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Tracing tremor: Neural correlates of essential tremor and its
treatment
Buijink, A.W.G.
Publication date2016Document VersionFinal published version
Link to publication
Citation for published version (APA):Buijink, A. W. G. (2016).
Tracing tremor: Neural correlates of essential tremor and
itstreatment.
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Chapter 8 Propranolol in essential tremor affects
motor control in a pattern fitting increased Renshaw
inhibition
Submitted as
Propranolol in essential tremor affects motor control in a
pattern fitting increased Renshaw inhibition.
AWG Buijink, W Mugge, S Sharifi, NM Maurits, AC Schouten, LJ
Bour, AF van Rootselaar.
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150 - Chapter 8
Abstract
Background
The tremorolytic site of action of propranolol in essential
tremor (ET) is unknown. It could be located peripherally, in the
muscle compartments, or centrally. Understanding its mechanism of
action will aid in the development of more effective
treatments.
Methods
To assess the effect of propranolol on motor control, 16
propranolol sensitive ET patients were tested on and off
propranolol. Using a wrist manipulator, ramp-and-hold stretches
were applied. M1 and M2 reflex responses were quantified.
Continuous wrist perturbations were applied during a passive and
two resist tasks (with/without external damping). Closed-loop
system identification determined the frequency response, which was
fitted with a neuromuscular model, including delayed position and
velocity feedback to represent afferent feedback from muscle
spindles.
Results
Repeated measures ANOVA revealed significantly decreased
afferent feedback and increased intrinsic muscle viscoelasticity
during the resist task in the on-medication condition. There was a
significant effect of task for afferent feedback and intrinsic
muscle viscoelasticity, reflecting varying levels of
co-contraction.
Conclusions
Our results suggest increased phasic co-contraction and
decreased reflexive activity in ET patients on propranolol.
Significance
Multiple sites of action combined can cause the tremorolytic
effect of propranolol, yet only increased Renshaw cell sensitivity
explains all findings simultaneously.
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Propranolol and essential tremor - 151
Introduction Essential tremor (ET) is one of the most common
neurological disorders, and is characterized by a progressive
postural and kinetic tremor.4 Propranolol is a non-selective
beta-adrenergic receptor antagonist and widely used as first choice
of treatment with a level A recommendation of efficacy.9 Several
randomized clinical trials show a mean decrease in tremor amplitude
of about 50% (see Deuschl et al., 20119 for a review of clinical
trials in essential tremor). Nonetheless, the efficacy of
propranolol was discovered by coincidence and the drug was
originally developed for other diseases. How the tremorolytic
action of propranolol is mediated is still unknown. It is of
crucial importance to understand the mechanism of action of tremor
medications to provide insight into the pathophysiology of ET and
possibly to aid in the development of more effective treatment.
Other beta-adrenergic blockers are less effective in ET than
propranolol.9,11 Propranolol, compared to other beta-adrenergic
blockers, has a greater lipid solubility and hence an increased
ability to cross the blood-tissue and blood-brain barrier.11,242
First, in the past, it has been suggested that the site of action
of propranolol in ET is located in the deep peripheral muscle
compartments, specifically at adrenergic receptors on the muscle
spindles.11 These compartments have a blood-tissue barrier similar
to the blood-brain barrier.242 How changes within the muscle
spindles might reduce essential tremor is uncharted. Elble and
colleagues suggested there is no evidence for unstable, or
oscillating, mechanical reflex activity in ET,243 but propranolol
itself might alter the reflex system in such a way that it
alleviates tremor. Two other plausible sites of action are located
within the central nervous system, considering the widespread
presence of adrenergic receptors.12,244 It has been postulated that
recurrent inhibition by Renshaw cells (RCs) within the spinal cord
is increased by propranolol, effectively filtering 10 Hz muscle
oscillations.13 Whether this hypothesis holds for other tremor
disorders is unexplored. Another possible mechanism of action is
through altering the properties of regions within the
cerebello-thalamo-cortical network, within which it is hypothesized
that pathological oscillations in ET are present.29
If there exists a site of action within the reflexive system,
either peripherally within muscle compartments, or centrally in the
spinal cord by affecting RCs sensitivity, this would in both cases
lead to altered properties of the stretch reflex in ET patients
taking propranolol.
