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Leo Koop (TU Delft) Simulating Hearing Loss April 9, 2015 1 / 35
Simulating Hearing LossDelft University of Technology
Leo Koop
April 9, 2015
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Outline1 Introductions and Motivation
IntroductionMotivationThe Ear and Cochlea
2 Modeling the CochleaThe General ModelLinear and Non Linear Models
3 Simulating Hearing LossApproachThe Linear Case; A Sound FilterResults
4 Testing and OutlookTestingOutlook
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Next Subsection1 Introductions and Motivation
IntroductionMotivationThe Ear and Cochlea
2 Modeling the CochleaThe General ModelLinear and Non Linear Models
3 Simulating Hearing LossApproachThe Linear Case; A Sound FilterResults
4 Testing and OutlookTestingOutlook
Leo Koop (TU Delft) Simulating Hearing Loss April 9, 2015 3 / 35
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Simulating Hearing Loss
• Applied Mathematics Department at TU Delft
• Supervisor: Kees Vuik
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Simulating Hearing Loss
• An incas3 project
• Supervisor: Peter van Hengel
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Next Subsection1 Introductions and Motivation
IntroductionMotivationThe Ear and Cochlea
2 Modeling the CochleaThe General ModelLinear and Non Linear Models
3 Simulating Hearing LossApproachThe Linear Case; A Sound FilterResults
4 Testing and OutlookTestingOutlook
Leo Koop (TU Delft) Simulating Hearing Loss April 9, 2015 6 / 35
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Motivation - Hearing Loss, Becoming morePrevalent
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Motivation - Uses of a Hearing Loss Simulator
• Education
• Hearing loss prevention
• Simplifying hearing aid development and testing
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Motivation - Uses of a Hearing Loss Simulator
• Education
• Hearing loss prevention
• Simplifying hearing aid development and testing
Leo Koop (TU Delft) Simulating Hearing Loss April 9, 2015 8 / 35
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Motivation - Uses of a Hearing Loss Simulator
• Education
• Hearing loss prevention
• Simplifying hearing aid development and testing
Leo Koop (TU Delft) Simulating Hearing Loss April 9, 2015 8 / 35
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Next Subsection1 Introductions and Motivation
IntroductionMotivationThe Ear and Cochlea
2 Modeling the CochleaThe General ModelLinear and Non Linear Models
3 Simulating Hearing LossApproachThe Linear Case; A Sound FilterResults
4 Testing and OutlookTestingOutlook
Leo Koop (TU Delft) Simulating Hearing Loss April 9, 2015 9 / 35
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The Ear
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The Cochlea, a Cross Section
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The Cochlea
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Next Subsection1 Introductions and Motivation
IntroductionMotivationThe Ear and Cochlea
2 Modeling the CochleaThe General ModelLinear and Non Linear Models
3 Simulating Hearing LossApproachThe Linear Case; A Sound FilterResults
4 Testing and OutlookTestingOutlook
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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
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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
Leo Koop (TU Delft) Simulating Hearing Loss April 9, 2015 14 / 35
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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
Leo Koop (TU Delft) Simulating Hearing Loss April 9, 2015 14 / 35
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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
Leo Koop (TU Delft) Simulating Hearing Loss April 9, 2015 14 / 35
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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
Leo Koop (TU Delft) Simulating Hearing Loss April 9, 2015 14 / 35
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Modeling the Cochlea
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
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Modeling the Cochlea
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
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Simplifying the equations
We introduce g(x , t) as follows:
g(x , t) = d(x)y(x , t) + s(x)y(x , t) (3)
Then rewrite my(x , t) as:
my(x , t) = p(x , t) − g(x , t) (4)
This allows us to then rewrite Equation (1) as:
∂2p
∂x2(x , t) − κp(x , t) = −κg(x , t) (5)
Where κ = 2ρhm .
