Note for MATH 250A with Professor Bergevin at UA
Note for MATH 250A with Professor Bergevin at UA
Popular in Course
Popular in Department
This 32 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Arizona taught by a professor in Fall. Since its upload, it has received 17 views.
Reviews for Note for MATH 250A with Professor Bergevin at UA
Report this Material
What is Karma?
Karma is the currency of StudySoup.
You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!
Date Created: 02/06/15
How Does an Ear Spontaneously Emit Sound University of Arizona Christopher Bergevin Quantitative Biology Seminar Math 596 9908 Overview urpose Starting Point Consider a complex biological sensory system that is difficult to examine directy Specific Means Use mathematics to quantify and model the system of interest m 1 Multidisciplinary approaches math biology MCB EEB etc physics engineering neuroscience etc 2 Get exposure to some usefulinteresting mathematics eg Fourier analysis statistics nonlinear oscillations wave mechanics 3 Translational researchmedicine thinking this way will help out in terms of 4 Experience presenting amp discussing while givingreceiving critical feedback SOAE Spontaneous otoacoustic emission recorded in the absence of any external stimulation http WWW6 mtamt eduUMHCDAUMHiMam sound pressure Pa sound pressure Pa Time D0main Spectral Domain quot0 time waveform recorded from ear canal Tonelike sounds spontaneoust emitted by the ear 1T Ana4 m E a 76577572 72 5 a timets I I E U as 005 5 Fourler transform a U4 zoomed in g 003 o 500 mun r500 2000 2500 some 3500 4000 4500 12 Frequency Hz 001 a 4 quot Digression One of the ear s primary 2 functions is to act as a Fourier transformer 005 or e rs 02 025 nmes Blackbird Turdus merua kHz 2 7 umckSemr l Mmmsah Sauna Mauve v Spectrogram frequency B ackaze r M a 7 SamvhngRaAe r mm gt gt We FFTsze l m s Wmdawsxze 39mu V ampmude wmgwwe l EMW 7 ScanSAeD 255 3 Dwsv ayHe gm 255 new 2 Wu osha 39 my l aquot n Time Waveform kaW th uvurrap15 l n I an n 583 U22 355 7m 2 m8 2 389 2 m 3 I72 3 m 3 755 m m WWW bwdsungs n 4Green9 Inner ear Middle ear Outer ear OAEs generated here OAEs measured here Inner ear Organ of Corti Three fluid filled compartments Sensory complex sits atop a flexible membrane Organ of Corti mn quot lxlllir u 39l n V Spiral organ Bazaar mcmbranc AMYquot If 1 piraz mam 39 39quot 1 Grey s Anatomy Bohne Inner Hair Cells IHCs vs Outer Hair Cells OHCs ENDOLYMPH Hair cell mechanoeecfro transducer e e 1 Mechanical stimulation deflects 9 e bundle opening transduction channels 2 HC membrane depolarizes 3 Vesicle release triggers Inner synapsed neuron to fire Hair Cell gt nonlinear saturation Afferent Auditory Nerve Fiber ANF a I u ll i I X i x Normalized HC Yransducticn Current 02 Normalized Bundle Displacement order of nm to um Martin 2008 BM Traveling Waves Mammalian Cochlea Uncoiled to Vestibular System TV gt Acoustic Energy g E stapes Helicotrema pliant amp mESSIVE to Middle Ear l A Round Window Cochlear Partition cu Geislev modified higher frequencies lower frequencies Stimulus induces propagating wave along BM Tonotopic organization Le a spectrum analyzer gt energy propagates to its characteristic frequency spot Membrane motion deflects HC bundles mn quot lxlllir u 39l n V Spiral organ Bazaar mcmbranc AMYquot If 1 piraz mam 39 39quot 1 Grey s Anatomy An Issue of Scale sound pressure Pa 004 o 06 I 30 006 0704 Measured Level dB SPL 1000 I500 2000 2500 3000 3500 4000 4500 Frequency Hz 560 time 5 NOTE different vertical scales one is logarithmic Pa Dynamic Range Humans hear over a pressure range of 120 dB that s a factor