AND SIGNAL PROCESSING Di VESTIBULO-ONLY CELLS … · NONLINEARlTY AND SIGNAL PROCESSING Di VESTIBULO-ONLY CELLS AND THE TRANSLATIONAL VESTIBULO-OCULAR REFLEX Sam MusaIIam A thesis

NONLINEARlTY AND SIGNAL PROCESSING Di

VESTIBULO-ONLY CELLS AND THE TRANSLATIONAL

VESTIBULO-OCULAR REFLEX

Sam MusaIIam

A thesis submitted in partiaI îidfillment of the requirements for the degee of

Doctor oEPhiIosophy

Depanment of Physiology

Lrniveaity of Toronto

G Copyri$t by Sam Musailam, 2001

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Abstract

NONLNLAEUTY AND SIGW-Ai PROCESSING IN

VESTIBULO-ONLY CELLS AND THE TRkUSLATIONAL

VESTIBULO-0CUL.M REFLEX

BY

Sam Musallam

Doctor of Philosophy

Department of Physiology

University of Toronto, 200 1

Recordings were obtrtined tiom 1 I O randomly selected vestibulo-only (VO) neurons

in the vestibutar nucleus oftwo rhesus monkeys. Sinusoidal stimuli were delivered at

several frequencies and velocities while position transients (steps) were delivered in the

naso-occipital, inter-aura1 and in directions 90 CCW, 60 CCW, 30 CCW, 30 CW, and 60

CW to the naso-occipital direction. The response to shusoidal stimuli was nonlinear.

Specifically, the response of VO neurons violated the principies of superposition and

homogeneity. The response to position transients was also nonlinear. Specifica!ly, the

responses were directionally asymmetric. One direction of step (fonvard step) elicited a

response that approximated the integral of the acceleration profile of the stimulus (velocity

direction). in the opposite direction (backward step), the ceIIs simpty encoded the

acceteration of the motion. This risymmetry could be attributed to an increase in the time

constant ofdecay of an excitatory response and the initial inhibition o f a neurons' response

in the opposite direction. A rate Limiter implemented as a procedure that extended the time

constant of decay (tirne constant enhancement) tvas used to mode1 these responses. Time

constant enhancement was dependent on spke arriva1 tirne in addition to the mean firing

rate of the cell. This proved to be a powerful cool enabling us to mode1 both the

nonlinearity during sinusoids and the a s p m e t r y during position aansients.

The tVOR was also investigated in response to sinusoids and position transients.

A simple mode1 is proposed that adequately simulates the tVOR in response to sinusoids.

However, the tVOR in response to steps of position revealed novel responses and exposed

the inadequacies of sinusoids due to phase reiationship ambiguity behveen the input and

output. Specifically, in response to position transients, the eye position traces were sirnilar

in waveform to head acceleration, an uncornpensatory response, which could be taken to be

cornpensatory if the stimulus was a sinusoid. Time constant enhancement kvas again used

to mode1 the tVOR in response ro steps.

Ac knowledgment

There is so much that my supervisor, Dave Tomlinson has done for me that a

paragaph of acknowled~gnent couId not describe. I owe al1 the successes in this thesis to

his tutelase and al1 my future successes to the confidence and scientific foundarion he built

within me. Dave is tmly a brilliant scientist and a good-hearted person and 1 will be

torever gratefd to the analytical mind and the gins of character he bestowed upon me. 1

could not have had a better supervisor.

This thcsis could not have been completed without the love and support of my wife

irene. Life is truly wonderîÙI with her. Irenc. i Iove you very much and 1 dedicate this

thesis to you,

Of course, rnany other people have helped me dong the way. Most notably is the

zroup at Journal Club and especially Dianne Broussard and Jim Sharpe. 1 tvouId especially - like to thank Dianns Broussard for her suggestions and for pre-reading portions of this

thesis and helping me rectify the nomenclature.

1 also want to thank my sister Mary. She is always ready to help me in any way she

cm, and 1 am ptefu l . i woutd also Iike to thank my parents, Siharn and Suteiman, and

Irene's parents, Michaei and Don, for their kindness and encouragement-

1 would also Iike to thank AIan BIakcman for his encouragement and technical

support.

Table of Contents

.. Abstract ................................................................................................................................. ii

Acknowledgment ................................................................................................................ iv

Table of Contents ................................................................................................................. v

List of Tables ......................... ... ........................................................................................... ix

List of Figures ....................................................................................................................... r

1.0 introduction .................................................................................................................... 1

1.1 Peripheril Vestibular Organs ................................................................................ 5

1.1.1 Semicircular Canals .............................................................................................. 7

..................................................................................................... L.1.2 Otolith Organs 10

1.1.2.1 Utricle ......................................................................................................... Il

.................................................................... 1.1.2.1.1 hatomy and Morphology 13

1.1.2.1.2 Striola .................................................................................................... 16

.............................................................................................. 1.1.2.1.3 Hair Cells 16

.................................................................................................... 1.2 Primary Afferents 17

1.3 Efferents .................................................................................................................... 29

1.4 Vestibular Nuclei ...................................................................................................... 30

..................................... 1-4LCentrai Termination of Regular and Irreguiar Afferents 32

1-42 Cells in the Vsstibular Nudei ............................................................................. 34

1.5 Vestibuloocular Refleres ........................................................................................ 41

......................................................... 1.5.1 Anglar Vestibulo-Ocular Reflex (aVOR) 42

1.5.1.1 Eye Plant ...................................................................................................... 44

.......................................................................................... 13-12 NeuraI Integrator 45

.................................................. 1.5.2 Translational Vatibulo-Ocular Reflex (tVOR) 47

1.6 Otolith Mediated Vestibulo-collic and Vestibulo Spinal Reflexes ....................... 55

1.7 Modeling ................................................................................................................... 56

1.8 Hypotheses ............................................................................................................... 59

Hl: Nonlinearity Using Sinusoids .............................................................................. 59

............................................................................. . H2 Nonlinearïty Using Transients 60

. .............................................................................................. H3 Modelino, the NOR 61

................................................................................... . HJ Non-compensatory tVOR 62

2.1 Animal Preparatiou ................................................................................................. 63

2.1.1 Surgical Procedures ............................................................................................ 65

2.2 Stimulus Ceneration ............................................................... ................................ 67

.................................................................................. 2.3 Data Collection and Analysis 68

2.3.1 Sinusoidal Stimutus ............................................................................................ 73

* * 2.3.2 Steps Of Posrcron ................................................................................................. 77

2.3.3 PuIodehg the tVOR .................................................................................. 79

................................................................................. 2.3 -4 Eye Movement Recording 80

3.1 Nonlinearity In Response To Sinusoids ................................................................. 92

3.1.1 Dynarnics of cells during eccsntric rotation ..................................................... 105

............................................................. 3.2 Nonlinearity In Response To Transients 110

3.2.1 Are the neurons sncoding direction? .............................................................. I I 5

3.2.2 Sional Processing .............................................................................................. L25 "

3.3 Translational Vestibulo-Ocular Reflex ................................................................ 132

3.4 Modeling ............................. .... .............................................................................. 136

2.4.1 Nonlinearity .................................................................................................... 137

3.4.2 Translational Vestibulo-Ocular Retlex ............................................................. 133

4.0 Discussion .................................................................................................................... 155

1.1 Failure of Superposition ........................................................................................ 156

4.2 Failure of homogeneity ..................................................................................... 159

.................................... 4.3 Direction of Motion is Not Encoded in Otolith Neurons 165

...................................... 1.4 Response Asymmetry and Approximating Integration 167

. 4.3 Spatio-temporal Convergence .............................................................................. 171

4.6 The tVOR in Response to Sinusoids ..................................................................... 176

4.7 The tVOR in response to position transients ....................................................... 180

5.0 Conclusion ................................................................................................................ 183

............... A1 . Equations Used For Fitting ................................................................ 185

vii

M. Spike Train Retrievd ................................ , ............................................... . ....... .. 187

References ..................................................................................... . .......................... 189

List of Tables

Table 2.1 Different velocities used for each frequency ................................................. 77

Table 3. 1 SIope (bl) and the standard error (SE) of the dope value for the linear regression

Table 3.2 Slope (M) of the regression of the bias shown in Figure 3.9 and the associated

p-value ................ ... ............................................................................................... 97

TabIe 2 .3 Tukey type cornparison of the sensitivities of al1 cells recorded as a fùnction of

frequenc y ................................................................................................................. 10 1

* . .................................... Table Al . Algorithm for computing fractional denvatives 187

List of Figures

Figure 1.1 Location of imer ear and vestibular organs ................................................... 6

Figure 1.2 The epithelial planes of the utticle and the saccuie are sufficient to encode

motion ...................................................................................................................... 11

Figure 1.3 Shape of the utricle is aimost elliptica1 in the chinchilla having dimensions .. 12

Figure 1.4 Morphology of the utricle . The utricle is composed of 3 layers .................. 15

Figure 1.5 Type i and type II hair cells ............................................................................ 18

Figure 1.6 Los of the number of fibers per kg of bnin weight ....................................... 20

Figure 1.7 Bode plots of regular and irregular afferents from the otolith organs ........... 28

Figure 1 . 8 The vestibular nucleus color coded according to the termination of afferent

originating fiom various peripheral organs ........................................................... 31

Figure 1.9 Off-mis rotation. or eccentric rotation ........................................................... 39

Figure 1.10 Neural substrate aVOR and tVOR ........................................................... 43

Figure 1.1 1 Steps OF position have jerk characteristics that are markedly different from

velocity ...................................................................................................................... 54

Figure 2 . 1 Example of auto-aligins several acce1eration cycles ............. .... ........ 72

Figure 1 . 2 Comparison benveen the ourput of che accelerometer ................................... 76

Figure 1.3 The acceleration profiles of nvo steps of position ..................................... 81

Figure 3 . 1 Example of the tVOR in response to position transienes ............................... 84

Figure 3.2 The response of a typicd ce11 co translation at 4Hz ...................................... 87

Figure 3.3 Example of a ce11 recorded during rotation h o u & an avis centered between the

interaurai line .......................................................................................................... 58

Figure 3.4 Example of a ceii recorded during eccentric rotation ................................... 89

................ Fi,w e 3 3. ExampIe of the firing rate of a ce11 durhg interaurd translation- 90

........................ Figure 3 . 6 The coordinates of a few cells fiom one rnonkey .. ........... 9 1

...................... Figure 3.7 Response of a cell to an interaural translation at 2 amplitudes 93

Figure 3.5 Velocity vs . Sensitivity for A) translation. B) eccentric rotation. and C) on-axis

rotation ...................................................................................................................... 96

. ............................................... Figure 3.9 Bias vs Velocity for the different frequencies 98

Figure 3.10A Sensitivity and phase for a single neuron recorded while the animal

translated in the naso-occipital direction ............................................................ 102

Figure 3.1 1 An example of a typical ce11 recorded while the animal undenvent 3Hz . .

oscillation ............................................................................................................. 106

Figure 3.12 Nonlinear response of vestibular neurons ................................................ 108

................... Figure 3.13 FaiIure of superposition depicted for a ce11 for al1 frequencies 109

.................................................... Figure 3. l4A X typicd step cycle used in this study I I 1

.......................................... Figure 3.14BTC Effect of Gaussian width on the response 111

..................... F r 3 . 1 The response of a ce11 to translations spanning 360 degrees 117

Figure 3.16 Surface plot of the conditional probability of cfetecting a direction Jiven the

tirin2 rate ............................................................................................................... 123

Figure 3.16 B. C. Probabilities calculated using Bayes' rule ........................................ 123

Figure 3.17 The response of a ce11 (mean = SE) to a backvard step (A) and a fonvard step

(B) in the naso-occipital direction ...................................................................... 126

Figure 3-18 Phase pIot of the response shown in Figure 3.17 indicating the asymmetry

present in the response of the neurons responding to steps .................................... 127

Figure 3.19 Acceleration (red). velocity fit ('Vel Fit' green). fiactional derivative fit ('FD

FitT(red). superimposed on the f ~ n g rate ............................................................. 128

....... Figure 3.20 A) Example showing the calcuIation of the rising a d f a h g slopes 130

Figure 3.21. Sensiùvicy and phase (r SE) of the sensitivity of tVOR io osciIlation

composed of Eequencies 1-5 Hz ............................................................................. 132

Figure 3.22 tVOR in response to steps of position ...................... ,. ........................ 134

Figure 3.23 Velocity profile of compensatory and uncompensatory stimulus and their

.................................................................................................. Fourier transforms 135

Figure 3.24 Model of the dynamics of the cells recorded that c m account for the failure of . . ......................................................... homogeneity and the failure of superposition 138

................. Figure 3.15 The output of simulations using Time Constant Enhancernent 142

Figure 3.26 The mode1 used here to mode1 sinusoidal data ......................................... 145

Figure 3.27 A cornparison of the sensitivity and phase of experimental tVOR data (dashed

line) and the mode1 ................................................................................................. 147

Figure 3.25 The output of the mode1 From an input composed of a combination of the

behaviourof the prirnary ai'fsrents t'rom Figure 3.27. .......................................... 149

............................. Figure 3.29 Gain and Phase of the plant descnbed by Equation 1. 151

Figure 3.30 Mode1 used to simulate the tVOR in response to steps ............................. 152

Figure 4.1 Response of a neuron to 4 Hz translation presented here to ernphasize the

.................................................................................... asymmetry in the response 161

............................... Figure 4.1 Neural nenvork used to simulate the data in this thesis 173

Figure 4.3 Denved primary afferent behaviour (cyan) as compared to measured behaviour

Erom nvo studies ........................................ 178

Figure 4.4 Example of a nonlinex acutuator ................................................................ 180

Figure 4.5 . Output of the rate limiter ............................................................................ 152

Figure Ai. accelention trace turned into a firing rate and its representaiive spike

train as obtained by the interspike interval method .................................. 179

xii

Ab breviations

Abbreviations are in alphabetical order.

aVOR

EF

EHV

a 3

IF

PVP

RL

STP

TCE

tVOR

VO

.hgular Vestibulo-Ocular Reflex

Excitatory First Direction

Eye Head Velocity

Acceleration due to gravity (9.8rn/s2)

Inhibitory First Direction

Position Vestibular Pause

Rate Limiter

Short Term Potentiation

rime constant enhancement

Translationai Vestibule-Ocular Reflex

Vestibular OnIy

1.0 Introduction

The vestibular system is quite remarkable in thac it gives animais a sixth sense.

The normal functioning of the vestibular system 1s essential for the detection of the

position oFthe head in space, the general maintenance of balance and posture, the normal

functioning of the sympathetic nervous system (Yates 1992), cardiovascuIar output

(Yates and Miller 1994), blood flow (Kerrnan et al. 2000) and pulmonary function

(Miller et al. 1995; Yates and W l e r 1998). In addition, spatial maps in the hippocampus,

and the auditory maps in the inferior olive are encoded in head-in-space coordinates and

accordingly, need the vestibular system to provide the location of the head in a

gravitational field for the precise compuration of the maps (Peusner 2001). The

importance of this system becomes cven greater when one considers that it allows us to

move and see at the s m e time by moving the eyes to compensate for rnovements of the

head. Other reflexes, such as the vestibuIo-collic retlex (VCR) rire driven by

monosynaptic input from the vestibuhr nucleus to the neck musdes in order to stabilize

the head in space (Sato et al. 1994; Ikegami et al. 1994). Even simple tasks mich as

reading in bed become impossible if patients suffering kom vestibular disease cannot

compensate for their head movements. Disease of the vestibular system leads to nausea,

dizziness and a general FeeIing of malaise and is even implicated in depression (Leigh

and Zee 1999). The research described in t h 3 thesis was performed in the hopes that Our

knowledse of the vestibular system, and more generaiiy, Ihe brain, will increase. The

uItimate applied goal of research into the vestibular system is to alteviate the suffering of

patients snicken by peripherd or centra1 vestibular rna1fùnction.

Very Little is known about the computational abiiities of vestibular neurons and

the signal processing that occurs in the vestibular nucleus. Uncovering the

transformation of input and sensory signals that give rise to the various vestib!llar

reflexes and the awareness of position of self in space is necessary in order to formulate

cures and remedies for systern malfunction. The irnrnediate goal of experiments

described in this thesis is to uncover the computational abilities of vestibular neurons in

response to translations and rotations of the head. We will then atternpt to understand the

fmctional relevance of the computation by applying it to the translational VestibuIo-

Ocular Reflex (tVOR). This is a necessary step as very little is known about the neural

substrate of the tVOR. the retlex that stabilizes the eyes in space in response to head

translation, This is in contrast to the wealth of knowledge available about the angular

VOR (aVOR) where it has been known for a long tirne that this reflex, which Iùnctions to

stabilize the eyes in space in response to a head rotation, involves three neurons in its

sirnplest fom: the prirnary afferent neuron conveying rotational head velocity, the

vestibular nucleus neuron in the brainstem which processes the afferent signais, and the

oculornotor neuron which activates the sye muscles (Lorente de No 1933, cited in Lei&

and Zee 1999). To complicate rnatters Further, the tVOR is much more demanding than

the aCrOR since the final output of the circuits driving the eyes is a Function of target

distance, target location and translationa1 head velocity (Viirre et al. 1986). In addition,

very iittle is known about how translational and rotational signals combine in the

bninstem to compensate for combinations of transiation and rotation. The need to

understand these circuits takes on geater importance in view of the hding that most

naturaI head rnovernents involve bath translations and rotations (Grossrnan et al. 1988;

Grossman et al. 1989).

Atternpts to elucidate signal processing in the vestibular nucleus rnay be fraught

with error. Information about head rotation and translation is delivered to the vestibular

nuclei by afferents that innervate the semicircuiar canals and the otolith organs

respectively, the peripheral orsans that detect rotations and translations. Since rnost

natual head rnovernents are cornposed of both kinds ofmovernents (Grossrnan et al.

1988; Crane et al. 1997), it is not surprising that there is wide spread convergence of

canal and otolith s iga ls in the vestibular nuclei (Uchino et al. 2000; McConville et al.

1994). Ongoing research in rnany labs assumes that various signals in the brainstem

combine linearly and that neurons in the brainstern behave as linear systems, without ever

having tested for the validity of linexity. In addition, many single unit recording

experimenrs in the brainstern have used sinusoids ris inputs. This is dangerous practice,

since if neurons in the brainstem are ever s h o w to be nonlinear, then any conclusion

about the behaviour of vestibuhr neurons to an input cornpriscd of ri combination of

s igals is invalid, and any ccnclusion about the output of these neurons to a sinusoidal

input cannot be seneralized to other foms ofinputs.

The processing that is achieved through canal and otolith signal convergence is

not strai&tfonvard as there are some differences in che nature of the signals carryin;

information about head motion. To begin with, afferent signais have different temporaI

charactenstics as canal afferents encode rotational head velocity while otolith afferents

encode translational acceleration of the head, inchding _onvity (Femandez and Goldberg,

L972; Fernandez and Go ldbe~ , 1976; Goldberg et al. 1990; Angelaki et al. 2000b). in

addition, otolith afferents deliver an excitatory and an inhbitory signal from the same

side in response to a translation (Wilson and Melvill Jones, 1972). indeed, it has been

shown that a vestibular nuclei neuron c m receive monsynaptic excitatory input and

disynaptic inhibitory input &om an otolith orsan on a single side (tenned cross-saiolar

inhibition) (Uchino et al. 1997; Ogava et al. 2000). Rotations on the other hand Iead

onIy to excitation of the side that is ipsilateral to the rotation while the inhibitory signais

must corne From polysynaptic ipsilateral circuits or the contralateral side. Given these

differences then, how are input signais cornbined in the vestibular nucleus?

The two major goals of this thesis are the etucidation of the computational

propenies of neurons in the vestibular nucleus and the application of these propenies to

the translational vestibulo-ocular reflex. Data presenred in this rhesis attempts to

describe the interactions benveen rotational and translational s ipals and the kind of

signal processing that may occur in the vestibular nucleus in response to sinusoidal

rotation. translation, and a combination of the iWO inputs. D3ta wiIl be presented that

supports the hypothesis that neurons in the vestibular nucleus are nonlinear elements and

that signals convergins ont0 neurons in the vestibular nucleus combine nonlinearly. In

addition, the behaviour of these nonlinear elements in response to a nonsinusoidal input

(position transients) will reveal powerfû1 signai processing abiiities. Specifically, the

nonlinearity could be used to approlcirnate the tempord i n t e p l of a sigaI. Xlthough the

nonlinearity adds complexity to the system, it faciiicates many of the required processing

steps that are curnbersome using linear elements aione. A mode1 utilizing rime constant

enhancement, a method used here to increase the tirne consunt of decay of a neural

signal, will be presented that sugsests mathematical integrahon of sigiaIs is achieved

which may be used centrally, dong with positive feedback loops, to mathematicdly

intepte. Finally, the tVOR will be reassessed based on new data obtained while using

position transients as the stimulus. Linear models of the tVOR in response to sinusoids

will be presented and will be s h o w to be misleading, failin; when the stimuIus is

changed to position transients. To that end, four hypothesis are put forth: 1) Cells in

the vestibular nucleus are nonlinear, 7) the nonlinearity is advantageous to the system, 3)

the tVOR can be modeled by the use of linear elements if the stimulus is restricted to

sinusoids, and 4) the tVOR in response to step transients is modeled best by the use of

nonlinear elements,

1.1 Peripheral Vestibular Organs

The vestibular nucleus functions to process vestibular, ocular and somatosensory

inputs via direct monosynaptic input and polysynaptic convergence. The results in this

thesis describe the response ofvestibular nuclei neurons to an input conveying head

motion information. Therefore. a thorougli understanding of these input signais is

required before we undertake the task of describing how these s igaIs are processed

centrally. Head acceleration is sensed by the peripheral vestibular organs Iocated in the

inner ear at the base of the shull just posterior to the cochlea (Figure 1.1). The peripheral

vestibular system functions as a sensor of head motion, responding to accelerations of the

head including pv i ty . To accomplish this, each ear contains three semicircular canals;

the horizontai, antenor and posterior canal. and hvo otoiith organs, the utricle and the

saccule (Lysakowski et aI. 1992). The semicircular canals detect angular head

acceleration while the otolith orsans detect transIationaI acceleration of the head, The

5

location of these organs in the head is depicted in Figure 1.1 relative to the cochlea. The

cochlea and the vestibular organs share many neural structures. For example, both

systems relay information to the brain via the VIU '~ nerve. whose vestibular portion is

divided into a superior and an inferïor section. The superior branch innervates the

anterior and horizontal canal and the uaicle, while the inferior vestibular nerve brancti

\ Hair Celb

Figure 1.1 A) Location of inner ear and vestibular orgüns. Shoivn lire the semicircular canrls, the

utricle and the saccule relative tu the cochlea. Note horv al[ these periphewl organs are

interconnected. B) Exagger~ted schematic of a canal s h o w to be occluded by the cupula.

Rotation of the canal causes the fluid rvithîn CO push agdinst the cupula, deflecting it. Embedded in

the cupula are the processes of hair ceits, which nlso get deîlected depolarizing (or

hyperpohrin'ng) the underlying hair cell.

Supplies the posterior canal and the saccule (Lysakowski et al. 1992).

1.1.1 Semicircular Canals

The three semicircular cmals are arranged approxhately orthogonal to each other

(Figure 1.1). The horizontal canal in hurnans lies ciose to the earth horizontal plane when

the head is tilted nose dotvn by 25 degrees tvith the body erect (Leigh and Zee, 1999). In

addition, the vertical canais lie in planes that subtend an angle of approxirnately 35

degrees relative to the vertical sagittal plane. The response of each canal is proportional

to the cosine of the angle betsveen the plane of the head rotation and the plane of the

canal. In addition, the canals are orgmized as functional pairs. The antenor canal on one

side is paired with the posterior on the opposite side while the horizontal canals fonn

synersistic pairs (Lysakowski et al. 1992; Lei$ and Zee 1999). Lt is remarkable chat the

pulling directions of the eye muscles are roughly in the same planes as the canals for

frontal eyed and lateral eyed anhals (Simpson and Graf, 1985). It has been argued that

it is the canai reference Crame- that has infiuenced the evolution of the oculomotor

reference fiame (Simpson and Graf, 19S5), ernphasizing the evolutionary importance of

signals generated by these organs. Each canal has an enlar~ernent known as the ampulla

At the base of the ampula is the sensory epithelium known as the cnsta. Hair cells Eom

the crista protrude into a gelatinous mas, the cupula, whch occiudes the canal. The

cana1 itself is tilled with a fluid, the endol-mph, and it is the relative force everted by the

endolymph on the cupula that causes the deflection of cilia prorruding into the cupula

(Figure I.1B and C) (Lysakowski et al. 1992)

As already mentioned, the aVOR ideally rotates the eyes with a velocity that is

equaI and opposite to the angular velocity of the head. Rernarkably, the velocity signal

does not have to be computed since the output of primary afferents innervating the canais

approximates head vdocity for the range oFnatura1 head movement Gequencies

(Fernandez and Goldberg 1971). Therefore, to drive the aVOR, the head velocity signal

is simpiy inverted approximating the desued eye velocity. Then, this signal is sent to the

eye muscles, which need a driving s iya l cornposed of a combination of eye velocity and

eye position (Robinson, 198 1). The velocity signal arises because the canals are

integrating accelerometers. The diameter of the sernicircular canals is small cornpared ro

their curvanire, so that when the canal is rotated, the fluid lags behind because of its

inenia (WiIson and Melvill Jones 1979). This causes the flow of the endolymph to be

proportiona1 to head velocity in response to an input ofacceleration. The mechanics of

cupular and rndolyrnph disphcement have been approximated by a torsion-pendulurn

mode1 (Steinhausen 1933, cited by Wilson and MelviI1 Jones 1979):

cf2e de I- = i-+p--t-x-e ri [ - d- dt

where 1=2.54 x loJ g-cm is the moment ofinenia of the endolymph, p is the angular

displacement of the head (and therefore the canais) in radians, 6 is the relative

displacement of the endolymph relative to the canal in radians, P = .OS poise (gfcm-s) is

the viscous damping, and k is the elastic restoring force of the cupula; k = 0.008--016

$cm-s' (Schwan and Tomlinson 1993). Fmm the values &en above, the displacement

of the cupula (0 in Equation 1.L) describes head veIocity (and therefore, canal velocity)

for an input of head acceIention for Gequencies benveen O.LHz and 8Hz (although at 8

Hz, the gain has aiready begun to fall). The response of the canai as descnied by

Equation 1.1 is characterized by hvo time constants: q=Lf/? and q = P/k. TI has been

measured to be 3 rns and represents the minimum duration of a srimuhs that can be

accurateiy transduced by the canals. Stated another way, afier initiation of a steady state

velocity of cana1 rotation, the cupula takes 3 ms to reach to within 37% of its final

displacement. Tl on the other hand has been calculated to be benveen 5 and 10 seconds,

and represent the time caken by the cupula to return to within 33 % ofits restin; position

in response to a construit velocity of rotation (Wilson and Melvill Jones, 1979). For

example, during constant velocity rotation, the cupula, powered by its restoring force,

will move back towards its resting position. This movement however will be opposed by

viscous forces created by the rnovement of the endolymph. The resultant cupular motion

\vil1 be exponential, reaching its resting position with a tirne constant ri.

Equation 1.1 is a simpliîïed mode1 of the integatin_o abilities of the semicircular

canals. it is derived using assumprions thar may not be accurare. For example, Equation

1.1 assumes that rndolymph flow is lamina excluding the possibility of turbulent

interaction between cupula and endolymph, which may not hold at higher fkequencies

(greater than 1 Hz) (Rabbitt and Damiano 1992). Recordings From pnmary affereiits

innewating the canals have s h o w that the actuai firing behaviour diverges fkom the

predictions made by Equation 1.1, Femandez and Goldbeg, (1971) attnbute this

divergence to hair ce11 adaptation. However, other modeling efforts by Rabbitt and

Damiano, (1992) replicatited the results of Fernandez and GoIdberg by taking into account

the variable cross-sectional geometry of the canais and taking into account the fiequency

dependence of the velociry of endotymph motion. En addition, Equation 1.1 is highly

dependent on the value of the canstants 1, P and k. For example, a canal with a Iarger

radius (such as canaIs of l q e r ztnimals) (Wilson and MeIvill Jones 1979) would increase

I, which without any simu1taneous change in/? or k would shift the inte-mtion

frequencies to lower values, and decrease the range of Eiequencies where integration

occurs.

1.1.2 Otolith Organs

The otolith organs detect translational acceleration inchding p v i t y . Al1

vertebrates, except the cyclostomes (e.g., the lamprey), possess some form of otolith

organs (Lewis et al. 1985). There are hvo otolith organs in marnmals, the utricIe and the

saccule, which Lie approximatsly perpendiculrtr to one anothsr and are therefore able to

detect translational accelention in any direction. Birds possess a third otoIith organ, the

lagena which is an extension of their otolith complex but is acnrally used for hearing

(Lewis et al, 1985). The utricle Lies approximately in the horizontal pIane with its

anterior portion tilted up while the saccule lies in the verticaI (or sagittal) plane

(Lindeman 1966; Curtho ys et al. 1999). Indeed, siven that the epithe lia of these

perpendicular structures is approximatsly a 2-(1 plane, then there exists an infinite nurnber

of vectors contained in the pianes of the bvo epitheiiwns that form a brtsis for 2

dimensional space (Fisure 1.2). Motion dong any vector (Iabeled 'A' in Figure L -2) can

be represented as a linear combination of the vectors lying dong the bases axes (Iabeled

e ~ , ez, and el in Figure 1.2). Therefore, motion dons any direction in space can be

represented as a linear cornbination ofvectors Iying in the epithe[ium of the utncle and

the saccule. Howeve. more precisely, the umcle and saccule are considerably curved, so

that acceierations in the horizontal and vertical plane stimulate both end-organs

(Rosenhall 1972; Curthoys et al. 1999). Translations presented here are confined to the

horizontal plane, therefore, what follows is an in depth review of the utricle.

Figure 1.1 The epithelial planes of the utriclo and the saccule are suffkient to encode motion in sny

direction since they contain vectors thnt can form r bnsis for threedimensional spnce, Therefore, an

accelerrtion along any vector .4 will have a projection ont0 the planes of the utncle and the saccule.

1.1.2.1 Utricle

As already mentioned, the uuicle Functions to detect translational acceIeration,

including pvity. Its anatomy is quite remarkable, being that it is sirnilar in design to a

classical mechanical accelerometer that utilizes the force exerted by an inertial system as

1 1

an indication of acceieration (much like a person's back presses against the seat o fa car

when accelerating). The shape of the utricle varies but is close to elliptical with an inlet

on the media1 side. The epithelium is demarcated by a single line m i n g the length of

1 - 1 mm

chinchilla

Human

Figure 1 3 Shape of the utricle is dmost ellipticd in the chinchilla hnving dimensions of 1.4 and 1.1

mm in the anterior-posterior and medio-lateral dimensions respectively. In the human, the utBcie

Iooks more like a trapezoid with cuwed edges. Note also that in the human, the striola occupies

considerable space. The scale is not the same betweert the human and the chinchilla utncle.

The utncle, the smola, separaring it into nvo seneraily unequal parts. The lengths of its

axes in the chinchilla are 1.4 and 1. i mm in the antenor-posterior and medio-lateral

dimensions respectively (Fernandez et al. 1990) (Figure 1.3). in humans, the utrÎcIe

resembtes a mpezoid with rounded corners (Watanuki and Schuknecht 1976).

The utricle can be subdivided into three parts that are stacked to form a

functioning accelerometer: the sensory epithelium called the macula, which contains hair

cel1s with processes that intrude into the second layer. The second layer is simply a

gelatinous mass capped by the third layer, which is composed of calcium carbonate

crystals known as otoconia (Figure 1.4). The specific gavity of the geiatinous-otoconiaI

mass is 2.7 times greater than the surrounding tndolymph (Money et al. 1971).

Therefore, the gelatinous-otoconial mass has a greater inertia which causes it to lag

behind during a translation, and causes a displacement of the hair ceIIs in the direction

opposite to the direction of accelention. The distribution of otoconial size and the

tliichess of the gelatinous membrane are not uniform throughout the utricle. The

geiatinous membrane is thickest in the middle and thins out nt the periphery of the utricie.

On the other band. small otoconial crystals line the periphel ofthe utride and the striola

(Lim 1984). In benveen the striola and the periphery, the otoconia increase in siza

OtoconiaI deftciency or malformation causes head tilts in animais (Lim 1984). indeed,

vestibular responses are absent in het' mice in response to trmslational accelerations

(Jones et al. 1999) and hamsters that had abnormal otoconial size had motor deficits, and

therefore the development of normal otoconia is important for noma1 vestibular function

(Sondag et al. 1998).

I het(het mice (abbreviated het) are munted micr which hck otoconia.