In the current study, stretch reflexes are therefore tested in
ET patients who were on and off propranolol medication.
Ramp-and-hold stretches and continuous perturbations to the wrist
were applied to induce stretch reflexes in a systematic way. With a
combination
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152 - Chapter 8
of system identification and neuromuscular modeling it is
possible to separate intrinsic muscular changes from alterations in
reflexive contributions.51,52,245,246 In this way, effects of
propranolol on specific parts of the motor system may be
dissociated.
Participants & Methods
Participants
Sixteen propranolol sensitive ET patients with a positive family
history were tested on and off propranolol medication. All
participants were right-handed according to the Annett handedness
questionnaire141 and patients were included when they fulfilled the
criteria defined by the Tremor Investigation Group,5 they reported
a positive subjective response to propranolol, they had a positive
family history of at least one affected relative in the immediate
family and an onset before the age of 65, a disease duration longer
than 5 years and were aged 18 years or over. Exclusion criteria
were neurological disorders besides ET and cognitive dysfunction
(i.e., Mini-Mental State Examination
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Propranolol and essential tremor - 153
A ground electrode was placed on the wrist joint of the
contralateral hand. EMG signals were digitally filtered with a
high-pass 3rd order Butterworth filter (20 Hz cut-off) to remove
motion artefacts, subsequently with a notch filter (45-55 Hz 3rd
order Butterworth) to remove line artifacts, rectified, and then
digitally low pass filtered (80 Hz 3rd order Butterworth filter,
causal filter for determining M1 onsets, non-causal filter for
determining M1 and M2 responses247).
Figure 1. Schematic representation of the experimental setup.
The subject is
seated in upright position with the forearm fixated allowing
unimpeded movement of the wrist. The actuated handle induces wrist
rotations to the subject since the axis of rotation of the handle
is aligned with the wrist flexion/extension axis. Electromyography
electrodes are placed on the flexor and extensor muscles (Adopted
from Mugge et al., 2012248).
Ramp-and-hold stretches
Prior to the stretches, subjects were requested to exert maximum
voluntary contraction (MVC); the EMG during the ramp-and-hold
stretches subsequently was scaled by the EMG at MVC. With the wrist
in its neutral position the subject was instructed to maintain a
constant contraction at 5% of the MVC force level, in the direction
opposite from the stretch perturbation. Two series of nine
ramp-and-hold stretch perturbations were applied, one in the
flexion, stretching the extensor muscles, and one in the extension
direction, stretching the flexor muscles, both with random time
intervals between the stretches (minimal interval of 2 seconds,
ramp velocity 4.0 rad/s, ramp amplitude 0.14 rad).248,249 Visual
feedback of the required force (line) as well as the exerted force,
filtered
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154 - Chapter 8
at 1 Hz (moving bar) were displayed on a monitor. EMG signals
obtained from the individual stretches from the flexor and extensor
muscles were averaged. The short latency M1 response was determined
as the area-under-the (EMG) curve (AUC) between 20 and 55 ms and
the long latency M2 response was determined as the AUC between 55
and 100 ms.250 Onsets of M1 and M2 were identified as the time
where the EMG passed the 3-standard deviations line of the average
background EMG (determined over the 200
ms period prior to the stretch). Paired t-tests were used to
assess differences in stretches in the on and off medication
conditions.
