ECE 598: The Speech ECE 598: The Speech ChainChain

Lecture 10: Auditory Lecture 10: Auditory PhysiologyPhysiology

TodayToday Outer Ear: Sound LocalizationOuter Ear: Sound Localization Middle Ear: Impedance MatchingMiddle Ear: Impedance Matching Basilar Membrane: Frequency AnalysisBasilar Membrane: Frequency Analysis

Mechanical PrinciplesMechanical Principles Frequency Response of Auditory FiltersFrequency Response of Auditory Filters Nonlinearity of Basilar Membrane Nonlinearity of Basilar Membrane

ResponseResponse Mechano-Electric TransductionMechano-Electric Transduction

Inner and Outer Hair CellsInner and Outer Hair Cells Neuro-transmitter Uptake ModelsNeuro-transmitter Uptake Models Neural Activation ThresholdsNeural Activation Thresholds

Auditory Anatomy: Auditory Anatomy: OverviewOverview

Localization of Sound: Inter-Localization of Sound: Inter-Aural Time Delay (ITD)Aural Time Delay (ITD)

r

rcosr(/2-)

ITD = (r/c)(/2-+cos)

Wavefronts (lines of constant pressure)

Wave traveling direction

Diffusion of sound around the head

Localization of Sound: Inter-Localization of Sound: Inter-Aural Amplitude DifferenceAural Amplitude Difference

f < c/4r ~ 1kHz: head << f < c/4r ~ 1kHz: head << =c/f; sound diffuses around head=c/f; sound diffuses around head f > c/2r ~ 2kHz: head > f > c/2r ~ 2kHz: head > , so sound is blocked by the head, so sound is blocked by the head

Low frequency, Long wavelength(shown: wave “troughs”, i.e., pressure minima)

High frequency, Short wavelength(shown: wave “troughs”, i.e., pressure minima)

Sound diffuses around the head; no shadow

Head shadow: Sound unable to diffuse around large obstacle

Localization of Sound: Echoes Localization of Sound: Echoes from the Pinna and Shouldersfrom the Pinna and Shoulders

Direct Sound

Pinna Echo

Shoulder Echo

Localization of Sound, Localization of Sound, Summary: Head-Related Summary: Head-Related

Transfer FunctionTransfer Function Source: Source:

s(t) = cos(s(t) = cos(t)t) Received at near ear:Received at near ear:

xxRR(t) = A(t) = ARR(() cos() cos(t+t+RR(()))) Received at far ear: Received at far ear:

xxLL(t) = A(t) = ALL(() cos() cos(t+t+LL(())ITDITD)) Near ear frequency response:Near ear frequency response:

HHRR(() = A) = ARR(()e)ejjRR(())

Far ear frequency response:Far ear frequency response:

HHLL(() = A) = ALL(()e)ej(j(LL(()-)-ITDITD))

Middle Ear FunctionsMiddle Ear Functions Impedance Matching: Impedance Matching:

Sound transmission in water (inner ear) requires Sound transmission in water (inner ear) requires much higher pressure than sound transmission in air much higher pressure than sound transmission in air (outer ear).(outer ear).

Without middle ear, sound incident on oval window Without middle ear, sound incident on oval window would bounce away (would bounce away (=1) =1)

Middle ear reduces g so that not all sound is Middle ear reduces g so that not all sound is reflectedreflected

Reduce Exposure to Loud EnvironmentsReduce Exposure to Loud Environments Strap muscles loosen in loud environments, reducing Strap muscles loosen in loud environments, reducing

the amplitude of sound transmitted to inner earthe amplitude of sound transmitted to inner ear Effect is relatively slow (hundreds of milliseconds), Effect is relatively slow (hundreds of milliseconds),

so not useful for adaptation to rapid sounds so not useful for adaptation to rapid sounds (gunshots)(gunshots)

Impedance Mis-Match Between Water Impedance Mis-Match Between Water and Air: Without a Middle Ear, What and Air: Without a Middle Ear, What

Would You Hear?Would You Hear?

Continuity of pressure at the boundary:Continuity of pressure at the boundary:

(p(pa+a++p+pa-a-) = (p) = (pw+w++p+pw-w-)) Continuity of volume velocity at the boundary:Continuity of volume velocity at the boundary:

(A/(A/aaccaa) (p) (pa+a+ppa-a-) = (A/) = (A/wwccww) (p) (pw+w+ppw-w-)) Densities: Densities: a a = 0.001 g/cc, = 0.001 g/cc, w w = 1 g/cc= 1 g/cc Speeds of Sound: cSpeeds of Sound: caa = 354m/s, c = 354m/s, cww=1000m/s=1000m/s Suppose pSuppose pw-w-=0, meaning that the only input sound is p=0, meaning that the only input sound is pa+a+

Then…Then…

The reflected sound is: pThe reflected sound is: pa-a- = ( = (wwccwwaaccaa)/()/(wwccww++aaccaa) p) pa+a+ = 0.9994 p = 0.9994 pa+a+

The transmitted sound is: pThe transmitted sound is: pw+w+ = 2 = 2aaccaa/(/(wwccww++aaccaa) p) pa+a+ = 0.0006 p = 0.0006 pa+a+

pa+ pa- pw-

pw+

Scala Vestibuli, contents: perilymph ≈ sodium water

Auditory Canal, contents: air

Oval Window

A

Hammer-Anvil-Stirrup = Lever-Hammer-Anvil-Stirrup = Lever-Based Impedance Matching Based Impedance Matching

SystemSystem

Lever system reduces the effective input Lever system reduces the effective input impedance (z=p/v) of water by a factor of Limpedance (z=p/v) of water by a factor of L22

