1. ECE 598: The Speech Chain Lecture 10: Auditory Physiology

2. Today Outer Ear: Sound Localization Outer Ear: Sound Localization Middle Ear: Impedance Matching Middle Ear: Impedance Matching Basilar Membrane: Frequency Analysis Basilar Membrane: Frequency Analysis Mechanical Principles Mechanical Principles Frequency Response of Auditory Filters Frequency Response of Auditory Filters Nonlinearity of Basilar Membrane Response Nonlinearity of Basilar Membrane Response Mechano-Electric Transduction Mechano-Electric Transduction Inner and Outer Hair Cells Inner and Outer Hair Cells Neuro-transmitter Uptake Models Neuro-transmitter Uptake Models Neural Activation Thresholds Neural Activation Thresholds

3. Auditory Anatomy: Overview

4. Localization of Sound: Inter-Aural Time Delay (ITD)  r rcos  r(  /2-  ) ITD = (r/c)(  /2-  +cos  ) Wavefronts (lines of constant pressure) Wave traveling direction Diffusion of sound around the head

5. Localization of Sound: Inter-Aural Amplitude Difference f < c/4r ~ 1kHz: head << =c/f; sound diffuses around head f < c/4r ~ 1kHz: head << =c/f; sound diffuses around head f > c/2r ~ 2kHz: head >, so sound is blocked by the head f > c/2r ~ 2kHz: 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

6. Localization of Sound: Echoes from the Pinna and Shoulders Direct Sound Pinna Echo Shoulder Echo

7. Localization of Sound, Summary: Head-Related Transfer Function Source: Source: s(t) = cos(  t) Received at near ear: Received at near ear: x R (t) = A R (  ) cos(  t+  R (  )) Received at far ear: Received at far ear: x L (t) = A L (  ) cos(  t+  L (  )  ITD ) Near ear frequency response: Near ear frequency response: H R (  ) = A R (  )e j  R (  ) Far ear frequency response: Far ear frequency response: H L (  ) = A L (  )e j(  L (  )-  ITD )

8. Middle Ear Functions Impedance Matching: Impedance Matching: Sound transmission in water (inner ear) requires much higher pressure than sound transmission in air (outer ear). 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 (  =1) Without middle ear, sound incident on oval window would bounce away (  =1) Middle ear reduces g so that not all sound is reflected Middle ear reduces g so that not all sound is reflected Reduce Exposure to Loud Environments Reduce Exposure to Loud Environments Strap muscles loosen in loud environments, reducing the amplitude of sound transmitted to inner ear 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) Effect is relatively slow (hundreds of milliseconds), so not useful for adaptation to rapid sounds (gunshots)

9. Impedance Mis-Match Between Water and Air: Without a Middle Ear, What Would You Hear? Continuity of pressure at the boundary: Continuity of pressure at the boundary: (p a+ +p a- ) = (p w+ +p w- ) Continuity of volume velocity at the boundary: Continuity of volume velocity at the boundary: (A/  a c a ) (p a+  p a- ) = (A/  w c w ) (p w+  p w- ) Densities:  a = 0.001 g/cc,  w = 1 g/cc Densities:  a = 0.001 g/cc,  w = 1 g/cc Speeds of Sound: c a = 354m/s, c w =1000m/s Speeds of Sound: c a = 354m/s, c w =1000m/s Suppose p w- =0, meaning that the only input sound is p a+ Suppose p w- =0, meaning that the only input sound is p a+ Then… Then… The reflected sound is: p a- = (  w c w  a c a )/(  w c w +  a c a ) p a+ = 0.9994 p a+ The transmitted sound is: p w+ = 2  a c a /(  w c w +  a c a ) p a+ = 0.0006 p a+ p a+ p a- p w- p w+ Scala Vestibuli, contents: perilymph ≈ sodium water Auditory Canal, contents: air Oval Window A

10. Hammer-Anvil-Stirrup = Lever- Based Impedance Matching System Lever system reduces the effective input impedance (z=p/v) of water by a factor of L 2 Lever system reduces the effective input impedance (z=p/v) of water by a factor of L 2 Resulting reflection coefficient Resulting reflection coefficient  = (  w c w  L 2  a c a )/(  w c w +L 2  a c a ) ~ 0.98-0.99 < 1 L units length 1 unit length Eardrum Velocity = (1/  a c a )(p a+  p a- ) Pressure = (p a+ +p a- ) Oval Window Velocity = (1/L  a c a )(p a+  p a- ) Pressure = L (p a+ +p a- )

11. Acoustic Impedance of Ear Canal Informative About Middle Ear Function Remember how to calculate impedance? Remember how to calculate impedance? 1. Impose a Boundary Condition at Far End p a- =  p a+ 2. Calculate z=p/v at Near End z = p/v =  c (p a+ e -jkx +p a- e jkx )/(p a+ e -jkx -p a- e jkx ) =  c (e 2jkL +  )/(e -2jkL  ) So by measuring the acoustic input impedance of the auditory canal very precisely, it’s possible to deduce  at different frequencies, and thus to learn something about health of the middle ear (product: Mimosa Acoustics) So by measuring the acoustic input impedance of the auditory canal very precisely, it’s possible to deduce  at different frequencies, and thus to learn something about health of the middle ear (product: Mimosa Acoustics) p a+ p a- Outer Ear, contents: air Eardrum -L 0 x

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

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

14. Cross-Section of the Basilar Membrane (image courtesy wikipedia)

15. Frequency Selectivity of Places on the Basilar Membrane Unroll Basilar Membrane (separates scala media & scala tympani) Base, x=0mm: High Stiffness Low Mass f c = (k/m) 1/2 /2  ~ 16000Hz Apex, x~3cm: Low Stiffness High Mass f c = (k/m) 1/2 /2  ~ 40Hz Oval Window In between: Each position, x, is tuned to a different mechanical resonance x(f c ) ~ 30mm – (11mm) ln(1 + 46f c /(f c +14700))

16. Frequency Selectivity of Places on the Basilar Membrane Wave p w+ e -j  x/c propagates forward at c=1000m/s until… Wave energy is absorbed by oscillation of the basilar membrane at x(f c =  /2  ) Scala Vestibuli Scala Tympani Oval Window Round Window

17. 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)

18. Bandwidth of the Auditory Filters: 100Hz at f c 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 f c

19. Velocity of Basilar Membrane Causes Inner Hair Cell Follicles to Bend

21. Bending of Follicles Causes Depolarization of IHC Scala Media (+80mV) Organ of Corti (0mV) Cations enter through follicle tips when follicles bend

22. Depolarization of IHC Causes Release of Neurotransmitter Cations enter through follicle tips when follicles bend Synapse, afferent neuron Neurotransmitter released

23. Neurotransmitter Dynamics (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)

24. Signal Processing in the Inner Ear (Simulated)

25. Neural Response to a Synthetic Vowel (Cariani, 2000)