Continuous force perturbations
Force perturbations were used to provoke proprioceptive reflexes
and enabled the separation of intrinsic and reflexive contributions
to human arm dynamics through closed-loop system identification and
subsequent neuromuscular modeling.51 During this experiment,
subjects had to hold the handle during a passive (“do not
intervene”) and resist task (“maintain position”), while continuous
pseudo-random force perturbations were applied for 20 seconds. All
multisine perturbations were designed in the frequency domain by
summing sines of 0.5 up to 20 Hz and optimizing crest factors.251
To facilitate the resist task, the position of the handle was shown
on a display as a reference to prevent drift. To minimize possible
non-linear effects, the standard deviation of the handle position
was equalized and minimized for all conditions and subjects by
scaling the torque perturbation magnitudes (appropriate scaling was
determined during training252).The following experimental
conditions were applied:
- Active, ‘stiff’, condition without external damping. During
the active condition, the task instruction was to prevent
displacement of the handle by resisting the force.
- Active, ‘stiff’, condition with external damping. External
damping is used to provoke reflex activity.51,52 Damping was set to
0.4 Nms/rad.
- Passive condition. Here the task instruction was different
from the other two: the subject was asked to relax his/her arm
muscles and not to react to the
perturbation.
Each condition was repeated two times, resulting in six trials
of 20 seconds each. In between the trials the subject could rest as
long as he/she wanted to prevent fatigue. In the time domain, EMG
signals were normalized to MVC and averaged over the total
measurement time to assess the average muscle activity, a measure
of the level of muscle contraction (mean normalized EMG).
Closed-loop system identification quantified the
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Propranolol and essential tremor - 155
admittance, the frequency domain representation of the
displacement or rotation magnitude due to a force or torque; see
Figure 2 for an example of a typical subject (next page). The
admittance captures the dynamic motor control behavior as a whole
and is commonly represented by a magnitude (the amount of
displacement) and a phase (the relative timing), hence
incorporating the effects of time delays.51
As a second step a basic neuromuscular model was fitted to the
experimental data to obtain physiologically interpretable
parameters (see Appendix A for the fit criterion and neuromuscular
model). The neuromuscular model incorporated a mass-spring-damper,
supplemented with time-delayed velocity and position feedback,
representing reflexive contributions to motor control.52,245,253
Output parameters of the model are thus hand
inertia i (kg m2), muscle viscosity b (Nms/rad), muscle
elasticity k (Nm/rad), and feedback
gains for muscle stretch kp (Nm/rad) and muscle stretch velocity
kv (Nms/rad) with a
reflexive time delay td (s).52,254 Hand inertia represents the
mass of the entire system, including the hands and fingers. Muscle
viscosity represents the non-delayed, instantaneous damping of the
muscles i.e. the resistance of the muscle against stretch velocity.
Muscle elasticity represents the stiffness of the muscle by
co-contraction, which is a non-linear property, i.e. the more
active the muscle, the more resistance against stretch. Reflexive
properties are subdivided into a position feedback gain and a
velocity feedback gain, representing the responses of several
afferents providing information about muscle stretch and muscle
stretch velocity.51,245 Units and fit boundaries are given in
Appendix B. These parameters were compared between task conditions
and medication conditions, using a repeated measures ANOVA design,
with a significance threshold of 0.05. Due to the explorative
nature of this study, we chose not to perform correction for
multiple comparisons.255
Results
Patient characteristics
Table 1 provides a full overview of demographic and clinical
characteristics. Due to hardware issues, two subjects did not
perform the flexion ramp-and-hold stretches (stretching the
extensor muscles) and four subjects did not perform the continuous
perturbation tasks, leaving 16 ET patients for the extension
ramp-and-hold stretches, 14 ET patients for the flexion
ramp-and-hold stretches, and 12 ET patients for the continuous
perturbations task.