of a million Gun shots Rock concen Highrisk threshold Threshold of pain Threshold of hearing Whisper Conversational speech Sound pressure 100 120 140 dBSPL I 10pm 100pm 1nm 10nm 100nm 1pm 10pm100um Disp39acemem of Eardrum m o N o 4 O 07 O on O Diameter of Thickness of hydrogen atom lipid bilayer 4 Width of red blood cell Thickness of human hair D Freeman The ear is capable of processing sounds over a remarkably Wide intensity range encompassing at least a millionfold change in energy Peter Dallos To appreciate this range we represent a similar range of potential energies by contrasting the weight of a mouse with that of five elephants gt Energy is related to the square of pressure WRONG ANALOGY 4 r 1 elephant 100 elephants 1 0000 elephants 1000000 5000000 elephants elephants SOAEs amp Threshold 40 m o r B o 39 39 39 human threshold curve Measured Level dB SPL 30 l l l l l l l l l 0 500 1000 l500 2000 2500 3000 3500 4000 4500 Frequency Hz 9 SOAEs typically have amplitudes down near auditory threshold Compression amp Amplification lose sensitivity for midlevels but acheive a reduced output range Central nervous system can 50 dB only encode incoming information over a limited range COMPRESSION OUTPUT Ideally want to maintain sensitivity at low levels AMPLIFICATION maintain lowlevel sensitivity the steeper the slope the more g i sensitive you are to changes Sound pressure 0 2h 41 so 50 non l2 Mn 0 dB 120 dB 4 O l l f O O O V mamquot INPUT mm mm m minim m mm mm WWW u Pym Commonly accegted hygothesis SOAEs are a byproduct of an ampli cation mechanism inside the ear OHC Force Generator Idea Hair cell can also act in reverse direction ie electromechano transducer OHC Somatic Motility Outer Hair Cell OHC Changes in cell Efferent 39 mfimbl39ane length Nerve Fiber stlffness From CNS Membrane changes thought to act mechanically Feedback control from CNS gt Possible mechanical mechanism for amplification and OAE generation Mammalian Cochlea Uncoiled t0 V3234 Traveling Waves Helicotrema 9 Acoustic Energy TV 3 pliant amp massive Stapes to Middle Ear Cochlear Round Partition Window CD Gelsler modified OHC Somatic Motility Outer Hair Cell 17 OHC I Changes in cell Efferent membrane length I Nerve Fiber 39 stiffness From CNS Bundle Force Generator A 120 nm l i 500 ms 4h 0 o 2 Observations N o 30 20 10 0 10 20 30 Bundle position rim C 5730 i Va 25 E 20 60 p g 15 Q 39U E 10 5 I D 0 5 10 15 20 25 Frequency Hz 80 40 80 Displacement nm bundle can oscillate spontaneously exhibits nonlinear and negative stiffness Martin 2008 Simple Model to Explain SOAEs Part ear is composed of resonant filters eg a secondorder filter such as a harmonic oscillator consider just one of these filters eg an individual hair cell or a particular location along the length of the basilar membrane Amplitude 515 l ij l L033 Aoewt T t 39i mass damping stiffness driving term term term term nEanANr mamm a mom NOTE quantities are complex so to describe both magnitude and phase to i3 2 25 m 35 sumz mm M om nmam De asiei 1953 Simple Model to Explain SOAEs Part cont need some sort of active term for selfsustained oscillation eg van der Pol 2 135 llllli v r v 4 A v r vviilllll 4 Hill y v v 1 39Avrllllllk 3 lllllhv39 r v A v iilll l l l l 0 till 2 ill v i lt 4 A 4 A l l l active term negative damping quot 39 39 39 39 39 39 39 39 V V H noninear yup 2 i lliw 3 l l l l l l l l l i one can readily envision adding in a driving term l l l eg stochastic force dueto thermal noise 3 A 393 392 r n i 2 3 A 5 ea Model Idea I SOAEs arise due to selfsustained oscillations of individual resonators eg a limit cycle httpen w