It is the deflection of cilia by the otoconia-gelatinous conlplex that is indicative of

the existence of acceleration. The ce11 body of the hair cells is embedded in the macula

with the cilia protmding into the gelatinous mass (Figure 1.4). Each hair ceIl gives rise to

several stereocilia, which have different heights but are arranged in a staircase pattern,

and one kinocilium, the tallest process arising from the hair ce11 (Figure 1.4) (Akoev and

hdrianov 1993). This staircase arrangement of the stereocilia indicates a functional

polarization direction of the ce11 pointing towards the kinocilium dong the increasing

heights of the stereocilia (Flock et al. 1977). Movement of the cilia in response to

movement of the gelatinous mass must be ensured for the pmper hct ioning of the

accelerometer. Therefore, the kinocilium is attached to the stereocilia bundle (Emstson

and Smith 1986; Ross et ai. L987) so that deflection of the kinocilia causes a deflection of

the stereocilia bundle which causes the hair ce11 to increase (or decrease) the prirnary

afferent neurons' Ievel of excitation. Similar to the variability in the thickness ofthe

gelatinous membrane and the variability in the size of the otoconia across the utticle, the

kinocilia heights are also not constant and decrease in height by up to 30% in the striola

of some species (Fontilla and Peterson 1000). This is in contrat to the thickness of the

~elatinous mass, which is thickest in the striolar region. Assuming uniform

elasticityistiffness of the gelatinous Iayer, then the above variables may lead to a large

deflection of kinocilium in the periphery and smaller deflections of the kinocilium in the

central region for a specific acceleration. The attributes of kinocilia deflection are highly

dependent on die variabies that govern the physical motion of the gelatinous-otoconial

mass and the osciilatory behaviour of the kinocilia and stereocilia. Besides the general

description of the otolith membrane relating otolith displacement to input acceleration

(Goidberg and Feniandez 1979, an in-depth theoretical analysis of local hair ceii

deflection and an analysis of the relative motion of the gelatinous-otoconiai mass bas not

yet been performed.

1.1.2.1.2 Striola

Acceleration that causes a deîlection of the stereocilia towards the kinocilium

depolarizes the primary afferent neuron while deflection away kom the kinocilium

hyperpolarizes the primary afferent neuron (Figure 1.4) (Wilson and Melvill Jones 1979).

The movernent direction which depolarizes the primary afferents is taken to be the

polarization direction of the hair cell. The striola is a specialized region on the macula

that demarcates the reversal of polarization (Wilson and Melvill Jones 1979). ln

addition, polarization vectors in the utncle and saccule point towards (Figure 1.3) and

away from the striola respectively. Since the striola is curved (e.~., semicircular in the

chinchilla (Femandez et al, 1990)). this has the consequence that acceleration in any

direction will be parallel to the polarizacion vector of nt Ieast one cell, Femandez and

colleagues (Femandez et al. 1972) estirnstted that the striola splits the macula into a 60/40

proponion (mediaVlatera1) in the squirrei monkey. initia1 growth of the macula starts at

the striola with the kinocilia initially not poIarized. bstead, the kinocilium is surrounded

by stereocilia and does not becorne polarized until it becomes eccentricaIIy positioned

towards the striola (Denman-Johnson and Forge 1999). indeed, differenccs in hair ce11

propenies benveen the striola and extrastriola regions are believed to lead to differences

in discharge properties of utricular afferents (KoIt et al. 1999). The signitïcance of the

difference behveen the striolar and exusmolar area wili be discussed below.

1.1.2.1.3 Hair Cells

Haïr cells in the macula of the otolith o y n s and the crists of the semicircular

canals are the first structure to initiate a signai upon detection of head movement. There

7 6

are two types of hair cells classified as Type 1 and Type 11 celis based on their shape

(Fi,yre 1.5), (Eatock et al. 1998; Lindeman 1966; Fernandez et al. 1990). Type 1 hair

cells are flask (or pear) shaped while Type Li hair cells are tlongated, resembling a

cylinder in shape. In addition, afferents innervating type I hair cells generally engulf the

ce11 in what is known as a calyx afferent terminal. On the other hand, type II hair ceIls

are simply innervated by bouton terminal endings (Figure 1.5) (Goldberg 1991; Baird and

Schuff 1994; Lysakowski and Goldberg 1997; Eatock et al. 1998; Goldberg 2000). It has

been estimated that in the chinchilla, 80% ofafferents give nse to both calyx and bouton

endings and therefore innervate both kinds of hair cells (Femandez et al. 1990). In the

sarne animal, type I hair cells are generally found in the smolar region while type iï cells

have a highrr concentration in the periphery of the utricular macula. In behveen the

striola and the periphery, both types of hair cells are found (Femandez et al. 1990) so that

the overall ratio behveen the hvo types of hair cells is I : 1 in the chinchilla (Femandez et

al. 1995). In amphibians and cyclostomes, only type II-like hair cells have been found

(HiIlman and Lewis 1971; Hiliman 1972). Therefore, type I hair celIs appear to be

phylogenetically younjer thnn type II cells ( U o e v and Andrianov 1993).

1.2 Primary Afferents

Pnmary afferent neurons cornpnsing the vestibular (vIIlth) nerve are the conduit

in which acceIeration sensed by the penpheral vestibuIar orgins reaches the brain. These

fibers form a major input into the vestibular nudeus and therefore are of prime

importance in this thesis.

Bouton

Figure 1.5 Type I and type II hair cells dong nith the afferent innervation they receive. Type I hair

cetls generdly receives a c d l ending rvhiie tvpe II hair cells are innervated by bouton terminais.

Afferent cells are bipolar neurons whose ce11 bodies lie in Scarpa's ganglion

(Wilson and blelvill Jones 1979; Richter and SpoendIin 1981). The vestibular nerve,

which is made up of vestibular afferents, is divided into the superior and inferior branch;

the superior branch contains about 65% of al1 neurons and innervates the anterior and

horizontal sernicircular canals and the utride. The remaining neurons make up the

infenor branch, which innervates the posterior semicircuIar canal and the saccule (Richter

and Spoendlin 198 1). Further branchine around a single end-organ has been found to

occur within each branch, For example, separate subdivisions of the supenor branch

innervate the strioIar and peripheral regions of the utric1e (Wilson and MetviI1 Jones

1979). Many studies have been performed that have determined the total nurnber of

fibers in the vestibular nerve of various species. There are about 3433 fibers in the

mouse (Baurle and Guldin 1998), 12,276 fibers in the cat (Gacek and Rasmussen 196 1 ),

7772 in the chinchilla (Boord and Rasmussen 1958, cited in Baurle and Guldin 1998),

523 1 in guinea pigs and 18,000 in rnonkeys (Gacek and Rasmussen 1961), 8720 in

pigeons (Landolt et al. 1973), 8449 in the nt (Alidina and Lyon 1990) and 18,500 in

humans (Richter 198 1). The differences in the above counts may be due to species

differences but also to differences in counting (Baurle and Guldin 1998). What is

notable, however, is the large number of fibers for small animals, indicating the

evolutionary importance of the signal being camed by the afferents. Figure 1.6 depicts

the log of the number of fibers per kilogram of brain weight for the various species listed

above (brain wei$ts were obtained from hnp:.~~facultv.washin~ton.ed~~!chudler

;'tàcts.htm). The large ratio for small anirnals indicates the importance of the s iga ls

carried by vestibular fibers for these animals. For example, if the mouse brain were

increased to 1 kg in weight, then close to 10 million fibers would occupy its vestibular

nerve. Given this disproportionality, it is interesting that in humans, therc are

approxirnately 6 tirnes more hair cells than fibers (Merchant et al. 2000) indicating that

on average, the output of at least six hair cells must converge onto one afferent if the

innervation is uniformly distributed. Therefore, aiready at the hair cell-afferent junction,

there is signal processing in the form of data compression which in general results in a

loss of information,

H MKCAT GP CH P R US

Figure 1.6 Log of the number of fibers per kg of bnin weight for humsns (H), rhesus monkey (MK),

CAT. guiner pig (GP), chinchilla (CH). pigeon (P), rat (R), mouse (blS).

Ciassic ivork by Wersiïl datin; back to the L960 (CVersSI, 1960) and others more

recently (Baird et al. 1988; Baud and Schuff 1994 Brichca and Peterson 1994) showed

chat thick afferents innervate type f cells in the central region of the end-organs while thin

fibers innervace type II cells in the periphery of both the crista and macuIa. Other

investigators vonntbia et aI. 1989; Naito et aii1. 1997) have confïrrned thai this

segregarion of ihick and thin fiers is rnaintained in the vestibuiar nerve, with the thick

fibers occupying the center wkile the thinner fibers occupying the periphery of the VIUh

nerve. The above diifferences have no effect on processing in the vestibdar nucleus

20

unless there also exist, dong with the diverse morphoIogy, behavioural differences.

Indeed, the discharge rate of primary afferents is aIso correlated with fiber size and the

site of innervation. Afferents with a regular discharge rate (low standard deviation in the

mean of interspike interval) are thin and innervate hair cells in the peripheral macula

while irregular afferents (having a high standard deviation in the mean of interspike

interval) are thicker and innervate hair cells more centrally (Baird et aI. 1988; Femandez

et al. 1990; Goldberg et al. 1990b; Baird and Schuff 1994; Bnchta and Peterson 1994).

Irregular afferents make more LYO-somatic contacts in the vestibular nucleus than do

regular afferents (Sato and Sasaki 1993). Glutamate is the primary neurotransmitter in

pnmary afferent neurons (Yarnanaka et al. 1997), but fiber size determines the type of

receptor in the vestibular nucleus that is accivated. Thin afferencs predominantly activate

.k'vIPA receptors while thick at'ferents activate both APclLPA and NMDA receptors. In

addition, the soma size of target vestibular nucki neurons m d the number of synapses per

tarirget vestibular neuron were larger for irregular afferents than for regular afferents (Sato

and Sasaki 1993). Given these observations, especiaIty cfie s a t e r number ofsynapses

formed by irregular fibers, one tvould expect the behaviour of vestibular nuclei neurons

to be better correlated with irregular fibers. However, as wilI be described later, this is

not the case. Additional differences benveen regulx and irreglar fibers were reponed in

the cat, where it was observed that some irregular vestibular affercnts increased their

activity in response to tone bursts preferentially benveen 500 and 1000 Hz (McCue and

Guinan 1995).

Intermediate behveen the reqlar and irregular fibers are the dirnorpbic fibers

which are found throughout the macukt but with some regional differences (Femandez et

al. 1990). Dimorphic units in the suiolarregion innervated fewer hair cells than

dimorphic units in the penpheral macula, which also gave nse to a greater number of

bouton endings (as opposed to ca1y-x endings) (Fernaridez et al. 1990).

For convenience, afferents are aIso named for the two types of connection they

make with the hair celIs: ca1y-x and bouton fibers. Type I hair ceI1s are innervated by a

calyx (bowl shaped) ending fiorn a calyx fiber while type II hair cells receive the bud-like

bouton sndings Fiom a bouton tiber (Eamck et al. 1998). CaIyx fibers can innervate up to

Cour type 1 hair celIs (cornplex calyx) although calyx fibers innervating a single type I

hair ce11 also exist (simple calyx). On the other hand, bouton fibers contact many type ii

haïr cells which in the cnsta can ranse over distances as large as 75 pm (Fernandez et al.

1990; Fernandez et al. 1995). Recall that in the crista, however, the polarization

directions of the hair cells are the samr so that rvidespread convergence of an afferent has

Little effect on the information transmitted. In the otolith organs however, innervation of

hair cells as far apart as 75 p n will lead to convergence of cells with different

poIarïzation vectors. However, this does not occur in the macula of the utncle

(Fernandez et al. 1990; Baird and Schuff 1994).

Given the loss of information that occurs wich s i g d conversence and the much

greater convergence that occurs for bouton tibers, it is possible that for the otolith organs,

bouton (or type II) fibers are generally concerned with s ignahg movements whiIe cdyx

(type i ) fibers may also be concerned with the direction of moùon. However, this is

uniikeIy since afferents in the umck innervate haïr ceIIs with sirnilar poIarization

directions (Fernandez et al. 1990; Baird and Schuff L994). As wiII be explained below,

this amngement Ieads to cosïne tuned behaviour in the afferents (where the amplitude of

the response is related to the cosine of the angle between the stimulus direction and the

polarkation direction of the cell), behaviour that is markedly different lÏom the behaviour

of central vestibular neurons (Blanks and Precht 1976; .Anselalci and Dickman 2000). In

addition, in the chinchilla (Fernmdez et al. 1990), 92% of al1 the fibers in al1 parts of the

macula were found to be dirnorphic fibers; units that make both calyx and bouton

connections, and only 6% were ca1y.v and 2% bouton. (However, according to Fernandez

et al. (1990), horsendish peroxidase has a predilection to label thick fibers which tends to -

underestimate the predominantly thin bouton units. The authors introduced a correction

and hypothesized that 12% bouton fibers in their population is a better estimate). In

connst, only 70% of fibers in the crista were Iabeled as dirnorphic, 10% as cdyx and

20% bouton (Fernmdez et al. 1988). Recently, it was hypothesized on theoretical

grounds that the advantage of the calyx terminal lies in the existence of the clef? between

the afferent and the hair cells. The accumulation of KI in the cleli may promote the

continued depolarizrttion of the afferent terminal and the hair cell, ensuring an accurate

transmission of the stimulus (Guldberg L996).

For most species, irreguIar fibers have hi* conduction velocities and therefore

Large avon diameters (Guldberg and Fernandez 1977; Howbia et al. 1989; Lysakowski

et al. 1995) while bouton fibers have low conduction velocities (Lysakowski et al. 1995).

irregular fibers generally make calyx endings ont0 type 1 cells while re~ular fibers make

bouton endings on type Il cells, Dimorphic fibers innervate both types ofhair cells

(Fernandez et al. 1995). One study (Yamashita and Ohmori 1990) found the opposite in

the chicken crista; the thin regular fibers made calys endings and that irreguiar Gbers

made bouton endings, Regardless of the above results, reylarity of discharge is a

function of the afferent terminal's ionic current, racher than the type of hair ce11

innervated or the type of terminal made (Goldberg 2000). For example, dimorphic fibers

have been identified that have simila. branching patterns but differ in their discharge

regularity (Baird et al. 1988; Gotdberg et ai. 1990b). These fibers however did differ in

their location on the epithelium which has led Goldberg, (2000) to suggest that it is the

different ionic currents throughouc the spi thehm that control the regularity of discharge.

blany studies have described the response properties of otolith primary afferents

although a complete description of the dynamics ofprimary afferent is still lacking

(Lowenstein. 1972; Loe a al. 1973; Fernandez and Goldberg L976b; Tomko et al. 198 1 ;

Baird and Lewis 1986; Goldberg et al. 1990a; Goldberg et al. 1990b; Dickman et al.

1991; Si et al. 1997; AngeIaki and Dickman 3000). [n ~ h e squirrel monkey, the average

resting rate of regular afferents is 64 spikedsec and irregular aiferents is 57 spikeskec

(Fernandez and Goldberg L976a). [n the pigeon, the resting discharge averaged LOS

spikeslsec (Si et al. 1997) while in the fiog, the maximum resting discharge recorded in

afferents was 28 spikeslsec (Blanks and Precht 1976). The different resting discharses

may have to do with the spectmm of frequencies achieved during head motion for the

different species.

The result that the resting discharge is greater than zero has a significant impact

on signal processing in the vestibular nucieus. For example, afferents c m increase or

decrease their discharge rate depending on the direction of translation or rotation. It has

long been known that the horizontal semicircular canais work in pairs. Hair ceils in the

crista of the semi-circuIar canaIs have the same polarity and therefore, excitation of

afferents by rotation to one side is accornpanied by inhibition of afferents irom the

opposite side (Leigh and Zee 1999). The side being inhibited can then disinhibit the

excitatory side, Ieading to a 'push-pull' arrangement onto secondary neurons (Shimazu

and Precht 1966; Goldberg et al. 1987). This amgement is advantageous in the event of

a disease to a single side, The brain c m rhen use the information Eom a single canal to

detect rotation in both directions in the plane of diat canal (Leigh and Zee 1999)-

The situation is less clear for translations, where a single sids has hair cells with

opposing polarization vectors. Recently, Uchino and colleagues (Uchino et al. 2001)

showed that 50% of their population of utricdarly activrtced vestibular nuclear neurons

receive inhibition from the contralateral utricdar nerve. In contrast, only 10% of

vestibular neurons receiving saccular input were inhibited by activation of the

contralaterai saccular nerve. The effect of this finding remains unclear since, for

example, in the utricle where polarization veccors point towards the saiola, interaurai

acceleration towards the letl will excite the Iatsrd portion and inhibit the medial portion

of the lsft utncle. Accelcration towards the ri$( wiI1 have the opposite cffect.

ïhereiore, this anatomy is conducive to a push-pu11 architecture from a single side

without the use of cornmissural pathways, This rnorphoiogy has been terrned cross-

sûiolar inhibition by Uchino and colIeagues (Uchino et al. 1997) and seems to be the nile

in the saccuk, where there exist very Few commissural connections (Uchino et al. 2001).

However, the validity of extensive use of cross-striolar inhibition in the utride is

doubtfiil. intemural translations towards the lesioned side in patients one week after ihey

had undergone unilateral vestibular neurectomy produced compensatory eye movernents

that were 13% of the responses of normals (Lernpert et al, 1996). Six weeks later, the

compensatory eye movements were back to normal (Lemperr et al. 1999), a time course

that is similar to the recovery for rotation (Smith and Curthoys 1989). in addition, a

greater percentage of neurons were found to have cross-striolar inhibition in the saccule,

than in the utricle (Ogawa et al. 2000).

Dynarnic afferent behaviour for primates is available for the squirrel (Fernandez

and Goldberg 1976c) and rhesus monkeys (hgelaki and Dickrnan 7000). Additional data

is available for pigeons (Si et al. 1997), Frogs (Blarks md Precht, 1976) and other

anirnals, however, the discussion of the dynamic behaviour of at'ferents will be restricted

to primates. Figure 1.7 depicts the frequency response of the transfer functions for

average regular and irreguhr libers imervating the otolith vrgans wtiich are depicted in

Table 1.1. The blue portion of the ploc is the extrapolaced Fernandez and Goldberg result

to frequencies geater than 3Hz.

The data from Fernandez and Goklberg is limited in that the ma..irnurn fiequency

tested was 2 Hz. On the other hand, AngeIaki and Dickman recorded From afferents for

I Regular

Frequencies up to 10 Hz. As can be seen frorn Fiame 1.7, both studies found that the

.hgelaki and Dickman, (2000)

Irregular

1

irregIar units are phasic, increasing markedly in sain as the frequency increased.

However, this is the mean of irreplar fibers, which show a spectnun of responses

Fernandez and Goldberg, (1976~)

s''.l5 (1 i 0.077s)' 'j R(s) = -82

(1 + 0-07s) 1 + . 1 8 8 ( 4 0 s ) ~ ~ ' ~ ~

I t 69s 1 i-,016s

Table t.1 Transfer function for otolith prirnary afferents for the squirrel monkey (Fernandez and

Goldberg 1976c) and for the rhesus rnonkey (Angelaki and Dickman 1000).

s"" (1 + 0.000 1s)' L2 [(s) = 0.70

(1 + 0.0 1 1s) I+IOls 1 + -009s 1

ranging iÏom low to high sensitivity. (Note that the Fernmdez and GoIdberg data has

been extended to IO Hz by using their models in Table 1.1). On the orber hand, regular

uni& only doubled in gain in going h m DC to 2 Hz. In addition, phase leads at Iow

frequencies were followed by phase lags at higher frequencies. The irregular units

depicted increased their gain 20 tirnes horn DC ro 2 Hz and had geater phase Leeds that

regular units. The only divergin; behaviour behveen the two studies is the phase of the

reguIar units. The extrapolated phase for the Fernandez and Goldbers smdy begins to Iag

acceleration as the Frequency is increased while the hgelaki and Dickman study actually

began to lead acceIeration as the fkquency increased. NevertheIess, both studies show

that otolith organ afferents do indeed carry accelerarion information to the brain. This is

in contrast to canal afferents which, as stated enrlier, carry a signal in phase with anpuIar

head velocity (Fernandez and GoIdberg 197 1). Therefore, vestibular nuclei neurons

receive information about the mgular velocity and translauona1 acceleration of the head

during morion chat includes both cranshtion and rotation. How vestibular nuclei neurons

process this combined information is one of the topics of this rhesis.

M a y hypotheses have been proposed as to the possible roIe for the different

dynamics of the afferents. Recenrly, it has been suggested that irregular afferents take

part in the viewing distance modification of the VOR (Chen-Huang and McCrea 1998;

Pingelalci et al. 3000). In addition, reguIar and UTepiar afferents are proposed to have

different functions for motor Iearning and adaptation of the VOR (Lisberger and Paveiko

1988; BronteStewart and Lisberger 1994; Minor et ai. 1999). Tt has even been proposed

that the different afferents with different dynamics drive different reBexes. Specificdly,

Fiirc 1.7 Bode ploe of rrgPlrr rad irngulir rflercnts fnw the otdiil ogm of tk sqaiml rad

rhcsm rnoakeys A&D: Aagchki and Dickmrn, (2000). R ~ g p l m am m b k k , lmeguhrs ha Rcd.

Femrnda r d G d d k r g ody tuîeâ abc+ rffercnts to f r e q r i c k op to 2 tTz T k erkœioi of*

rcspoa~e of theu iifertnts is s b m in Mut.

The regular afferents have ken proposeci to drive the VOR, and the kgular affaents

the vestibulo-coüic reflex (VCR) (Highstein et al. 1987; Minor and Goldberg 1991). No

proof exists that any of the above hypotheses is correct.

Merents in general innervate hair ceh with simïiar morphoIogical polarization

vectors (Feniande2 et al. 1990; Baird and SchuE 1994) and thetefore may be expected to

exhiiît cosine tuned behaviour. Cosine tuning refers to the modulation of the magnitude

of the response as a fiuiction of the cosine of the angIe betwew the stimulus and the

polarization vector of the hair cek For example, ifthe stimuius is paraüel to the

poiarization vector, then the hait ceIl is m;uùmally excited whiIe ifthe same stimuius is

oriented 90' to the polarization direction, then the stimulus sbuld produce no response.

28

On the other hand, if the stimulus is antiparallel to the polarization direction, then the hair

ce11 should be hyperpolarized. Afferent innervation ofhair cells widi various polarization

vectors (spatio-temporal convergence or STC) has been proposed as a means of

generating dynamics that could be used to generate signals that drive the tVOR (Angelalci

1992; Angelalci et al, 1992; .Angelalci et al. 1993). However, Angelaki and Dickman did

report that their afferents were indeed cosine tuned. (Note that this does not prec1ude

STC in the brainstem). However, Fernandez and Goldberg (Femandez and Goldberg

1976b) found that the nul1 directions of their afferents were on average 224' apart, not the

180" expected from a cosine tuned behaviour. This suggests an asisymmetry behveen the

excitatory and inhibitory directions. Indeed, Fernandez and Goldberg did find such an

asyrnrnetry and even demonstrated that orthogonal forces have an excitatory effect on the

primary afferents. This behaviour however may not affect the signal processing in the

vestibular nucleus since vestibular nuclei neurons presented in this thesis exhibit no nul1

direction and therefore receive conversence fiom many afferents (see also Angelaki and

D i c h a n 2000).

1.3 Efferents

Efferent Libers arïse laterd to the abducens nucleus (Goldberg and Femandez

1980) and have been shotvn to synapse on the calyx terminals fibers innervating type 1

hair ce1ls (Sans and Highstein 1984) and directly onto type II hair ceIls (Gleisner and

WersalI 1975; Sans and Highstein 1984). Like afferents, efferent fibers also travel Ï n the

eighth nenre but make up Iess than 0.3?/0 of the total nurnber of fibers (Goldberg and

Fernandez L980). The purpose of the efferent system is still subject to debate. The time

29

course of the falling phase of the respome of efferent fibers is irregular and proionged

indicating possible multisensory convergence on efferent neurons (Precht et al. 1971).

Goldberg and Fernandez, (1980) have proposed that the efferent system, by

exciting the afferents, could serve CO prevent inhibitory saturation. However, this

hypothesis has received little support since efferent activation has been shown to excite

and inhibit the prirnary afferents (Rossi et al. 1977; Rossi et al. 1980; McCue and Guinan

1994; Brichta and Goldberg 1996; Brichta and Goldberg 2000). It has also been

suggested that if the efferent systern is activated in anticipation of movement, then it

could be used to svitch the vestibular system h m a postural mode to a volitional mode

by inhibiting units thar couId be saturateci by Iargs head movsmenrs and activating units

that have large dynamic ranges (Brichta and Goldberg 1996; Brichta and Goldberg 2000).

Highstein and Baker, (1955) reported that efferent vestibular neurons in the toadfish

increased their tiequency of discharge when the fish was aroused Iending support to this

hypothesis. Althou$ many theories exist, the exact function of the efferent system

remains elusive.

1.4 Vestibular Nudei

The vestibular nuclei, Iocated in the medulla and pons, are divided into a medial

(MW), IateraI (Lw, superior (LVN) and inferior vestibular nucleus (NN). In

addition, there are several subgoups dismbuced around the major nuclei named x, y, z, f

a d 1 goups and the interstitial nucleus of the vestibdar nerve (Gacek L969; Brodal

1984). The y-goup is by far the larges of the s u b p u p s and predomùiantiy receives

Figurt I I Tbt vcstibulrr nucleus cdor codd according to the terminaiions ofafkrcots

originatiag from varioirs pcripheral organs. R d indicatcs innervation h m tht burimatal rad

anterior csar4 yellow is h m the pmterior mm4 stars are from the sicetût rad s q u i r n from

the atricle. DoMd pattern is innemation f m al1 three canals. Widespread coovergence h m the

various eodorgaas is strrsJed in tbis f i i re . SVN: Supcrior Vcstibnlir Nockm; LYN: LaCd

Vestibular Nucleus; IVN: Inferior Vcstibular Nucleus, MVN; Medial VcstibPlir Nucltm.

Saccular affèrent input (Gacek 1969) and pmjects to the oculomotor nucleus. In addition,

it receives floccuiar input and additional head velocity information probably h m the

superior vestibuiar nucleus (Partsalis et al. 1995). Additional and miprocal cerekllar

connections exist between Groups f and x (Buttaer-Ennever 1992).

1.1.1Central Termination of Regular and lrregular Afferents

Sato and Sasaki, (1993), using a combination of intra-auond staining and electron

microscopie techniques on horizontal semicircular canal afferents sliowed that regular

and irregulrtr fibers contacted many vestibu1ar nuclei neurons prirnarily in the superior,

medial, and inferior vestibular nucleus. in addition, they strowed rhat Iarge vestibular

neurons were innervated exclusive1y by irregular fibers while srna11 vestibular neurons

were innervated by both regular and irregular fibers. Large diarneter alferents from the

vertical canals in the turtle have been s h o w to terminate in the rostrai region of the

medial and infenor vestibu1a.r nuckus while smaIIer fibers innervate the caudal regions OF

the sarne nuclei, which plays a different role in the control of head movement than the

rostrai region does (Huwe and Peterson L 995). There fore, these studies suggest that

morphological segregation of aff~trent innervation is accompanied by hcrional

specificity.

Gtricular fibers project to regions in the vestibuiar nucleus ba t overlap with the

innervation patterns of the horizontal semi-circular canals (Dickman and Fang 1996).

These fibers project mainly to the intërior and lateral vestibular nuclei although few

projections EO the superior and rnedid nuciei do exist (Imagaiva et al. 1993; Buttner-

Ennever 1999) (SVN c o ~ e c t i o n s of utricular ongin are not shoivn in Figure 1 .S).

Saccular fibers innervate regions that aiso receive verticai canal fibers (Dickman and

Fang 1996)- in addition, specidized gangiiit within the vestibular nucreus, such as the

regions that are presumed responsible for the VOR or the VCR, receive inputs that differ

in their behaviour. Neurons that make up the VOR pathway receive regular and irre,dar

input wtiiIe the region that projects to the cervicâi section of the spinal cord receives ody

irregular input (Highstein et al. 1987; Boyle et al. 1992). However, this se,sregation is Far

5om comprere since there is extensive arbonzation in the vestibular nuclei (Lysakowski

et al. 1993,; Goldberg et al. 1994). There are, however, contradictory srudies as to the

types of inputs received. Funcrional ablation of irreguIar afferents achieved by injecting

modal current into the e u ddoes not affect the aVOR (Minor and Goldberg 199 1) which

implies that there is no i r reyhr fiber input in the aVOR pathways. However, Arigelaki

and colleagues (hgelaki and Perachio 1993) did observe a dtcrease in eye velocity

dunng periods of galvanic stirnuhtion (injection of current which reversibly silences the

irregular fibers) during constant veiocity rotation. One possible explmation for the

discrepancy of the Minor study with the results of Boyle et al. (1992) and Highstein et al.

(1987) mentioned previously is that the irregular inpuc to the vestibular nucleus may

serve to modi@ the behaviour of the VOR and thrir efkct is ihcrefore unobservable

under certain conditions (Chen-Hum2 and 5TcCrea 1993; Chen-Huang and McCrea

1999). For example, functional ablation studies found that the irre;ular afferents are

important for viewin; distance modification of the aVOR but have IittIe effect on the

VOR during rotation about an x i s in front or behind the animal (eccenmc rotation)

(Chen-Huang and McCrea I998). The different sffects observed during eccentric rotation

were attributed to changes in the aVOR component (Chen-Hum3 and McCrea 1998). in

contras, other studies usin,o hc t iona l ablation of irregular rifferents during ri pure otolith

stimulus noted a rnarked decrease in viewing distance reIated changes (hge lak i et al.

2000). One problem with the Chen-Huang et ai. (1998) result is that interaction between

aVOR and tVOR siyrtls may be nonlinear. As will be discussed behw, the generally

accepted assump~ion of Iinearity is widdy used in vestibular research and desperateiy

needs to be tested. Part of this thesis is dedicated to the elucidation of signal interaction

in the vestibular nucleus, As will be shown later, we found the interaction of rotational

and tnnslationai signais in the vestibular nucIeus to be clearly nonlinear.

1.4.2 Cells in the Vestibular Nuclei

None of the neurons described in the cesurts section of this thesis have any eye

movement s igals on them (see Methods). However, the neurons in the vestibular

nucleus are diverse and are narned based on the types of signals they convey. These cells

include t ) Position-vestibuIar-pnuse (PVP) neurons, 2) Burst-tonic (BT) cells, 3) Eye-

head velociry (EHV) netirons ,4) Floccular Target Neurons (FTN) (although these may

be the same as EHV, see below), 5 ) VestibuIar-only (VO) cells and 6) Vestibular pause

cells (Miles 1974; Fuchs and K i m 1975; Keller and Oaniels 1975; Keller and Kamath

1975; Lisberser and Miles 1980; Tomlinson and Robinson 1984; Scudder and Fuchs

1992; McConville et al. 1996; TomIinson et ai. 1996).

The firing rate of PVP ceHs is proportiond EO angu1ar head verocity and eye

position when the head is stationary and ceases during a saccade. it is thought to be the

second neuron in the hee-neuron arc of the aVOR (Chubb et al. 1984; Tomlinson and

Robinson 1984; Scudder and Fuchs 1992; Cullen and McCrea 1993). Evidence for this

cornes t'rom the tïnding that PVP cells involved in generating horizoncd eye movements

project directly to the contralateral abducens nuclei and that aeren ts have been s h o w to

monosynaptically activate PVP celIs (McCrea et al- 1980; Scudder and Fuchs 1992)-

PVPs aIso can make irihibitory connection to the ipsilatenl abducens (11% of the

popuiation of Scudder and Fuchs, 1992). There are aIso PVPs that rnake monosynaptic

34

connections to the oculomotor (third) nucleus and participate in vertical eye movements

(Tomiinson and Robinson 1984; McCrea et al. 1987). Eye and head veiocity signais

converging onco PVP cells act synergistically, since eye position sençirivity is in the

opposite direction to head velocity sensitivity (Scudder and Fuchs 1992; McConville et

al. 1996). This is true for both type t and type U PVPs, where type 1 indicates an increase

in the firing rate in response to ipsiiateral head velocity and contralateml eye velocity and

type U is just the opposite. Mmy researchers have fiequently used linew techniques in

order to ascertain the head or eye velocity sensitivity ofthese cells (Scudder and Fuchs

1992; PvIcConville et al. 1996). In general, the sensitivity of PVP neurons to eye

movements is measured by having an animal pursue a target. Similady, the head

veiocicy sensitivity of these cells cm be measured by recording dunng VOR cancellation

jlookin; at a tarset that rotates with the body). it is then common practice to use these

sensitivity values to predicc the behaviour ot'PVPs. However, this form of Iinear analysis

has not yer been validated. hdeed. it has been known for many years that linear

summation of signais poorly predicts their behaviourdu~g scable gaze (Tomlinson and

Robinson 1984).

The EKV cek , in contnst to the PVP, fire for eye and head movement in the

same direction- Contralateral EHVs increase their firing rate in response to contralaterd

eye and head velocity (Scudder and Fuchs 1992; McConville et al. 1996) whiIe ipsilaterai

EHV have opposite characteristics (Angelaici et al. 2001). It is beiieved that these cells

are a subset of floccuku tarset neurons (FTN) (Lisberger and Fuchs 1978; Lisberger et al.