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156 - Chapter 8
Table 1. Demographic and clinical characteristics. Extension
ramp-
and-hold stretches (n=16)
Flexion ramp-and-hold stretches (n=14)
Continuous perturbation tasks (n=12)
Male/female 8/8 8/6 8/4
Age in years 55.1 (16.1) 53.5 (16.0) 54.5 (18.4)
Disease duration in years
33.7 (17.7) 30.5 (17.7) 34.1 (18.4)
TRS A+B off propranolol
28.3 (11.0) 26.8 (10.8) 25.8 (11.6)
Propranolol effect TRS A+B
- 4.3 (3.0) - 4.1 (3.3) - 3.8 (2.7)
Propranolol dosage in mg
86.8 (76.2) 91.4 (84.5) 95.0 (84.7)
TRS: Tremor Rating Scale. Propranolol effect: improvement
determined by difference between TRS A+B on and off propranolol
medication. Results are presented in means with standard deviations
between parentheses. Characteristics for the ramp-and-hold
stretches are derived from all 16 ET patients performing the
extension ramp-and-hold stretches.
Figure 2. Task and medication effect on admittance of a typical
subject. For each of the three conditions during on and off
medication measurements, the magnitude (top panel) and phase (lower
panel) of the admittance are shown for the passive (solid), active
(dashed) and damped (dotted) conditions. Each line represents the
average of two trials per condition. It describes the rotation
magnitude due to torque, as a function of frequency. At frequencies
above the eigenfrequency, the second order decline of inertia is
visible, with expected overlap of all conditions. The on-medication
condition is depicted in black, the off-medication condition in
grey. Low gain values represent higher stiffness i.e. at low
frequencies the wrist is stiffer in the active condition than in
the passive condition.
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Propranolol and essential tremor - 157
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158 - Chapter 8
Ramp-and-hold stretches
There was no significant effect of medication condition for the
M1 and M2 reflex
responses and M1 reflex onsets (paired sampled t-test, Table 2).
There was no significant difference in maximum voluntary flexion
contraction (paired sampled t-test, Table 2).
Table 2. Results ramp-and-hold stretches
Without propranolol
With propranolol
p-value*
M1 response extension [-] 3.83 (1.61) 3,42 (2.04) 0.40
M2 response extension [-] 3.91 (1.32) 4.01 (3.13) 0.85
M1 onset extension [ms] 16.34 (19.33) 16.64 (21.03) 0.97
M1 response flexion [-] 2.66 (1.15) 2.27 (0.88) 0.23
M2 response flexion [-] 2.89 (1.49) 2.32 (1.04) 0.16
M1 onset [ms] flexion 22.50 (22.76) 22.50 (17.21) 0.98
Mean MVC [Nm] 10.06 (4.86) 9.04 (5.02) 0.16
Results are presented in means with standard deviations in
parentheses. MVC: maximum voluntary contraction. *paired
t-test.
Continuous perturbation task
A repeated-measures ANOVA revealed significant task and
medication condition effects in the fitted neuromuscular
parameters. There was a significant effect of medication
condition for muscle elasticity k, afferent position feedback kp
and a trend towards a
decrease of afferent velocity feedback kv in the on-propranolol
condition (p = 0.056, Table 2, Figure 3). Individual post-hoc
t-tests revealed no significant effect for a specific medication
condition. There was a significant effect of task condition
(passive vs. active
vs. active plus damped) for muscle visco-elasticity (b and k),
afferent position feedback kp
and afferent velocity feedback kv. Individual post-hoc t-tests
revealed the following: for b and k, a significant difference
between the passive and active conditions (b on medication
Figure 3. Results for the fitted reflex parameters for the
continuous perturbation task. Bars represent means, error bars
represent standard error of the mean. I: hand inertia, b: muscle
viscosity, k: muscle elasticity, kp: reflexive position feedback
gain, kv: reflexive velocity feedback gain in, td: reflexive time
delay. *: significant task effect, paired t-test, p < 0.05. ~:
significant medication effect, one-way analysis of variance, p <
0.05. For exact p-values see Table 3.
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Propranolol and essential tremor - 159
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160 - Chapter 8
Ta
ble
3.
