ECE 598: The Speech Chain
Lecture 10: Auditory Physiology
Today
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Outer Ear: Sound Localization
Middle Ear: Impedance Matching
Basilar Membrane: Frequency Analysis
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Mechanical Principles
Frequency Response of Auditory Filters
Nonlinearity of Basilar Membrane Response
Mechano-Electric Transduction
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Inner and Outer Hair Cells
Neuro-transmitter Uptake Models
Neural Activation Thresholds
Auditory Anatomy: Overview
Localization of Sound: Inter-Aural
Time Delay (ITD)
Wavefronts (lines of
constant pressure)
r(p/2-q)
Diffusion of
sound around
the head
rcosq
q
r
ITD = (r/c)(p/2-q+cosq)
Wave traveling
direction
Localization of Sound: Inter-Aural
Amplitude Difference
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f < c/4r ~ 1kHz: head << l=c/f; sound diffuses around head
f > c/2r ~ 2kHz: head > l, so sound is blocked by the head
Low frequency, Long wavelength
(shown: wave “troughs”, i.e.,
pressure minima)
Sound diffuses
around the head;
no shadow
High frequency, Short wavelength
(shown: wave “troughs”, i.e.,
pressure minima)
Head shadow:
Sound unable
to diffuse
around large
obstacle
Localization of Sound: Echoes from
the Pinna and Shoulders
Direct Sound
Pinna Echo
Shoulder
Echo
Localization of Sound, Summary:
Head-Related Transfer Function
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Source:
s(t) = cos(wt)
Received at near ear:
xR(t) = AR(w) cos(wt+fR(w))
Received at far ear:
xL(t) = AL(w) cos(wt+fL(w)-wtITD)
Near ear frequency response:
HR(w) = AR(w)ejf (w)
Far ear frequency response:
HL(w) = AL(w)ej(f (w)-wt )
R
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L
ITD
Middle Ear Functions
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Impedance Matching:
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Sound transmission in water (inner ear) requires
much higher pressure than sound transmission in air
(outer ear).
Without middle ear, sound incident on oval window
would bounce away (g=1)
Middle ear reduces g so that not all sound is reflected
Reduce Exposure to Loud Environments
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Strap muscles loosen in loud environments, reducing
the amplitude of sound transmitted to inner ear
Effect is relatively slow (hundreds of milliseconds), so
not useful for adaptation to rapid sounds (gunshots)
Impedance Mis-Match Between Water and Air:
Without a Middle Ear, What Would You Hear?
Auditory Canal, contents:
air
pa+
pa-
Oval
Window
Scala Vestibuli, contents:
perilymph ≈ sodium water
pw+
pw-
A
Continuity of pressure at the boundary:
(pa++pa-) = (pw++pw-)
 Continuity of volume velocity at the boundary:
(A/raca) (pa+-pa-) = (A/rwcw) (pw+-pw-)
 Densities:
ra = 0.001 g/cc, rw = 1 g/cc
 Speeds of Sound: ca = 354m/s,
cw=1000m/s
 Suppose pw-=0, meaning that the only input sound is pa+
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Then…
The reflected sound is: pa- = (rwcw-raca)/(rwcw+raca) pa+ = 0.9994 pa+
The transmitted sound is:
pw+ = 2raca/(rwcw+raca) pa+ = 0.0006 pa+
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Hammer-Anvil-Stirrup = LeverBased Impedance Matching System
Eardrum
Velocity = (1/raca)(pa+-pa-)
Pressure = (pa++pa-)
L units
length
Oval Window
Velocity = (1/Lraca)(pa+-pa-)
Pressure = L (pa++pa-)
1 unit length
Lever system reduces the effective input
impedance (z=p/v) of water by a factor of L2
 Resulting reflection coefficient
g = (rwcw-L2raca)/(rwcw+L2raca) ~ 0.98-0.99 < 1
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Acoustic Impedance of Ear Canal
Informative About Middle Ear Function
Outer Ear, contents: air
pa+
pa-L
0
x
Remember how to calculate impedance?
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Eardrum
Impose a Boundary Condition at Far End
pa-=gpa+
Calculate z=p/v at Near End
z = p/v = rc (pa+e-jkx+pa-ejkx)/(pa+e-jkx-pa-ejkx)
= rc (e2jkL + g)/(e-2jkL - g)
So by measuring the acoustic input impedance of the
auditory canal very precisely, it’s possible to deduce g
at different frequencies, and thus to learn something
about health of the middle ear (product: Mimosa
Acoustics)
Inner Ear Anatomy
(image courtesy Alec Salt, Otolaryngology, Washington University)
Inner Ear Anatomy: Charged Fluids
(image courtesy of Alec Salt, Otolaryngology, Washington University)
Cross-Section of the Basilar Membrane
(image courtesy wikipedia)
Frequency Selectivity of Places on the
Basilar Membrane
Basilar Membrane (separates
scala media & scala tympani)
Oval Window
Base, x=0mm:
High Stiffness
Low Mass
fc = (k/m)1/2/2p
~ 16000Hz
Unroll
Apex, x~3cm:
Low Stiffness
High Mass
fc = (k/m)1/2/2p
~ 40Hz
In between: Each position, x, is tuned to a different mechanical resonance
x(fc) ~ 30mm – (11mm) ln(1 + 46fc/(fc+14700))
Round
Window
Oval
Window
Frequency Selectivity of Places on the
Basilar Membrane
Scala Vestibuli
Wave pw+e-jwx/c propagates forward at c=1000m/s until…
Scala Tympani
Wave energy is absorbed by
oscillation of the basilar
membrane at x(fc=w/2p)
Frequency Selectivity of Places on the
Basilar Membrane
Traveling waves in the
cochlea.
“Concerning the pleasures
of observing, and the
mechanics of the inner
ear,”
Nobel Lecture, 1961,
Georg von Békésy
(courtesy of Pacific
Biosciences Research
Center Hawaii)
Bandwidth of the Auditory Filters:
100Hz at fc<500Hz, 0.2fc at fc>500Hz
(image courtesy Julius Smith and Jonathan Abel, CCRMA, Stanford)
Equivalent
Rectangular
Bandwidth
(ERB) =
Bandwidth of
an ideal
BPF that
passes the
same total
energy as
the basilar
membrane
section at
the same fc
Velocity of Basilar Membrane Causes
Inner Hair Cell Follicles to Bend
Velocity of Basilar Membrane Causes
Inner Hair Cell Follicles to Bend
Bending of Follicles Causes
Depolarization of IHC
Scala Media (+80mV)
Cations enter through
follicle tips when
follicles bend
Organ of Corti (0mV)
Depolarization of IHC Causes Release
of Neurotransmitter
Cations enter through
follicle tips when
follicles bend
Neurotransmitter
released
Synapse, afferent neuron
Neurotransmitter Dynamics
(Three-Store Model: Meddis, JASA 1986)
Neurotransmitter
Re-uptake (several ms)
Neurotransmitter release (instant)
Neurotransmitter binding (several ms)
Result: probability of neuron firing is a smoothed
(lowpass filtered) version of the IHC voltage
Signal Processing in the Inner Ear
(Simulated)
Neural Response to a Synthetic Vowel
(Cariani, 2000)