1994; McConviIk et al. 1996). Like the EHIrs. FT;Nç also encode eye velocity, eye

position and head vetocity ahhou& their eye ve1ocity signal can be contraiateral or

ipsilaterally directed (Lisberger and Paveko 1988; Broussard and Lisberger 1992;

Lisberger et al. 1994; Zhang et al. 1995).

Vestibular-only neurons fire dwing translation and rotation of the head and have

no eye position on them (Tomlinson and Robinson 1981; Scudder and Fuchs 1992;

Tomlinson et al. 1996; McCrea et al. 1999b). Ai1 of the single unit data descnbed in this

thesis came fiom this type of ceII. Aithou$ there are vestibular-only cells that receive

pure otolith or pure canal input, most of the ceils described in tliis thesis received both

types of input. Their behaviour is perplexing and rheir exact role unknown. Recently it

was shown that VO neiirons decrease their sensirivity to head motion during a head on

body movements (Roy and Culien, 200 1) and a cornbined eye-head gaze shift (McCrea et

al. 1999b) leading to the hypothesis that efkrence copy of the neck motor command

suppresses the activity of these cells (McCrea et ai. 1999b; Roy and Cullen, 200 1).

However, there are hvo problerns with this interpretation. Specifically, the auis of

rotation of the head during head on body movernents is in the back of the head whkh

activates the otolith organs to a qreater degree than wouId passive rotation through the

interaura1 a.uis. In addition. there is no guarantee that the plane of head rotation dunng

head on body movement is the same as during passive head movements. These

objections render the efference copy conclusion moot. Aitemarively, these neurons,

especially ones in the LW, MW, and IVN (but noc in the SV'i) project to the spinal

cord via the laterat vestibuio-spinal tracts (LVST), the medial VST (MVST), and the

caudal VST (CVST) (Akaîke 1982; Boyle et ai. 1992). h addition, these ce1Is project to

the rostnl tàstigiai nucleus in the rhesus monkey where most of the neurons also exhibit

a combined canal and otolith input (Siebold et al. 2001, 1997)- Endeed, the rostrai

fastigial nucleus receives extensive input From the vestibular nucleus (Siebold et al. 2001)

and minor input kom vestibular afferents (Sato et al. 1989; Siebold et al 2001) making

the cerebellum the most Likely target of these vestibular neurons. The exact function of

these cells is h o w n although there do exist some hypotheses. For example, they could

be a part of a pre-processing circuit for the VOR (Tomlinson et al. 1996) or more likely

contniute to vestibulospinal reflexes as suggested by their projections to the fastigial

nucleus (Siebold et ai. 1999; Thach et al. 1992). In this thesis, we specifically sought out

cells without any eye position on them in order to eliminate the possibility that the

observed response differences during different paradips might be due to differences in

the eye movements evoked by the vanous stimuli.

VO neurons are ideal for the study of convergence of rotational and translational

sigals. Given that natural head movements are composed of a combination of

translation and rotation (Grossman sr al. 1988; Grossman et al. 1989), then elucidating

the types of interactions behveen thesr s iga ls is paramount for the understanding of

vestibuiar reflexes. Up to now, both these stimuli have been introduced simultaneously

by using eccentnc rotation (rotation around an a i s removed fiom the interaural line).

(Tomlinson and Robinson 1984; Viirre et al. 1986; Gresty et al. 1987; Tomlinson et al.

1996; hge lak i and Dickman 2000). This paradi-em introduces tangentid and centripetal

accelerations and rotational accelerations (Figure 1.9). Given the different dynarnics of

centripetai and tangential acceleration, care c m be taken in the design of the experiment

to eliminate the effect of centripetal acceleration. This can be easily accomplished by

noting that the centripetal acceleration is sirnila- to a high pass tiltered signal, white the

tangentiaI acceteration is aIso hi&-passed, but with a lower corner fiequency. By

conducting the expenment in the stop band of the centripetal acceleration, one c m ofien

study the effect of only two stimuli on the VO cells. The centripetal and tangential

cl) 7

acceleration induced by eccentric ratation can be descnbed by a,=r(-)- = r ( ~ o ) ' and dt

d'v u,=r* = .clro2 respectively, where y is the angular position of the head, A is the

clr-

amplitude of rotation, o is the fiequency and r is the radius of rotation. Therefore,

when a, and a, are peak accelerations, a,=rla, and by making A sufficiently small, it is

always possible to keep the peak centripetal acceleration below the threshoid of

detectability for the otolith organs (0.005 g; 1; = 9.8mls') (Wilson and MeivilI Jones,

1977).

In the past, before the advent of the sled, linear techniques have been applied to

PVP, FTN and VO celIs in order to calculate the sensitivity of the various individual

signais converging onto them. Experiments utiIizing the methods outlined above

calculated the translational sensitivity of the VO ce11 by subtracting the Iinearly

calculated rotational contribution to the firing me. Specifically, an animal wouId be

rotated on-ir~is (about an ~ x i s centered on the interaural line so that no translationa1

acceleration exists) while the response of a neuron is being recorded. Given the

rotationai attributes, such as veiocity or acceleration, the sensitivity of rhe ce11 to the

stimulus can then be easiIy calculated. Then, the animal is shîfted off-ais, so that

eccentric rotation c m be applied inuoducing a cangenual acceleration. Note that the

rotational stimulus does not change during the eccentric condition since the sernicircuIar

c d s continue to sense the same rotationai acceleration. The total forces during this

condition do change though, as tangentid and centripetai accelerations, which

d A x i s of rotation 1

acceleration

Figure 1.9 Off-aris rotation. o r eccentric rotation, is an ideal stimulus that generated both tangential

and rotational acceleration. Centripetal acceleration is also generated but careful choice o f

rotational attributes csn render i t insignificant. Also note that although the rotation does not change

between the ovo conditions depicted (nose in vs. nose out), the tangential and centripetal

mielerations change direction.

Are dependent on the distance of the head from the a i s of rotation are introduced, Given

that the rotational sensitivity has been calculated, then the rotational contribution to the

response of the cet1 during eccenmc rotation was removed, leaving behind a residuai

signal- Since translationai accelerations represented the additional stimuli during

eccentric rotation, then the additional si_enals recorded (the residual) were assumed to be

otolith in origin. This methodology makes the bold assumption that the interaction

behveen the rotational and translational contribution to the firing rate is linear (Chen-

Huang and McCrea, 1999; Tomlinson et al. 1996; McConville et al. 1996). No proof of

linear behaviour exists in the vestibular nucleus although there may be linear interaction

between vestibulo-ocular reflexes. S q e n t and Paige, (19911, by studying the VOR

during eccentric rotation, have suggested that signais tiom different end organs sum

linearly aithough .hastasopoulos et al. (1997) have found evidence of nonlinearity.

Nevenheless, the assumption of linearity in the vestibular nucleus was necessary since it

was the only way to obtain an estimate of the otolith sensitivity given that sIeds capable

of delivering tnnslational stimuli have only recently become available. Therefore, by

assuming linearity, the otolith response was obtained by subtracting on-mis responses

fiom eccentric responses (Chen-Huang md McCreli, 1999; McConville, et al. 1996;

Snyder and King, 1991). This method has been applied to cells in the vestibuiar nucleus

with and without eye position sensitivity.

However. with the advent of the sled, an apparatus that can deliver pure

translational motion without ruiy rotation. one cm calculate the otoiith sensitivity of

vestibuhr nuclei neurons. The first part ofthis thesis repeats the sxperiments described

above but without the assumption oflinearity. instead, the sensitivity of neurons is

obtained by recording fiom neurons during pure transIations and rotations and comparing

the sum of firing rates decîved From those values to the values obtained during eccenuic

rotation.

1.5 Vestibuto-ocular Reflexes

The main motivation to study s igals in the vestibular nucleus is co elucidate

mechanisms and signal processing that rnust occur in order to drive the various vestibular

refiexes. Although experirnental setups usually elicit pure rotations or translations, in

nature, pure rotations seldorn occur since the posterior location of the axis of rotation of

the head also excites the otolith organs. Since rnost natural head rnovements are

cornposed of simultaneous translations and rotations (Grossrnan et al. 1985; Crane and

Demer 1997), it is not surprising that there is wide spread (but not exclusive)

convergence ofcanal and otolith signais in the vestibular nuclei (Uchino et al. 2000;

Buttner-Ennever, 2000). It has also been suggested that a convergence in the vestibular

nucleus is necessary in order to cornpensate for inadequate vision stabilization achieved

by otolith stimulation. (Fukushirna and Fukushirna 199 1) although the poor performance

of the tVOR in Fukushima's study may be due ro the low t'requencies used (c 0.85 Hz in

the vertical plane). Nevertheless, numerous anatomical experiments have been conducted

that have verified the existence of a I q e number of cells in the vestibular nucleus that

receive peripheral signal convergence . This convergence, dong with the cornbined

VOR, has been extensively studied (.kgelalci et al. 2000; Viire et al. 1986; Crane et aI.

199%; Snyder md King, 1997; TeIford et al. 1996; Anastasopoulos et al. 1996; Barmack

and Pettorossi. 1988; Sargent and Paige, 199 1; Bronstein and Gresty, 1991).

The discussion to foiiow will focus on eye rnovements eIicited dusing pure

rotations (aVOR) and pure translations (tVOR) Additional discussion \vil1 be given on

the vestibulo-collic reflex (VCR).

1.5.1 Angular Vestibulo-Ocuhr Reflex (aVOR)

The aVOR produces compensatory eye movements in response to rotations of the head.

It is the most thoroughly studied vestibuhr reflex (Schwarz and Tomlinson 1993). There

does not exist a complete mode1 based on kno~vn pathivays in the brainstern that c m

relate head translation to eye movernents for the tVOR in contrast, the aVOR has long

been known to be based on a three-neuron arc; the primary afferent, the secondary neuron

in the vestibular nucleus, the most important being type 1 PVP neuron and the

contralateral EHV neuron, and the oculomotor neurons [TomIinson and Robinson, 1984;

McCrea et al. 1987; Scudder and Fuchs, 1992; McConville and Tomlinson, 1994)

(Figure 1.10). A head rotation to the right requires an eqital and opposite eye rotation to

the left, a task ideally accomplished by the reilex if the rotation occurs in the fiequency

range (0.5 - 5 Hz) (Leigh and Zee 1999). The aVOR is driven by canaIs from both ears.

ipsilateral rotations excite the ipsilateral canals and inhibit the contralateral canals. The

inhibitory signal is then invened and contributes co the excitation of central neurons

dready being excited by the ipsilateral canals. This push-pull arrangement between the

canals leads to a more robust system. .At Lower Frequencies where the aVOR develops a

phase shift and is unable to compensate fuly for the rotation, the visual system is capable

of providing additional compensation. Movement of the right eye in response to a

rotation to the lefi requires the excitation of the contralateral Iateral rectus and inhibition

of the contralateral media1 rectus muscle of that eye. This is accomplished by having

vestibular neurons excite the contralateral abducens nuclei, which is done with a latency

of 1.2-2.0 ms (Baker et al. 1969). internucIear neurons in the abducens project to the

third nucleus via the medii longitudinal fasciculus in order to contact the medial recbu

motoneurom (Figure 1.10).

rotation translation

tVOR

F i i 1.10 Neural sulastrate o f the mgdar r d (propoacd saktmte of tk ) tnulrbioirl v e s t i b

oelilrr rekx s b m daring a kmirrrd r o r i k (SVOR) rad 8 rigLhvrrd brulition (tVOR). Bliw

lines arc inbibitory wbik r d limes arc rscititory. Somc of tk celb ard iw ak rVOR rmd tk tVOR

may k tk srme. Primrry atlbcrcats Lirrm the amb synapse oato v d b a h r nœki ncrrow wbich U

km, actirite t& cwtralrbrnl abdacens For the tVCîR, shami krt is 8 hypotbctirrl arrimgewrt

smggcsted by stvcnl studiu ( d l y Aigehki d rL 2001) empbuizhg its ipsllilrrrl imngcacit

The inbibitory cwacetions for the tVOR are Mt siarvi. Tliimgdmr cd prtiripîhg im c m

striolir inhibitioa is of unkaara type. 't' in kgend is erritriory, 'i' in @id ù inbibitory. rVOR

circuit f m L e i i and Zœ, 1999 wbik tWR iroir Augehki tt d. 2001,21cClilo et a l 1994; Uckiia et

rL 1997.

1.5.1.1 Eye Plant

The ocuiar motoneurons are thought to require signais proportiond to eye

velocity and eye position and c m be appro'iimated by (Robinson and Keller 1972;

Robinson 198 1):

where R is the tiring rate in spikeslsec, Ro is the background firing rate (or the firing rate

dE when the eye is in the primary position), E and -are the eye position and eye vetocity

rit

respectively and k and r are thought to be constants. Equation 1.2 was actually

developed to mode1 behaviour during saccadic eye movements but has frequently been

used to describe slower eye movements (KelIer and Robinson 1972; Robinson and Keller

1972). For the aVOR, the velocity command cornes from the afferent signa1 which

encodes head velocity, while eye position is obtained by intept ing the eye velocity

cornrnand. Other models similar to Equation 1.2, but that include higher order

derivativss of eye position have been proposed to better approximate VOR eye

movements (Fuchs et al. 1988; Minor and Goldberg 1991). Sylvestre and Cullen, (1999)

hnher vdidated the need for higher order decivatives in Equation 1.2. More importantly

however, they have shown that Ro, k and r are not constants but are functions of eye

velocity. Specifically, in response to an increase in eye velocity, the sensitivity to

velocity and position decrease, wïth the velocity sensitivity decreasing by a greater

amount than the sensitivity to position. In addition, the backgound h g rate (%)

increases as the eye velocity increases. This is a signifrcant result since di modeIs of the

VOR assume the plant that is being driven has constant viscous and elastic coefficients,

The authors attribue this behaviour to a change in the behaviour of the antagonistic

muscle ofthe eye, whose behaviour is not considerzd in Equation 1.2. Surprisingly, data

presented in this thesis obtained Erom the vestibular nucleus will be shown to behave in a

simiIar manner.

1.5.1.2 Neural Integrator

The velocity s i p a l is then fed through the neural integrator in order to obtain the

position signal required by the eye plant (Skavenski and Robinson 1973). The need for a

position signa1 c m be appreciated if one considers that animnls are able to hold eccentric

eye position &ter cessation oFa rotation. It is generally established that circuits for the

horizontal neural integrator lie in the nucleus prepositus hypoglossi - medial vestibular

nucleus (WH-b1V-u) complex (Cannon and Robinson 1987; Cheron and Godaux 1987;

McCrea and Baker, 1985) even though other locations could also exist as part o f a

distributed integrator (Kaneko 1999). Recent pharrnacological inactivation of the

paramedian tract (PMT) in the brainstem, whose exact function is unknown, produced a

leaky integrator (Nakamagoe et d,7000), suggesting that PMT cells provide the

cerebellum with signals essential for neural integation. This is not surprising as lesions

of the flocculus and the paraflocculus, areas which receive input kom the PMT, also

effect neural integraion (Robinson, L974; Zee et al. 1981). It should also be mentioned

that afferent signais fiom eye muscle proprioceptors have been found to have an effect on

activiry in the NPH and the M W (Ashton et al. 1988). Therefore, NPH could distribute

eye position signals derived Erom muscle proprioceptors (Donaldson, 2000).

Nevertheless, untiI more work is done to elucidate the exact function and on,@ of s iga l s

in the WH, we shall adopt the classic view of a neural integator that functions to

transfocm velocity into position signals.

The neurai integrritor has been modeled by positive feedbacks circuits (Cannon et

al. 1983; GaIiana and Outerbridge 1984; Robinson 1989)- Cannon et ai. (I983), building

on positive feedback models of a neural integrator of Keller and Kamath, (1979)

presented a mode1 that accurately integrated the input signal while leaving the

background discharge rate intact-as required. Additiond modeling efforts have

improved the rnodeling of physiological data (Arnold and Robinson 1997; Anastasio

1998; Seung et al. 2000). However. al1 these developments rely on positive feedback

loops with a gain dangeroudy dose to 1.0 in order to extend the time constant of the

integator. Assuming the time constant of the membrane o f a neuron to be 5 ms, then the

gain of the feedback loop must be in the order of 0.99975 in order to extend the time

constant to a physiological value of 20 seconds. in addition, assuming that therere are

4,000 neurons in the circuit and each neuron contributes equally to the feedback gain (for

exarnple, each one would contribute 2.4993e-004 to the overall feedback gain), then if

one neuron should stop contributing, the time constant will be reduced to 10 sec! 4,000

neurons may not even be available for use in the integator. For example, the goldfish

integator has a time constant of about 10-20 seconds but only has 25-40 neurons

participating in the neurai circuit that perfoms the integation (Pastor et al. 1994; Aksay

et ai. 2000). Shen, (Shen 1989) suggested an alternative to positive feedback in the form

of Short-term Potentiation (STP). The use of STP is of great benefit to the stability of

neurai integraror designed using a positive feedback since it increases the time constant

of the membrane. However, more recently, Seung et al. (2000) suggested that STP is

indeed usehl if it is used by the system in conjunction wïth positive feedback to extend

the time constant ofthe membrane to 100 ms. This c m be accomplished by using

predominantly NMDA receptors to depolarize the ce11 resulting in a much more stable

and robust feedback integrator mode!. Given that the integator extends into the

vestibular nucleus, then NhlDA receptors could aiso participate in the signal processing

of vestibular afferent signals.

1.52 Translational Vestibulo-Ocular Reflex (tVOR)

In contrast to the wealth of information available about the aVOR, relatively Little

is known about the tVOR. Vestibular neurons have an abundance of input signais

relaying information about the transtacion of the head and its position with respect to

,gavity (hgelaki and Dickman 3000; Fernandez and Guldberg, 1975; Uchino et a1.1997;

Ogawri et ai. 1000). The at'ferents that supply the inpur seem to be fairly consistent in

their behaviour, simply encoding the accekration of the movement in a pmicular

direction. In contrast, cells in the vestibular nucleus that receive otolith input (otolith

cells) have cornplicated dynarnics that deviate Iiom the aiTerent behaviour (Angelaki and

Dickman, 2000; Tomlinson and McConville, t 996 ). It has been suggested that the

complexity is an outcome of spatio-temporal convergence of otolith afferents (hgelaki,

1992; Angelaki, 1993; Bush et al. 1993). Additional complications a i se when one

considers that accelentions due to gavity elicited d u ~ g a head tilt and while translating

are indistinguishable to the otolith organs, and yet pmduce diEerent and compensatory

eye movements (Paige and Tomko, t 99 1 ; -hse[aE;i 1998).

The complications for the tVOR are mainly due to the fact that no eye rotation

can compensate for the retinal slip produced dunng translation. As a result, the tVOR is

highly dependent on target distance and the direction of gaze (McHenry and Angelalci,

2000; ,Angelalci, 1998; Paige and Tomko, I992a, 1991b; Telford et al. 1997). For

example, the eye movements necessary to stabilize ;aze during an interaurai translation

are dependent on the tarset distance, target eccentricity, and translational head velocity

(Viirre et al. 1986; Paige and Tomko 199 1; Snyder and King 1992; Telford et al. 1997;

hge lak i et al. 2000). Even more complicated are the eye movements elicited dunng

naso-occipital translation. Translating foward whiIe fixating on a target in fiont of the

left eye requires no movement !rom the left eye, but ri Iehvard rotation fiom the nght

eye. Remarkably, this behaviour has been shown to occur (McHenry et al, 2000). In

addition, based on our knowledge of the appropriate s iga ls that could drive the plant,

otolith s iga ls seem to require more cornputation than canal siynals since the afferents

encode acceleration.

P n m q dferents onginating in the utricIe predominantly innervate the Iateral and

infenor vestibular nucleus with some overlap into the mediai nucleus(Ima,oawa et al.

1995). The lateral and inferior nuclei are more associared with spinal rather than

oculomotor reflexes (Buttner-Ennever 1999 Kushiro, 2000 k7 1 1). Nevertheless,

geometric considerations for translations dictate that translations require eye movements

for gaze stabilization and this has recentiy been a motivation for the various studies on

the characteristics of the tVOR and its neural substrate (Bronstein and Gresty 1988; IsraeI

and Berthoz 1989; Bush and PvIiIes 1996; McConvilIe et ai. 1996; Telford et ai- 1996;

Tomiinson et al. 1996; Tefford et ai- 1997; ,bgeIaki L998; AngeIaki et ai- 1999; McCrea

and Chen-Huang 1999; Angelaki and Dickrnan 2000; Angelaici et al. 2001). As already

mentioned, the aVOR iitilized the processing of type 1 PVPs and contralateral EHY in

order to drive the eye in the appropriate direction. Recently, .Angelalci et al. (2001)

hypothesized that the tVOR could be driven by type iI PVPs and ipsilateral EHVs (Figure

1-10). This arrangement, dong with anatomical evidence fiom other studies (üchino et

al, 1994; Uchino et al,, 1997), is depicted in Figure 1.10 (tVOR). Note that the Function

of cross-striolar inhibition depicted by the blue line c o ~ e c t i n g hvo vestibular neurons

(NOR), is not known and is included for completeness. As can be seen by the

arrangement depicted in Figure 1.10, the tVOR is depicted as actively driving the eyes on

a single side, while the aVOR is shown to cross over, and activate the abducens on the

opposire side. Of course, both eyes must rnove, and so both systerns have ipsilateral and

contralateral connections. Howevsr, the arrangement shown in Figure 1.10 for the tVOR

is conducive to disjunctive eye movement since the ipsilateral lateral recrus is s h o w to

be activated by signals originating in the ipsilateral utricle.

Ln addition, since trie otolith orsans encode head acceleration, then there is a

potential ambiguity as to whether the acceleration being sensed is due to translation or to

gravity. Although ambiguity can also arise in the saccule since it is also an

accelerometer, studies attempting to resolve the ambiguity problem have concentrated on

the equivalence of stimuli benveen tilts and translations in the horizontal plane. Primary

otolith afferent neurons have been shoivn not to discriminate benveen tilts and intemural

(utricular) translations (Femandez and Goldberg 1976a; Dickman et al. 1991) but the eye

movernents eticited by the identical otoiith afferent input do differ; intemuni translations

have been shown to generate compensatory horizontal eye movements whfIe tiIts eIicit

ocular torsion (Tweed et al. 1994; Telford et al. 1997; Angelaki et al. 1999). Therefore,

the differentiation between tilts and translations must occur centrally.

There are bvo competing hypotheses as to how the brain can resolve this

ambiguity problem, The first, the fiequency filtering hypothesis, states that the fiequency

content of a signal is enou@ to discriminate the stimuli that elicited it (Mayne, 1974;

Paige and Tomko 199 1 ; Telford et ai. 1997). For exarnple, translational signals are

composed of a hi& fiequency spectnim while tilts are of Iow frequency. The second

hypotliesis states that the brain must consider the activity of the semicircular canais to

differentiate tilts and translations (Angelaki et al- 1999). (It is worth noting h a t Mayne,

(1971) did recognize the importance of canal signals in relieving some of the otoIith

m bigui ty.)

If this ambiguity is resolved using a tiequency filtering mechanism, then low

tiequency interaural translations shouid produce Low pass filtered ocuhr torsion. As the

Frequency increases, the low p a s fittered torsion should give way to high pass filtered

horizontal eye movements. Proof that the torsional and horizontal components OP

interaural sye movernents were segregated in frequency came fiorn Telford et al. (1 997)

and (Paige and Tomko 199 1). However, rhese authors espressed the torsional eye

movements and the horizontal eye movement in different units, and therefore, the

characteristics of the responses can not be compared. However, when the different eye

movements are expressed in similar units (such as "/cm), no fiequency segregation of

torsional and horizontal eye movements is observed (Angelaici 1998). instead, it was

hypothesized that the persistent torsion during hi& fiequency translations is related to the

kinematics of 3-D eye movements and its interaction with vergence (AngeIaki et al.

2000). in addition, hi* frequency roll tilts of the squirrel monkey did not produce any

horizontal eye rnovernents, as would be required by the fiequency segregation hypothesis

(Merfeld and Young 1995).

The use of rnultisensory inibrmation was shown to be a better rnechanisrn to

differentiate behveen tilts and translations than that of fiequency filtering (Angelaki et al.

1999). in a recent study, (Angelaki et al. 1999) rhesus rnonkeys that had their

sernicircuIar canais plugged could not discriminate behveen tilts and translations as

indicated by horizontal eye movernents that occurred during tilts. From this result, it

folIows that patients with vertical canal lesions will exhibit horizontal eye movements

upon tilting their head, a simple and srraightfonvard test to conclude vertical canal lesion.

However, al1 4 vertical canals were plugged in the Angelaici study. The effect of a

unilaceral vertical canal plug on eye rnovement during tilt is not yet known. However,

recent anatomic data has estimated that 33% of utricular activaced vestibular neurons

receive posterior canal input (Zakir et rit. 7000). More recently, humans were asked to

assess the degree of tilt dunng eccentric rotation before and after the semicircular canal

signal had decayed (Merfeld et al. 100 1). These authors found that semicircular canal

cues had a large effect on the perception of tilt. However, the paradi-9m to produce tilt

sensation, on-axis rotation for 5 minutes until al1 canal signals decayed and then

increasing the radius of rotation while rotating (translation in a rotating reference h e ) ,

induces a coriolis acceteration in addition to the cenmpetai and tangentid acceleration.

(Translational motion in a rotating reference fnme creates a coriolis acceteration equal to

2 0 v (where w is the angular velocity of the rotating reference and v is the translational

velocity), rvhich is perpendicular to the motion and therefore causes a sideways

deflection), No mention of the effecc of the coriolis force on the sensation of tilt was

made.

The use of semicircular canal signak to indicate tilts is convincing. However,

during the static portion of the tilt, the cana1 signal decays in less than 6 seconds leaving

behind the continued excitation of the otolith organs. Do horizontal eye rnovements

begin to occur afier a prolonged tilt? An ambiguous horizontal translation to a prolonged

(steady state) tilt is a step of acceleration in the opposite direction of tilt, a stimulus likely

not to occur in nature but that occurs everyday in cars and planes. Irregular afferents are

known to adapt &er prolonged stimulation but regular afferent continue to fire

(Fernandez and Goldberg 1976a). Neicher of rhe above hypotheses c m explain why

horizontal eye movements are not elicited during prolonged tilts, afier the cessation of

vertical canal activity.

it has long been knoivn that a disynaptic input exists fiorn the utricle to the

abducens nuclei (Schwindt et al. 1973). Surprisingly, utricular fibers have also been

found to monosynaptically innervate rhe abducens nucleus (Uchino et al. 1994; Imagawa

et al. 1995; Uchino et al. 1996; Uchino et ai. 1997). ï h e role of these connections

rernains unclear as acceleration s i p h carried by ocolith primary afferent fibers are

thou;ht not to be appropriate to drive the eye plant. Models by our lab and others have

shown that such a signal, given a low gain, could in principle provide the proper phase

fead to ensure proper dynamics (Green and G a h a 1998; Musallam and Tomlinson

1999). However, the problem is what exactly are the proper dynamics? Angelaki,

(1998) has conducted a study on the tVOR emproying a Iarge range of frequencies. This

study concluded that horizontal eye velocity was in phase with head velocity for

frequencies between 2-10 Hz, as required for compensation. However, even if eye

velocity was found to be in phase with head jerk, the denvative of acceleration, this

would have been taken as compensatory since for a sine wave, head velocity and head

jerk are L80 degees out of phase, and therefore, eye velocity c m in fact be taken to be in

phase with head velocity. (The only difference between the velocity and jerk of a sine

wave is the amplitude and its sign). However, this kature is an idiosyncmy of a

sinusoid and may evsn be misleading. Other stimulus waveforms such as transients of

head position (approximate steps, where the rise time is finite), have jerk characteristics

that are markedly different from their velocity characteristics (Figure 1.1 L). As c m be

seen in Figure t -1 1, the jerk of a transient is nor identical to the velocity. Therefore, eye

velocity being in phase with jerk does not imply that it is also in phase with velocity once

the stimulus is not a sinusoid. If sye velocity did look Iike the head jerk shown in Figure

1.11, then the eye position wouId have the samc waveform as head acceleration and this

would be the response of ri purely eIastic system.

Part 4 of the results will describe the tVOR in response to such steps. Eye

velocity tvill be çhown to have a similar waveform to head velocity durin5 low

frequencies and head jerk during high frequency steps of position (maximum power of

hi& fiequency spectrum peaks - L O Hz).

The analogy with an elastic system is delibente. Single ce11 recording data

presented in this thesis exhibited behaviour that c m be describecf as an increase in the

'eIasticity7 of the response (see Results). More relevant however is the work by

Sylvestre and Cullen, (1999) who faund that a single Iinear plant mode1 cannot descnbe

both slow and fast eye movements. Instsad, tt nonlinear plant mode[ is needed, They

noted that as the eye velocity increased, the sensitivity to eye position and eye velocity

decreased (see section entitled 'Eye Plant'). However, their data indicates that the

decrease in velocity sensitivity is more pronounced than a decrease in position sensitivity,

fime (sec)

Fi- 1.11 In coitrrst to &mi&, slcp of poaitioa bave jerk c h r r c k m c s tbrt ar t mrrlrediy

difftreot k m velocity. Note tbrt k r e are 3 pcrks in tk jerk Errnct but ody 1 in the veloeity

met.

hdicating an increase in the stiffness of the system, and hence an increase in the spring-

like properties of the plant.

1.6 Otolith ~Mediated Vestibulo-collic and Vestibulo Spinal Reflexes

in addition to the VOR, the canal and otolith organs function to stabilize the head

and body dunng locomotion. Stimulation of the otolith organs has been shown to Iead to

activation of neck extensors by vestibulospinal neurons that originate in the lateral

vestibular nucleus (Sato et al, 1994; lkegarni et al. 199J; Li et al. 1999). The medial

vestibulospinal tract, which arises fiom the media1 vestibular nucleus has also been

shown to give off collaterals to neck muscles (Shinoda et al. 1992) and is the soIe

innecvator of the stemocleidomastoid (Wilson et al., 1995). in addition, the cerebellum

is innervated by a 1ar;e projections of afferents that originate tkom the medial and inferior

vestibular nucleus (Voogd et al. 1996). indeed, the rosual fastigial nucleus has been

shown to modulate with head movements alone suggesting that this area of the

cerebellum is involved in vestibulo-spinal reflexes (Büttner et al. 1991). FinaIIy,

neurons in the vestibular nucleus innervate an area of the reticular formation which in

tum projects to the spina1 cord and neck muscles (Wilson and Melvill Jones, 1972). As a

resuit, signais Gom the vestibular nucleus directly and indirectly work to stabilize the

head and body in space.

Stabilization of the trunk and head may be the predominant hnction of the otolith

organs. The majority of inputs kom the umcle and the saccule terminate in the lateral

and intèrior vestibular nucleus jhagawa et al. 1995). Recent studies of neurons that

receive utricular or saccular input in the decerebrate cat have revealed very few neurons

having solely oculomotor firnction (Kushiro et al. 2000; Zakir et ai. 2000). Specifically,

Kushiro and colleagues identified 91 neurons in the vestibular nucleus that receive otolith

and saccular input by stimulating the uuicular and saccular nerve. Once a neuron was

identified, they then stimulated the ocuIomotor nerve and found that only 3 out of the 91

identified neurons were solely antidromicdIy stimulated From that nerve while 9 others

responded to both spinal and oculornotor antidromic stimulation (Kushiro et al. 2000).

However, this data is confmed to neurons in rhe Iateral vestibular nucleus which is

responsible for spinal retlsxes and the preponderance of vestibulospinal neurons (79191)

was expected. In addition, there is sparse innervation by utricular af'ferents of the MVN

and the 1W which are not considered in the Kushiro study. [n addition, stimulation of

the saccular nerve elicited a response in 13% of al1 oculomotor neurons tested, (30% if

the type of motor neurons are reduced to those in a sample that is involved only in

vertical eye movements) and these response were trisynaptic (Isu et al. 2000). Therefore,

the maintenance of posture is an important function for the otoIith system, but this does

not preclude the need for circuits that drive the tVOR.

Data obtained in the experiments described in this thesis wil1 be modeled in the

hope that the resultant simulations wi11 lead to an increased insight of the system under

study. Most modeling techniques utilized are straightfonvard and are descnied

eIseivhere except for a transformation we have corne to cal1 rime constanr enhancement

(TCE), which needs a bnef introduction. in many places in this thesis, a Rate Limiter

56

and TCE will be used interchangeably since a rate limiter functions as an approximation

to TCE.