Resu
lts
cont
inuo
us p
ertu
rbat
ion
task
Wit
hout
pro
pran
olol
W
ith
prop
rano
lol
pass
ive
acti
ve
dam
ped
pass
ive
acti
ve
dam
ped
p-va
lue*
Mea
n EM
G fl
exor
[-]
0.01
06
(0.0
094)
0.
0777
(0
.050
6)
0.11
69
(0.0
831)
0.
0105
(0
.006
9)
0.10
28
(0.0
576)
0.
1282
(0
.092
4)
0.27
(m
edic
atio
n ef
fect
)
< 0.
001
(tas
k ef
fect
)
Mea
n EM
G
exte
nsor
[-]
0.02
68
(0.0
184)
0.
1999
(0
.074
5)
0.23
54
(0.0
832)
0.
0195
(0
.017
3)
0.19
63
(0.0
819)
0.
2088
(0
.098
8)
0.41
(m
edic
atio
n ef
fect
)
< 0.
001
(tas
k ef
fect
)
I [kg
m2 ]
0.
0025
(0
.001
1)
0.00
25
(0.0
009)
0.
0027
(0
.000
8)
0.00
26
(0.0
010)
0.
0025
(0
.000
7)
0.00
26
(0.0
006)
0.
96
(med
icat
ion
effe
ct)
0.60
(tas
k ef
fect
)
b [N
ms/
rad]
0.
0764
(0
.040
6)
0.10
59
(0.0
463)
0.
1127
(0
.041
9)
0.06
66
(0.0
229)
0.
1001
(0
.050
6)
0.10
55
(0.0
521)
0.
26
(med
icat
ion
effe
ct)
< 0.
001
(tas
k ef
fect
)
k [N
m/r
ad]
0.36
57
(0.6
281)
3.
1199
(3
.005
9)
3.97
98
(2.8
275)
0.
2666
(0
.339
5)
4.49
95
(4.1
929)
4.
5415
(2
.397
6)
0.04
6 (m
edic
atio
n ef
fect
)
-
Propranolol and essential tremor - 161
p = 0.009 and off medication p = 0.009, k on medication p =
0.005 and off medication p
= 0.007), and passive and damped conditions (b on medication p =
0.005 and off
medication p = 0.007, k on medication p < 0.001 and off
medication p = 0.001). For k, an additional significant difference
between the active and damped conditions was found
(off medication p = 0.022). For kp , a significant difference
between the passive and
damped conditions (kp on medication p = 0.005 and off medication
p = 0.007, kv on
medication p = 0.015 and off medication p = 0.070), and active
and damped condition (kp on medication p = 0.030, kv on medication
p = 0.032). See Table 2 for an overview of all tested variables.
There were no significant interaction effects between task and
medication condition. Furthermore, a repeated-measures ANOVA
revealed no significant medication effect for mean normalized EMG
during tasks. There was a significant task effect (flexor p <
0.001, extensor p < 0.001, Table 2). Individual post-hoc t-tests
revealed significant task condition effects for the flexor muscle
(passive vs. active p < 0.001 on medication, p < 0.001 off
medication; passive vs. damped p = 0.001 on medication, p = 0.001
off medication; active vs. damped p = 0.008 off medication) and for
the extensor muscle (passive vs. active p < 0.001 on medication,
p < 0.001 off medication; passive vs. damped p < 0.001 on
medication, p < 0.001 off medication; active vs. damped p =
0.025 off medication).
Discussion In the current study, we demonstrate an effect of
propranolol on several physiological model parameters fitted to
motor control in patients with essential tremor. Our results
indicate that in the on-propranolol condition, compared to the
off-propranolol
condition, there is an increase of muscle elasticity during
active muscle contraction (k), a
decrease of afferent position feedback (kp) and a trend towards
a decrease in afferent
velocity feedback (kv). Furthermore, we have observed changes in
muscle elasticity (k),
muscle viscosity (b) and afferent position and velocity feedback
(kp & kv) related to task
condition (passive vs. active vs. active and damped) as
expected.252 We will interpret our findings within the framework of
possible locations of sites of action of propranolol, leading to
these parameter changes, and subsequently to a reduction of tremor
amplitude.