kipediaorgwikillmagsVanDerPoIOscillatorpng Simplest Model to Explain SOAEs Part II Wave motion sets basis for reflection of energy SWquot Cochlear Partltlon Effective Stiffness Mammalian cochlea Uncolled tu Vestibular System T7 i Acoushn Energy Y Helicutrema pliant amp massive to mm Ear I 23353 wmm mm Sources of Reverse Traveling Waves 39 Preexisting mechanical perturbations Resonant caViW 7 Nonlinear gain mediurn SOAE cochlear amplifier Middle ear Peak region of base Cochlear Location gt apex traveling wave Shera 2003 Model Idea ll SOAEs arise due to standingwaves set up along the length of the cochlea Summary OHC Somatic Motility Outer Hair Cell oncl changes in cell l Elterenl 1 mamhnne length Nerve Fiber stillness r 3 rpm cusp mph quotm E39EP39W 0000 elepha m 1000090 5000000 elephants zlzphamslll lililillallwill enormous dynamic range of inputs limited output range to CNS EM quot39l 39 l W E possible amplification mechanism inside ear can also provide compression Commonly accepted hypothesis SOAEs are a byproduct of an amplification mechanism inside the ear Model Idea I SOAEs arise due to selfsustained oscillations of individual resonators eg a limit cycle Model Idea ll SOAEs arise due to standingwaves set up along the length ofthe cochlea The Papers Week 2 916 Week 3 923 To Do 1 Zurek JASA 1980 Initial empirical observation on SOAEs 1 2 Bialek amp Wit Phys Rev 1984 Early SOAE model likening to a quantumlimited oscillation 1 3 van Dijk amp Wit JASA 1990 Linearnonlinear noisedriven oscillator 2 4 Talmadge et al JASA 1991 Selfsustained oscillators variations 2 5 Shera JASA 2003 Cochlear global standing waves 2 6 Vilfan amp Duke Biophys J 2008 Series of coupled oscillators for the lizard ear 2 thoroughly read your assigned paper prepare a 2025 min presentation that outlines the basic model ideas results and mathematical techniques used nonpresenters are expected to a write a one page critique and b form two critical questions prepare for a roundtable discussion on 930 GoalsThings To Think About Can you summarize the logic of the model How are the mathematics and underlying biology woven together What types of statistics are performed to analyze SOAE data What are the basic underlying assumptions present in the model Why do you think the authors chose the approaches they did What might one gain by taking different approaches towards analyzing a given model eg a dynamical systems perspective Compare and contrast the points of view expressed in the papers introductions What do the papers initial paragraphs reveal about the authors modeling approach Make a list of arguments statements conclusions equations etc that you do not understand or think are incorrect or unjustified Do you get the sense that the authors understand their model How well is that understanding conveyed Are theory and experiment compared on the same graph On the same scales Are there reasons why or why not gt Provide a chance for you to collect and analyze your own SOAE data 1 Zurek JASA 1980 Initial empirical observation on SOAEs 1 Week 2 2 Bialek amp Wit Phys Rev 1984 Early SOAE model likening to a quantumlimited oscillation 1 916 3 van Dijk amp Wit JASA 1990 Linearnonlinear noisedriven oscillator 2 4 Talmadge et al JASA 1991 Selfsustained oscillators variations 2 Week 3 923 5 Shera JASA 2003 Cochlear global standing waves 2 6 Vilfan amp Duke Biophys J 2008 Series of coupled oscillators forthe lizard ear 2 LEVEL dB SPL HUMAN THRHOLD OF AUDIBILITY FOR PURE TUNES Stevens 1998 Frequency Hz
Are you sure you want to buy this material for
You're already Subscribed!
Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'