TCE, as the name suggests, is a mechanism that hnctions to enhance the time

constant of the decay of a post-synaptic response. Although this is a theoretical

algorithm used to simulate the behaviour of neurons recorded here, it has a direct

correlate with neuronal activity. SpecificdIy, it hc t ions to perseverate the activity of

the post-synaptic cell, rewarding the post-synaptic neuron for being activated. This could

be achieved by eliciting an EPSP in the post-synaptic ce11 that has a time constant that is

a hnction of the interspike interval ofthe firing rate ofthe presynaptic ce11 (and hence

the rate ofvesicular release). For exampk, a spike arriving at the terminal will elicit (by

some mechanism) an EPSP. If a subsequent spike amves within a time window, (less

than lOms for the algorithm used here), another EPSP is eiicited with an increased time

constant, with the size of rhe time constant being proportional to the inverse of the

interspike interval (see Appendix). Othenvise, the tirne constant of the EPSP does not

chanse. This methods assumes that the temporal structure of the arriving spikes carries

additional information. beyond the information transrnitted by the mean firing rate

(deChams and Zador, 2000). This idea proved suificient in simulating the response of

vestibular neurons to steps (see Figures 3.19 and 3.25).

As already mentioned, TCE and a rate limiter wilI be used interchangeably. The

rate limiter can be descnbed by the function:

where S is the cising or falling slope imposed by the rate limiter and r is defined by

~ ( i ) - y(i - 1) r = where tr is the input and dt is the sarnpling rate. If the rate of change of

nt

the input signal in soing fiom y(i-1) to y(i) is bounded by the slew rate S, then the output

is simply equal to the input. The definition given above assumes an equal rising and

faIling slew rate but this is not necessary. As a consequence of this definition, there are

two major differences betiveen TCE and a rate limiter. The first is that the decrease in the

activity of a rate limiter is linear while that of TCE is exponential. The second

difference is that TCE is impIemented in such a ivay that the increase in the tirne constant

is a function of the activity of the neuron, while the rate limiter simply saturates the rate

of chanse of a signal. Despite these differences, the rate limiter could be used as an

approximation to TCE by settins slew rates that are dependent on the activity.

The behaviour of TCE is also similar to short-term potentiation (STP), where the

probability of vesicuhr release increases afier the terminal has been potentiated (Brown

and Johnston, 1983). Let n be the number of reIease sites on the presynaptic terminal,

and if we let p be the probability of reIeasing a quantum of neurotransmitter, then the

mean response size at the postsynaptic terminai d e r the arriva1 oFa spike can be

described by R=npq where (1 is the size of an EPSP. Afier a high frequency stimulus is

delivered to the terminal and potentiation achieved. it has been shown that the probability

changes, from p to p, where p, =p. pp and p, is the ridded probability of release due to

potentiation. Eventually, pl decays exponentiaily and the efficacy of the synapse r e m s

to presynaptic values. According to this definition of R, the response to a step input wiII

be a step output that has its amplitude modulated according to the degree of potentiation.

In order to implement TCE from this definition of S V , an addition term is needed.

58

Specifically, TCE can be implemented if the response size is now defined by

R = npq(1 + =lev' ) where rr is the enhanced time constant and is a function of R, the rnean

response, and A is some constant. (Note that this is equivalent to the enhanced time

constant being a function of the interspike interval, since a l q e firing rate will produce a

large response R, which wili affect r,.). The tffect of this representation of R is that as

EPSP's are generated, r, is increased, which causes EPSP's to be continuously generated,

where in the absence of srimulation, the seneration of EPSP's decreases with time

constant rr. In response to a step input, this definition of R is not a step output, decaying

with a time constant r, beyond the ~ i m e that the step input has vanished. An increase in

the amplitude of the step leads to an increase in the time constant and therefore, an

increase in the time R wiIl be greacer than zero afier the input is zero. This

implementation, although theoretical, aIlowed us to mode1 the asymmetric behaviour of

neurons to be described in the Results section. The spike train extraction used for TCE is

described in the Appendix.

1.8 Hypotheses

Hl: Nonlinearity Using Sinusoids

There is wide spread convergence in the vestibular nucleus. Previous

investigation of the response of vestibuIar neurons to a varïety of stimuIi has relied on the

assumption that celIs in the vestibuiar nudeus behave as linear systems Linearity in a

system cornes about From the nature of the system's excitation and response. Two

general principles, superposition and homogeneity, need to be established before a

system c m reliably be determined to be linear. The principle of superposition has to do

with the additivity of sigals. Thus, suppose a neuron provides a response Ri to an input

Si and a response Rz to an input SI, then to conclude linexity, the principle of

superposition, that the neurons respond with RI + RI to an excitation SI + Sz must be

satisfied. It is aIso necessary that magnitude scale factor, or homogeneity, be preserved

in a linear system. Again, consider a neuron that provides a response RL to a stimulus Sr.

Then for any constant multiple u, the response of the neurons must be URI to a stimulus

USI. SatisQing both these principles ensures that there is no interaction between signal

components and that the amplitude of one sisna1 cannot influence the a m p h d e of

mother. The need to ascertain whether cells in the vestibular nucleus are nonlinear is

necessary since there is extensive convergence in the vestibular nucleus. Here we show

that the underlying assumption of linearity in the some celis in the vesribdar nucleus is

incorrect.

The jirsr Izyporhesis ir thar vesribtilo-only (VO) cells are non-linear and that rorarional

and tmnsfational sigttals converging onro these cefls cornbine nonlinearfy.

H2. Nonlinearity Using Transients

it is misleading to atternpt to ascertain the possible signal processing taking place

in the vestibular nucleus using sinusoids, especially since the finding of nonlinearity.

Often, studies of vestibuiar nuclei neuron will mesure the phase of the output of a

neuron and conclude that caIcuIus is being performed if the phase difference is found to

be leading (or Iagging) 90 degrees. Hoivever, tirne deIays also contribute to phase lags.

In addition, sine waves recorded bom the vestibular nucleus are ollen asyrnmetric, with

the rising phase have a large absolute slope than the falling phase. This feature too, will

lead to erroneous measurement ofthe phase. In order to ascertain the type of signal

processing taking place in the vestibular nucleus, position transients (also called steps of

position) will be used as the p r i r n q stimulus.

Perhaps the biggest advanrage of using steps of position as stimuli is that the

acceleration and the velocity \vavefoms differ not j u s ternporally, but also spatially.

Under ideal circumstances, the inte,ml of a biphasic acceleration curve is a curve that

resembles a Gaussian, peaking as the acceleration undergoes a transition fiom its positive

to its negative values. By using steps of position as the primary stimulus, we will show

that there may exist rime comranr enliancenienr in the vestibuhr nucleus, enabling celIs

CO encode velocity of motion in one direction of the step and therefore inregrating.

Oiv second hyporltesis is rhat poiverfid signal processing ntay be nchieved by urilizing

certain kinds of rionlitzeariries. ,.ln aciciirional /ypodtesis abolir possible ways ro inregrate

rvill be presertred

H3. bIodeling the tVOR

So Far, models of the tVOR have focused on the type of processing that the

p r b q afferent signa1 must undergo before reaching the neural integrator. Here, we

propose a mode1 that does not require any pre-filtering if the input is restricted to

sinusoids of low amplitude and kequency. WC propose that the velocity s iga i is

obtained directly from the neural întegator, whik the position signal is obtained directly

fkom the primary afferents synapsing onto the oculomotor nuclei. This design proved

sufficient to simulate eye movements in response to translational motion.

For oiu third hypothesis. we propose thar tire t VOR c m be modeled by the use of linear

elenierits ifthe stimdrts is resrricted ro sinzrsoids. Specifically, a combiization of afferent

signals along with integrated afferent signal proved adeqtiare to simtilare the t VOR in

response to sinrtsoids.

HJ. Non-cornpensatory tVOR

Our fourth hypothesis is again related iu the NOR. Bode plots depicting the

frequency performance of the tVOR obtaincd using sinusoidal translations have indicated

that eye velocity continues to compensate for head velocity even at IO Hz. However,

even if eye velocity was found to be in phase with head jerk, then the natural conclusion

would be that the tVOR is compensating for the translation, since head jerk during a

sinusoid c m only be distinguished tiom head velocity by the its s i a . However, the use

of other stimuli, such as seps of position, have starkiy different jerk and velocity profiles.

We wiil show that for steps of position composed of a spectrum dominated by low

frequencies, eye velocity is indeed compensaring for head velocity. However, for higher

frequencies, eye velocity Iooks similar to head jerk, a signa1 that is not compensatory. In

addition, the eye velocity during the hish Gequency steps is shown to be the response

expected from an elastic systern. Otrr fotrrti~ ityporiresis is that nonlinear elernents are

needed to model the t VOR in response ro non-sinirsoidal data.

2.0 Methods

The purpose of the studies presented in this thesis is to shed light on the behaviour

of ves t ibu l~ nuclei neurons in response to a combination of rotation and transIation and

to uncover the s iga l processing that otolith signais undego in the brainstem. The

experirnentd equipmenr and the procedures each monkey undenvent reflect the methods

necessary to achieve these goals. The methods outlined in this section serve the purpose

of allowing the investigators to elicit a controiled stimulus of rotation, translation, and

combination of the two while recording from individual neurons in the vestibuhr nucleus

and the position of each eye. In the following sections, the necessary procedures that

ailowed us to Conduct these experiments are outlined in detail.

2.1 Animal Prepariition

Al1 the surgery, expecïments and training rnethods presented in this thesis are

carried ouc in accordance with the Animal LTse Protocol administered by the Office of

Research Services of the University of Toronto through the Division of Comparative

Medicine. In addition? the candidate compieted the Short Course on Animal Care given

by the ~ iv i s ion of Comparative Medicine and therefore was trained in the handling of

mimals.

The data in this thesis was obtained f3om hvo female rhesus monkeys weighing

6.5 and 5.9 kg. One monkey tvas 4 years oId when experiments comrnenced (born: June

27,1996), whik the other was 5 years old. Animais were quarantined for 3 weeks upon

arriva1 and tested systematically (once a year) for the Herpes Sirnian B Wus, Simean

retrovirus (SRV), Simian Imrnunodeficiency Virus (SIV), Simian T-Lymphotropic Virus

-1 (STLV-1) and Measles, and once every 6 months for tuberculosis. Ali tests on atl

occasions were negative. In addition, neither monkey had any history of exposure ta

vestibulotosins.

Upon completion of the quarantine period and the establishment that the monkeys

were fiee of disease, the monkeys were allowed a few days of leisure to become

acquainted with the investigators. Thereafter, the monkeys were fitted with plastic light

weight collm and trained to come out of their cage and sit in the primate chair by the use

of the pole and collar method. The primate chair was made fiom Plexiglas and reinforced

in order to minimize the natural oscillations that could a i se during translations and

rotarions. A few days Iater, the monkeys were brought into the lab and introduced to the

room were experiments were to take place. The room has an ares 8x8 foot squared and

is light-seaied and covered with a steel mesh in order to keep electric fields on the outside

so that interference is minimized. The monkeys were rewarded with fruits and peanuts

for not vociferously compiaining about being in the primate chair. Eventually, the

rnonkeys became servile and would sit in the chair without feu. This is a necessary step

and constitutes a milestone for the investigator. Water deprivation is prohibited by the

animal protocol and therefore, training by the use of positive reinforcement can only

commence upon the zstabiishment of a tmsting relationship bebveen monkey and

investigator.

2.1.1 Surgical Procedures

Al1 surgical procedures were carried out in sterile operating conditions at the

University of Toronto under the supervision of a veterinarian. The monkeys were

initially anesthetized with ketamine which was injected intramuscularly. A tube was

then expeditiously inserted into the monkeys' trachea in order to administer Halothane

and oxygen during surgery. The monkeys were then prepared for surgery by scrubbing

the areas to undergo incision with Becadine. Oxygen saturation, heart rate and

temperature were continuously monitored throughout the duration of al1 surgeries.

Binocular search coils (Robinson, 1963) were used to measure eye position. The

search coils were planted subconjucativally xcording to the methods of Judge et al.

(1980). Each monkey undenvent nvo surgical procedures; during the first procedure, the

head-holder was fixed to the skuIl and one eye coi1 was implanted. The head-holder is

cornposed of titaniurn and is T-shaped when observed Eom above. It has a height of 1.5

cm and a dorsoventral length of 2.2 cm. On top, the bar is circular so as to fasten into a

U-shaped head-holding bar that also attaches to the chair and renders the head immobile.

ï h e head-holder has perforated rectangular staidess steel anchoring bars that protrude

from the left and right side so that upon placement of the head-holder on top of the skull,

they were oriented perpendicular to the midline. The anchoring bars were curved so as to

follow the contour of the skull. An incision thraugh the midline about 2 cm posterior CO

the brow was made along with mother incision that was perpendicula. to the k t . The

skull was then exposed by ciearing away the tissue that occupied an area equivaient to

that of an e1Iipse d e h e d by a major and minor axis composed of the hvo incisions. Four

stainless steel screws and hvo inverted titmÏum T-boIts were passed through the

anchonng bars and secured to the skul1. Holes for the screws were predrilled using a

hand drill and threaded at the exact locations where perîontions of the anchonng bars

rested. Cranial cement, which will be poured ont0 the screws to reinforce the rigidity of

the head holder, will not be used until the eye coil is in place.

During the sarne surgery, a singIe eye coil was implanted. The eye coil was

cornposed of three ioops of teflon coated stainless steel wire. (The word 'coil' refers to

the three loops and al1 residual wire). The diameter of the loops was 17mm. The \ i r e s

emanating fiom the loops where then tightly hvisted together so that 2 wire leads

remained about 2 cm in length frorn the end of the twist co the end of the coil. The eyes

were forced open using an eye Lid retraccor. The conjunctiva was carefül pinched and

Iifted by forceps and an incision was made 0.5 mm fiom the limbus. The incision was

chen extended around the perimeter of the limbus. The coil was then inserted through

the cut conjunctiva while ensuring thac the plane of the loops remained parallel to the

surface of the eye. The leads were then threaded thoush a needle that was 8.5 cm long,

which was inserted into the periglobal recess, and passed subcutaneously to an incision

next to the head holder. Rie coil leads were then passed though the needle. The teflon

was then removed from the leads and male gold pins were soldered onto each end. The

gold pins where then inserted into a plastic connector placed next to the head holder.

Fast drying cranial cement was then used to cover the anchoring screws, T-bolts and the

plastic connector with the open end of the connector facing laterally. Extra skin \vas then

sutured around the cranial cernent.

The monkeys were given ancibiotics (BayûiI1) for cen d q s and aIIowed to recover

€or six weeks before the next surgery. During this recovery time, the monkeys were

triUned to fixate on a visual targec projected ont0 a tangent screen, with a distance of 100

cm h m the eyes, in exchange for an apple, strawberry, or cherry juice reward. During

the second procedure, the second eye coi1 was imphted dong with the recording

chabe r .

The recording chamber tvas a stainless steel cyiinder 3 cm in dimeter. A

monkey was anesthetized and placed in the stereotaxic frame. The recording chamber

was then mounted onto an arm of the stereotaxic Irame and Iowered at an angle of 30

degrees from the stereotaxic verticai unti1 it touched the skull. Its location on the skuil

was then rnarked. A hoIe with an approximate diarneter of 2 cm was then driI1ed in the

skul1 at the exact location where the chamber landed. The recording chamber was then

placed on top of the hoIe and anchored in place with cranial cernent and stainless steel

screws. The stereocaic coordinates were predetermined and were set such that an

elecmde going through the origin of an x-y grid centered on the charnber passed directly

behveen the abducens nuclei (Smith a al. 1972). The vestibular nucIei were then found

simply by moving hterally or posterioIaten1ly from the abducens. The chamber was

kept closed with a plastic lid, After e x h experiment, the chamber was cieaned with

hydrogen peroxide and was tilled with 10 mgiml of chloromycetin .

2.2 Stimulus Generation

Both rotations and translations rvere used as stimuli d u h g experiments presented

in this thesis. Rotations were delivered by a servo-controlled rate table, which had a

seno-controlIed sled mounted on top. Therefore, rotations couId be elicited ~4th the ded

parked in any position. The length of the s1ed is 26 cm so that monkeys codd be rotated

6 7

either 13 cm nose in (facing the center of rotation), 13 cm nose out, or at any distance

from the axis of rotation benveen = 13 cm. The exact radius of rotation used, dong with

the various velocities and accelerations memireci durin; the various experimental

paradi,ms are described in detail below. The sensitivity of cells to eye movements was

ascertained by having the monkeys track a Iaser target. The laser target could be moved

in the horizontal or the vertical plane by adjusting galvanonieters that were controlled by

bvo amplifiers (General Scanning).

2.3 Data Collection and Analysis

The chair and sied position, eye position, accelerometer output and neural spike

train were digitized by a Data Translation DE000 card ai 1000 Hz and recorded onto a

Pentium III computer running Labview (National instmenrs) on a Windows 98

operating systcm. Juice rewards were also dispensed Eom the same computer. Eye

position was measured by the use ofthe magnetic search c d technique (18 inch cube)

that rnoved with the animal. The horizontal and vertical eye positions were measured

with 2 phase detectors, one for each eye (CNC engineering, Seattle, Washington). A 3-D

Iinear accelerometer (Crossbow) was placed on the head holding barcentered behveen

the monkeys' ears on the intenurai Iine. The accelerometer had a range of = 2 g (where

Ig = 9.8 m/s2) and a bandwidth ofDC to 125 Az and noise of 1.5 mg rms which was

more than an adequate for the rance of accelerations used in the experiments. Recordings

were obtained by using tungnen electrodes (impedance = 1M!2) coated with paraiene 'C'

(Microprobe) and fitted into a polymids tube for additionai insuIation. The electrode was

then threaded through the guard tube that was attached to the microdrive. The imIation

68

fiom the top end of the elecerode (side opposite to the end with the tip) was then bumt off

and a male gold pin was soldered at that tip. The position of the electrode in the guard

tube was then adjusted so that the recordiig tip of the electrode was 1 mm from the end

of the guard tube. The impedance of the electrode was measured with a BAK electronics

impedance tester by inserting the electrode into a saline solution and attaching the

electrode lead to the preamplifier. The electrode was then placed into a solution of

Virox STF (accelented hydrogen peroxide) disinfectut. Before inserting the electrode

into the brainstem, it was thoroughly rinsed with saline.

A vernier ;Y-Y platform was placed over che recording charnber before the

beginning of sach experiment. The dura was first pierced with a sterilized needle and

then the electrode was inserted through the pierced hole. The height of the electrode in

the g a r d tube was controlled by a hydraulic microdrive with a resolution of 1 0 ~ .

During the very first expenment for boch rnonkeys, the X-Y was set for 1 mm lateral of

(0,0), which stereot~~ically represented a location in benveen the abducens. For both

monkeys, the vestibular nucleus was simply found by moving lateral to the abducens.

The electrode signal was pre-arnpIified and passed thmu& a coaxial cable to

another amplifier with the gain set nt around 2000 (possible ranse LOO-10,000). The

signal was also filtered (DC to 8.3 N z ) to remove coi1 noise and fed into a window

discrirninator ( B a ) whose output was displayed onto an oscilioscope (Tektronix). (This

is not an antialias filter since we are dïgitizing acceptance pulses). The total input

impedance was 200 Megaohms. The signal was also channeled through to a speaker.

The activity oFa vestibular cell was Grst noticed by the characteristic sound outputted

fiom the speaker. It was then isotated by a d j u s a the trigger and the width of the

window through the tvindow discriminator. An acceptance pulse lasting 50 ps was

generated whenever the electrode signal fell within the window. The duration of the

acceptance pulse was extendsd until the data acquisition card read the pulse, at which

tirne it was reset. in order not to miss acceptance pulses that were generated while the

previous pulse was being read or reset, subsequent pulses were placed in a buffer. in this

way, there was no dead time. The spike times were recorded with a resolution of Ims.

The firing rate of each neuron was calculated with the use of the Gaussian

technique (Richmond et al, 1990) by convolving the spike train with a Gaussian profile

1

defined by G(r) = eT . The width of the Gaussian (O) was set to 15 ms when the

stimulus was a sinusoid (range of frequencies 1-4 Hz during rotations and 1-5 Hz during

translations), and S ms when steps of position where used. Stsps had appreciable high

fiequency power and therefore, by choosing ci to be srnall! low pass filtering of the signal

is avoided. (Convolving with a Gaussian with a width o f a = 15 ms is equivalent to low

pass filtering the data with corner frequency = 1 1 Hz. Lowering the width to o = 8 ms

leads to a low pass filter with corner frequency = 70 Hz).

Cycles were automatically aligned by programs tvritten in Matlab. The time of

occurrence of the peak of the cross correlation was used as an initiai estimate of the Iag or

lead between cycles. OF al1 the potential cycles that were to be aligned, a single reference

cycle was chosen that was statisticaIIy the closest match to the mean of al1 cycles. (This

is an arbitrary choice, any other cycle wiII do as the reference cycle. However,

smoothness of the reference cycle increases the effrciency of the aIlnthms). AIL

subsequent cycles were then to be aligned to this reference cycle. Initially, the tirne

difference between the peaks of two cycles was computed and compared with the initial

result of the cross-correlation. If the hvo values were within * 1% kom each other, then

the peak of the cross correlation value was used to shifi the waveforms in order to align

them. If the hvo values did not agree, which indicates the cycles are noisy (or at lest ,

not smooth), subsequent cross-correlations were computed until either convergence

(cross-correlation time retmed zero (or more accurately, the cime of the peak

corresponded with the time for a single cycle)), or divergence (cross-correlation bounced

around incoherentIy). If convergence occurred, then the cycle was shifted by the sum of

al1 the lags returned by the cross-correlations. Cycles whose h g estimates diverged were

discarded. After ali,ment, al1 cycles were presented to the investigator for verification.

The investigator courd then cliscard m y cycles. 10-60 cycles were used in the alignment,

dependinz on the noise level and Iength of the recording. In generaI, the initial peak of

the cross-correlation proved to be an accurate estimate of the time difference benhreen

peaks. Figure 2.1 depicts a typical a l i v e n t plot produced by the above algorithm by

usin; the initial estimate of the pe& of the cross-correlation. Additional detail about the

methods can be found in the appendix,

The position signa1 and the accelerometer's output were used for aligning

sinusoidal rotations and translations respectively. Dunng steps of position, the output of

the accelerometer was inte_=ted yielding velocity, and it was the velocity s i p a l that was

digned. The intecg1 of a biphasic acceleration stimulus yields a monophasic Gaussian-

Like waveform. Al1 cycles were al iged to this velocity peak. The Einng rates were then

fined wïth the appropriate fiinctions and the cell's sensitivities computed using custom

wïtten stand-alone software and progams in Matlab (Mathworks).

Time (sec)

Figure 2. 1 Exûmple of auro-aligning sevenl accelention cycles by the use o f the cross-correla~on

rnethod. Al1 a c e s shown in this plot were digned by shifting the peak of the integnl of these mces by the

peak oFthe cross-correhtion betwern n plot and ihr rekrencr plot (see rext for deuil).

Once a ce11 was isoiated, the monkeys had to track the tarset in order to determine

the eye position sensitivity of the isolated cell. Al1 the neurons used to test our

hyporheses exhibited no eye position sensitivity. This was necessary in order to eliminate

the possibility that the observed response differences during different paradigrns rnight be

due to differences in the eye movements evoked by the various stimuIi.

2.3.1 Sinusoidal Stimulus

Chair and sled position, dong with the accelerometer's output were fit by the

equation Y = bins, +a, sin(or + 8) where Y is in degees for the chair and centimeters for

the sled position, c d s ' (or equivalently ing's) [or the accelerometer, biar, is the stimulus

offset, a,, is the amplitude of the modulation (peak amplitude), o is the frequency and 8 is

the phase with respect to a sine wave. Sirnilarly, for each average of cycles, al1 spike data

was fitted with the equation FR = bim, + fp sin(or +p) where FR is in spikeslsec, bias,

is the response offset, j; is the amplitude of the modulation (peak firing rate), and yl is the

phase of the firing rate with respect to a sine wave. A!1 fits were performed in Matlab

with a non-linear least-squares weijhted algorithm using the Levenberg-Marquardt

method with the inverse of the standard deviation as weights. (Cycles that had a portion

of their firing rates clipped (driven to zero) were given zero weights in the fit while they

were clippeu). For the rotational paradigms, head velocity was determined by

differentiating the head position using a central difference algorithm which was then

smoothed using a SavitzSf-Golay third order polynomial filter (Orfanidis, 1995). The

translational velocity was obtained by intepting the accelerometers output using the

trapezoid method with an interval of 0.5 ms (haIf the samphg penod) (Kahaner et al.

1989). The trapezoid method entaiIs breaking ~ h e time series into pieces of equat width.

Then, if we let rl and r l be the s t m and stop time of any piece, then the area under the

curve behveen rl and it is A= O.5*(t,--)*[f(tI) 7 f(cI)] which is the area of a trapezoid.

The interval chosen (O.5ms) is ma i l enough so that Simpson's method, which is

descnied as being a more accurate estimaee of the integcal of a c w e , does not yield a

better approximation (Kahaner et ai. 1989). The sensitivity of the ceIls to on-axis and

fP translational stimuli was calculated as peak firing rate divided by peak vehcity ( S r = T;-

where Vp is the peak velocity) and has units of spikes/sec/deJisec for rotational stimuli,

and spikes/sec/cm/sec for translational stimuli. Although it is more naturd to calculate

sensitivity re acceleration for translational motion, sensitivity re velocity was used for

anaiysis for both translation and rotation because the magnitude of their respective

sensitivities are comparable, and this facilitates the overall presentation of the data.

Figure 3.10A is the only exception, where the sensitivity was calculated with respect to

acceleration so that the dynamics of the cells could be compared with other studies.

Switching from sensitivity re velocity (from the units above) to sensitivity re acceleration

(in g's and degisec') is a trivial task, and can be accomplished by multiplying the

sensitivity by 98 l f w or l!o for translation and rotation respectively. The phase with

respect to velocity was calculated simply as the difference in phase benveen the firing

rate and head velocity. Al1 values for the mean sensitivity and mem phase are reporred

as + standard error. Al1 statistical analysis was performed in Matlab either using

prepared or custom written functions with the algorithms comin; from Zar, (1996).

in this section of the rhesis. the response to four stimulus conditions are described;

1) on-a is (pure rotational stimuius), where the center ofthe interaural line is also the

center O C rotation; 2) animal oriented nose-in (eccentrïc or OR-ais rotation) such that the

mis of rotation was Iocated in fiont of the interaural line; 3) animal oriented nose-out,

such that the a..s of rotation was Iocated behind the interaural line, and 4) pure

translationaI stimulus directed dong the interaural zxis. Recordings which had stimulus

spectrums composed of additional unexpected harmonies as detected by the

acceIerometer were not used in the anaIysis presented here. The centripetal and

74

tangentid acceleration induced by eccentric rotation can be caiculated using the

4 d ly equations nc=r(-)' and a,=r -, =druz respectively, where y is the angular position dr dt-

of the head, A is the amplitude of rotation, w is the fiequency and r is the radius of

rotation. The stimulus mplitude during eccentric rotation was designed as co keep a, at a

minimum so that the only contribution to the firing rate was due to rotational and

tangential accelerations. Figure 2 3 depicts an example of tangential and centriperal

acceleration as detected by the accelerometer during eccentric rotation at 4 HZ with a

peak to peak mplitude of 0.48 degrees, md a radius of I O cm fiom the center of rotation.

The centripetal acceleration (&) is well below the threshoId of detectability of the otolith

organs (-005 g; lg = 9.8mis2) (Wilson and MeIvil1 Jones, l972), and as a resuIt, it was not

necessary for us :O compensate for it during the analysis of eccentric rotation. However,

the tangential acceleration (labeled At) a,gees wel1 with that computed analytically usine

the equation relating tmtngential acceIerarion to the radius of rotation described above.

During rotacional stimulation, the sied wvas locked so that it couid not slip

relative to the rotator. SirniMy, during umsIationd acceleration, the rotator was locked

in place. Stimuli were senented at 1,2,3, and 4Hz during rotations and 1,2,3,4, and 5

Hz during ms1ation. At each fiequency, the stimulus was composed of at Ieast 2

mpIitudes. As can be seen korn TabIs 2.1, only 2 amplitudes were used for Iow

fiequencies and 3 or 4 amplitudes for hi;her frequencies. This was necessary since cells

had to be held for a Iong time in order to unde30 the paradigms listed above and longer

time series are needed d u ~ g low kequency oscillation in order to obtain a sufticient

number of cydes. Limiting the number of different amplitudes to hvo during Iow

fkquency expedited the recordhg rime. Two amplitudes were dso used during 4 Hz

75

rotation since this was the Iimit of our rotator. htially, the monkeys were rotated nose-

in at a radius of 10 cm Erom the avis of rotation.

Figure 2.2 Cornparison bcmen the output of the accelerometer for tangenrial and centripetal.

accelerations during -!Eh off-axis rotation with a radius of IO cm. The proper choice of the

amplitude ensured that the centripetal acreleration is below 0.00Sg and therefore below the threshold

of detectability. As expected, the centripetal ûcceleration is twice the tangential.

Translation (cmlsec) t

Once a ceil was Iocated and isolated, the anima1 was subject to rotations at ail 4

Rotation (degls)

1Hz 2Hz :Hz 4Hz SHz

frequencies. Then, the animals were moved to the on-ais and nose-out position and

once again subjected to the paradigms. Finally, the animais were transiated dong the

Table 2.1 Different velocities used for each Irequency (defined lis the amplitude or the stimulus)

during translation and rotation, The values listed below are peak amplitudes as reported by the

accelerorneter and the chair controller, and not the desired amplitude as set by the user. Note that

rotation refers to both eccentric and on-axis rotation.

14.7; 35.4 4.5; 13.7

3.+ 6.5; i 1-1 ; 15.5

interaural line at the 5 frequencies mentioned above. After all the paradigms were

15.3; 35.7 7.5; 14.0; 18.5

3.1; 6.5; 10.7

complete, the animals were once again rotated nose-in and nose-out at varying distances

2.1; 3.6; 5.6; 1 1.6 I 3.0; 5.5 1.5; 2.6; 4.7; 8.9;

Eom the center of rotation (r=5 md t=12 cm). This sequence or paradi-ns was strictly

followed in order to record as many 'complete' cells as possible; i.e., cells that had

undergone the four paradigms hted exlier. This was necessay as ttvo types of

nonlinearities are discussed in this section of the thesis: failure of homogeneity and

faiiure of superposition.

2.3.2 Steps Of Position

In this section of the thesis, steps were used as the primary translationai stimulus.

Steps of posiuon were deiivered in 7 different orientations, cIockwise (CTIV) and

counterclockwise (CCW) to the naso-occipital (NO) direction. Specifically, the steps

delivered were 90 CCW, 60 CCW, 30 CCW, O, 30 CW, and 60 CW degrees (O degrees

refers to NO and 90 refsrs to LI). Initially, the monkeys were translated sinusoidaDy

unril a ce11 that responded to the oscillation was located. Once isolated, the ce11 was then

tested for eye movement sensitivity by having the monkeys saccade behveen eccenaic

targets and follow a target oscillating with a variable Erequency ranging between 0.2-1.5

Hz using smooth pursuit. Fits to the firing rate were also performed in Matlab with a

non-Iinear least-squares weighted algorithm using the Levenberg-Marquardt method.

The function used CO fit the firing rate was any combination of:

where B is the b i s , ( r t , m < O implies intsgation and t1.m > O irnplies differentiation) and

ALI and - 4 , ~ ~ are the accelerometer's output in the [A and NO directions respectively.

Note that n and nr do not have to be integers but can take on riny real number. For

purely IA or NO steps, only the term that corresponded to the direction of motion was

used. ,411 the variables (B. u, b. n, m) were optirnized during the fitting process. ïhe

acceieration trace was shified relative to the liring rate untii the optimal fit was abtained.

The optimal time shift was taken to occur at the peak of the cross-correlation behireen

the acceleration and the firing rate. However, this peak did not always give the best mean

squared error (MSE) for the fitting function. in those cases, we heuristically and

iteratively adjusted the time shift until the MSE was minimized. Fractional integrals

T(n) is the gamma function (yislding a constant in this case) where O < n < 1 for

75

htegmtion (note the negative on the exponent of D), (Or equivalently, in the frequency

domain. the fractionai derivative can be calculated ushg: 3'(3 64 *(ici$) where 3 a n d

F' are the Fourier and inverse Fourier transforms respectively). Integration ( n = -1)

was also computed by using the trapezoid method with a base qua1 to half the sarnpling

period (0.5 ms) (Kahaner et al. 1989). Both methods produced identical results.

Steps of severai amplitudes and durations were used resulting in severd peak

accelerations for each direction of motion. The rise urne of the step was varied by

1 passing the step instruction through a sigmoid function of the form - . The slope of

I+e-'

the sigrnoid, and therefore of the step, was varied by varying the value 0F.r. The resulting

peak acceierations thrtt were used in this experiment were: O.?. 0.?5,0.3,0.4,0.5,0.6,0.8

g's where g = 9.8 m/s2. A simple rnodel using urne constant enhancernent was used

to mode1 the data presented in this section oFthe thesis.

