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Leo Koop (TU Delft) Simulating Hearing Loss Using a Transmission Line Cochlea ModelOctober 28, 2015 1 / 53

Simulating Hearing Loss Using a

Transmission Line Cochlea ModelDelft University of Technology

Leo Koop

October 28, 2015

Outline1 Introductions and Motivation2 Modeling the Cochlea

The General ModelModel Output

3 Inverse ModelThe IdeaInverse Filtering Method

4 Energy ReflectionThe Problem

5 Sound ResynthesisTuning Curves and Inverse FiltersFilter Contribution Regions

6 Simulating Hearing LossModeling a Damaged CochleaThe Resulting SoundComparison of Sound


Simulating Hearing Loss

• Applied Mathematics Department at TU Delft

• Supervisor: Kees Vuik


Simulating Hearing Loss

• An incas3 project

• Supervisor: Peter van Hengel


Motivation - Hearing Loss, Becoming morePrevalent


Motivation - Uses of a Hearing Loss Simulator

• Education

• Hearing loss prevention

• Simplifying hearing aid development and testing



• Education





• Education




The Ear


The Cochlea, a Cross Section


The Cochlea


Next Subsection1 Introductions and Motivation2 Modeling the Cochlea







Modeling the Cochlea

The Main Equation

∂2p

∂x2(x , t) − 2ρ∂2y

h∂t2(x , t) = 0, 0 ≤ x ≤ L, t ≥ 0 (1)

• y(x , t): The excitation of the oscillator

• p(x , t): Pressure on the cochlear partition

• ρ: Density of the cochlear fluid

• h: Height of the scala

• L: Length of the cochlea

• t: Time



The Main Equation

∂2p

∂x2(x , t) − 2ρ∂2y

h∂t2(x , t) = 0, 0 ≤ x ≤ L, t ≥ 0 (1)






• t: Time



The Main Equation

∂2p

∂x2(x , t) − 2ρ∂2y

h∂t2(x , t) = 0, 0 ≤ x ≤ L, t ≥ 0 (1)






• t: Time



The Main Equation

∂2p

∂x2(x , t) − 2ρ∂2y

h∂t2(x , t) = 0, 0 ≤ x ≤ L, t ≥ 0 (1)






• t: Time



The Main Equation

∂2p

∂x2(x , t) − 2ρ∂2y

h∂t2(x , t) = 0, 0 ≤ x ≤ L, t ≥ 0 (1)






• t: Time



The pressure term

p(x , t) = my(x , t) + d(x)y(x , t) + s(x)y(x , t) (2)

• m: Mass of the membrane

• d(x): Position dependent damping

• s(x): Position dependent stiffness



The pressure term

p(x , t) = my(x , t) + d(x)y(x , t) + s(x)y(x , t) (2)

• m: Mass of the membrane

• d(x): Position dependent damping

• s(x): Position dependent stiffness


The Stiffness Term

Linear stiffness term (theoretical)

s(x) = s0e−λx


The Stiffness Term

Linear stiffness term (theoretical)

s(x) = s0e−λx

Scaled length of the cochlea0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Stiffnessvalue

×104

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

s(x)


The Damping Term

Linear damping term (theoretical)

d(x) = ε√m s(x)


The Damping Term

Linear damping term (theoretical)

d(x) = ε√m s(x)

Scaled length of the cochlea0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Dam

pingvalue

0

1

2

3

4

5

6

7

8

d(x)









Model Output

Oscillators in scaled cochlea length0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1O

scillatordisplacement/velocity

(nm/m

s) ×10-5

-5

-4

-3

-2

-1

0

1

2

3

4

5progress 151.00 steps, t tilde = 0.00

osc. velocity

osc. displacement


Model Output



(nm/m

s) ×10-5

-5

-4

-3

-2

-1

0

1

2

3

4

5

progress 1101.00 steps, t tilde = 0.00

osc. velocity

osc. displacement


Model Output



(nm/m

s) ×10-5

-5

-4

-3

-2

-1

0

1

2

3

4

5

progress 4101.00 steps, t tilde = 0.01

osc. velocity

osc. displacement


Model Input and Output

Time (ms)80 90 100 110 120 130 140 150 160

Amplitude

-0.5

0

0.5

Singing sound

Time (ms)80 90 100 110 120 130 140 150 160

Amplitude(nm)

×10-5

-4

-2

0

2

4

Singing sound single oscillator trace









Simulation Approach

• We have a model of the normal cochlea

• Can we find the Cause given the Effect?

Idea

Find a method to get back the original sound from the model of ahealthy ear. Use this method on a model of a damaged ear tosimulate hearing loss


Simulation Approach

• We have a model of the normal cochlea

• Can we find the Cause given the Effect?