Interpretation of parameter differences
Figure 4 presents a schematic overview of the
neuromusculoskeletal system.245,253,256 Within the
neuromusculoskeletal system, taking into account the different
reflex and feedback loops, RCs play a central role in our
interpretation with regard to the observed parameter changes. RCs
recurrently inhibit motor neurons.13,257 Furthermore, RCs
inhibit
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162 - Chapter 8
group Ia interneurons and antagonistic RCs.258–260 An increase
in RCs sensitivity would result in the following three observed
changes of 1) decreased muscle elasticity in the passive condition
(not significant), 2) increased muscle elasticity due to increased
antagonistic contraction in response to agonist muscle stretch in
the active conditions and 3) reduced reflexes:
1. Through increased RCs activity, inhibition of the motor
neuron increases, which results in less muscle activity in the
passive condition and reduced MVC (did not reach significance).
2. Increased inhibition of the Ia interneuron by RCs
consequently results in decreased inhibition of the antagonistic
motor neuron (causing an increase in
antagonistic contraction leading to increased muscle elasticity
(k) in the active, on-propranolol, conditions).
3. Increased inhibition of the agonistic motor neurons
(observation 1) and reduced reciprocal inhibition on the
antagonistic motor neuron from Ia interneurons (observation 2) both
decrease the effectiveness of reflex responses
(kp & kv), a notion supported by a trend of decreased M1
responses upon
flexion and extension stretches in the on-propranolol
condition.
An alternative explanation is that decreased reflexive position
and velocity feedback could be mediated peripherally, by altering
muscle spindle sensitivity.253 However, considering the additional
increase in muscle elasticity, reflecting improved phasic
co-contraction in the on-propranolol condition, the possibility
that differences are based solely on an effect on muscle spindles
is unlikely. Furthermore, in our study, we did not observe a
medication effect on the M1 and M2 response after ramp-and-hold
perturbations, supporting the idea that muscle spindles do not play
a solitary role in mediating the effect of propranolol.
Alternatively, one could postulate that presynaptic inhibition is
affected by propranolol through changes in supraspinal control.
Presynaptic inhibition influences Ia afferent input onto the motor
neurons.261 However, if propranolol would affect presynaptic
inhibition, one would solely expect a change in reflexive activity.
What we observe however is that a muscle stretch not only leads to
less reflexive activity, but also to increased muscle elasticity.
Finally, we cannot exclude that our results could have been
influenced by the fact that patients exhibited significantly less
tremor in the on-propranolol condition. However, we hypothesize
that an effect of tremor on the modelled
parameters would cause a decrease in muscle elasticity in the
on-propranolol active conditions, as we found in the passive
condition, rather than an increase in muscle ela-
-
Propranolol and essential tremor - 163
Figure 4. Neuromusculoskeletal model. An antagonistic muscle
pair actuated in a one degree of freedom joint while being
controlled by a spinal network with motor neurons (MN), group Ia
interneurons (IA), Renshaw cells (RCs), inhibitory interneurons
(IN), excitatory interneurons (EX) and group Ib interneurons (IB).
Feedback is provided by Ia, Ib and II afferents. The locus
coeruleus exerts descending inhibitory input on RCs. Adapted from
Schuurmans et al., 2011.253 On the right the proposed influence of
propranolol on the system is depicted. (1)RCs increase motor neuron
inhibition (2) Increased inhibition of the Ia interneuron by RCs
decreases inhibition of the antagonistic motor neuron, and (3) as a
result of the prior two the effectiveness of the reflex response is
reduced (reduced activation of the agonistic motorneuron and
increased activation of the antagonistic motorneuron in response to
muscle stretch).