2.3.3 Modeling the tVOR

The mode1 shown in Fizure j.26 was writtrn in Matlab (Mrithworks). The neural

inteerator and the oculomotor plant are expressed as (Fuchs et al. 1988):

The open loop t r ade r fiinction of the mode1 in Figure 326A is simply

t5 - = ( K , + & H,,, ) H,,r "' u

where KI provides the system with position information. K2Hint with velocity information,

e."' repreçents a 10 rns delay and a is the accelention. The oatput fiorn Equation 2.1 was

compared to Angelaki's data (Angelaki, 1998) and the values Ki and Ki optimized to

minirnize both phase and gain errors. For a pure acceleration input, the appropriate

values for KI and K2 tvere deduced by minimiùng the least squared difference between

the experimentally obtained cornplex number geb ( where g is the gain and p is the

phase) and the one produced by the mode[. Other minimization methods tvere aIso used

without ruiy significant change to the values of KI and Kz. Then. the diEerence benveen

the output of the mode1 using the cierived KI and K2 and the e'cperimental data was

computed. This difference corresponds to the required tiltsrhg of the accelention signa1

to adequately simulate the esperimental data. The diKerence between the two outputs

was tiited to an equation according to the Goldberg et al. (1 990) classification of

afferents.

2.3.4 Eye Movement Recordings

The horizontal and vertical position of each eye was measured by the use of the

magnetic search coi1 technique ris descnbed above. The sue coils tvere calibraced at least

once every nvo experimental days. The sys position recording range is i= 40 degrees.

Caiibration \vas carried out by rotating the animal at 1 Hz and ensuring that the gain of

80

the VOR was appropriate. In addition. smooth pursuit eye movements and saccades were

utilized for caiïbration. The 40 degree eye position range was mapped so that 10 degrees

was 5 Volts. This resulted in a resoiution of -125 Videgree. Digitizing this s i g a i on a 12

bit AiD card leads to a resolurion of 1.21. m W i t or .O097 degreedbit. Eye positions

were measured during steps of position whiie the eyes were diverged (or close to being

0.05 0.1 0 0.1 5 0.20

Time (sec)

Figure 2.3 The acceleration proliles of two steps of position chat were used as stimuli in order to

measure the compensatory nature of the tVOR. A) Bigh frequency acceleration (peok amplitude of

Fourier spectrum is 10 Hz) 6) low frequency acceleration (perk amplitude of Fourier spectrum is 5

m.

Diverged since the target distance was 100 cm, McConviiie and Tomlinson, 1994). In

order to ascertain whether the eye movement was compensatory to the steps for severai

frequencies, nvo kinds of steps were used. Both steps had sirnilar waveform

characteristics but differed in frequency content (Figure 2.3). Figure 2.3A depicts

acceleration traces that Ilas a frequency spectnim that peaks at 8 Hz while Fi,aure 2-38

has a frequency spectmrn ihar peaks at 4 Hz. In general, the 1ow &equency steps peaked

at frequencies less than 5Hz while the high Frequency steps peaked above SHz. As will

be s h o w in the Reçules, these wo acceIention traces lead to very different eye

movement responses, AI1 data analysis and modeling was perforrned in Matlab

(Mathworks). The monkeys used durin; the experirnents are the same as the ones used

for the other expenments and as such, information regarding their training and other

pertinent information is described above.

3.0 Results

in order to uncover the existence and describe the type of nonlinearity present in

che vestibular nucleus, the response of 135 cells is described in the first 2 sections of the

Results. Eye movements in response to translations are also presentsd in the latter parts

of this section. Position transients' proved a worthy stimulus that allowed us to destribe

vestibuIar nuclei ce11 dynarnics and to elucidate tVOR characteristics. For example, it is

simple to discern whether eye movements in response to steps of position are

compensacory simply by looking at the waveform of the response. In contrast, if

sinusoids were used, the phase of the response would be taken as indicative of the degree

of compensation, a metfiodology which could be misleadhg Figure 3. l depicts eye

movements in response to position transients with variable fiequency content. It is easy

to discem the noncompensatory nature ofthe eye movements in response to the first set

of steps (the acceleracion of the steps is shown). in contnst, the second and third set of

steps (t >1.1 seconds) lead to impressive and compensatory tVOR responses. The eye

rnovemenr seen behveen 0.0 and 0.4 seconds are sirnilar in wavefom to head

iicceleration, bvhich cm esily be mistaken to be compensatory if the stimulus was a

sinusoid. These ideas, including the response of the tVOR to sinusoids, will be discussed

in more detail in sections 3.3 and 3.4.

Figures 3.2 -3.5 are examples ofthe response and the average firing rate of typicd

celis. Figure 3.2 depicts the firing rate of a neuron whose activity as recorded while the

' The terni -stepsr. .seps of position', and 'position transieut.' wiI1 be used interchangeably in the texL rüthough the ansients are clearly not steps, (but they approximate them to a degree dowed by the hardware), we beIieve that this wiII faciIinte the discussion and wvüi not Iead to any ambiguiy about the meaning intendd

moakey was oscillating at 4 Hz The response show illustrates the high fiequency

robustness of this ceü, which is typicd of al1 our tek. This particular ce1 has had its

background discharge removed so that only the modulation is apparent. As can be seen,

the stimulus (top trace) spans 3 amplitudes which daer in magnitude by 55%. The peak

firing rate, however, does not reflect this magnitude change. Therefore, it is easy to see

that the sensitivity increases as the stimulus amplitude decreases. This and other forms

of noniinearities will be eiaborated on in section 3.1.

Time (sec) Tirne (mc) Tirne (sec)

Figure 3.1 Ersmpk of the tVOR in rcspwsc to positioa trPisui& (Red ir eye positioa). Note tbt

compeasrtory stcp in eye for P1.0 seroids. In motrut, the drst îwo steps (dcsfribed by the

a c c r k n h ) c lk i t e p movcwit thrt are simihr to k8d reeckrrtioi, 8 rrsporrc t h t is c k u l y

iincomptnsrtory, bot mry k trkcn as compeasrtory if tbt stimuiœ wm a simILlOid T k eye position

s h m fmm t=S sccoads ir coa~pcwrtory, since it rrscmbks t k doobk irtcgil of the rccrkrioioi

Wace (bcrd ~*tioa).

AdditionaI experiments presented in this thesis are designed to address the

following question: 1s the response recorded fiom a neuron during off-auis rotation

sirnply a sum of the rotational and translational responses or is there nonlhear

interaction? Specificdly, the response during off-auis rotation will be compared to the

sum of the responses during on-ais rotation and translational acceleration. h example

of these three responses is presented in Figure 3.3-3.5. At hish fiequencies, the firing

rates shotcn in Fijure 3.3 and 3.4 are in phase with head acceleration. Note that

translation also exists in 3.4 since there exists a tangentid and centripetal acceleration

due to the increased radius. As the frequency decreases, the phase of the firing rate

increases in lead with respect to the position trace until at 1 Hz, the lead is considerable

and approaches 90 degrees. On the other hand, the response during translational stimuli

(Figure 3.5) is opposite to that just mentioned. SpecificaUy, at Iow frequencies, the firing

rate leads the position trace by a small phase. As the frequency increases, the phase lead

also increases, approachin_e a 90 degee lead. These properties wi11 also be elabonted on

in the section 3. L .

To what extent do the responses presented in Figures 3 3 - 3 3 describe the amount

of calculus being performed by the cells depicted? in Figure 3-5, the phase has advanced

up to 70 degrees behveen L and 5 Hz, and this may be interpreted as an arternpt by the

systern to perIbrrn mathematical integration. However, during sinusoidal oscillations,

clynarnics, delays, nonlinearities and asyrnmetries contribute to the recorded phase hg.

In section 3.1, it will be s h o m that the phase shift acmally depends on the amplitude of

the stimulus, a nonlinear feature which is inconsistent with the procedure of caicuiating

phase shift in order to ascertain integratiorddifferentiation. In section 3 2 , position

transients will be used as the prirnary stimulus. Here, a hypothesis based on the

asymmetric firing rate will describe how nonlinearities cm lead to integration. in

addition, it will be shown that onIy 3 cells are needed in the vestibular nucleus to robustly

encode the direction of motion. In the Iwt nvo sections of the results, the topic wiIl

switch fiom single ceIl recordings to the tVOR. In section 3.3, eye movement recordings

during position transients will reveal that once again, conclusions about the machinery of

a system ascertained during the use of sinusoids do not generalize to other forms of input.

In section 3.4, models will be presented that attempt to sirnulate the nonlinearities found

in individual cells. in addition, 2 models will be presented that simulate the tVOR. The

first describes the simplicity in which sinusoidal data can be replicated by the model. in

addition, a hypothesis will be presented as to the type of afferent behaviour required to

drive this linear model. The second model wilI suggest that an element resembling the

nonlinearity found in the brainstem needs co be included in the mode1 in order to

adequately simulate the tVOR in response to steps of position.

2 4 6

Time (sec)

Figure 3.2 The response of a typical ceil to translation at 4Hz The response of this ce11 has been

detrended in order to depict the small change in the modulation of the firing rate in response to a

large decrease in the stimulus. The detrending \vas performed piecemeal, since the background

discharge for the rvhole time series shown in this figure is not a constant. Detrending occurred at t=û

- 3.2 sec and thcn from r4.4 to t=8 sec. In generel, cells responding to translations were high p m

filtered, responding much more robustly to hi@ frequency oscillrtions.

Fipre 3 3 Example of a ce1 reeorâed duriag robtion tbmugb r i lrIs ctmdrred bctwœm t k

interauml lint. Red üae is the rotothg chair position.

Tirne (s)

Fiin 3.4 Esampk of a al1 mordcd during rncairic mîmîioo. Arh of tohtlor U 10 cm ia front of

the aaimiL Red lint is chair pœitioa. Note tbrt iatcriurrl rccckntion also txists duriag tu

pradigm in tbe farm of îangentirl rmleratioa.

Interaural Translation

Time (sec)

F'igure 3.5 Exampk of the liriag na of a cell dmring intenuml tnaslrtîom. Rtd is Iht positioi of

Figure 3.6 The coordinates of a few cclIs from one monkey. The PA-LR plane is the plane the

electrode egressed the guard tube. The lines indicste n hypothetical path to a cell, which is

represented by the solid circles. On average, the cells were clustered farther t h m -i2mm around

the origin. which is in good agreement with the Ioeation of the vestibulnr nucleus and its location

around the nbducens (Smith cc 31.1971).

Finally, a description of ceII Iocation is needed before delvin; into the results.

Fi,gue 3.6 depicts the distribution of some of the cells recorded f?om one monkey. The

origin (0,O) of the base (Posterior-Anterior, Lefi-Right) corresponds to the or@ of the

X-Y that guided the s a r d tube (see Methods), which stereotaxicaiiy, was the Iocation

between the abducens nuclei. The Iocation of the vestr'bular nucleus was then simply

found by moving lateraliy to the abducens. Tbe depth on the z-auis is the distance the

electrode traveled fiom its starting point (1 mm in the y a r d tube, see section 2.1). The

location relative to the X-Y is consistent with previous recordings with the same system

(McConville PhD. Thesis, 1994).

3.1 Nonlinearity In Response To Sinusoids

The first series of expenments to be described will test the validity of the

assumption of Iinearity in the vestibular nucleus. To that end, the response of 73 cells,

which were free of eye position (vestibular-only cells), was recorded fiom the vestibular

nucleus in response to sinusoidal stimuli at various fiequencies. ~Most cells (6 1/73) (al1

the ce1I.s used in superposition) responded to both translation and rotation. This result is

consistent ivith previous work in the same Iab (Tomlinson & McConville, 1996;

McConville et al. L996).

Figure 3.7A depicts the response of a ce11 undergoing translation at 4 Hz at

different amplitudes (and hence velocitics). As crin be seen in Figure 3-7A, the response

ofthe ce11 during the hr;e amplitude portion is risyrnrnemc, with the nsing portion of the

response having a l q e r dope than the falling portion. This asymmetry does exist durint

the low amplitude portion of the time series but is less discernible due to the low

amplitude of the response. This asymmetry is not present in the stimulus. Furthemore,

this behaviour was a generai property of many neurons' response to sinusoids. However,

these responses were fit to sinusoids in order to test the principles of hornogeneity and

superposition since the question of validity of these principle is not affected by the

asymmetry, although the processes that $ves cise to the asymmetry and the fdu re of

these principles may be related. in later sections, the asymmetry is ïnvestigated by

92

lime (s)

Figure 3.7 A) Response of a ce11 tu an interaurd transtation at 2 amplitudes (top trace). Note that the

response of the ce11 to the increased amplitude of the stimulus is an increase in the b i s and a

decreïse in the sensitivity B) The response of one cefl during translation to a stimulus a t 3 Hz during

4 different amplitudes. Points a re * SE.

Acceleration (g)

Figure 3.7C Sessitinîy ami birs (ùackground discharge) for n single ce0 dnriag trrwhtioa rt rii

frequeacies. The iacrcasc in the bias and the decrease in the semitiriiy is c k i r for i l 1 licqwnciw.

utiiizing position transients as the prirnary input. The sensitivity of this ce1 during the

small amplitude portion of the stimulus is 387 spfsedg (9.91 sp/sec/cm/sec) while at the

larger amplitude it is 193 sp/sec/g (4.94 sp/sec/cmfsec). However, the bias (defineci here

as the mean discharge) aIso changes during the daerent amplitude profiles. The b i i

during the s m d amplitude portion of the stimulus is 39 s p k c but increases to 98 spfsec

as the stimulus increases. Therefore, the response of this neuron to an increase in the

stimulus amplitude is to modulate with a smder sensitivity around an increased bias.

This change in bias in central neuroas has already been predicted by Galiana and

coiieagues (Galiana and Outerbridge, 1984).

An exarnple ofthe sensitivity of another ce11 undergoing translation at different

velocities (frequency = 3 Hz) is depicted in Figure 3.7B. The sensitivity to velocity

clearly decreases as the velocity increases, although it seems to be approaching an

asymptote at higher velocities, This would be true even if the sensitivity is plotted

against acceleration. -hother ce11 recorded dunng cransrarion is depicted in Figure 3.7C.

Once again, as the acceleration increases, the sensitivity decreases for al1 fiequencies.

This decrease is accompanied by an increase in the bias. The significance of this

behaviour is illustrated in the discussion.

The sensitivity as a fùnction of velocity at each individual tiequency for al1 cells

undergoing interaural translation, on-ais and eccentric rotation is depicted in Figure 3.8

As can be seen, the mean sensitivity of the population ofcells in not constant but

decreases as the velocity increases. This decrease is dso evident at individual

frequencies. (Note that at this point, the sensitivity during eccenuic rotation is simply

taken to be the finng rate of the ce11 divided by the rotational velocity, even though there

exists a tangentid acceleration). Sulid lines are the straisht line fits of sensitivity vs.

velocity for erich tkequency. The points at each frequency are depicted for completeness.

Althou$ Figure 2.7B suggests that the decrease in sensitivity is better fit by an

exponential h c t i o n , linear fits were used in Figure 3.5 since generalIy, 2 or 3 different

Velocities were used per fiequency, not enough points to justib an exponential fit (Table

7-1 page 73). For al1 3 plots, the line with the Iowest dope is for 1 Hz data For each

additional Erequency, the slope continues to increase in increments with higher

fiequencies having higher slopes widi a few exceptions (Table 3.1). Table 3.1 depicts

the dope and the standard error of' the siope for al1 Lines in Figure 3.8. MI slopes are

Translation

Veiocity (cmlsec)

Offaxis rotation

Velocity (deglsec)

C .7 On-Axis rotation

O 10 20 3 0 4 O 5 O Velocity (degisec)

Figure 3.8 Velocity vs. Seositivity for A) transIation, 0) eccentric rotation, and C) on-& rotation.

For ail plots, Circles 1 Bz; triangle pointing down; 4 E k Square, 3 tIz, dkmond, 2HZ Straight

lines are the Cits bctween seositivity and velocity for each individud Crequency. For each plot, the

steepest line is the highest frequency (4 Hz for rotarion and 5 Hz for translation) while the Iine

with the smaiiest dope is the fit rt a frequency or L f[z

Translation

1 Hz HZ

Eccentric Rotation

Translation

i'able 3.2 ~lo'pe (M) of the reg;ession of the bis* shown i" Figure 3.9 a i d the assorinte?d p-value for '

On-his Rotation

I Hz 2Hz

the hypothesis that the slope=Q at an a=0.05

M (sp-s/cL) -. 1582

3Hz 1 -392 1.098 -.61U 1.15 i -27 1.110

Eccentric Rotation

significantly greater than zero (pc.00 1,7-raiIted t-test at u = .05) cxcept for On-ais at L

SE .O367

On-Axis Rotation

Slope p-value i SIope p-value 1 slope p-value

Hz (t=-,562). In addition, the on-z~is data exhibits the least amount of difference

-.3 52

M(sp-sidL)

I H z 5Hz

benveen the slopes as compared with the eccenrric and the translation trials. The

ma..imum correlation coefficient out of d l the linear fits depicted in Figure 3.8 was 0.62

SE M(sp-sldL)

Table 3.1 Slope (81) and the standard error (SE) of the slope value for the linear regression of the

sensitivities shown in Figure 3.8 (sp-SIC': spikes-secondslcm2; sp-s/d2: spikes-secondsldeg').

- 3 3 .-- -.6 13 1 .[O7 1 -1.5 1.311 l

-2.17 1 .3?5 i I

1 .O6

(range -18 to -62; rnedian -28 1). Et is clear from Figure 3.8 that the sensitivity at a

-.19

SE

.IO7 / -.O87 ! -06 1 -.O7

.O537 1

O 1 -49 <. [ 1 .O5

particular frequency is not a constant but is dependent on the amplitude of the stimulus.

.O1 1

Accept 1.98 1<.001 12.18 ] <.O01 1 -.O6

The nonlinear behaviour mentioned above is liccompanied by an increase in the bias at

.O31 1 -.O5

Accept

higher velocities. Fi,we 3.9 depicts a re,gession Line for the bias for al1 the data

.O39

O I O 20 30 Velocity (deglsec)

Figure 3.9 Bias vs. Velocity for the different frequencies. Points are the binned mean sensitivïties

*SE ptotted at the center of the bins according to velocities Iisted in Table 1. Circles: 1EEz.;

Squares: 2H2, Triangies pointing up: 3Hz; Triangles pointing down : 4Hz Note that for on-aris

rotation, the b i s change was not significant across velocities at 1 and 2 Ez

kom rotation, translation and eccentric rotation for each frequency tested. Table 3.2

depicts the slope and the p-value that this slope is equivalent to zero (one-sample t-test),

Note chat the on-mis rotation only had slopes that were si,pificantly different fiom zero

for 3 and 4 Hz. On the other hand, the bias For translation and eccentric rotation

increased as the velocicy increased for al1 the frequency tested. As can be seen, the

positive slope of bias vs. velocity is geater for higher frequencies. In response to an

increased stimulus magnitude, this results in a modulation around an increased

background discharge as depicted in Figure 3.7A. Therefore, these cells increase their

bias and decrease their sensitivity as the stimulus amplitude increases.

Given this nonlinearity, a single frequency vs. sensitivity plot cannot be presented

for these cells without considering the effect of the stimulus amplitude. However, the

effect of the nonlinexity can be reduced if the stimulus magnitude is divided into

subranges to restrict the variability of the amplitude. Figure 3.10C depicts the sensitivity

and phase 3s a function of frequency for translation. on-ixis and eccentric rotation

gouped according to stimulus magnitude. The velocity ranges for the rotational

subgroups (both eccentric and on-asis) are O < RGi < 7 , 7 < RG, 5 12, and 12 < RG3 5

30 deg/sec. The translational velocity subgroups are O< TGI I 5 , s <TGï 19,9 < TG3

514, and 14 < TG4 I 30 cdsec. As c m be seen fiom Figure 3.10C, not only does the

sensitivity încrease as the Frequency increases, but it also depends on the magnitude of

the stimulus. However, recently, Angelaki and Dichan , (3000) presented evidence for

the existence of a diverse population of neurons that respond to translational acceleration.

The vaying dynamics depicted in Figure 3. LOC, therefore, could have come fiom

combining the data fiom cells with variable dynamics. However, Figure 3.10A and

3.1OB depict individual cells, and clearly, the sensitivity of these ceIls is not a constant

for varying acceleration but is dependent on the ma,gnitude of the acceleration. Less can

be concluded about the phase of these neurons, since they generally exhibited large

variations. Fi,gre 3.lOA has phase characteristics of a 'high-pas' ce11 as reported by

Angelaici and Dickman, (2000). Fi,we 3.10C, however, depicts the average of a number

of ceIIs that have similar phase behaviour, similar to the 'low pass' cells in the AngeIaki

study. This nomenclature is based on the behaviour of their sensitivity curves. However,

Figure 3.10 shows that 'iow-pass' and 'high-pass' behaviour can occur in the same cell.

For example, the mean sensitivities at 3 Hz during translation are (mean * SE) 503 * 16,

3 18 i= 16,218 = 8, and 163 = LS spisecig for TG[, TG,, TG3 and TG4 respectiveIy.

Therefore, a single bequency is associated with several gain vaiues, depznding on the

magnitude of the input. This was not the case for al1 frequencies however. A Knrskal-

Wallis test verified that most of the sensitivities Çom different groups at a single

kequency were indeed significantly different. However, another test is needed in order

to compare the individual results at each fiequency between al1 velocity subgroups.

Table 3.3 depicts the result of ri non-parametric Tukey type test with unequal samples

compared to the criticaI Q-values (known as the 'Studentized range') (Zar, 1992) at a=.05

using the error degrees of freedom From the analysis of variance. This test enables us to

eficientIy compare mmy means with any assumptions about the distribution of the data.

Specifically, the nuIl hypothesis (Ho: p1~ü,y~3=,u+ ) of equaI sensitivities during different

amplitude of the stimulus is tested by simply computing a q-value between each mean.

The q-varue is defined as q= O<[ - ,u2)/SE where SE = and MSE is the

mean squared error obtained fiom the analysis of variance performed on ail the means

100

(Zar, 1992). If the resuItant q is greater than the critical Q , then Ho: pi=pz is rejected.

The results for al1 the velocity groups is depicted in Table 3.3. Note that al1 the vaiues

above 2Hz are indeed different (excspt for g o u p 3 vs. soup 3 at 4 Hz during

Translation). At Iow i?equcncies. a change in velocii, has lirtIe effect on the sensitivity

Ieading ro rt failure to rejcct the nu11 hypothesis of equal sensitivities at low

Translation, q.05=3.633

1 Hz 1 2 Hz

TG1 vs. TG2 TG1 vs. TG3 TG1 vs. TG4 TG2vs.TG3 TG2 vs. TG4 TG3 vs. TG4

q I conc 1 q 1 conc i q 1 conc 1 q 1 conc 1 RGI vs, RG2 1 3.97 / R 1 .94 1 A ! 6-74 j R 1 27.57 1 R

;Hz 1 3 Hz

[ H Z i HZ I HZ 4 HZ - q ! conc : q conc i Q / conc / q conc

I 1 1 l I 1 I I 1 RGl vs. RG3 13.68 1 R

q , , values are for p.05, k=5 (number o f means being comprred) for transiations and l& Cor

q ] conc j q 1 conc 1 Q ! conc

RG1 vs. RG2 1 2-75 ! A 2.22 i

rotations; v= the error degrees of freedom from the analysis OC variance. Standard error hm been

9 32.28

27.54

A i 3.54 / R ! 74-37

rdjusted to îcrount for unequoi sizcs (Zar, 1W2). Nuil hypothesis for dl triols is Ho: pi=p1=p3=p+

conc R R

1.35 1 A / 19.21

R

RGIvs.RG3 RG2 vs. RG3

-

R=reject nul1 hypothesis. A=accept nuIl hypothesis

R R

2.56

R R

R 1 17.62

A j 24-65 6.12

3,12

Eccentric Rotation, q.os=3.314

2.17 1.4 1 - 8 8

1.12 1 A i 2.93

R

A 13.72 /Et 79.13 1 R A 1 3.85 1 R / 24.30 1 R

R 1 29.69 R 1 4.91

19.85 R R

4-95

4.35

R 1 23.35

On-Axis Rotation, qe05=3.3 14 I

A 1 10.53

A / 3.88

20.32 5.13 A 3.72

R R

3.18

-795 R R

3.85 / R 1.53 1 A

Peak Accelention (g's)

Figure 3.10A Scnsitivity and pbuc for a siagie meiroa m d wbür the animal tnasbtcd in the

naseoccipital direction. Accclentiws i r e calor codecl in A. Tbe dynamics of the scasitivity d t b Y

neoron is depcndatnt rpm the s k o f t k acakmtiar. For low rrcckntioirs, tk scnsitivity c a m

continues to incretase witb inereasingfimencitn Houever, for bigb accekratioa, the wnsitivity

curie actually dccrruc as the frqiicacy iaerrrs. No stitirtierl difkftmce exist bctweei the pbuc

plots. B) The eff'ct accckntim b u oa the semitMy a d pbuc of anather ceii at P3& I n this

partkalit ce& the phase is clearely affeeted by the imkntia

700 - Translation

12- l2 - On-Axis Rotation

400

rl) O T , r t t t 1; O * i 0 I I I i

0 1 2 3 4 5 6 0 1 2 3 4 5 0 1 2 3 4 5 - 120 - 150 - > C 120 - 120 - O 90 O -

30 al 0 0 - al Q -30- 5

-30 - 3 0 - a

-60-t , , , t 4 O . 1 t 5 1 r -60 t t t 8 i

0 1 2 3 4 5 6 O 1 2 3 4 5 O 1 2 3 4 5 Frequency (Hz) Frequency (Hz) Frequency (Hz)

Figure 3.10C Sensitivity ( in spikes/sec/g where g=9.8 d s for translation and splsecldeg/sec f o r

rotation) and Phase vs. Frequency for translation, On-bis rotation and Eccentric rotation. F o r

translation, TGl=Fil led Circles; TGI= Open Circies; TG3= Filled Triangles' TG.l=Open Triangles.

For Rotation: RGl=Filled Circles. RG2= Open Circles; RG3= Filled Triangles. See text fo r the

numerical ranges described b y these groups. As can be seen, the dynamics o f a cell is not constant bu t

is dependent on the stimulus amplitude.

fiequencies. Possible reasons for this behaviour are described in the Discussion. As can

be seen from the translational data- the same cell cm be described by different filters

depending on the choice of srirnuius. For example, the top curve in Figure 3.LOC (labeied

'Translation') is a result of TG, (stimulus with the lowest veIocity) and has high pass

filter charactenstics while the second curve 6om the top (labeled TGr), which is in

response to TG2 is consistent wïth low p a s fiIter dynamics. Therefore, the same ce11 can

exhibit differing dynamics depending on the choice of stimuius. The rotational data also

L03

had differing dynamics for different ve1ocity groups. The standard error of the phase was

too large to conchde a difference for most frequencies and groups, especiaily for the

rotationai data. However, a generai trend c m be observed with increasing Erequencies

resuking in increase phase lead with respect to velocity. Trrinshtions had phase Iags re

accderation increase as the group numbrr increased (velocity increase). As cm be seen,

the phase of this goup of cells approaches icceIeration as the Gequency increases and as

the velocity decreases. Other celis not included in the mean had the opposite behaviour

(see F i g u ~ 3.10A for example). If the system depicted in Fi,we 3.10 was a description

of a linear systern, then the cuves for each pa rad ip would be superïmposed, and clearly

they are not, indicatiag the existence olnoniinearities. Figure 3.10 also reveaIs that the

sensitivity for the eccentnc paradi,gns is geater than that of the on-ais for al1 groups

and at al1 frequencies above i Hz (p«.001; Tukey test not shown). Since the response

of a ce11 during eccentric rotation reflects iis response to both translation and rotation, it

seems reasonabie io zxpect that its firing rate will be different during on-auis rotation

provided che rotationai stimuIus is the sarne. Tiie tolIowing seccion discusses the relaiive

contribution of the translacional and rotarional component of che stimulus to the response

during eccentnc rotation.

3.1.1 Dynamics of cells during eccentric rotation

The analysis of the superposition principle requires a comparison of a cell's

response during eccentnc rotation with the sum of a cell's on-a.s and transIationa1

responses and therefore requires that cells undergo al1 the paradigms stated in Methods.

This was accomplished for 31 cells.

Recordings Eom cells during eccentric rotation were already s h o w to behave in a

nodinear fashion. The sensitivity of the cells during eccenmc rotation increases not only

as a h c t i o n of frequency (and inverse of velocity), but also as a function of the radius of

rotation since the tangential accelention increases as the radius increases. An example of

a ceII undergoing 3 Hz rotation during the on-auis, nose-in and nose-out paradi,gns is

depicred in Figure 3.1 1.4. Note that the change in gain for the nose-out condition is

accompanied by a change in phase compared to the nose-in condition. This is consistent

with the change in the direction of the acceleration vector benveen the nose-out and the

nose-in conditions. Also depicted in Figure 3.1 1A is the position trace that elicited the

firing rate. Note that almost identical stimuli leads to different firing rates in the three

conditions. Figure 3.1 1B depicts the mean sensitivities + SE of al1 the cells tested for

superposition, during eccentric rotation for different radii. The generai shape of the curve

in Figure 3.1 1B (increased sensitivity as the absolute value of the radius increased) was

eidiibited by al1 velocity groups and therefore, the curves in Figure 3-1 1B include the

values across a11 velocities. During such a paradigm, both a tangentid and a rotational

stimulus exist activating the semicircuIar canals and the otolith or,aans. The sensitivity

durin; pure rotation (axis of rotation centered on the interaurd h e such that the otolith

acavation is minimÏzed) are the values at r = O. Clearly, the sensitivity increases with

105

0.4 - A

0.2 - = 5 0.0 - 'a 3 0.2 - a

4.4 - 4.6 .

0.0 0.1 0.2 0.3 0.0 0.1 0.2 O. 3

Tirne (s) tirne (s)

a 1 -10 4 O 5 10 15

Distance trom centor of rotati*on (cm)

Figure 3.1 1 A) An esample of a t ypa dl mordcd whik tk animal Dadcrncnt 3Hz osciilitioi

during Ibc 00-rris (mi), nosc-in (tbick biack linc), nad nùscsut conditions (bloc). Note tbit the

nase-om eonditioa bsd in invctîed pbme rtiattve to the m d n cwditmi. B) Scasiîhity for nrhm

distaacrs f m the intemural line. It ïs ciur tôat tbc sas i t~ ty incrwsrs as the mdjm ~BCCCIISCS

increasing radius, rnaking clear the apparent contriition of the otolith organs because

the rotationai stimuhs does not change at different radius locations. The addition of the

oto iith signal onto the rotational signal has always been assumed to equal the ihear sum

between the rotationai arad traaslaûonal response (Chen-Huang and McCrea, 1999;

McConviiie, et ai. 1996; Snyder and King, 1992). According to this idea, the response of

celis to translational stimuli is simply e q d to the respoase of the cell at some r # O

minus the response at r = O. However, note that the sensitivity increases for both the

nose-in and the nose-out condition, which is inconsistent with a simple swn of the signals

since the transIationa1 signal reverses phase behveen the nose-in and nose-out condition,

To Further test the linearity hypothesis, monkeys were translated and rotated on-ais.

Then, while we still recorded fiom the same cell, rnonkeys were moved to an eccentric

position and rotated with the sarne stimulus applied (identical amplitudes for a particular

frequency) during the on-mis paradiam. Note that the radius was carefuIly chosen so

that the tangential acceleration produced dunng eccentric rotations approximated that

during translation. During off-line analysis, the eccentric response was appropriately

scaled if the eccentric tangential acceleration was found to deviate from this equivalence.

We found that the assumption of linearity is tvrong.

Figure 3.12 depicts the response of a neuron to rotation, translation, and a

combined rotation and translation at a fiequency of 3 Hz. if the ce11 behaves in a Iinear

fashion, then the sum of the response of this ce11 to a translation at a peak velocity of 14.6

cmisec (labeled 'translation' in the plot), and a rotation at 8.4 delsec ('on-ais'), should

be equal to that recorded when these nvo stimuli are presented sirnultmtneous~y ('actua17).

As c m be seen [rom Figure 3.17' this cell clearly violates linearity when presented with

the velocities mentioned above. The amplitude of the firing rate of the recorded signal

('actual') is aImost nvice what one would predict based on Iinearity ( blue trace labeled

'linex'). The blue trace labeled 'mr' is the maximum amphtude obtained by Iinear

sumrnation. This was obtained by aliging the peaks of the individual responses to

nitnsIation and rotation before sumrning those responses. As can be seen, no phase

adjusmient of the response to the single combined stimulus can compensate hily for the

1 translation

Tirne (sec)

Figure 3.12 Nonlincar rrsponsc of vcstibdir acurws. Bdtom. Rcsponsc of i acaron to iitemarril

translation at 3 Hz with a trioshtioaal velocity of 14.6 cm/sce. Middk: Rcspoost of the srmc

nearon to au-ixis rotation at 3 Hz witb r rotatioarl velocity of 8 4 de@sce. Top: The respoase of

the same oearoa to a combiacd tnashtionrl and rotatioa at 14.6 cmlsec rad 8 4 dwsec

resptively ('actril'). If tbe cd1 rcspoaded as a liaear sptem, then tbe blœ üw 'iistir*, wbkh

equrfs the vcctor sam of the bottom two trices, shodd k i n rppronuution to the mpme The

-mm p i b k signal tb i t coPld k obhincd by lincar slimmrtioa (ml üw mrrLcd 'nu'),

obtained by pbue adjiatment of the bottom two trices, io di weU sbort of the amplitude of tk

actual mordcd si@

discrepancy. Linear summation for a ceII at d l 4 frequencies tested is depicted in Fiume

3.13. The length of each vector represents the h g rate, Note that the principle of

superposition fails at al1 frequencies. When cornputing the translational contribution to

the firing rate during eccenmc rotation, we took into account the sensitivity profile shown

in Figure 3.7 and used high sensitivity values for each cell.