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Simplifying the equations
Equation 5 can be further reduced to 2 first degree ODEs byintroducing v as follows:
∂y
∂t(x , t) = v(x , t) (6)
∂v
∂t(x , t) =
p(x , t) − g(x , t)
m(7)
Which can then be solved with a numerical integrator, say ClassicalRunge Kutta 4
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Next Subsection1 Introductions and Motivation
IntroductionMotivationThe Ear and Cochlea
2 Modeling the CochleaThe General ModelLinear and Non Linear Models
3 Simulating Hearing LossApproachThe Linear Case; A Sound FilterResults
4 Testing and OutlookTestingOutlook
Leo Koop (TU Delft) Simulating Hearing Loss April 9, 2015 18 / 35
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Damping and Stiffness Terms
The pressure term
p(x , t) = my(x , t) + d(x)y(x , t) + s(x)y(x , t)
Linear damping term
d(x) = ε√m s(x)
Non-linear damping term
d(x , y) =
{(1 − γ)(δsat − δneg )
[1 − 1
1 + e(Λ−α)/µα
]+ γ(δsat − δneg )
[1 − 1
1 + eΛ−β/µβ
]+ δneg
}√m s(x)
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Damping and Stiffness Terms
The pressure term
p(x , t) = my(x , t) + d(x)y(x , t) + s(x)y(x , t)
Linear damping term
d(x) = ε√m s(x)
Non-linear damping term
d(x , y) =
{(1 − γ)(δsat − δneg )
[1 − 1
1 + e(Λ−α)/µα
]+ γ(δsat − δneg )
[1 − 1
1 + eΛ−β/µβ
]+ δneg
}√m s(x)
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Damping and Stiffness Terms
The pressure term
p(x , t) = my(x , t) + d(x)y(x , t) + s(x)y(x , t)
Linear damping term
d(x) = ε√m s(x)
Non-linear damping term
d(x , y) =
{(1 − γ)(δsat − δneg )
[1 − 1
1 + e(Λ−α)/µα
]+ γ(δsat − δneg )
[1 − 1
1 + eΛ−β/µβ
]+ δneg
}√m s(x)
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Damping and Stiffness Terms
The pressure term
p(x , t) = my(x , t) + d(x)y(x , t) + s(x)y(x , t)
Linear stiffness term
s(x) = s0e−λx
Non-linear case; an additional delayed feedback stiffness term
c(x , y) =
{(1 − γ)(σzweig )
[1
1 + e(Λ−α)/µα
]+ γ(σzweig )
[1
1 + eΛ−β/µβ
]}(8)
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Damping and Stiffness Terms
The pressure term
p(x , t) = my(x , t) + d(x)y(x , t) + s(x)y(x , t)
Linear stiffness term
s(x) = s0e−λx
Non-linear case; an additional delayed feedback stiffness term
c(x , y) =
{(1 − γ)(σzweig )
[1
1 + e(Λ−α)/µα
]+ γ(σzweig )
[1
1 + eΛ−β/µβ
]}(8)
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Damping and Stiffness Terms
The pressure term
p(x , t) = my(x , t) + d(x)y(x , t) + s(x)y(x , t)
Linear stiffness term
s(x) = s0e−λx
Non-linear case; an additional delayed feedback stiffness term
c(x , y) =
{(1 − γ)(σzweig )
[1
1 + e(Λ−α)/µα
]+ γ(σzweig )
[1
1 + eΛ−β/µβ
]}(8)
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A Sample Model Output
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−0.2
−0.15
−0.1
−0.05
0
0.05
0.1
0.15
0.2progress 50000.00 steps, t−tilde = 10.00
Oscillators in % of Cochlea Length
Oscill
ato
r D
ispla
cem
ent / V
elo
city (
nm
/ n
m/m
s)
osc. velocity
osc. displacement
Figure: Modeling the response of the basilar membrane to a tone sound
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Next Subsection1 Introductions and Motivation
IntroductionMotivationThe Ear and Cochlea
2 Modeling the CochleaThe General ModelLinear and Non Linear Models
3 Simulating Hearing LossApproachThe Linear Case; A Sound FilterResults
4 Testing and OutlookTestingOutlook
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Simulation Approach
• We have a good 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
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Simulation Approach
• We have a good 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
Leo Koop (TU Delft) Simulating Hearing Loss April 9, 2015 23 / 35
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Next Subsection1 Introductions and Motivation
IntroductionMotivationThe Ear and Cochlea
2 Modeling the CochleaThe General ModelLinear and Non Linear Models
3 Simulating Hearing LossApproachThe Linear Case; A Sound FilterResults
4 Testing and OutlookTestingOutlook
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The Model Viewed as a Convolution
0 2 4 6 8 10 12 14 16 18 20 22−1
−0.5
0
0.5
1Sound: A cappella singing
Time in seconds
Am
plit
ude (
dB
FS
)
0 2 4 6 8 10 12 14 16 18 20 22−2
−1
0
1
2x 10
−7 Oscillator trace
Time in seconds
Oscill
ato
r d
isp
lace
me
nt
(nm
/ms)
Leo Koop (TU Delft) Simulating Hearing Loss April 9, 2015 25 / 35
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Finding the Inverse Filter
If the original sound is x and the result from the model is y then themodel is h
y(t) = x(t) ∗ h(t)
Performing a Fourier Transformation results in:
Y (f ) = X (f ) · H(f )
A change in basic operation from convolution to multiplication
Leo Koop (TU Delft) Simulating Hearing Loss April 9, 2015 26 / 35
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Finding the Inverse FilterThen H and H−1 are:
H(f ) =Y (f )
X (f )
H−1(f ) =1
H(f )
X (f ) Can then easily be found
X (f ) =Y (f )
H(f )
And then:
x(t) = Inverse Fourier Transform of (X (f ))
Leo Koop (TU Delft) Simulating Hearing Loss April 9, 2015 27 / 35
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Next Subsection1 Introductions and Motivation
IntroductionMotivationThe Ear and Cochlea
2 Modeling the CochleaThe General ModelLinear and Non Linear Models
3 Simulating Hearing LossApproachThe Linear Case; A Sound FilterResults
4 Testing and OutlookTestingOutlook
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Some Results
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0
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1Sound: A cappella singing
Time in seconds
Am
plit
ude (
dB
FS
)
0 2 4 6 8 10 12 14 16 18 20 22−1
−0.5
0
0.5
1Resynthesized sound
Time in seconds
Am
plit
ude (
dB
FS
)
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What Affects Sound Reproduction Quality
• Length of impulse response!!
