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