Resulting reflection coefficientResulting reflection coefficient

= (= (wwccwwLL22aaccaa)/()/(wwccww+L+L22aaccaa) ~ 0.98-0.99 < 1) ~ 0.98-0.99 < 1

L unitslength 1 unit length

Eardrum Velocity = (1/aca)(pa+pa-)

Pressure = (pa++pa-) Oval Window Velocity = (1/Laca)(pa+pa-)Pressure = L (pa++pa-)

Acoustic Impedance of Ear Canal Acoustic Impedance of Ear Canal Informative About Middle Ear Informative About Middle Ear

FunctionFunction

Remember how to calculate impedance?Remember how to calculate impedance?1.1. Impose a Boundary Condition at Far EndImpose a Boundary Condition at Far End

ppa-a-==ppa+a+

2.2. Calculate z=p/v at Near EndCalculate z=p/v at Near Endz = p/v = z = p/v = c (pc (pa+a+ee-jkx-jkx+p+pa-a-eejkxjkx)/(p)/(pa+a+ee-jkx-jkx-p-pa-a-eejkxjkx))

= = c (ec (e2jkL 2jkL + + )/(e)/(e-2jkL -2jkL )) So by measuring the acoustic input impedance So by measuring the acoustic input impedance

of the auditory canal very precisely, it’s possible of the auditory canal very precisely, it’s possible to deduce to deduce at different frequencies, and thus to at different frequencies, and thus to learn something about health of the middle ear learn something about health of the middle ear (product: Mimosa Acoustics)(product: Mimosa Acoustics)

pa+ pa-

Outer Ear, contents: air

Eardrum

-L 0x

Inner Ear AnatomyInner Ear Anatomy(image courtesy Alec Salt, Otolaryngology, Washington University)(image courtesy Alec Salt, Otolaryngology, Washington University)

Inner Ear Anatomy: Charged FluidsInner Ear Anatomy: Charged Fluids(image courtesy of Alec Salt, Otolaryngology, Washington University)(image courtesy of Alec Salt, Otolaryngology, Washington University)

Cross-Section of the Basilar Cross-Section of the Basilar MembraneMembrane

(image courtesy wikipedia)(image courtesy wikipedia)

Frequency Selectivity of Places on Frequency Selectivity of Places on the Basilar Membranethe Basilar Membrane

Unroll

Basilar Membrane (separates scala media & scala tympani)

Base, x=0mm:High StiffnessLow Massfc = (k/m)1/2/2 ~ 16000Hz

Apex, x~3cm:Low Stiffness

High Massfc = (k/m)1/2/2

~ 40Hz

Oval Window

In between: Each position, x, is tuned to a different mechanical resonancex(fc) ~ 30mm – (11mm) ln(1 + 46fc/(fc+14700))

Frequency Selectivity of Places on Frequency Selectivity of Places on the Basilar Membranethe Basilar Membrane

Wave pw+e-jx/c propagates forward at c=1000m/s until…

Wave energy is absorbed by oscillation of the basilar membrane at x(fc=/2)

Scala Vestibuli

Scala Tympani

Oval

Win

dow

Rou

nd

Win

dow

Frequency Selectivity of Places on Frequency Selectivity of Places on the Basilar Membranethe Basilar Membrane

Traveling waves in the Traveling waves in the cochlea.cochlea.

““Concerning the Concerning the pleasures of pleasures of observing, and the observing, and the mechanics of the mechanics of the inner ear,” inner ear,”

Nobel Lecture, 1961, Nobel Lecture, 1961, Georg von Békésy Georg von Békésy

(courtesy of Pacific (courtesy of Pacific Biosciences Research Biosciences Research Center Hawaii)Center Hawaii)

Bandwidth of the Auditory Filters: Bandwidth of the Auditory Filters: 100Hz at f100Hz at fcc<500Hz, 0.2f<500Hz, 0.2fcc at at

ffcc>500Hz>500Hz(image courtesy Julius Smith and Jonathan Abel, CCRMA, Stanford)(image courtesy Julius Smith and Jonathan Abel, CCRMA, Stanford)

Equivalent Equivalent RectangulRectangular ar Bandwidth Bandwidth (ERB) = (ERB) =

Bandwidth of Bandwidth of an ideal an ideal BPF that BPF that passes the passes the same total same total energy as energy as the basilar the basilar membrane membrane section at section at the same the same ffcc

Velocity of Basilar Membrane Velocity of Basilar Membrane Causes Inner Hair Cell Follicles to Causes Inner Hair Cell Follicles to

BendBend

Velocity of Basilar Membrane Velocity of Basilar Membrane Causes Inner Hair Cell Follicles to Causes Inner Hair Cell Follicles to

BendBend

Bending of Follicles Causes Bending of Follicles Causes Depolarization of IHCDepolarization of IHC

Scala Media (+80mV)

Organ of Corti (0mV)

Cations enter through follicle tips when follicles bend

Depolarization of IHC Causes Depolarization of IHC Causes Release of NeurotransmitterRelease of Neurotransmitter

Cations enter through follicle tips when follicles bend

Synapse, afferent neuron

Neurotransmitter released

Neurotransmitter DynamicsNeurotransmitter Dynamics(Three-Store Model: Meddis, JASA 1986)(Three-Store Model: Meddis, JASA 1986)

Result: probability of neuron firing is a smoothed (lowpass filtered) version of the IHC voltage

Neurotransmitter release (instant)

Neurotransmitter Re-uptake (several ms)

Neurotransmitter binding (several ms)

Signal Processing in the Inner Ear Signal Processing in the Inner Ear (Simulated)(Simulated)

Neural Response to a Synthetic Neural Response to a Synthetic VowelVowel

(Cariani, 2000)(Cariani, 2000)