תתתתתת תתתת תתתתת תתתתתת תתתתת ת' תת"ת://www.eng.tau.ac.il/~mira/Se 2009 Virtual Lecture 4
Jan 14, 2016
עבוד אותות במערכת החושיםסמסטר א' תש"ע
http://www.eng.tau.ac.il/~mira/Senses2009
Virtual
Lecture 4
Cochlear model’s geometry
helico trem a
ova lw indow
roundw indow
basila r m em brane
sca latym pan i
sca la vestibu li
x
baseapex
x
The Cochlear Model Equations:I. Linear ApproximationII. OHC are not Active
2
2BM BM
BM BMP m x r x s xt t
x x x
BM OHCP P P
2
2
2
2 2
tAx
P BM
x 0 2 OW
Px
xx
, 0P L t
( ,0) ( ,0) 0bm bmx xx x
0OHCP
Frequency Domain Solution
22
2
2
22
0
,, , 0
2,
,
Re ,
Im ,
,2 ; , 0OW
x
d P xk x P x
dxj
k xAZ x
Z x r x
s xZ x m x
d P xP L
dx
x
Resonance Frequency
CF x s x m x
Resonance Frequency= Characteristic Frequency
Resonance Frequency is obtained at the frequency that yields:
; 0 CFZ x
OHC Anatomy
OHC’s model
OHC model’s equation
AP BASI I
SMAPAPSMAP VCdt
dGVI
dt
CdGI BAS
BASBAS
0
0
APAP BAS
BAS SM APAP
AP BAS AP BAS AP BAS
dCG G G V dCd dt G
dt C C C C C C dt
0
80
70SMV mV
mV
Known Facts & Assumptions
• The outer hair cell motility is proportional to the basolateral membrane voltage drop.
• The membrane electric analog is a low-pass filter with a cutoff frequency less than 1 kHz.
• The capacitance changes with the partition motion.
• The current flow through the basolateral membrane is a function of the partition displacement and velocity.
Assumptions
.SMSM BAS
BAS AP
VV C const
C C
.
APAP BAS
BASOHC
AP BAS BAS
dCG G Gdt const
C C C
AP BAS
AP BAS
C C
G G
1500OHC Hz
0AP
OHC APdCd
Gdt dt
OHC Properties: Linear Approximation
0
0
AP G G BM
AP C C BM
G
C
x
x
0OHC l ll
OHC Force
OHC OHC BM OHC
OHC OHC
F K l
P x F
x
γ(x) - is the relative population of OHCs per unit length
OHC Pressure Equation
tP
t
P BM2BM1OHCOHC
OHC xx
ClOHC
GlOHCOHC
K
K
12
1
- Substituting the linear approximations in the OHC electrical potential equation yields:
The Embedded Cochlear Model
tP
t
P BM2BM1OHCOHC
OHC xx
BMBMBM
BM txst
txrt
xmP xxx
,,
2
2
BM OHCP P P
2
2
2
2 2
tAx
P BM
x 0 2 OW
Px
xx
, 0P L t
Parameters Estimation
1x CF s x m x
For
and
1 2
Re , Im , 0
; OHC
Z x Z x
r x s xx x r x
m x
Frequency Domain Equations
22
2
2
1 2
2 2
1 2
2 2
22
0
,, , 0
2,
,
Re ,
Im ,
,2 ; , 0
OHC
OHC
OHC
OHC
OW
x
d P xk x P x
dxj
k xAZ x
x xZ x r x x
s x x xZ x m x x
d P xP L
dx
x
WKB Approximation
1 2
0 0
; exp ; exp ;; ;
x xA AP x j K d j K d
K x K x
• A1 and A2 are determined by the boundary condition
Model’s Simulation
Cochlear representations of Chirp
Cochlear representation
21 0
01
( )( ) cos(2 )
2
f f tS t f t
t
Cochlear representations of “SHEN”
Cochlear representation
Impaired Hearing
Audiograms
Sensorineural Hearing Loss CONDUCTIVE HEARING LOSS
Simulated Audiograms 2
0 0
1,
T L
d BML x t dxdtT
x
sin(2 )
1/
s t ft
T f
Estimated Loudness:
- For Input Signal:
Estimated Hearing Level is defined as: ; ; 0.5 ;d dHL f L f L f