Idea

Find a method to get back the original sound from the model of ahealthy ear. Use this method on a model of a damaged ear tosimulate hearing loss









Inverse Filter Approach for a Single Oscillator

If the original sound is a and a result from the model is c then anoscillator in the model is b

c(t) = a(t) ∗ b(t)

This in the frequency domain is:

C (f ) = A(f ) · B(f )

A change in basic operation from convolution to multiplication


Finding the Inverse Filter

• b(t) is the impulse response of an oscillator

• B(f ) is the frequency response of an oscillator

In the frequency domain B−1(f ) is easily found:

B−1(f ) =1

B(f )

Given C (f ) and B(f ), A(f ) is:

A(f ) = C (f ) · B−1(f )

An inverse Fourier transform yields a(t)


The Idea









The Cochlea


A Good Impulse Response

Time in ms-2 0 2 4 6 8 10 12

Amplitude(nm)

×10-5

-2

-1

0

1

2

Clean Impulse Response


Non-Finite Impulse Response

Time in seconds0 0.05 0.1 0.15

Trace

ofoscillator410of600

×10-6

-4

-2

0

2

4

Impulse response with no update


Energy Build-up in the Model

Time (ms)0 500 1000 1500 2000

Amplitude(nm)

-0.05

0

0.05

Unstable CM output


The Solution

Scaled length of the cochlea0 0.2 0.4 0.6 0.8 1

Dam

pingvalue

0

5

10

15

20

25

d(x) updated


A Better Impulse Response


Trace


×10-6

-4

-2

0

2

4

Impulse response with no update


A Better Impulse Response


Trace


×10-6

-4

-2

0

2

4

Impulse response with update









Tuning Curves

frequency in kHz10

-110

010

1

Amplitude(dB)

-200

-180

-160

-140

-120

-100

-80

-60

-40

B(f ) - tuning curves

osc.#: 5

osc.#: 30

osc.#: 55

osc.#: 80

osc.#: 105

osc.#: 130

osc.#: 155

osc.#: 180

osc.#: 205

osc.#: 230

osc.#: 255

osc.#: 280

osc.#: 305

osc.#: 330

osc.#: 355

osc.#: 380

osc.#: 405

osc.#: 430

osc.#: 455

osc.#: 480


The Inverse Filters

frequency in kHz10

-110

010

1

Amplitude(dB)

40

60

80

100

120

140

160

180

200

B−1(f ) - filter functions

osc.#: 5

osc.#: 30

osc.#: 55

osc.#: 80

osc.#: 105

osc.#: 130

osc.#: 155

osc.#: 180

osc.#: 205

osc.#: 230

osc.#: 255

osc.#: 280

osc.#: 305

osc.#: 330

osc.#: 355

osc.#: 380

osc.#: 405

osc.#: 430

osc.#: 455

osc.#: 480


Error Amplification

frequency in kHz

10-1

100

101

Amplitude

0

500

1000

1500

2000

Frequency Content of Result

Sound

inv. Filt.









Choosing Contribution Bounds per InverseFilter

frequency in kHz10

-110

010

1

Amplitude(dB)

60

80

100

120

140

160

Two inverse filters and f and f

tilde f f









Modifying the Damping Term

Oscillator number in the cochlea model0 100 200 300 400 500 600

Dampingvalue

0

5

10

15

20

25

Damping while simulating damage









The Resulting Sound

frequency in kHz10

-110

010

1

Amplitude

0

200

400

600

800

1000

1200

1400

1600

1800

Frequency Content of Result


The Resulting Sound

frequency in kHz

10-1

100

101

Amplitude

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Ratio between damage and original signal









A Normal Cochleogram


Simulating Damage


Cochleogram in Response to Damaged Sound


Comparing the Cochleograms

Oscillator number in the cochlea model

0 100 200 300 400 500 600

Averageresponse

level

intime

-60

-55

-50

-45

-40

-35

-30

Average of cochleogram per oscillator in time

Original sound

While simulating damage

Response to resynthesized sound


Sound Samples

• “1, 2, 3” From the TIDigits database• “1, 2, 3 w/ noise” With background noise• “1, 2, 3 w/ noise” Resynthesized without simulating damage• “1, 2, 3 w/ noise” Approximate hearing loss of a 40 year old• “1, 2, 3 w/ noise” Approximate hearing loss of a 60 year old• “1, 2, 3 w/ noise” Approximate hearing loss of a 90 year old


Accomplishments

• Fixed an energy reflection problem in the model

• Found a way to combine contributions from different oscillators

• A transmission line cochlea model can now be used to simulatehearing loss


Accomplishments





Accomplishments





Recommendations

• Sound resynthesis from a nonlinear transmission line cochleamodel

• The best method to solve the energy reflection problem

• How to best modify the cochlea model to simulate various kindsof hearing loss


Recommendations





Recommendations





The End

“He who has an ear, let him hear...”

- Revelation 2:17


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