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164 - Chapter 8
-sticity in the active conditions, which is what we observed in
our study. A decrease in tremor severity (in the on-propranolol
condition) would lead to less muscle activity, resulting in
decreased muscle elasticity in the active conditions.
Possible beta-adrenergic receptors mediating Renshaw cell
sensitivity
Propranolol, which is lipophilic, is significantly more
effective at both reducing tremor11 and penetrating the
blood-tissue barrier262 than the hydrophilic atenolol. This
supports the notion that its sites of action supposedly lie also
within the central nervous system or within another site separated
by a blood-tissue barrier.242 In the light of our results and those
of others,11–13 it seems likely that there is a central mechanism
of action of propranolol in essential tremor, possibly by mediating
RCs sensitivity. There is no available data on the presence of
beta-receptors on the RCs themselves. However, it has been known
for a long time that locus coeruleus activity suppresses RCs
discharges.263 The locus coeruleus possesses adrenergic
receptors.13,264,265 It is therefore conceivable that beta-blockade
through propranolol suppresses locus coeruleus activity. As
mentioned previously, Williams and Baker have hypothesized that
propranolol increases recurrent inhibition by RCs in the spinal
cord, effectively filtering 10 Hz muscle oscillations.13 They
suggest that this reduction also occurs at lower frequencies, and
can therefore potentially be the mechanism in which propranolol
alleviates tremor in tremor disorders such as ET and Parkinson’s
disease. They suggest that strengthening RCs feedback could result
in a reduction of tremor amplitudes,13 which fits with the clinical
benefit propranolol gives in several tremor disorders. Our results
support the hypothesis by Williams and Baker for essential tremor,
as well. Considering the widespread presence of β-receptors in the
rest of the brain, it is necessary to consider an alternative, or
additional, mechanism of action, somewhere within the
cerebello-thalamo-cortical loop. Whether anti-tremorogenic effects
are mediated through one specific class of beta-adrenergic
receptors is unclear. All subtypes are widely distributed
throughout the central nervous system, including the cerebellum,
midbrain, inferior olive, thalamo-cortical neurons and superficial
dorsal horn of the spinal cord.264–269 Many studies have reported
pathophysiological changes in the cerebellar cortex in ET, with a
possible decrease in the number and function of Purkinje
cells35,270 and dysfunction of the cerebellar cortex and dentate
nucleus.39,40,140 Noradrenergic projections from the locus
coeruleus to the cerebellar cortex are thought to be an important
modulator of fine motor control.271 Interestingly, local
application of norepinephrine or stimulation of the locus coeruleus
results in an inhibition of the spontaneous activity of Purkinje
cells.271,272 One could speculate that adrenergic blockage
-
Propranolol and essential tremor - 165
of this effect increases spontaneous activity of Purkinje cells,
which could have an additional tremorolytic effect. These effects
are however beyond the scope of this study.
Methodological considerations
Due to the experimental setup, the on-medication condition was
always during the first visit. Better task performance through
learning and familiarization would cause an increase in reflexive
activity, which contrasts with the observed decrease in reflexive
activity in the second off-medication visit in our study.
Furthermore, our study was not set up to make a definitive argument
in favor of, or against, an effect of propranolol within the
cerebello-thalamo-cortical system, therefore an effect of
propranolol on this system cannot be excluded.
Conclusions In conclusion, our results provide novel support for
a central mechanism of action of propranolol in terms of increased
Renshaw inhibition, hence alleviating tremor in ET. Further
understanding of the pharmacotherapeutic mechanism of propranolol
could help future development of more specifically targeted
therapies for ET.