Figure 3.13 Failure of superposition depicted for a celi for dl frequencies. L: Linear summation of

on-aris (ON) and translation (TR) response' OFF= off-mis. Radial distance is the firing rate.

Numbers in italics on the 1Bz polar plot represent phase angle. (Velocity at O degrees),

3.2 Nonlinearity In Response To Transients

The finding that cells in the vestibular nucleus respond in a nonlinear matmer

sheds new light on the signal processing accomplished in the brainstem. The firing rate

shown in Figure 3.3 has a clear asyrnmetry. However, the dynarnics of this asymmetry

are hidden by the idiosyncrasy of a sinusoid. It wouId be more instructive to use a

stimulus whose position, velocity and acceleration curves are rnarkedly different fiom

one another. This way, the possibirity that the asymmetry observed leads to any form of

calculus is clearly discemible. To that end, a total of 62 cells were recorded from the

vestibular nucleus of 2 fernale rhesus monktys in response to steps of position. 4 6 2 cells

had responses that encoded pure acceleration and wil1 not be discussed in this paper. Of

the rernaining 58 cells, 39/58 were from the lrft nucIeus and the remaining 19 from the

ri$t nucleus. No eye movement signa1 was detecced on any of the 33 cells (vestibular-

only cells).

Figure 3.14 X depicts typical steps almg with the velocity and acceleration as

reported by a 3D accelerometer placed on the monkey's head. The position trace is the

feedback signal from the sled whiIe the velocity trace is the uapezoidal integral of the

accelerometer's output. The firing rate that this stimulus produced in a vestibular nudei

neuron is s h o w at the bottom. This neuron responded quite weI1 to the hi& fkequency

ringing in the sled as wel1. Al1 the ceris described in this paper exhibited this hi&

frequency robustness. in addition, the shape of the response of the ce11 was fairIy

consistent despite changes in the amplitude of the stimuIus (not shown). The peak

acceleration for the stimulus in Figure 3.14 varied benveen 0.42 and 0.50 g in the

0.0 0.5 1.0 1.5 2.0 2.5

Time (sec)

Figure 3.14 A) A typical step cycle used in this nudy Top trace is the sled position and is the

feedback from the sled. The middle trace is the veloeîty of the steps, and is obtained by integrating

the acceleration (third trace). The bottom trace is the firing rate in response to the acceleration.

IF: i n h i b i t o ~ First. EF: Excitatory First.

1 .O 1 .S 2 .O

Time (sec)

Figure 3.14 B) Three second time series of the ce11 depicted in Figure 3.1JA. The kernel widîh

affects ihe response amplitude but does not affect the Wmmetry to be described. Standard

deviations of the Gaussian that was convolved with the spike train is wntten on the figure. (See

3.14C to see the eîïect averaging bas on the amplitude.

-15 rns s 0.0 0.1 0 3 0.3 0.4 0.5

Time (sec)

Figure 3.14 C ) The mean of 14 cycks d u h g tbt EF poitioa of the pasitioa trrmunt of the ccll

whost time series is shown in 3.148. Bhck is tbc Wng rate iad red is tht firing rate + tbe Jtradrrd

devirtion of the bring rate. Notc Iht as the rtradrrd d-tioi o f the Ciasira k c d decrasw, the

standard deviatioa o f the mponse increascs The me o f the puk fviag rate ia sabsqucat railysk

w u obtaincd by wing d ms

positive direction, and was consistentiy O.4g in the negative direction. However, the

rising and faliing phases of the steps eIicited different responses. Specifically, the fmt

acceleration pulse elicited a biphasic pattern in the firing rate, initially driving this ce11 to

zero (labeled '1 ' in Figure 3.14) before exciting it to fire at approximately 180 spikestsec

(Iabeled '2') . We shall refer to this stimuIus as Inhibitory First (TF) direction. M e r the

stimuius is over, the cell passively decays back to basdine (taken here to be 80

spikedsec) with a tirne constant of 60 ms (labeled '3'). On the other hand, once the sied

reverses direction, so that the acceleration reverses poIariry (referred to as Excitatory

First (EF) direction), the finng rate (labslsd '4 ' ) no longer clearly represenrs the biphasic

nature ofthe stimulus, but instead has adopted a monophasic response approximating the

integal of the stimulus. Even though the acceleration has gone korn 0.54 g to a -0.48 g

in 36 ms (-39.23 g/s) and maintained this minimal value for approximacely 80 ms, the

firing rate of the ceil is decreasing at a much slower rate. in contrast, in the IF direction,

the acceleration peaks at 0.4 g and returns to baserine in 65 rns (-6-15 g/s) resulting in the

firing mts taking almost three rimes as long to return to basehe. Thus, the acceleration

returns co baseIÏne ive11 in advance ofthe evoked firing rate.

in order to ascertain that the aqmmetry just descn%ed is not due to the

characteristics of the kernel, Figures 3-14B and 3.142 depict the effect different kernel

widths have on the response. The standard deviacion of the Gaussian kemel used in

witten on the plot. As is sho~vn in the figures, as the standard deviations decrease, the

amplitude increases (compare Figure X14B a=3 ms with o = 20 ms). This is expected

since the area under the Gaussian is 1 in al1 cases. Therefore, a decrease in the standard

deviation must be accompanied by an increase in the height of the Gaussian.

Nevertheless, the asymmetry is still present regardless of the width of the kernel

(compare first second of al1 plots in Figure 3.14B). The mean of 14 cycles is shown in

Figure 3.14C only for the EF directions. The large deviations in the heights depicted in

Figure 3.14B is less conspicuous here. However, as c m be seen, as the standard

deviation decreases, the noise in the average increases. This is also expected, as

convolution with a Gaussian applies a moving average filter to the time domain data.

ha lys is to follow will rely on the calculation of the peak. We have chosen (T = 9 ms as a

representative value of the peak since the peak obtained with this standard deviaaon is

the mean of the peaks shown in Figure 3. LJC.

3.2.1 Are the neurons encoding direction?

Given the asyrnmetry described above, cari a single otolith n e m n encode

direction or are several of thern required? Figure 3.15 depicts the shape of the waveforms

for another ceil for al1 orientations used in this stuciy. The stimulus for a11 orientations

was the sarne and is depicted in the upper rïght and lower lefi corner. For each

orientation, the rnonkeys were sirnply stepped in one direction, and then stepped (back) in

the opposite direction, resulting in the acceleration profiles shoivn in the piot. The

behaviour of this ce11 is consistent with that shown by others, (e-,o., AngeIaki and

Dickman, 1000), responding to translations in al1 orientations, Therefore, afferents with

different on-directions must be conversin; onto centra1 neurons (Angelaki, 1992;

Ano,eIaki et al, 1993; Angelaki and Dickman, 2000). Note atso that the diffirence in

behaviour of the neuron benveen the IF and the EF directions is not generated pduai Iy

as the angle of stimulus sweeps through different orientations. hstead, what one fin& is

that the ceIl clearly demonstrates its robust tuning, firing vigorously as to approxhate the

velocity of the motion in d l forward directions spannin; 180 degrees, and producin; a

biphasic signal rerniniscent of the input signa1 for the rest of the angles. The only

difference arnong the responses for the EF direction is the modification in amplitude and

changes in the standard deviation of the k g rate fiom one angle to the next. The sarne

is tme for the IF direction. Given these responses, this ceil can theoretically distinguish

behveen a transIation that is soing fonvard and ri translation that is going backward.

However, it is still not apparent whether the exact orientation of the motion is also

encoded. Figure 3.15B depicrs the peak firing rate (mean = SE ) for al1 the orientations

in the EF and IF directions. (Note tliat che peak firing rate for the IF direction occurred

much afler the peak for the EF direction since IF stimulus inhibits the neuron first (Figure

3.15A)). As can be seen tiom Figure 3. LjB, and for both EF and IF directions, the naso-

occipital directions elicited the grexest response which sives the impression that the ceII

may be encoding a specific orientation. However, there does not seem to be a difference

in the CCW firing rates (Figure 3.IjB) between the EF and the IF directions. For

exarnple, for translation dong the 60 degrees CCW orientation, we cannot reject the nul1

FFgrirt 3.15 A) T k respoasc of r ceIl Lo traiulrtioas ayaiing 360 degrces NO: Nmo=occipibL Li:

lnterrml. Sbown arc the respmw at 30 d q p e iarremrats. The trradition Is aiways ia tk NO

direction (Plang the ml iine). !r bbck axes witb the a m w s arc tk d k t h tbe wiikcy is

looking. For eacb as& the stimdus is compoeed ofa SftP in t k dimtjOa of tbt a m , 8 4 8 stcp

hck in the oppsite direction. Tbt M n g mC d e is shmm oa tk kit T k stiadm is s h in

the top right and bottom right coratm. Notc tbat the mpomm only diilcr nbci tbc trrnsbtioa ip in

tbe EF or IF dirrctiw, a d do sot diiftr nbta chmg@ elit rigk within r toamrd or bitlmud

trposhtroa

-60 -30 NO 30 60 IA CCW CW

Orientation

Figure 3.15 B) The maximum amplitudes (mean ISE) in the EF and TF directions. This cell was

sharply tuned in the naso-oceipiial direction. Xote that the maximum amplitude did not differ

significantly in CCW direction.

hypothesis of equal rneans of firing rate in the EF and iF directions (t = 1.842, sigmficant

at the P=.O 1 level). On the other hand, mean firing rates in the CW direction are very

different with the EF direction clearly reriching higher firing rates with relativciy srnailer

SE. The points in this plot are based on the average of 16 - 10 cycles, depending on the

direction of motion. Therefore, given the standard deviation inherent in the f i ~ g rate for

one particda- direction. c m ive accuracely state that this single ceII is encoding direction

in addition to magnitude'? We shaii use Bayesian uiference, which reiies on the

conditional probability distribution of the neuraI response to answer this question (Orarn

et ai. 1998; F o l d i a 1993). For each orientation, the probability distribution of the firing

rate was calculated without any assumption about the distribution of the firing rate, The

nurnber ofspikes elicited during a 200ms window in response to a train of stimuli were

separated into buis 6 spikes wide and counced. The frequency distribution that was

obtained by this method was divided by the total number ofspikes in order to get a

probability distribution. The distribution of one ce11 dong al1 orientation is depicted in

Figure 3.16A. The height of the plot in Figure 5.16A (represented by colour; red is the

highest, blue is the iowest) is the probability of obtaining a particuIar firing rate given the

orientation. Therefore, the plot in Fisure 3.16.4 is the distribution P(r 1 s ) (the

probability of the response, given the stimulus) while the sum of al1 the probabilities at

each orientation is one. P(slr) can then be obtained by using Bayes' mle as:

[t is clear from Figure 3.16A that the responses dong different orientation are not

identical. For example, response ofthis neuron to a transhtion 60 degrees CW fiom NO

leads to a broadly tuned probability response, as indicative by the persistence of coIor in

Figure 3.16A at hi@ firing ntes and the lack of yellow and red. On the other band, 60

degreed CCW to NO, the probability of recording a response geater than 150 spikedsec

dong this direction is very low, as most of the activity occurred at low Firing rates.

Given this distribution, we can now proceed to use Bayes' rule to ask what direction are

we moving in if the ce11 is firing at (for exiimple) 48 sp/sec, 90splsec, LSOsp/sec, 210

spisec and 270 spikeslsec? Figure 3.16 B depict the conditional probability distribution

given the finng rates mentiuned cibove calcuIacsd using Bayes' ruIe for the ce11 in Fi,we

3.16A . Note that there is ambiguity for a l the f ing rates tested. For the 270sp/sec

his to-m, the probabiiity is quite hi& that the tramration that is occurring is dong the

119

60 CW direction. Nevertheless, this is an isolated case since a firing rate this high is

rarely recorded. No conclusion can be made about the direction of translation fiorn the

histogram calculated at 150 spikedsec, a more average firing rate. Bayes' rule c m be

used to combine information from several cells in order to increase the estimate at any

particular level, Xssurning the stimulus has a uniform probability of being presented, the

cornbined conditional probability c m be calculated fiom (Oram et al. 1998):

The probability distribution afier using 3 cells is depicted in Figure 3.16C. Note that of

the additional 2 cells used. one did not have a response at 30 CCW (and therefore 120

CW). The values Cor this direction were interpolated From neighboring values. Note that

the firing rates r,, r~ and r~ in the above equation were the mem ofeach of the three cells

respectively. As c m be seen, the distribution changes slightly but the probability that the

system can guess the correct orientation by using this technique remains low. The

distribution of the 110 spikeslsec level has begun to indicate a possible direction, while

the probability that the monkey is translating at 60 CW if a firing rate of 270 spikesisec is

being recorded is almost 1. As can be seen, Little is gained a the lower Ievels where the

bulk of the responses occuned in most cells. Certainly, if more cells are included in the

analysis, then the probability distriburion may change. The present analysis presents just

one way of calculating stimulus probability. In addition, by combinin; celIs with sharp

tuning curves, better estimates will sureIy result. Nevertheless, the resuIts presented here

rnay indicate that connections between ceIIs in the vestibutar nucleus is ordered according

to tuning curves, so that the pecipheral topology remains accessible to the system.

However, the possibility does exist that the system is weak at discerning orientation.

Indeed, cosine tuned systems, such as the otolith organs, have very poor resolutions,

since for example, a transiation along the polarization vector of an af3erent and a

translation 15 CW fiom the polarization vector lead to a difference of 3.5% in the

response (cos(15)=.965, cos(O)=L), a very small value. This may be the reason for

convergence of afferents in the first place.

Figure 3.16 A). Surfice plot of tk c o a d i i l probabiliîy of detecîing 8 directioa givei the iùiig rate.

TbiP plot was comtmctcd by computiiig tht probrbiiity distribiitim of îhc firing rite withort prior

rsstimptim of any disîribPtioa and pkttiig ibe proimbiüty agiinst the 8- mte iid tlie dimctioo. By

noting t k a m O€ r d and y e k in the plot, oie can romclde that îkre am ambiguitics in direcruhg

direction. For eampie, 200 spilrrs/scc, the ptobrbüity i9 q& law f'or i U sîimili Red: Blgbcst

probmbüity, Bk: lowcst p r o b r b i i Colot in the vrrîial dition ir P(rIs)

B 1 Cell

Orientation

Figure 3.16 B: C(slr) calculated using Bayes' rule for the cell shown in Figure 3.16A. The question k i n g

nsked is: given a firing rate of, what is the orientation of the stimulus? Little can be said about the

direction of motion at low value of the firing rate (150 and below) sincr the probabiiity distribution is

quite broad.

3 Cells

Orientation

Figure 3-16 B: P(s]r) cdculated using Bayes' rule for the threedinerent cells shown in Figure 3.16A. For

the 48.90 and 150 level, not much improvernent has occurred indicating that more cells rnay be needed.

A definite improvement can be seen in the 210 spikeslsec, wbere the probability thrt the direction of

translation is 60 CW to NO is slightl greater than 0.6.

3.2.2 Signal Processing

Figure 3-17 depicts the firing behaviour of another ce11 (mean i SE) in response

to a position transient in the naso-occipital direction. The nvo plots in Figure 3.17

represent a single step cycle; Le., the sled moved backward and then forward as depicted

by the insets in the upper right corners of the plot. Once again, the asyrnmetry between

the nvo directions is obvious. As the sled translated backwards (Figure 3.17A), the

response exhibits a biphasic waveform, being inhibited first and then excited, suggesting

that this ceil is encoding the acceleration of the movement. However, once the sied steps

in the opposite direction, the ceil is excited by rhis acceleration direction, and the

excitation lasts much longer than the stimulus. This behaviour renders the ce11 unable to

encode the reversal of the acceleration as robustly as it could when it was ulitially

inhibited, resulting in a firing rate that resembles the velocity of the motion. in both

cases, the firing rate decays back co baseline slower than a linear response to the stimulus

would suggest. As in Figure 3.14, the time constant of decay of the response in Figure

3- 17A is approximateiy 60 ms, whiie in 17B it is 20 ms. This value is surprishg since

the stimulus in 17B is forcibly driving the response in the opposite direction.

The difference in the response benveen a stimulus composed of a step forward

and a step bacbvard is best presented by a phase plot (Figure 3-18), The acceleration

and its integral (velocity) are plotted against the tiring rate for both directions of motion.

A coilapsed pIot (Figure 3.18% and C) indicates that the stimuli and the response are well

correlated with features occurring close to unison, while an infiaeed surface indicates that

the biphasic stirnuhs is being plotted againsi a monophasic curve rvhich is the description

of its integral (Figure 3.13, second and third row). The existence of both types of these

curves for a single cycle (step forward and a step back resembling a square wave, see the

top trace of Figure 3.14) indicates that stimulus velocity is a better M to the data in one

direction while accelecation is a better fit in the opposite direction.

l i m e (sec)

Figure 3.17 The mponse of8 ceII ( m a n S6E) to a backward step (A) and 8 f o m r d sbtp (B) in

the nrisooecipital direction (response in r d supcrimpmed on stimulpr in blut ). A) The ceIl

erhibiîs r biphisic mpoose rcmiabeit of the stimuiia if it b h t inhibittd bmt dctiys sbwly

back to M i n e a f k the p a î t nring rate is rchicvtd. 6) The respoase in Uni direction is mon

rcminisceat of i mwopbsii sipal, appmximtuig the integral of the stimdirn ïüû ir dut to the

iaability of t k stimdirp to expeditiody drive tbe firing rate into inhibition Traces im the kft

corner oftach plot is the skd position.

-0.50 -0.25 0.00 0.25 0.50 -25 -20 -1 5 -10 -5 O 5

Acceleration (g) Velocity (cmlsec)

Figure 3.18 Phase plot of the response shown in Figure 3.17 indicsting the asymmetry present in the

response of the neurons respanding to steps, A) Acceleration vs, firing rate in the fomard

direction. B) velocity vs. firing rate in the forwsrd direction, C) accelerntion vs. Ilring rate in the

backward direction. D) velocity vs. firing rate in the backwnrd direction.

More accurately, the best fit to the response of this ce11 Ieads to a hctionaI

denvative exponent of velocity of 0.82 in the EF direction and 0.21 in the IF direction.

ïhese Fractional dynamics (plus a bias) were better at fitting the responses (hi$er

correlation index) than a bias pIus any combination of velocity, acceleration, jerk or

dF*R/dt ( Iow pass filter fit). This was due, at Ieast partiy, to the differences in the rîsing

and falling phases of the response. The difference benveen a velocity fit and a iÎactionaI

derivative fit of 0.2 is more pmnounced after the peak of the firing rate rather tfian before

since the tirne taken for the neural response to return to baseiine is greater than the time

0.0s 0.10 0.15 0.20 0.25 0.30 0.36

Time (sec)

Figure 3.19 Acœkntioa (red), velacity fit ('Vel Fit' green), frictiond derivative fit ('FD Fit'(d),

supcrimpd on the firing rate.

taken to reach the peak (Figure 3.19). in addition, the direction approximating velocity is

affécted by the biphasic nature of the stimulus, with the response going below b l h e

before setthg (see Figure 3.178 at F0.2 sec). This drive below baseline dong with the

graduai retum to basehue is the portion of the velocity direction that takes advantage of

the fiactional exponents. indeed, there is no reason why exact velocity or acceleration

shouid be encoded centrally given the varying dynamics of the various plants dnven by

these signais.

Figure 3 -20 depicts the asymmetric effêct difEerhg rates of change of acceleration

have on the 6nng rate of a ceii that has undergone 7 separate trials in the inter-aura1

direction using different step amplitudes (see Methods). For each trial, the response was

separated into the rising and falling phase and subsequently fit with a Iinear regression

(Figure 3.70A). Only the linear portion of the curve will be fit in order to compare the

rising and faIlhg rate of change of firing nte.

The stimulus that gave rise to the portion of the response used in the linear

regression was also separated into 2 groups composed of a rising and fallin; phase and fit

usin5 a Iinear regression (Figure 3.20A, cyan). Figure 3.20B depicts the linear lit of the

slope of the firing rate plotted against the linear fit of the slope of the acceleration Gerk).

in Figure 3.20A, linear fit to the rising phase of the response (red) is: FR = -157 + 3850t

(r2 = 0.98) while the fallinp, phase produced a fit of FR= 633 - 3054r (r" -96). (The

slopes calculated in Figure 220A are points in Figure 3.20B). Since the response is

obviously curved, only the linear portion of the rising and falling phase of the response

was used in the regression. For the rising phase, this usually included the response at a

time after the response crossed the baseiine to about 10% from the peak. This was

expected since at the peak rhe derivative is zero and the average rising slope must

decrease in order to reach this zero. Note that the bonom mis in Figure 3.20B refers to

the rate of decrease of accelention (slope of the falling phase) and therefore belongs in

the third quadrant of the plot but has been placed dong side the rising acceleration line

for comparison (note sign of bottom s-stuis). For the sarne reason, the absolute and not

the m e value of the rate of change of firing rate is shown. What is notabIe for positive

jerk (increasing acceleration, top mis in Figure 3.20B) is that the rate of change of f i n ;

is not very sensitive to different rates ofjerk values, as depicted by the srnaIl dope of the

Iine Iabeled 'Rising AcceIeration7 (srope = 27.1 + 4.3 spikes/g*sec: mean

Time (sec) Time (sec)

B Jerk (lncreasing Acceleratioir g(s)

5 10 15 20 25 30 35

Rising Acceleration

Jerk (kreasing Acceleration gls)

Figure 320 A) Ernmpk showing the crkulrtioa of the rang and bliing slopes uscd io B. The

Lincar 6ts to the rising and falling phase o f t b rwpwoe am ploltrd as thidc mi lines for the

mponse and in thick cyan lines for t k stimiiltm For tbk particoûr direcîbc Riring pLuc:

stop = 3850 spürcs/secz ; FaUing phase: dope=-IM0 spikedwe'. Nouaber ofcycks : 21 B): Thick

liac U the liaur regrcssioa of the jerk vs c h m in firing rate wûik Ut ILii Iincs are utcasiws of

the ünear ngrrssioa to tbc extent of the plot.

dope t 95% confidence interval). (Note that the greater the value ofjerk, the steeper the

change in acceleration). The opposite is true for decreasing acceleration as shown by the

greater slope of the negative jerk vs. chanuige in firing rate regression lint (79.5 k 6.4;

P<.001; 7-tailed t-test with DF=39). However, even more notable is the large difference

in y-intercepts which will lead to an increase in the time it would take the finng rate to

return to baseline given a decreasing negative jerk. For example, for srna11 jerk values

(e-g.: -10 g/s in Figure 3.20B) it will take the acceleration 100 ms to fa11 back to zero

fiorn a value of I g. However, assuming that the ce11 was just driven to 1 g with a jerk of

10 g/s, then the firing rate would be at 300 spikeslsec (increases at 3000 spikes/s' for 100

ms (see Figure 3.308) but would now decrease at 1000 spikesls' requiring 300 rns to

return to baseline. -4s the absolute value of the negative jerk increases (rate of decrease

of acceleration increases, so that the ceil is being driven harder), the firing rate is driven

back to baseline at a tàster rate. In addition, the risin3 rate of the firing rate differs Erom

the faliing rate tor equd jerk values. As seen by the difference in the slopes oFthe nvo

regression Iines in Fi-me 520B, a ce11 responding to a biphasic acceleration puise with

equal positive and (absolute value of the) negative amplitudes wiIl reach its peak f i n g

rate much quicker than it will return to baseline, as seen by the differing slopes for the

same positive and negative jerk values. This feature expresses itself as the response

depicced in Figure 3-17, where the negative jerk in the IF direction is smailer than the

negative jerk, in the EF direction. Therefore, given this, and that the absoiute rate of

change of firing rate is smaller for smaller jerk values (Figure 3-20), the finng rate takes

longer to return to baseline than it does to reach its peak.

Figure 3.21, Sensitivity and phase (ISE) of the sensitivity of tVOR to oscillation composed of

frequencies 1-5 Hz. Dotted line is the data from Angelalci. (1998). .As can be seen, Our results

agree nlthough Angelrki's dain errend to much higher frequencies. where at 10 Hz, the phase

leads accelerrtion by 65 degrees.

3.3 Translational Vestibulo-Ocular Reflex

So fa , the dynamics of the ceIIs in the veshiular nucleus have been

descnbed without much detail on the reflexes benefiting fiom this signal processing.

132

Important to the study of vestibular signais is the study of the tVOR, one of the systems

driven by these brainstem signais. Most studies of the tVOR have used sinusoids as the

main f o m of stimulus (Telford et ai. 1997; Paige & Tomko, 199 1; Angelaki, 1998).

Here, we present the result of tVOR recordings in the dark in response to sinusoids and

position transients. Swpnsingly, high kequency data obtained with the steps are not

consistent with previous descriptions of the reflex, Figure 3.2 1 depicts a bode plot of the

tVOR in response to sinusoidal data, Supenmposed on the plot is also the results of

Angelaki, (1998). The results agree well up to 5Hz, which is the maximum translational

tiequency used in Our study. The reflex is indeed compensatory at these fiequencies, eye

velocity being in phase with head jerk (180 degrees out of phase with head velocity) . As

can be seen, the sensitivity for these plots has been expressed as dep/sec/cdsec. This is

the form of the Angelaki data and therefore, to facilitate cornparison, we chose CO also

present our data in this way. However, not so obvious in Figure 3.21 is that eye position

is d so in phase with head acceleration (take the derivative of both to get eye velocity in

phase with head jerk). For a sine wave, this is desirable as eye position and head

acceleration are opposite in phase. However, steps of position do not possess this

simplifying feature. Specifically. as shown in the Introduction (Figure 1.1 1 page 53), eye

position having a similar wavefonn to head acceleration is uncompensatory. Therefore,

is the compensatory eye rnovement obsewed during a sinusoid compensatory because of

reflex computation or because of the idiosyncrasy of a sinusoid. The answer is both-

Figure 3.22 depicts the eye movements elicited by steps of position, As can be seen, the

eye movement to the fmt step (Fiqre 3 . 2 2 ~ ) is cornpensatory. A step in position

(Ieading to a biphasic acceIeration) leads to a step in eye position in the opposite

C

I Eye Position

. - -

0.5 0.2 1 Sled Position B

0.0 Eye Position 0.1 -

4.5

-1.0 0.0

-1 .s 4.1 -

0.0 0.1 0.2

T i m (sac)

Figure 322 tVOR in respoasc to step ofpaaitioa A) Tbe eye positioi trace is simihr Io the berd

position (ml) and so this step ka& to a compeasatory cyt movemcnt. B) The eye position trrœ b

similar to head accelcration and dots mot compensate for the step in head pasho.

direction (inverteci in Figure 3.22 in order to facilitate cornparison). Note thai unlike

sinusoids, the compensatory movement here Is not to have eye position be in phase with

head acccleration but d e r with head position. Note aIso that the final eye position is

maintainecl which indicates tfiat an integrator is participating in the signai proçessing that

produced this eye movement. In Figure 3.228, however, the eye position is very simiiar

to the head acceIeration. As aIready mentioned, this wouId be taken as compensatory if

the stimuIus was a sinusoici, but here it is uncompensatory. CtearIy, the eye seems to be

acting as a mere spring in Figure 3.22B since the position of the eye is proportional to the

acceleration of the bead.

Head velocity (the integral of the acceleration puise) is depicted in Figure 3.23A.

As cm be seen, the vetocity of the ieo waveforms d s e r in amplitude by 10 cdsec, with

the iarger velocity king the integral of the acceleration pulse that gave rise to the

compensatory eye movement. if Figure 3.23B depicted the larger velocity ofthe two,

30 - 8 2 s - A compensatory fi $ 20 -

1 5 - a 'B 10 - O = 5 . >

0 - W

-5 1

0.0 0.3 0.S

T i (sec) T i (sec)

Figure 3.23 A) Velority pnk of cwipcurtory stimolm, B) velocity p6k of ~aeoaipcmsatory

stimdpn C) Tbe Fourier spcctra ofthe two piilses do dincr hanever, with tbe compsatwy (rd)

peaking at a €tquency ssmriier thin tbe scroad Note the difkrent hime s a k s in A and B.

then we could be observing the effect'already reported by Sylvestre and Cullen, (1999).

Specifically, they reported that as the eye velocity increaçed, the eye plant became less

dependent on its viscous properties. Instead, it acquired an slastic type of behaviour.

Clearly, since the velocity of the stimulus that led to the expression of an elastic system

(Figure 3.228) is srnaller than the velocity of the compensatory response, this effect is

not being observed. However, the two waveforms do differ in their respective frequency

content. Figure 3.23C depicts the frequency spectnun ofthe two waves. Note that the

frrst, the one that eiicits the compensatory response, peaks at 3.8 and again at 5.8 Hz and

7.8 Hz, while the second pulse peaks at 8.3 and 11.6 Hz. Unlike sinusoidal data, it is

clear that the tVOR may not be as robust as once assurned and that at around IOHz, it is

unabie to compensate for translation.

This section will present models for both the single unit data and the eye

movement data. Firçt, a simple mode1 is presented to expiain the failure ofhomogeneity

and superposition shown in section 3.1. Then, this model wiIl be expanded on in order to

accommodate the data presented in section 3.2. FinaHy, a mode1 wïll be presented for the

tVOR that adequately sirnulates the sinusoidal data. Sli@t modifications of this model

d 1 be shown to model step data as isvell. More detail about the models can be found in

the Discussion.

3.1.1 Nonlinéarity

Figure 3.24A depicts a simple circuit that is adequate to replicate the failurt of

homogeneity and faiIure of superposition. Specifically, signais fiom the canals and the

otolith organs pass throuph a rate Iimiter (Ieads to Mure of homogeneity), and then are

multiplied (leads to failure of superposition). The rate limiter functions to limit îhe

derivative of the input signai. Figure 3.248 depict the output of the model to two

sinusoidal inputs 90 degrees out of phase, representing the acceleration that is encoded by

otolith afkrenrs and velocity that is encoded by canal afferents (Fernandez and Goldberg,

197 1; Fernandez and Goldberg, 1976; Goldberg et al. 1990; Angelah and Dichan,

2000b). For Figure 3.24 Bi, the rate Iimiter was kept out of rhe simulation in order to

emphasize the multiplication property. In addition, the filter placed aRer the rate limiter

is reduced to simply be F(s)=l for the purpose of the simulations shown in Figure 3.21B

and 3.24C reducing rhe model in Figure 3.24h CO its simplest fom. (With these

limitations, rhe output of the model is simply the rate Iimiced product of the input

signais). Figure 3.4Bl was produced by setting the rising slew rate of the rate limiter to

infinite (meaning there is no limit on its rate of change) whik the falliny sIew rate is

restricted to -12 (80 % of rnaimum denvative) (see the Discussion for an explanation of

these vdues). Note that these values are arbitrary and depend on the magnitude of the

input signal. F igre 224B cIearly shows the faiIure of superposition that results fiom this

model. The red trace labeled 'Linear Sum' is the sum of the responses of the mode1 to

each stimulus alone. Note that the inputs rnodulate around a vdue of 2 units with an

a m p h d e of 1 unit which mirnics a modulation around a b i s in 3.21Bt. Figure 3.24Bz

0.0 0.4 0.7 1.0 1.4 1.8

fime (sec)

Figure 334 A) Mode1 of the d p i m i u of the œl$ mcorded thit c m rccwat for the füliut of

homwneity and t k fiilam of superposition, BI) sumrmtioa ia ml (liœar) and multiplication of

signaki in bloekckarly diar . BI wm not ntt limiteà krc in ordcr to empbuh tbe muitipüahm

intenction. Dcerrrsing the slew ntcs krds to the saw r d t buî inerrrscs tbe prrdiirity of the

response. C) Rcspoasr of a sin& pthway to a change in tbc stimuira: doubliog the sîimilpr

impühide dcerrucs the resuitrnt seasitivity 1.667 to 1.333. Only the rate l imiter nrs aiW

ia the simplrtiw, kaving the fiitcr for the Discopsion (sec F i Al).