• Type of window used, Gaussian seems to be a good choice
• Which oscillator is used
• Integration time step used (affects sound quality)
• Number of oscillators in the Model
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What Affects Sound Reproduction Quality
• Length of impulse response!!
• Type of window used, Gaussian seems to be a good choice
• Which oscillator is used
• Integration time step used (affects sound quality)
• Number of oscillators in the Model
Leo Koop (TU Delft) Simulating Hearing Loss April 9, 2015 30 / 35
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What Affects Sound Reproduction Quality
• Length of impulse response!!
• Type of window used, Gaussian seems to be a good choice
• Which oscillator is used
• Integration time step used (affects sound quality)
• Number of oscillators in the Model
Leo Koop (TU Delft) Simulating Hearing Loss April 9, 2015 30 / 35
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What Affects Sound Reproduction Quality
• Length of impulse response!!
• Type of window used, Gaussian seems to be a good choice
• Which oscillator is used
• Integration time step used (affects sound quality)
• Number of oscillators in the Model
Leo Koop (TU Delft) Simulating Hearing Loss April 9, 2015 30 / 35
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What Affects Sound Reproduction Quality
• Length of impulse response!!
• Type of window used, Gaussian seems to be a good choice
• Which oscillator is used
• Integration time step used (affects sound quality)
• Number of oscillators in the Model
Leo Koop (TU Delft) Simulating Hearing Loss April 9, 2015 30 / 35
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Next Subsection1 Introductions and Motivation
IntroductionMotivationThe Ear and Cochlea
2 Modeling the CochleaThe General ModelLinear and Non Linear Models
3 Simulating Hearing LossApproachThe Linear Case; A Sound FilterResults
4 Testing and OutlookTestingOutlook
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Testing
• Objective testing may be limited
• Subjective testing• Comparing two sounds on Right and Left channel does not work• Consecutive listening tends to work better• System limitations should be considered
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Testing and Optimization, a Possibility
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0.5
1Resynthesized sound
Time in seconds
Am
plit
ude (
dB
FS
)
0 2 4 6 8 10 12 14 16 18 20 22−1
−0.5
0
0.5
1Resynthesized sound
Time in seconds
Am
plit
ude (
dB
FS
)
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Next Subsection1 Introductions and Motivation
IntroductionMotivationThe Ear and Cochlea
2 Modeling the CochleaThe General ModelLinear and Non Linear Models
3 Simulating Hearing LossApproachThe Linear Case; A Sound FilterResults
4 Testing and OutlookTestingOutlook
Leo Koop (TU Delft) Simulating Hearing Loss April 9, 2015 34 / 35
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Outlook
• We have a good model of the ear
• Can we get good sound back from the model?
• Improving the sample rate
• Using multiple oscillators
• Look for optimality using the settings required for the Non-linearmodel
• Resynthesizing sound from the non-linear model
Leo Koop (TU Delft) Simulating Hearing Loss April 9, 2015 35 / 35
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Outlook
• We have a good model of the ear
• Can we get good sound back from the model?
• Improving the sample rate
• Using multiple oscillators
• Look for optimality using the settings required for the Non-linearmodel
• Resynthesizing sound from the non-linear model
Leo Koop (TU Delft) Simulating Hearing Loss April 9, 2015 35 / 35
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Outlook
• We have a good model of the ear
• Can we get good sound back from the model?
• Improving the sample rate
• Using multiple oscillators
• Look for optimality using the settings required for the Non-linearmodel
• Resynthesizing sound from the non-linear model
Leo Koop (TU Delft) Simulating Hearing Loss April 9, 2015 35 / 35
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Outlook
• We have a good model of the ear
• Can we get good sound back from the model?
• Improving the sample rate
• Using multiple oscillators
• Look for optimality using the settings required for the Non-linearmodel
• Resynthesizing sound from the non-linear model
Leo Koop (TU Delft) Simulating Hearing Loss April 9, 2015 35 / 35
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Outlook
• We have a good model of the ear
• Can we get good sound back from the model?
• Improving the sample rate
• Using multiple oscillators
• Look for optimality using the settings required for the Non-linearmodel
• Resynthesizing sound from the non-linear model
Leo Koop (TU Delft) Simulating Hearing Loss April 9, 2015 35 / 35
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Outlook
• We have a good model of the ear
• Can we get good sound back from the model?
• Improving the sample rate
• Using multiple oscillators
• Look for optimality using the settings required for the Non-linearmodel
• Resynthesizing sound from the non-linear model
Leo Koop (TU Delft) Simulating Hearing Loss April 9, 2015 35 / 35