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166 - Chapter 8
Appendices
Appendix A: Model derivation
The neuromuscular model is based on a linearized Hill-type
muscle model.(van der Helm
et al., 2002) The model is briefly discussed in this appendix; a
more detailed description of the model is provided in.(Schouten et
al., 2003)
Note that the model is represented in the frequency domain where
s denotes the Laplace operator. The admittance of the complete
neuromuscular model is described by:
𝐻𝐻𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 =1
𝐻𝐻𝑖𝑖 + 𝐻𝐻𝑣𝑣𝑚𝑚 + 𝐻𝐻𝑎𝑎𝑎𝑎𝑎𝑎𝐻𝐻𝑚𝑚𝑚𝑚
with Hi describing the inertial dynamics, Hact the muscle
activation dynamics, Hve the
muscle visco-elasticity, Hms the muscle spindle activity. The
equation was condensed using the following equations:
Inertial dynamics, where I represents the hand inertia:
𝐻𝐻𝑖𝑖(𝑠𝑠) = 1𝐼𝐼𝑠𝑠2
Muscle activation dynamics:
𝐻𝐻𝑎𝑎𝑎𝑎𝑎𝑎(𝑠𝑠) = 1
0.03𝑠𝑠 + 1
where Hact describes the activation dynamics (the process of
active muscle force build-up following a neural activation signal)
with an activation time constant assumed to be 30 ms.(Schouten et
al., 2003)
Muscle visco-elasticity:
𝐻𝐻𝑣𝑣𝑚𝑚(𝑠𝑠) = 𝑘𝑘 + 𝑏𝑏𝑠𝑠
with k the intrinsic stiffness and b the intrinsic damping of
(contracted) muscles.
Muscle spindle activity:
𝐻𝐻𝑚𝑚𝑚𝑚(𝑠𝑠) = 𝑒𝑒(−𝜏𝜏𝑑𝑑𝑚𝑚) ∗ �𝑘𝑘𝑣𝑣𝑠𝑠 + 𝑘𝑘𝑝𝑝�
The parameters kp and kv represent the gains of respectively the
monosynaptic stretch and
stretch velocity feedback. A single short-latency time delay τd
is used to model the neural
latency of signals travelling to the spinal cord and back to the
muscle.(De Vlugt et al., 2002) Muscle spindles are often reported
to have an excitatory effect on the alpha motor neuron: a positive
gain results in activity that resists muscle stretch, decreasing
the admittance. In the model fit negative values are allowed, and
represent inhibitory effects.
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Propranolol and essential tremor - 167
As a fit criterion the total of the squared logarithmic
difference in admittance was minimized(Pintelon et al., 1994) over
all conditions and frequencies; fitting all parameters
for each subject in one optimization, according to:
𝐸𝐸 = � 𝑚𝑚
𝑛𝑛=1
� 𝑔𝑔
𝑓𝑓=1
𝛾𝛾𝑛𝑛2(𝑓𝑓)1 + 𝑓𝑓𝑓𝑓𝑒𝑒𝑓𝑓(𝑓𝑓)
∗�log𝐻𝐻𝐹𝐹𝐹𝐹𝐹𝐹𝑛𝑛(𝑓𝑓)𝐻𝐻𝑀𝑀𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑛𝑛(𝑓𝑓)
�2
where the error is summed over all frequencies (f) with freq(1)
representing the lowest
frequency, freq(m) the highest, and over all experimental
conditions (n=1,…,m). HFRF represents the frequency response
function from the system identification (admittance) and Hmodel the
frequency response function of the model.
Appendix B: Parameter descriptions, units and fit boundaries
Parameter Description Lower bound
Upper bound
Unit
I Hand inertia 0.0001 0.006 [kg m2]
τd Reflexive time delay 0.015 0.05 [s]
ba Muscle viscosity 0.001 1 [Nms/rad]
ka Muscle stiffness 0 20 [Nm/rad]
kp Reflexive feedback gain -30 30 [Nm/rad]
kv Reflexive velocity feedback gain -20 20 [Nms/rad]