138

on the other hand had the input signal modulate around 3 units. As c m be seen, the

response in 3.34Br is increasingly peculiar, with the inhibitory curve behaving differentiy

han the excitatory curve. Decreasing the slew rate even M e r to undesirable values

results in even stranger products (not shown). However, the slew is ncver intended to

reach these very low values.

increasing the bias avoids negative values of the input signais which ensure that

no additional fkquencies are produced in the output due to the rectification of the

multipkation element. (The rate limiter, however, does introduce additional frequencies,

at integer harmonies of the fundamental), Failure of hornogeneity is best illustnted in

Figure 3,242. As can be seen, the sensitivity decreases and the bias increases for an

increase in the stimulus (lower trace). However, there is an additional peculiarity to the

output. Specifically, as can be seen in Figure 3.242, the rising portion ofthe resultant

sinusoid is different From the falling phase. This is directly attributed to the rate limiter

and is aIso a feature of many of the cells described in this thesis. As shown in Figure

3.24C, the nonlinear behaviour of the rate limiter is suficient to repiicate the failure of

homogeneity. A signal with nvice the amplitude has its derivative reduced to the rate of

change allowed by the rate limiter. The rate limiter used in this simulation leaves the

rising phase of the sinusoid intact, but limits the rate of decrease of the response. This

difference in the slope of the change of the response (the king rate), is dkectly

responsible for the increase in bias produced by the simulation. The f a l h g phase of the

output takes longer to return to baseline, and before it c m reach the basehe, it is once

again excited by the next phase ofthe simsoids. The change of the bias c m be directly

controIled by dtering the allowable slope. This in tuni reduces the sensitivity of a

system since it cannot change its firing rate Fast enou@ to account for the increase in the

stimulus. However, how do we go tiom a mechanical entity like a rate limiter to real

neuronal behaviour? The simulation in the following £&es wilI show that Time

Constant Enhancement is partly a rate limiter.

Figure 3.25 depicts the tiring rate in response to position trmsients dong with

simulations produced by passing the acceleration s i s a l b u g h a single branch (no

rotation is present here). However, instead of the rate limiter, Time Constant

Enhancement was utilized. LVhat is being depicted in Figure 3.25 A, C and D is several

excitatory post-synaptic potentials (EPSP) convolved with the spike train representation

of the input. The input, which we took to be the output of the accelerorneter, was

deconvolved so that a spike train mirnicking the output of aeren ts c m be utilized (see

the Appendixj. (The spike min ofan aiTerem convolved with a Gaussian will reproduce

the analog acceIeration trace.) This represencation iyores rhe dynamics of the afferents

but is a generalized case. Equivalenrly, the anaiog acceIention signal was tumed into a

senes of spikes by usin; the amplitude of the signai as an estirnate of the interspike

interval. This method was preferred to the deconvoIution methods since the accurate

representation of the signal by spikes is highly dependent on the accurate heuristic choice

of Gaussian charactenstics. This proved tedious at tirnes since some accelerorneter

signals were contarninated with osciIIations and vibrations that depended on the direction

of the stimulus. Nevertheless, both methods were used, one being used as a test for the

other. Once the spike train representation of the acceleration signal was obtrùned, it was

convolved tvith several EPSP's that differed in Ume constant. -4n EPSP is simply

defined by e-'= where r is the time constant of decay. ive used severai EPSP7s in our

simulation having differing time constants depending on the h g rate so that as the

firing rate increases, so does the time constant. This is the same as having the post

synaptic neuron 'charge' so that as the firing rate increased, the time constant of the

decay increased, simulating Tirne Constant Enhancement. The time constant of the EPSP

( eTUr ) was defined as:

where ri is the time of spike occunence. For example, if the firing rate at any particular

instance is 230 splsec, then r, - r,., = 4 rns (the interspike interval), and the time constant

becomes 3ro. The upper limit that we allowed the reconstructed firing rate to reach was

330 spikesisec. However, the mavirnurn arnount by which the time constant was

sxtended was 3 . 5 ~ ~ . These values are of course arbitrary and highly dependent on the

average tinng rate assigned to the acceleration signal. Any other representation of the

acceleration as a series ofspikes c m easily be simulated by adjusting the definition fort .

Nevertheless, it is a simple idea that does a remarkably good job in simulating Our data.

The acceleration waveform (thin trace), before being converted to a spike train, dong

with the simulated firing rate (thick trace) is the depicted in Figure 3.25A. The

acceleration was transformed frorn a pe& of O.7g to the firing rate shown in Figure

3.25A (Iabeled 'input' in Fisure 3.15A). Note that the expected behaviour is easily

replicated. CVhen the acceIention rises tirst (EF direction) (Figure 3 . 5 4 at t = 0.2 sec),

the response of the mode1 is to produce an approximate integrai of the input. However,

when the input reverses direction, so that it is inhibited first, then, the response is

biphasic, decaying with a time constant greater than the time constant ofthe EF dÏrect io~

Cornparhg the actuai finng n te dong with the simulated trace (Figure 3.25C and D), one

141

c m see that Time Constant Enhancement of the input signal produces a good

approximation to the f i ~ g rate observed in this cell. For the simulation shown in this

Time (sec)

Factor multipling the tirne constant

D I

lïme (sac)

Figure 3.15 The output of simulations using Time Constant Enliancement. -4) Output of mode1

(thick black linc) iii response to the accelcratiun (thin line) after the acceleriition signal w u

transformed into a spike train and convolved with an EPSP with a base tirne constant of 16 ms (see

text for detail). The ncceler;ition trace is an esample of the transformation that the input (ncturl

rcceleration trace) undenvent. The original acceleration trace hrd a peak of 0.7 g, which we

transformed to the Gring rate shown, B) The relative amount of enhancement to the time constant

neeessary to produce the results shown in C and D. Note that 40% of a11 points received no

enbancement (r,, = 16 m.) while over 75 % of al1 points receive less than 24 ms enhancement. C and

D) Simulation (thick black line) using Time Constant Enhancement superimposed ont0 finng rates

(black) for EF and ïF input profiles.

Figure, rO = 16 ms so that the maximum time constant was 56 ms. This amount of

enhancement is sufficient in order for us to simulate our data. Figure 3.258 depicts the

normalized Frequency of use of various time constants in the simulation for Figure 3.25A

C, and D. As cm be seen h m Figure 3.25B, the time constant was low for most of the

duration of the motion. SpecificaIly, Iess chan 1% (0.7%) of dl the points were

convolved with an EPSP having a tirne constant of 56 ms while 78% of the points were

convolved ivith an EPSP with a tirne constant Iess than 25 ms,

3.4.2 Translational Vestibulo-Ocular Reflex

Sinusoïdal data ivill initially be used to consmct a mode1 for the tVOR

Architecture borrowed fiom the aVOR will be used to show that models of the tVOR

need not be complicated by supertluous tilters that mold the simulations in order to

mimic ;idequate ssperimental pertomance. For h e firsr model. ive shail assume that the

eye plant requires a s iga l in phase with head velociry and position and chat the plant is

constant across frequencies (Robinson, 1975). The hypothesis that the eye plant actually

constructively manipdates the incoming signal wiIl be implemented (Green and Galiana,

1998; MusaIlam and Tomhson, 1999). In addition, afferent dynamics that can drive this

linex mode1 wiil be derived. It will be shown that the ease in which sinusoidd data can

be modeIed is deceiving by atternpting to vaiidate ihe mode1 ivith the transient stimuli.

Subsequeneiy, the tVOR in response to steps of position wiii be rnodeled. Here, we s h d

assume that the eye plant is not a constant but a function of Eequency. The use of

nonhear eIements in modeting the tVOR Ïn response to sùiusoidal input cannot be

justifieci $yen the ease in ivhich sinusoida1 dara c m be modeled. Hoivever, this clearly is

142

a misconception and the use of nonlinear elements is needed in order to model the tVOR

in response to the position transients. In the Discussion, a 2" order nonlinear saturating

actuator will be built and it will be shown that the rate limiter (described previously as

Time Constant Enhancement) and the saturating actuator have sirnilar characteristics.

Figure 3.26A depicts the model that will be used to sirnulate sinusoidal

behaviour. As can be seen, it is composed o fa monosynaptic pathtvay (Uchino et al.

1994; Imagawa et al. 1995; Uchino et al. 1996; Uchino et al. 1997) and another pathtvay

running through the integrator. For a pure sinusoidal acceleration input, the appropriate

vatues for KI and K2 were deduced by rninimizing the Ieast squared difference between

the experimentally obtained complex number gelP ( where g is the gain andp is the

phase) obtained from Angelaki, (1998) paper and the one produced by the mode1. Other

minirnization methods were also used without any sigificant change to the values of KI

and K2. Then, the difference benveen the output of the model using the denved Kt and

Kz and the experimentd data was computed. This difference corresponds to the required

filtering of the accelention signal to adequateiy simulate the experhental data. The

difference benveen the nvo outpurs was fitted to an equaiion according to the Goldberg et

al. (1990) classi~ïcation of afferencs (see below). Figure 3.26 A-C depict the output of the

model (solid line) for Kr=l and KI=lOO as compared to experimental data (Angeiaki,

1998 and Telford et al- 1997 up to 4 Hz). There is a fairly good phase agreement

behveen the hvo plots tvith the larzest phase difference occurring at 2 Hz where the

output of the mode1 Iags the experirnental results of AngeIaki by less than 20 degrees.

However, the value of the model's sensitivity curve is greater than those found

experimentaity beIow 1 Hz. As the fiequency hcreases, the slope of the model's

sensitivity curve is smaller than the experirnental one and as the fiequency increases

Fwther, the sensitivity curve levels off. Note that at hi& kequencies, this is the

behaviour of Angelaki's e-qerimental data (see for example Angelaki, 1998).

From Figure 3.26, it can be seen that in order to accurately simulate the

experirnental data, the model still needs a slowly nsing high p a s filter and an almost flat

phase response, exhibiting a 20 degree phase lag as the frequency increases. Up to 2 Hz,

0.1 1 .O 10.0 0.1 1 .O 10.0

Frequency (Hz) Frequency (Hz)

Figure 3.26 A) The model used here to model sinusoïdal data. a(t): acceleration; NI: Neural Integrator;

EP: Eye Plant; Kt and & are as discussed in the Methods section. B) Cornparison of sensitivity and

phase (C) values for the output produced by the model (solid line) shown in Figure LA. with K,=.1.2

and KL=L50 for a pure acceleration signal, and data from Angelaki (1998) (dashed line) and Telford

(1997), (dashed line up to 4 Eh). The phase from the model leads by up to 20 degrees at 2 & whiie the

sensitivity has r smaller slope and a greater intercept

145

this is the behaviour of utricular regular af'ferent neurons recorded by GoIdberg et al.

(1990). The two curves depicted in Figure 3.26 reaching 10 Hz were divided into each

other and the rcsult Iabeled Hatr. Hur represents the required t'rltering of the acceleration

signal (primary afferent behaviour) so that the output of the mode1 agrees with the

AngeIaki data. Han was then fined according to Goldberg et al. (1990) classification of

primary afferents. Specifically, the overall transfèr function describing otolith primary

afFerent behaviour is (Goldberg et al. 1990):

where

HI- is a velocil sensitive operator and provides a gain enhancement and a phase lead, HA

represents an adaptation operator tvhile HL, provides the system with a lag and may

represent otolith motion (Goldberg et al. 1990; Fernandez and Goldberg, 1976). The

input to the mode1 will be fit riccording to the above equations and the time constants and

the exponents optimized. Rcpresentative values of the parameters are tabfi=3s, r.tpO-lOs,

K.L~~=O.I~, s4=15s, KA=0.13. tvI=200s and rt? t s (Goldberg et al. 1990). For H&& ail

values were as above except for t ~ = O . ? j . WO.15 and ~ ~ = [ ( ~ + s t ~ ) ( l - s t ~ ~ ) ] ~ ' : This

results in a s i p a l that has a phase response consistent with a very reguiar primary

afferent but with a gain described by a dimorphic af5erent. indeed. this couid be the

behaviour ofsome afferents above 2 Hz, since for primary affcrents recorded by

Goldberg et al. (1990) the phase begm to Lag acceleration as the Frequency increased.

Figure 3.27 A) A comparison of the sensitivity and 3) phase of experimentsl cVOR data (dashed

Iine) and the mode1 (solid line) in Figure 1 for a prima- alferent input with Kp.16 (dimorphic) , A;=3.9 and KL=80. The sensi t ivi~ curve is almosc identical with that of Angelaici (1998), and with a

slight adjustment in gain. can aIso be made to accurately reproduce Telford (1997) data. Bowever,

up to a 60 degree phase lead is introduced. C) A comparison of the sensitivity and D) phase of

aperimentd tVOR data (dashed Iine) and the modei (solid line ) in Figure 3 1 6 for a pr imay

ïfferent input with &=.O1 (highly regular). &=0.8 and &=l. In contmst with Figure 3.27.A and

3.27B. the phase curve is almost identic~i with that or Angeiaki (1998). However, the sensitivity is

flat and exhibits o high intercept.

Kowever, primary afferent phase lags at high fcequencies is not supported by the data o f

Angelaki and Dickman, (2000).

F ig re 3.27 depicts the output of the model in response to an input cornposed of

the representative values given above for afferents. The dirnorphic afferent (KV=0.L6)

(Figure 3.27A and B) converges onto the experirnentally deduced sensitivities but with as

much as a 50 degree phase lead at 1Hz. In contrast, the regular afferent (K&,Ol)

approxirnates the experirnental phase curve alrnost perfectly but with a large loss in

sensitivity (Fisure 3.27C and D). Figure 3.28 depicts the output of the model to the

combined behaviour derived above. The rnodel's sensitivity curve (soiid line) closely

resembles that of Angelaki (Angelaki, 1998) while the mmimurn phase difference is a iag

of 10 degrees and occurs at about 1 Hz.

The model shown in Figure 326A adequately sirnulates the tVOR for known

sinusoidal behaviour. At first aiance, ic looks as if it could also simulate the eye

movements in response to steps of position as well. RecalI that the ocolith afferents

encode acceleration . Thsretore, the rnonosynaptic connection h m the uuicle to the

abducens provides the acceleration signal and is responsible for the eyc movements

elicited during the high fiequency step (Figure 3.22B). During such hi& frequcncies, the

signal on the integrator pathway is very small since the integator is a low pass filter. For

the low fiequency pulse however, the inte,wtor could in turn produce the velocity signal

that drives the plant to the appropriate position. However, there is a probiem with this

interpretation: even at 5Hz, the amplitude of a signal that has been integrated is also srnail

and therefore, the model used above to simulate sinusoidai behaviour fails when given a

step of position.

Figure 3.25 The output ofthe mode1 from ;in input composed OC a combinotion OC the bebaviour of

the primary afferents from Figure 3.27. The model's sensitivity curve (solid line) is quite close to

experimentai values whilc the phase exhibits up to a 10 degree Iag below 4 Hz.

In al1 the preceding discussion of madeling the tVOR, we have ignored the

synergistic or antagonistic îùnction OF the eye muscles. It has Long been known that the

aVOR is a push-pull system (Leigh and Zee, 1999). However, no such information is

available for the tVOR where the activation of eye muscles may deviate fiom what is

already known. There Xe other unknowns as wel1, including the high frequency

behaviour of the plant, To mode1 the steps of positions, we shall make another

assumption: that the dynarnics of the plant is a nonIinear function of frequency. It is

already know that the viscous and elastic propenies of the plant are inversely

proportional to velocity (Sylvester and Cullen, 1999). Here, we theoretically extend this

finding of nonlinearity to the fiequency domain. An indication of this behaviour was

given earlier and is depicted in the frequency s p e c t m shown in Figure 3.23C. As can

be seen, the high frequency pulse elicits an eye movement (Figure 3.22B) that is the

response of a purely elastic system. Therefore, we shall use a plant model whose viscous

properties exponentially decrease as the Frequency increases. The pImt model is

described by

where

The gain and phase of Equation 3.1 are depicted in Figure 3.29. Note that beIow 4 Hz,

Figure 3.29 is simply a iow pass filter and agees weli with the experirnentally measured

dynarnics of the plant (Fuchs et al. 1988). At appmxirnately 4 Hz, where the viscous

properties no longer have any cffect, the dynamics c m be described as being

increasingly elastic. There is no experimental description of the behaviour of the plant at

higher fiequencies. However, the eye position during t< lsscond (Figure

Figure 3.29 Cain and Phase of the plant described by Equation 3.1. .As can be seen, the viscous

propenies of the plant decrelises as the frequeocy increases.

Tirne (sec)

1 im e (sec)

Fium 3 3 . A) Modcl med to simrlitt tâe tVOR in rrspwsc to stem B) The rrspwsc to lon

frcqmency (top trace) and bigb fkquency (boî!om tnce) rccekrition p u b . Red is simolitioa rad

blrck is actwl eye movemcnt, Acrckrrtion ip indiutcd on the boîîom for ach trace.

3.29B) does suggest that in response to high fiequency pulses, plant dynamics may be

approximated by Fiame 3.29. The mode[ used to simulate the tVOR in response to steps

of position is depicted in Figure 3.30A. Note that once again, there exist monosynaptic

innervation of the abducens (Uchino et al. 1994; hagawa et al. 1995; Uchino et al. 1996;

Uchino et al. 1997). Note that the high frequency behaviour of the plant described by

Equation 3.1 (which makes the plant elastic) functions to correctly simulate the high

Gequency pulses depicted in the simulation. The integrator present in the model for

sinusoids (Figure 3.23A) has been repiaced by an approximation to TCE in the form of a

rate limiter. Here, the rate limiter asain acts to rnirnic Tirne Constant Enhancement in

order to approximate the velocity of the motion but with a much higher corner kequency

than an integrator'. in addition, the rate limiter avoids saturathg of the systern by

increasing its bias, as alrcady shotvn in section 3.1. in effect, what this has accomplished

is the same as what the leaky integrator in the model of Fi-mire 3.23 accomplishes, to

supply the system with an estimate of the in t ep1 of the stimulus.

Simulations in response to rhe actual accelerarion are depicted in Figure 3.30B.

Note the eye movement trace is contaminated with eye drift and a change of vergence

(not show). However, the model is indeed rtdequate in modeling the steps in eye

position. Not immediately apparent is the persistence of the monosynaptic input For

exarnple, the oscillation present at ~3.0 seconds (arrow in Figure 3.3OB) disappears h m

the simulation if the monosynaptic pathway in the mode1 is severed. This is a

' AcntalIy, it is not correct to nlk about caner Frequencies as related ro tate lirniten but hem, the term

corner fiequency is merely used to suggest hat the nte ii iter approiumates the integnl of a signal in a

linear inteptoc's stop band.

dernonsixation of a persistent contamination of compensatory eye position by the

monosynaptic acceleration signal. Durin% high frequency acceleration bumps, the

rnonosynaptic pathway is driving the eye moirernents which results in the eye position

mereiy mimicking the acceIeration of the head. This is clearly not compensatory

behaviour which renders the monosynaptic connection a mystery. This subject will be

expanded on in the Discussion. In addition, it will be shown that the use of the rate

limiter (Tirne Constant Enhancement) to drive the tVOR is sufficient and that it is an

approximation to a typical nonlinear actuator (with saturation).

4.0 Discussion

So far, we have shown that cells in the vestibular nucleus are nonlinear.

Specifically, we have demonstrated that neurons in the vestibular nucleus tend to

decrease their sensitivity and increase their bias in response to an increase in stimulus

magnitude. Previous studies have genenlly relied on linearity in order to deduce a

translational signal from an eccentric response. We have shown that this assumption is

incorrect and that the principle of superposition is not obeyed in the vestibular nucleus.

Based on the data presented in section 3.1. the assumption of linearity can no longer be

used.

The behaviour of vestibular neurons was also tested in response to steps of

position in order to uncover how the nonlinearity described in section 3.1 manifests itsetf

with nonsinusoidal stimuli. Surprisingly, what emerged was an asymmetry that could

provide the system with an approximation of! the velocity of the head in one direction of

motion, and an approximation of acceleration in the other direction. We successfully

used TCE and rate Iimiters to simulate the behaviour of vestibular neurons in response to

positional transients and sinusoidal inputs. Prolonged NMDA receptor activation could

be used to implernent TCE since it c m prolong post-synaptic dynamics in response

increased activation (Land field and Deadder , 1988).

The tVOR was also studied in response to sinusoids and steps of position. The

mode1 that simulated the tVOR in response to sinusoids was used to generate a

hypohesis about tfie afTerent dynamics that could drive the reflex when restricted to

sinusoidai input. Mary ideas exist on the vaxying roles played by the regular and

irregtilar afferents. For example, the differing dynarnics of afferents may fùnction to

155

modi@ the gain of the VOR (Chen-Huang and McCrea 1998; Angelaki et al. 2000) or

contribute to motor learning (Lisberger and PaveIko 1988; Bronte-Stewart and Lisberger

1994; Minor et ai. 1999) or even drive different reflexes (Highstein et al. 1987; Minor

and Goldberg 1991). Here, the type of input necessary to drive the simple circuit of

Figure 3.26A wilI be compared to known regular and irregular behaviour. As was shown

in the Results, in order to correctly simulate sinusoida1 tVOR behaviour, an input in with

dynarnics in between chat of regular and irregular afferent dynamics was utilized.

Although sinusoidal data tvas readily modekd by rhe use of linear techniques,

rate Iimiters simulating TCE were urilized in order to sirnulate eye position durhg steps

of position. A nonlinex saturating actuator, which functions to move a device with a

precision conuolled by its damping factor and bandwidth, will be shown to approximate a

rate limiter and therefore TCE.

4.1 Failure of Superposition

We have s h o w that a neuurn in the vestibular nucleus increases its Eiring rate in response

to a combined transIationa1 and rotationa1 input more than e'xpected based on a h e a r

decomposition of the same input. Given that most head movements simultaneously

activate both the cmals and the ocolith organs (Grossrnan et al. 1989), then the vestibular

system may have adapted co always expect simultaneous input from the different end-

or;ans, Functionai~y, these neurons may send axons to the cerebeitum or the

vestibulospinril m c t to Form part of the body smbiIizing system. Nternatively, but not

rikely, they may form parts of the g z e stabirizing nenvork (Tomlinson et ai. 1996).

Even if hey do not, could the behaviour observed here in VO ceus be advantageous to

156

the VOR? If they are involved in gaze stabilization, or if there exist similar nonlinear

behaviour in the gaze stabilizing system, then would one expect to observe this

nonlinearity manifest itseIf during the VOR? Many studies have addressed the nature of

convergence of the tVOR and the aVOR (Viire et al. 1956; Crane et al. 1997; Snyder and

Kuig, 1993; Telford et al. 1996; .hastasopoulos et al. 1996; Barmack and

Pettorossi, 1988; Sargent and Paige, 199 1; Bronstein and Gresty, 1992). There is sonie

disageement on whether simple linear summation c m account for the combined VOR.

In one study, simpie summation consistently fell short of adequately explainhg the

responses during combined stimulation in humans (Anastasopouios et al. 1996). These

authors concluded that the translational VOR is more robust in the presence of canal

stimulation. This behaviour is similar to the cells described here. Simitar results have

aiso been presented in rabbits (Barmack and Pettorossi, 1988). However, other authors

could account for their own results using models utilizing linear summation between

rotational and translational responses (Crane et al. 1997; Sargent and Paige, 1991).

There are severat possible mschanïsms that cm explain the failure of superposition

shown in this paper. The most obvious nonlinearity is that the inputs into the system are

not independent but interact in some way. For example, dendrites f?om afferents

originating in different endorgans could converge presynapticalIy, wtuch could lead to

mutual facititations benveen the afferents. This would resuIt in the sensitivity of cells in

the vestibular nucIeus to a particular stimulus not being a constant but dependent on the

variety of stimuli present (in addiaon to the sensitivities' vm-ation across veIocities).

Recently, using the multisensory inte-mtion in the superior colliculus as their b e w o r k ,

Anastasio et ai. (2000) suggested that nonlinear superposition is necessary in order to

increase the probability that a weak stimulus wil1 be recognized. Specifically, this novel

idea uses BayesT mle (Oram et al. 1999; Foldiak, 1993) to compute the conditional

probability that a stimulus exists given the existence of a sensory input, With respect to

the present study, this suggests that simultaneous rotation and translation is a much better

indicator of motion than either one alone and that nonlinear superposition enhances the

signal coming from a single sensor.

The presynaptic interaction benveen afferents was modeled as a multiplicative

interaction between rotational and translational signals. Figure 3.24A depicts a simple

circuit used to simulate the failure of superposition. The circuit is quite simpIe in that it

involves a rate limiter, which lirnits the race of change of the input signal, and a

multiplication. Multiplication of sigals in the brainstem has been proposed by many

investigaton (Le., Angelalci, 1992, Hain, L986, Poggio and Torre, L97S). Tweed and

Vilis, (1987) proposed it as being necessrtry for 3D eye rnovements. This was recently

reconfirmed by Smith and Crawford (1998). More recently, multiplication of canal and

otolith signals was proposed by hgelaki et al. (1999) as part of a network that can

differentiate tilts 6-om translations. AIthough the results described in this paper came

from anirnals rotating around an earth horizontal axis where no head tilt with respect to

,mvity exists, this multipliczition may be a general way for the canal and the otolith

signal to intenct centrally. Figure 3.24B depicts the tailure of superposition that results

frorn this simple model. The [race labeled 'Modd Output' is the product of the input

s igals whiIe the sum is labeled 'Linex Sum'. The increased amplitude ofthe mode1

output (due to the product of the input signals) is expecced and even obvious. However,

not so obvious is that a producr: will resu1t in a decrease in the bias in response to an

increase in the input. This is not a problem though, since, as will be shown below, the

rate limiter in the mode1 hnctions to decrease the sensitivity and increase the bias in

response to large inputs, as experimentally observed. Therefore, the result of this

architecture is an arnp lified output (failure of superposition) which is restricted kom

saturation by the rate limiter, The rate limiter (or 'Tirne Constant Enhancement'), with

its Iimiting abilities, proved a powerful signal processing feature.

4.2 Failure of homogeneity

.hother feature ofthe behaviour ofvestibular cells described in this thesis is the

failure of homogeneity. Thus, changes in stimulus intensities are not accompanied by

linear changes of the response. The increase in bias was also shown by Fernandez and

Goldberg (1 976) to be exhibited in the dferents. Specifically, they showed that the

discharge rate of regular (but not irregular) otolith afferents increased d u ~ g sinusoidai

stimulation and that regular afferents could be asymmetrically biased in the excitatory

direction. For the neurons in this study, this behaviour c m simply be attnbuted to the

neurons increasing their firing rate. The neuron is limited by the inhibitory cutoffbut not

in the excitatory direction since the tirhg rates used here are well below excitatory

saturation. Therefore, by increasing its firing rate in the excitatory direction, and leaving

the inhibitory cycle intact, then the bias is perceived as increrising. However, more

importantly, the same neuron simultaneously decreases its sensitivity so that large stimuli

will not saturate the response. In addition, the same ce11 can e.xhibit diffenng dynmics

depending on the magnitude of the stimulus at a particular frequency. To complicate

rnatters tiirther, not al1 cells have the sarne dynamics for the same magnitude of the

t 59

stimulus ampiinide. For exarnple, when one ce11 is behaving as a low pass filter to a

particuIar stimulus, another ce11 may be behaving as a high pass filter to the sarne input,

dthough both have the ability to assume the spectrum of responses. As can be seen from

Figure 3.8 and 3.9 and Table 3.2 and 3.3, this is more evident at higher fiequencies for

the whole population. Specifically, the decrease in sensitivity in response to an increase

in velocity had a greater variation and range during low fiequencies than during high

Frequencies. Given the low values of the sensitivities, these large standard deviations

caused a failure of statistical tests. However, the failure of homogeneity is also tme at

Iow fiequencies on a ce11 by ce11 basis, Similar results have been obsewsd by Sylvestre

and Cullen (1999) who have s h o w that abducens neurons' transfer function depend on

eye velocity, in addition to Iiequency. It follows that plant models need to be used that

have stiffness and viscosity that are Functions of eye velocity.

As WU s h o w in Figure 3.24, the nonlinear behaviour of the rate limiter is

sufficient to replicate the failure of homogeneity. The asyrnmetry generated in the

response is clex, including the increase in the bias. The magnitude of the bias is

proportional to the slew rate of the rate limiter. For exarnple, setting a very low slew rate

would cause the response to decay much less than it would with a higher slew rate. In

addition, since the peak to peak modulation is reduced, this in tum reduces the sensirivity.

The feature of the rate limiter that allows it to process the input signal in this desirable

way is its ability to lirnit the derivative of the input signai, In this particular case, the rate

limiter places a Iimit on how f a t the signal Eom a ceii decays, making the nsing and

faIIhg phase of a signal asyrnmetric (Figure 4.1).

Time (sec)

Figure 4.1 A) Rcsposse of a nearoa to 4 Hz tmmhtioa prrscrîed kre to empbmizt t4e asymmttry

in the respse. Note how tôe absdate valut of tbe dope of the 6 l h g phase of the firing mtt is

smallcr tbrn t k slopc of the rising p h B) Rtspwe of 8 rite ümiîcr to a siammicial input wïîh

ampiihide of 1 and a fteqwncy of 4Ez The output of the rate limiîtr (RL) ii pssscd to a lm prss

filter (LP) with a corser fquency of14&, in order to smooth the shrp edgu prodiirai by the rate

output

B

input - LP RL >

(Figure 4.1 (continued frompreviouspage) limiter. Note that this îilter does not change the

dynamics of the response. Here, it is ssumed that this LP is an intrinsic property of a neuron.) and

therefore, no separate filter implementation is required. The stimulus is shown in black, and the

response in color. Blue and red traces have the falling phase of the rate limiter reduced to 9 and 12

respectively and the rising phase slightly belon the derivative OC the input. The green trace has the

rïsing phase of the rate limiter decreased to 18, giving the impression that the phase of this trace has

shifted. Time constant enhancement was used to model the falling phase feature ofthis behaviour.

Figure 3-1 depicts an example ofthe effect a rate limiter has on an input signal.

Figure 4 I A depicts the response of a neuron during 1Rz sinusoidal translation. The

asymmetry in the response is clear, This asymmetry, however, is even more evident in

traces recorded during position transients, as depicred by Figure 3.25. A single branch

bom the model in Figure 3.244 is reproduced here in Figure J.1B. Note that the rate

Iimiter (RL) and the low pass filter iLP) rire lumped together as a single entity, as

indicated by the box surrounding them. This was donc in order to indicate that we are not

proposing the addition of another filter to the circuit, but that LP is simply an intrinsic

property of the neuron. Specifically, the corner ftequency of LP is 14 Hz, and is placed

there to rernove the abrupt transition benveen s i p d s that the rate limiter impinges on the

output. Note thrtt this filter has M e effect on the actual s ipa l (amplitude and phase)

since rnost of the information contained in the response occurs well below 14 Hz. The

effect different slew rates of the rate limiter have on the input signal (sine wave with an

amplitude of 1 and a frequency of cl Hz) are color coded in Figure 4.1B. Specifically,

the blue and red responses were produced by Iimiting the slope of the failing phase to 9/w

and 1Yw respectively, where, w= 4*2*;c. As already indicated, this results in an uicrease

in the bias, and a marked asymmetry. In addition, by setting the rising slew rate to be 23/

CO, the response appears to have shifted its phase as well, By further decreasing the

rising slew rate to 1810 (green trace), a much greater phase shifl occurs.

By slowing the decay of a signal, the rate Limiter acts to extend the t h e constant

of decay, similar to the function ofTime Constant Enhancement. Indeed, the rate limiter

and the Time Constant Enhancement produce approximately the sme results. The major

difference is that TCE generates an exponential decay in the output while the rate [imiter

simply saturates the rate of change of the signal, resulting in a Iinear change in activity.

Since Our data exhibited exponential decays in firing rate, then TCE was used to mode1

the data, especially, in response to position rransients (see Figure 3.23). In general, if the

rate of change of the input signai is yater than che slew rate of the rate limiter, then the

rate limiter can be descnbed by the function y(i) = y(i - 1) + Snt where S is the nsing or

falling dope imposed by the rate Limiter. Note that if the rate of change of the input

signal in going Fromy(i-1) to y(ij is bounded by S, then the output is simply equal to the

input.

Failure of homogeneity is necessary in order to avoid saturation at large values of

the stimulus. A neuron that maintains an even rnodenrs sensitivity for very high

velocities will easily saturate well before any appreciable velocity is reached. However,

inhibitory saturation may be a worse problem for the vestibular systern since it can be

encountered more often. For exampIe, a neuron with a resting rate of 100 splsec and a

fixed sensitivity of 1 sp/sec/dee/sec will reach inhibicory cutoff at a velocity of 100

degisec. However, a mechanism must exist to prevent this situation since human

subjects c m compensate for head velocities greater than 300 degsec (Pulaski et ai.

198 1). -4ny ce11 that is drïven h to inhtiitory saturation wiIL no Longer have the ability to

provide the system tvith any specific information about heaci rnovement. In addition, this

information in unrecoverable. The decrease in sensitivity coupled with the increase in the

bias for hi& velocities is necessary to minimize this loss of information. Note that the

increase in the b i s and the decrease in the sensitivity rnay also lead to some ambiguity.

However, the system rnay have circuits that c m remove the ambiguity, something that

cannot be done if there is saturation. In addition, any system that c m easily be saturated

has a reduced dynamic range. The nonlinearity showri in this paper increases the

dynamic range of the vestibular sysrem and actually biases it towards a higher Eequency

spectmm. Indeed, most natural movements are composed of high fiequencies (Grossman

et al. 1989). Therefore, the increase in the bias and the decrease in the sensitivity for

increasing stimulus magnitude are necessary for the normal operation of the vestibular

system.

Neurons presented in this study were shown to have varying dynamics that is

dependent on the magnitude of the stirnuIus. Previous studies has s h o m that there is a

diverse behaviour in neurons that respond to translational acceleration. Angelaici and

Dickman, (2000) identified three classes of neurons narned 'Iow-pass', 'high-pas' and

'flat' neurons. -4lthough little can be concluded about the effect acceleration has on the

phase of the response, the effect on the sensitivity is clear. As was shotvn in Figure 3-10,

hi& pass, low pass, and flat sensitivity dynamics c m emerge from the same neuron

dependins on the rnagnkude of the acceleration. In addition, different dynamics emerge

at different amplitudes dependinz on the ce11 under study. Given the varie- of dynamics

present, then the properties of these ceils in the fkequency domain rnay not be as

important as the noniinear temporal computation that rnay be taking place. Time constant

enhancement, for example, can produce the estirnate of the temporal integral of a signal,

but not appezir as an integrator in the frequency domain. In general, the nonlinearity and

the rich behaviour exhibited by vestibular-only celIs recorded here preclude them from

being labeled with Iinear nornendature without accompanying the label with infinnation

about the stimulus. in addition, some of these cells rnay accomplish heir goals with

methods that are unrelated with linear filtering techniques.

4.3 Direction of Motion is Not Encoded in Otolith Neurons

As already s h o w by Angetaki and Dichan, (2000) and by die data presented in

this thesis, there is convergence in the vestibular nucleus. However, the peripheral otolith

organ's epitheliurn is topologicaly organized. 1s this topoiogical organization lost due to

convergence. Put another way, c m single neurons in the vestibdar nucleus encode

direction? Afferents are rictually cosinc tuned (..g&ki and Dichan , 2000) -

However, cosine tuning has a very poor resolution. For example, rhe difference between

cos(0) and cos( 10") is 1.5 %, (cos(O)=l, cos(lOO) is .9548), a difference that may not be

detected if represented as a difference in firing rate. Therefore translations that are 10"

apart rnay not be discerned by an animai. We attempted to shed Iight on this issue by

translating monkeys at various orientations (Firure 3.154). Figure 3.L6 depicts the

ability of cens in the vestibular nudeus receiving otoIith input to encode the direction of

motion, F6Idiak and CoiIeagues (Omaret ai. 1998; Foldiak, 1993) devised ri method that

utilizes Bayes' rule which c m indicate the popdation coding of neurons, and used it to

show that neurons in the primary visual cortex are poor estimators of the orientation of a

sine ,orting presented to an anesthetized car. Using Bayes' rule, rhey showed that a

165

population of neurons is required to encode direction but that only a few of them are

needed. This is in contrat CO population vector encoding used in the rnotor cortex

(Georgopoulos et al. 1998; Sch~vartz et al. 1998) which requires a geater number of

neurons to achieve similar results (Omar, 1998). As c m be seen from Figure 3.16,

however, otolith neurons are not well suited for discerning a particular orientation given

a firing rate, except at firing rate levels which are outliers. Figure 3.16A shows a surface

plot of the conditional probability for al1 orientations. The cross-section at m y value of

the firing rate results in the probability distribution describing the Iikelihood of obtaining

the observed response jiven the specific stimulus. As can be seen by the large area

colored yellow and red (highest probability), the encoding of direction at that level is

arnbiguous, since a îèw firing rates correspond to many directions. As was s h o w in

Figure 3.16B the conditiona1 disrribution P(s 1 r ) , calculated usin: Bayes' rule for a

response of 270 spiksstsec had a sharp peak at 60 CW direction- However, this was a

unique case as cells with a tuning curve peaking at other orientations exhibited broader

curves. However, as cm be seen in Figure 3.16, using the cornbined conditional

probability fiom 3 cells sampled at their respective responses does not improve the

system's reliability in detecting direction when usin; broad curves. Note that the

additional nvo ce1Is did not have such a s h q tuned conditional probability plot at their

respective peaks as did the cell depicted in Figure 3.15A- Nevertheless, the combined

probability plot (Figure 3.16C) shows that the combination ofthese cells, even if

individually broadly tuned, cannot encode direction with a substantive accuracy. It is

worth noting that this result is arbitnry and is dependent on the tuning curve ofthe

neurons pooled, Nevtrtheless, more cells are needed to increase the probability of

detecting the correct orientation, Given the poor resolution of cosine tuned systems, then

it is also possible that the system cannot discern the direction of motion.

4.4 Response Asymmetry and Approximating Integration

In a linear system, except for a change in s ig , it rnakes no difference to the

system wherher the stimulus is ~ o i n g Eom an amplitude of .rl to .r., or frorn .rI to 11 (Dorf

and Bishop, 1998). There is a cIear violation of this rule presented in this report as

opposiceIy directed srimuli slicirs much differenr responses. This has long been known to

occur in the smooth pursuit system, where a step in target velocity eiicits eye velocity

overshoot and subsequent oscillations whiIe stopping the target elicits an exponential

decay in eye velocity with a time constant of 90 rns (Robinson et ai. 1986). This pursuit

behaviour has been attributed to separate subsystems controllhg eye movements and

tixation (Leubke and Robinson, 1988; Huebner et al. 1992). However, we have shown in

section 3.2 that asymmetric behaviour cm anse from the sarne syscem by saturating the

ce11 in one direction and deIaying its remrn to baserine once the ceII is excited jsee for

example Figure 3.20). This may just be a passive property of the ceIl, but it serves a real

purpose. [t is able to provide the system ~ l t h an estimate of head velocity without the

need for additional circuitry. Figure 2-19 shows the sarne ceII as in Figure 3.1 7 dong

with the acceleration (red), a fit based on the inte,@ of acceIention (green) and a

fiactionai derivaiive fit (bIue), The best fit regression for velocity was FR43 + 8.3*V

where V is the integrai of the acceleration trace (2 = 0.78). Note thar if the fit is

restncted to t < 190ms, the correIation index of the velocity fit jumps to r' = 0.91- In

p z , , , contrast, the best fit regression using fiactionai derivatives is F R 4 6 + 9.8 (r- =

0.89). It is clear that the use of &actional denvatives better approximates the response by

utilizing the inhibitory swing of the acceleration. There is no reason why the exact

differentials of signals should be encoded by neurons, especially in light of the finding of

nonlinearities in the system. indeed, fractional derivative exponents have been used by

Femandez and Goldberg, (1976) and Iater by Goldberg et al. (1990) to describe afferent

dynamics. Given that the afferents are the inputs to the system under study, then it

should be expected that s igals bener fit by fiactional exponents also exist in the

vestibular nucleus.

Time Constant Enhancement proved to bs a powerful feature that allowed us to

easily simulate the results presented in this paper ( see the Introduction for a definition of

Time Constant Enhancement). Time constant enhancement is similar to Short Term

Potentiation (STP) in that i t increases the time constanc of decay of signais which may be

interpreted as increasing the time constant of the membrane. This can be accomplished

by hriving the excitation of the post-synaptic neurons mediated by M I D A (N-rnethy1-D-

aspartate) receptors (Landfield and Deadlwler, 1988). N h D A receptors (and Nitric

Oxide, also implicated in Time Constant Enhancement) are known to exist in the

vestibular nucleus and are implicated in r e s t o ~ g the vestibulo-ocuIar reflex afier a Iesion

( Smith et al, 1990; Grassi et al. 1999; Caria et al. 1996; Grassi et al. 2000 ). In addition,

it has been shown that there is a large number of ?&IDA receptors in the vestibuIar

nucieus (Sato et la., 1995; Kinney et al. L994) wich various functions (Serafim et al.

199 1).

The use of Tirne Constant Enhancement to perseverate the signal on a neuron is

aiso of great benefit to the stability of newal integator designed using a positive

feedback. The neural inteptor provides the eyes with a static signal of the desired eye

position, and is necessary for oculomotor systems in order to deliver a signai to the eye

plant that has appropriate dynamics (for a review, see Robinson, 1989; Leigh and Zee,

1999). As already mentioned in the Introduction, modeling efforts of the integator rely

on positive feedback loops with a gain equal to 0.99975 in order to extend a 5ms tirne

constant of the membrane to a physiological value of 20 seconds. SIight variations in the

feedback gain have deleterious effects and therefore, the system must have some way of

circurnventing this problem. One obvious solution is to increase rhe thne constant of the,

membrane (Shen, 1989: Seung et al. (2000)), a solution that could be accomplished by

the use of NMDA receptors. Given that there exist NMDA receptors in the vestibdar

nucleus, then these receptors could be responsible for ce11 depolarization in response to

otolith input. This in turn could provide the many systems that depend on otolith

processing with the velocity and accelention of the input signal with little additional

circuitry. However, Although Time Constant Enhancement cm assist in producing a

compensatory signal during dynamic signal processing, it cannot be a substitute for an

integator since eccentric gaze can be maintained in the dark with a time constant of 20

seconds, a time constant that cannot be achieved by TCE as it is presented here.

However, during signal processing of a dynamic s i p l , whether an în tep tor has a time

constant of 20 seconds or 2 seconds does not affect processing. Therefore, we propose

that TCE is a dynamic processor, there to provide the plant wvith sipals with appropriate

dynamics-

Under certain resmctions, the use of tirne-constant enhancement is an

approximation to a fiactional integal (or derivarive). The convolution of the spike train

O

with the EPSP can be defined by Ih ( r ) f (x - r )dr where h(tj is the EPSP and fer) is the

spike train. We are using the variable cime constant of the nonlinear kernel in the

convolution integal as a piecewise approximation ro TCE. In the time domain, the

fractional integral of acceleration (O < n < 1) c m be computed using:

1 ' D-" f ( r ) = - fit -x)~- ' f (+)& where r(n) is the gamma function (which in this case, U n ) ,

T(n) merely yields a constant). Shce n is Iess than 1, m = n-1 is less than zero, so that

(I -x)"' represent a h i l y of curves rhat c m be approximated by decaying exponentials

having differing time constants depending on the value of .r. Correct choice of a scaiing

factor to the fractional integral and appropriate time constants for the EPSPs results in

having the fractional integral become rt good approximation tu the convolution integral

shown above.

In section 3.3, we used a rate limiter in order to simuiate the response of

vestibular neurons to sinusoidal stimuli. The hnction of the rate limiter is similar to that

of Time Constant Enhancement. For example, the Timc Constant Enhancement is also

responsible for raising the bias. The firuig rate takes longer to return to baseiine and

therefore any stimulus that begins whiIe the firing rate is decreasing, will cause the

response to appear to be modulated around an increase discharge. As mentioned earlier,

this is advantageous for the system since it increases its dynamic range. However, we

have just established an additional advancage to tfiis mechanism: that the same process

can provide the system ivith an estimate of the integrai of the stimuIus. This is essenaal

270

for the vestibular and oculomotor systems whose many reflexes depend on the ability to

integrate. Note that we are not suggesting that cells in the vestibular nucleus have rate

liming behaviour but that this ferinire of their behaviour may be used in conjunction with

other circuits, including integrators. Recall that the otolith afferents supply the vestibular

nucleus with information about the accelerstion of the translation. As will be shown

below, the output of a rate limiter as an approximation to the velocity of the signal proved

suficient to simulate the tVOR in response to steps of position.

4.5 Spatio-temporal Convergence

Time Constant Enhancement is not the only mechanism that c m account for our

data. Spatio-temporal conver;ence (STC) (Angelaki, 1993a; hgeIaki 1993b; Angelaki,

et al. 1993; Angelaki, 1991) has been proposed as a possible mechanism chat can be used

to process otolith sigals. The result of Figure 3.15A clearly shows convergence of

afferent signak, but c m this convergence rilso lsad to the nonlinearity s h o m here?

Although we were not able to design a mode1 thnt utilizes STC to simulate our data, using

STC in a neural nehvork proved trivial once the input data was appropriateiy modified

(see below). The nenvork architecture is shown in Figure 4.2.4. It is cornposed of 2 feed

fonvard input layers, each receiving 10 inputs, 7 fully comected cells in the intermediate

layer, and one output layer with no feedback. The training data for the neural net was

composed of a time series representing acceleration transients as shown in Figure 4.B.

The network was then vaIidated using sinusoidal data. M e r constnicting the üainhg

data fkom accelention profiles from the sled, we passed those profiIes through the regular

and irregular afferent traosfer functions as reported by AngeIak and Dickman (2000) in

171

order to set a better idea of what the afferents firing behaviour would be, given such a

stimulus. This filtering had minimal effect but did produce a slight phase difference and

gain difference betsveen the inputs. The ma!cimum delay in the input signai was set to 15

ms. In addition, the training data was not symmerrically centered around zero.

Specifically, we simulated saturarion by not allowing the input to go below a certain

value. In general, the excitatory portion of the stimulus was held at a maximum

of 1.4 times the amplitude in the negative direction. This was done in order to gain a

realistic input signal into the network, where a newon, (primary afferents in this case) can

increase its firing rate rnuch more than it can decrease it.

The neural network was rmdomly initialized and then trained using a Levenberg-

Marquardt backpropa;ation algorithm. Backpropagation has been shown not to be a

bioIogical plausible learning mechanism (Stork, 1989), and we are not suggesting that

training of the neüral net sheds any li&t on how the vestibular nucleus acquires its

behaviour, However, after tnining has been completed, the weights between neurons in

the network and the robustness (or lack thereofj of the network's response do suggest a

possible mechanism for the vestibular nucleus' behaviour. We initially had more than 30

neurons in our intermediate Iayer but were abie to reduce the number of neurons to 7

input

S im u la t i o n

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Tirn e ( s e c )

Figure 4.2. A) Xeural network used to simulate the data i n this thesis. The network hûs 2 Iinear

input layers that receive oppositely polarized input, Each input byer receives 10 inpuis with

differing on-directions as described in the teut. The 1 input layers then feed to e ~ c h of the 7 h l l y

connected intermediate neurons with nonlinear sigrnoid activation functions. Finally, al1 7

neurons feed the output neuron which is rlso Iinear. B) Output (top trace) of the network in

response to the input shown in the bottorn trace (Iabeled 'input'). Note that the input is

symmetric, reacfiing rn amplitude of20 in the escitatory direction but on& -10 in the inhibitory

direction. This sîmulated the inhibitorq- cutoffpresent in a saturating qstern.

without increasing the mean squared error between the output and the training data The

neurons in the intermediate layer al1 had identical dynmics composed of a nonlinear

sigrnoid activation Function and a iow pass filter wih a corner Eiequency O C 15 Hz. The

training data dong tvith the perfùmance of the network is depicted in Figure 5.23, As

c m be seen, the nenvork performs quite well in producing an asymrnetry in one direction

but not in the other in response to the accelerometer signa1 (IabeIed 'input' in Figure

42B). The accelerornecer's output was first sorted into the IF and EF directions. Then,

the IF traces were concatenated with other IF direction traces, and the EF traces where

concatenated only with EF traces given a time series that does not represent a series of

square waves as in Fisure 3.14, but is a sequence of steps going one way followed by a

sequence of steps going back. ('tnpur' in Fisure 4.1B becornes 'Training Data'). This

signa1 was chen presented 10 rhe nenvork. However: furthsr rransfotmations were needed

in order to get the nenvork to converse. The neuraI net had a totaI of 20 input vectors

(ai.. .aZO), with each veccor representing an activation direction separated by a polar angle

of 18" fiorn its adjacent vectors, In addition, each vector was muitipIied by the cosine of

the angIe benveen it and the vector chosen co have motion along ics activation direction

(ur in this case) (AngeIiiki and Dichan, 2000). This represented a cosine tuned

approximation OF the afferents (even though Femandez and Goldber;, (1976) found b a t

prirnary afferents were not exactly cosine m e d but exhïbited zero crossïngs separated by

about 220 degrees). Assurning chat the first input vector (a!) was produced by an afferent

Uinervating a cet1 wich its polarization vector in the direction of motion, then vector ai 1

was assurned to corne fiom the orher side of the strioh and hence have opposite

poIarïzation to ai (Ogawa et al, 3000) , The s m e opposition pairing was appiied to a11

the input vectors. The variation in amplitude in the input signal does not affect the

training of the network directly, but does however affect the phase shift given to each

input (see below)). The input data was then alternatively passed through the reglar and

irregular transfer b c t i o n (Table 1. in Angelaki and Dickrnan, 2000). This resulted in

each adjacent vector inheriting a phase (or equivalently, time) shift relative to its

neighbor. Thus, these 20 input vectors act like the responses of 20 different oriented

oto lith afferents. Findly, the input vectors were allowed to increase in magnitude

without limit but were saturated at their minimum values (see input vectors in Figure

4.2B). The first vector in the input to the nehvork is shown in Figure 4.2B as 'input7.

Only aAer this procedure was compieted did the network finally converge ont0 the

training data.

Many training sessions were conducted with the input being a subset of the set

described above. Hoivever, the nehvork could not converge until the number of inputs

was suf'fïcientIy high, with the mean squared error bstween the simulation and the actual

data consistently becoming smaller as the number of inputs increased, However, even

tvith n large nurnber of inputs, ive were unable to set the network to converge without

subjectins the input vector to the transformation rnentioned above. Although this

nenvork could also simuiate the asymmetry seen in sine waves, it coutd only do so

within a limited amplitude window. increasing the amplitude of sine waves beyond a

threshold value led to unpredictabIe behaviour. in generai, the solution of the network

couid r,ot be generalized to other form of inputs \vîthout extensive retnining In addition,

the network could not be cross-validated. On the other hand, Time Constant

Enhancement could aiso simulate the non1inea.r behaviour of sinusoids (asymmetry and

increased bias for an increased stimulus) and was a more nama1 and even simpk way to

accomplish this complicared behaviour. The I q e number of afferent inputs used here is

important for convergence suggestins that afferent s igais play a dominant roie in the

s ipa l processing of the nehvork. Perhaps given a different nenvork, the simulations

could be made more robust. Neverttieless, the success of this neural nehivork c m o t be

ignored although the ease in which Time Constant Enhancement simulated Our dara Ieads

us to conclude that it may be a more natural way to process otolith signais.

4.6 The tVOR in Response to Sinusoids

The tVOR in response to sinusoids was sirnuhted using the simpie mode1

depicted in Figure 3 2 6 A Woughout this rhesis. the convenience (section 3.L3.3) and

ineffecciveness (section 3.2.3.4) of using sinusoids h a been repeatediy stressed. Hem,

once again, this simple linear model is a testament to the ease with which sinusoids couid

be rnodeled but also serves as an example of how the idiosyncrasies of sinusoids may

conceat the worltings of a nodinear system. A second nonIinear mode[ was needed in

order to model the steps of position. However, we shall use the Iinear mode[ in order to

hypothesize about the dynamics of the input sigal. Recall chat otoIith afferents have

varying dynamics whose tùnctional roles rernain a mystery.

The mode1s presented are simpie in that they take advantage of known pathways

in the brainstem- The linex mode1 utiIizes an integxcor in order to achieve its goals. For

horizontal conjugate eye movements, the nuctear preposinis hypoglossi (NPH) is an

important site for neurai inte_mtion. There is a Iarge projection of inputs fiom the Iateral

vestibuhr nucleus (LVN) ont0 the WH in the squirrel monkey ( B e b p et ai. 1988) and

176

a correspondhg large projection of utricular afferents onto the LVN (McCrea et al.

1987). No second integration of the otolith signal is required. The 'position' signal (the

signal necessary to augment the velocity signal to compensate for the plant) is obtained

directly from the primary afferents with a modification in gain. Utricular afferents

synapsing directly onto oculomotor nuclei have been reported by Uchino et al. (1996).

As a sinusoidal acceleration signal is in phase with position (with negative amplitude),

this makes the signal that the otolith primary afferents cany adequace to code position.

However, here lies the problsm in that this is untrue for nonsinusoidal data. In addition,

this relies on the verity of the hypothesis that the eye plant requires a signai in phase with

velocity and position for al1 reflexes and fiequencies. The nonlinear model does not

utilize to this convenience. Instead the rate limiter functions to provide a nonsaturathg

input to the plant. There is, of course, a disadvantage to this architecture; specificaily, the

reflex is rendered imperfect by the limiting behaviour of its nonlinear elements.

in deriving the dynamics of the afferent input to the linear model, it became clew

rhat the behaviour of regular afferents is more suited to drive the system. However, the

derived input may be an indication of the type of afferent behaviour needed in order to

realize the Iinear mode1 presenced here. It is consistent with extrapolated regular Se ren t

(bordering on dimorphic) bshaviour; ri slow rising high pass tilter with a flat phase

response increasing in las 3s the fiequency increases. The transfer function used to fit

the input signai bat will serve as the input to the model is defined as H n ~ H , ~ I H ~ I f - t where

(Goldberg et al. 1990):

and T &s, tAm=0.l0s, Kb~0.15, tA=15s, KA=0.13, tvi=200s and ~ d . 2 5 , K*.15.

Figure 1.7 is reproduced here as Figure 4.3 with the bode plot ofthe above transfer

Fmquency (Hz)

Fi i re 43. iktived prima y offennt bebaviour (cyan) as comprred to wuid ôehatkur rtom two studies. AU labels art as in Figure 1.7 and are reproduced àcrr for convtaicnrc. A&D:

Aagcbki rad Dickmaa, (2000). RtguIm art ia b k k , Imgplrrs in Reâ. Fnaiida r d Goldbtrg

oaly tcsted thcir affercnts to frqucacics up to 2 Hz The exteasion of thc rrspoa~c of tbcir alrerenb

is shown in btuc.

tùnctions. As çan be seen, the derived transfer fùnction (cyan) does not agree with the

plot fiom AngeIaki and Dickrnan (2000) nor does it agree with the extnipoiated

Femandez and Goidberg af5erent descriptions. However, it does seem to possess

dynamics that are in between those of the reguiars and irregulars and thetefore, such

behaviour couId theoreticaily mise fiom a convergence of reguiar and irreguiar primary

The high fiequency phase Jag exhiiited by the response of the mode1 is partly due

to the 10 ms delay that was used while fitting the afferent transfer hction. This shoa

latency is consistent with Angelaici's result (Angelaki, 1998). One weakness of the

model presented here is that upon cessation of movement, the position signal disappears

leading to an inability to hold eccentric ;aze in the dark. However, the tVOR reflex is

only robust in the light and when the eyes are converged on a near target. Therefore, this

might be the way the system functions. In addition, the model does not attempt to

include translationltilt differentiation. It onIy deals with the generation of horizontai eye

movements in response to sinusoirial oscillations.

For angular rotations, an inregrator lesion l e d s to an inability to keep gaze steady

(no position signal) ( Cannon and Robinson, 1987). Perhaps the most suiking

consequence of our model is that upon inteptor lesions, a partial loss of eye movements

in response to translational motion will occur although some eye movement may still

occur due to the monosynaptic prirnary afferent connection to the plant. This is also tme

if a lesion affects the Tirne Constant Enhancement abiIity of the rate limiter of the

nonlinear model shown in Figure 3.2OA. h o t h e r consequence of this model is that

irregular primary afferents have little or no effect on the behaviour of the tVOR. Since

the behaviour of primary afferent neurons for frequencies geater than 2 Hz is not known,

this prediction is based solely on theory. Galvanic current studies (current injected into

the inner ear which reversibly silences the irregular afferents) of the aVOR have shown

that irregular afferents do not contribute co rhe aVOR (Minor and Goldberg, 199 1). In

addition, regular and irreylar inputs remain segegated at the Ievel of the vestibular

nuclei (Goldberg et al. 1957) aithough this segegation is incomplete, However, this

could result in parallet pathways for the prirnary afferents that have distinct functions.

We have shown here that it is possible for the h c t i o n of the reglar afferent to provide

the inte-grator with input in order to obtain the velocity command. The function of the

irregular afferent remains a question. The VOR is not the only reflex that these afferents

drive. Therefore, the ineguiar af%erents could be used for the vestibulocollic reflex

(Goldberg et al. 1987) or even adjust the gain of the tVOR for vergence sensitivity.

4.7 The tVOR in response to position transients

Figure 33OA depicts the model used to sirnulate the tVOR in response to steps in

head position. The difference benveen this figure and the linear model of Figure 2.26A is

the substitution of the integrator in Figure 3.26A with a rate limiter and the modification

of the plant (see Equation 2.1). Note that the rols of these wo elements are equivalent.

However. as will be shown below. the rate limiter. ~vith irs limirauon on the derivative of

the fdling phase o f a signal, hnctions more like a controller with varying time constant,

Figure 4.4A depicts a typical actuator that is generalIy used in the description of DC

Figure 4.4 A) example of a nonlinear actuator, whose equivelant linear transfer function is shown

in B. The box labled 'Actuator' is sirnply 1 sytern thot crin npprorimate many mechanical

systems and is defined by K s(ins t b )

motors or hydraulic actuators (or with slight modifications, even a hi& precision

telescope and many other devices) placed in a feedbrick loop and cascaded with the plant.

An actuator is a device rhat moves (or provides the power to move) an object (Dorfand

Bishop, 1998). Here, the object that being moved is the eye. Note chat the overall

transfer function ofthis system is simply a second order system with bandwidth on and

darnping c(Figure 4.4B). A rate limiter simply approximates this second order system

but with a rime constant that is dependent or! the amplirude of the input (the tirne constant

1 of the accuator is - ). Figure 4.5 ciepicts die response of nie limiter with a slew rate of (3 ,,

=13 g/s (which is the vaIue used in the simulations of Figure 3.30) and the saturated

second order system (Figure 4-44) in response to the acceieration data used in the

simulation of Figure 3.30. As can be seen, the output of the rate limiter, is a good

approximation to that of the actuator. Given that section 3.2 proposes that the rate

limiter is actually implemented ceniralIy by die use of Time Constant Enhancement, then

ttiese simulations suggest that the Time Constan& Enhancement. besides providing the

system (or contributing) with an estimate of the velocicy of the translation, also functions

as a nonlinear controIIer for the nodinear properties of the eye plant. it is generaily

riccepted in the literarure rhat circuits should suive to cornpensate for the dominant time

constant of the plant, which is taken CO be 750ms (Robinson, 197 1). However, since the

plant we used ha a variable tirne constant that depends on fiequency, and Sylvestre and

Cullen (1999) showed that the tirne constant is also a f ic t ion of eye veiociy, chen it

would be advantageous for the system to have varying constants in its circuits. This is

accornplished by the rate limirer since its restriction on the derivative of the input sipal

is similar to a vxy& rime constant in a second order systern. These results suggest that

181

the tVOR is much less robust than once thought. In addition, the successfbl use of the

rate iimiter in modehg the tVOR sheds new light on processitg techniques for the

tVOR.

O 1 2 3 4

Time (sec)

Figure 45. Output of tbe rate iimitcr rvith a sien rate off 13%~ (ml) and a n o i i i i a r wtaator

(black) sbom in Figrire R4A. Noce tbat the output o f tbe rate limiter n i a d d 8 g d estimate of the

output of a control system. The input to tbe rate limiter and the coatrolkr is s b m in blue.

5.0 Conclusion

The nonlinearity shown in this thesis to exist in the vestibular nucleus sheds new

light on the processing of input signais in the vestibular nucleus. The existence of

noniinearity removes the limitations set by h e a r models of vestibular functiun but also

precludes the use of linear techniques in data analysis. For example, an otolith signal,

caIculated during translation can no longer be subtracted from the signal of a neuron

recorded during eccentric rotation. in jenerai, it was shown that sinusoids are a poor

choice of stimuli as shown by the tVOR elicited during steps of position. The

conclusions of the work presented in this thesis are:

1) Cells in the vestibiilar nucleus are nonlinear.

2) The nonlinearity could be ussd to approximate integration without the limitation

of linex techniques.

3) Monosynaptic connections from the uuicle to the abducens and the integration of

a combination of regular and irregular neurons rnay drive the tVOR in response to

sinusoids.

4) A rate Limiter is needed to drive the rVOR in the presence of a nonlinear plant and

in response to seps of position. in addition, the rate limiter is actually an

approximation to a nonIinear controller.

There are advanrages to this nonlinearity. Plant compensation achieved h o u &

neuraI processing is simple to achieve by taking advantage of the negative output of

the rate limiter. Surprisingly, the use of a rate limiter showed that in one direction of

translation, its output is equivdent to taking an approximate integral of the input

signal. The integation may be achieved by spatio-temporal convergence or short-

term Time Constant Enhancement (or both).

There have been many attempts to mode1 otolith reflexes, such as the translational

VOR, by utilizing a sepante and detached neural integation, an operation necessary

to obtain the velocity of motion (Telford et al. 1997; Green and Galiana, 1999;

Musallam and Tomlinson, 1000; AngeIaki et al. 1998). in section 3.2 we showed that

integation of otolith signais is inherently (and perhaps passively) produced by otolith

neurons, and does not necessarily require addition circuitry. The necessary dynamics

would simply come about h m the increased tirne constant ofdecay. This feature

takes on greater importance when one considers that the eye plant changes its

viscosity and stiffhess in response CO an increase in eye velocity. Here, we have gone

further and assurned that the time constant of the plant is also a function of frequency.

The use of nonlinearity in the processing of otolith signais to produce the tVOR easily

compensated for the nonlinearity imposed on the plant. Nonhearity does indeed add

complexity, but it also simplifies the computation for a wide variety of tasks.

Al. Equations Used For Fitting

Al1 fits to the various fonns of stimuIi (acceleration, position), firing rates and eye

position were fit into L of 10 possible equations chosen by the user based on the

correlation coefficient of the fits;

Note tiat Equation 8 refers to the hctional derivative 6ts discussed in the Methods

section. In addition, as was depicted in Fi,gu-e 3-15, sreps of position were gïven dong

many different orientations. Therefore, both a naso-occipital and an interaural

accelention exists for orientations that are intemediate behveen the two. For these trials,

fits were performed with a combination of the above equations. For example, fitting the

firing rate using Equation 1 for a translation directed 15 degrees clockwise to the naso-

occipital direction resulted in the equation y = b, + bzV, + b3V,,, . Note also that some of

the equations were simply tried for cornpleteness and were never utilized (e.g., Equation

3,6,7). This was due to the unjustifiable increase in the cost of a higher order equation in

relation to an incresed lit. In addition, not a single neuron e.xhibited any usehl

correlation with Equation 3, and hence the jerk vector was nevsr utilized. Al1 fits were

carried out using the Levenberg-Marquard nonlinex fitting routine with the inverse of the

standard deviation of the firing rate as weijhts. The computation of the fiactional

1 ' derivative was already given in the Methods and iis D-" f ( r ) = - I(t -+)"-If (x)& m) , where T(n) is the gamma tùnction (yielding a constanc in this case) where O < n < 1 for

integration (note the negative on the exponenc of D). Equivalently, in the frequency

domain, the fractional derivative cm be caiculated using: F'(F(A *(iwjn) where Fmd

3' are the Fourier and inverse Fourier transforms respectively. The algorithm below (

Table Al) describes the calcuIation of the partial denvatives in the frequency domain:

Inputs: Data, hctional exponent

Step 1. Calculate the Fourier trmsform of the data-

Step 2- Define a comptex fkquency vector

Step 3. Raise the cornplex Frequency vector to the tiactional exponent I

Step 4. Multiply the result from Step 3 wirh the data.

Step5. Obtain the Inverse Fourier Transform (ET) of the result

Step 6. Real d u e of the [FT is the fractional derivative.

Table Al . Algorithm for computing fractional derivrtives.

A2. Spike Train Retrieval

The enhancernent shown in Figure 3.25 was obtained by convolving the spike

1 - train representation of the acceleration with a variable EPSP defined by r "" where ~ ( i )

is the time constant of the EPSP which varied depending on the amplitude of the input

signa1 (il. Therefore, the convolution integaI is used to create a piecewise time series

thar is the approximation to the nonlinear response. We are assuming that the rnean firing

rate and die incerspike interval are conuibuting to sliciting activity in the pos-synapcic

cell. The acceleration trace was tint convened into a firing rate based on recorded

afferent firing rates (Angelaki and Dickrnan, 2000). Note that the waveform of the

acceleration shown in Figure Al is quite different ti-om the sinusoidal stimuli used in the

AngeIaki and Dickman study. However, primary afferents are known to encode

acceleration and d I that was used from the aforementioned study was the sensitivity of

the afferents (in spikes/sec/g) to an acceleration input. The output of the accelerometer

(fïrst row of Figure Al), was then scaLed according to this sensitivity in order to obtained

the hypotheticai king rate (second row in Figure AL.). Then, the a m p h d e of the

discharge at hvo adjacent times (1 ms) was used as an estimate of the interspike interval

and a spike piaced in the center between the adjacent points. R e p e a ~ g this step for al1

points led to the spike train shown in Figure Al.

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