Seminar 5. Biophysics of the senses

Transcription

1 Seminar 5 Biophysics of the senses Vision. The eye as a compound lens. Limitations of visual acuity. Colour vision. Imperfect human vision. Correction of vision. Audition. Physics of sound waves. Parameters of the human voice. Theories of hearing. Basic measurements of ear function. Hearing defects. S5 1

2 Perception of the outside word depends on five senses 1) Sight (~70%) 2) Hearing (~15%) 3) Touch 4) Taste 5) Smell Stimuli sensory receptor Receptor is a transducer that produces electric signal (nerve pulse) from the form of energy (mechanical, thermal, light, etc.) peripheral nervous system central nervous system brain Considerations are limited to Sight Hearing S5 2

3 Vision Anatomy and physiology of the eye Eye sphere ~2.5 cm in diameter Pascal law Spherical shape intraocular pressure (IOP) S5 3

4 IOP measurement applanation tonometer Tonometer applied to the cornea the cornea is locally flattened the pressure within the eye ball is related to the force applied and the deformation of the cornea Air-puff tonometer S5 4

5 Intraocular pressure (10 20) mmhg Remark: Different thickness of the cornea may introduced an error of the IOP S5 5

6 Eye operation 1. Formation of the image of an object at the retina optical system of the eye 2. Detection of the image by the retina Retina light detector photoreceptors Two types of photoreceptors 1) cones (~6*10 6 ) 2) rods (~120*10 6 ) Remark: Cone diameter = ~µm S5 6

7 Schematic of the retina in the eye with the arrangement of rods and cones as well as other retinal cells The absorption of light by the rods and cones is a fundamental quantum-mechanical process in which one photon of light is absorbed by the pigment rhodopsin Rhodopsin consists of a chromophore (the part of the molecule responsible for its colour retinal which is a derivative of vitamin A) attached to the protein opsin (348 amino acids) The absorption of a single photon of light isomerizes (changes its molecular conformation) the chromophore a sequence of sensory transduction processes S5 7

8 The response time of the human eye critical frequency the fastest rate of light pulses a person perceives with no fluctuation in light intensity usually ~30 Hz computer monitor is typically refreshed every 1/50 s (50 Hz) or 1/100 s (100 Hz) Problem of signal transduction There are about 10 6 nerve fibres in the eye, so there are some cones as well as rods connected to the same nerve cells the brain is also involved in the image perception S5 8

9 Optical system of the eye Different shapes of lens Focusing of the light in air F focal length R1 and R2 curvatures of the first and second surfaces d thickness of the lens thin lens approximation d 0 S5 9

10 Lens immersed in a material medium index of refraction (n) dimensionless quantity R1 > 0 R2 < 0 Focal length of the lens 1 nl - n1 nl - n = 2 - F R1 R = FP focusing power 2 1 [FP] = dioptre = D = m S5 10

11 Optical system of the human eye consists of 2 lenses Formation of an image at the retina is determined by the indices of refraction (n) and geometry of each eye component A model of the eye contains only one lens standard eye model S5 11

12 Image Q = 17 mm Property of the object and image triangles O = P I Q Focal length of the lens 1 F 1 1 = + = Focusing power P Q Accommodation changing the thickness and curvature of the lens Focusing of the cornea and lens needs to be achieved far and near point vision S5 12

13 Standard eye model Object far point (FPO) P = Object near point (NP) P = 0.25 m Image Q = m 1 FFPO = + = Focusing power = 58.8 D P Q m 1 FNP = m = 62.8 D Necessary accommodation 4.0 D Accommodation is age dependent Age (y) Accommodation (D) S5 13

14 Limits of vision Visual sensitivity for proper vision image should be neither too dim nor too bright illumination The light transmission to the retina is governed by the diameter of the pupil (entrance aperture) change from the maximum (~8 mm) to minimum (~2 mm) pupil diameter corresponds to 16-fold decrease in the amount of light incident on the retina Minimum number of photons to give visual signal ~100 photons at the cornea Remark: Flash lamp emits ~10 18 photons each second S5 14

15 Photometry light-meter device to measure illumination Photometric units 1) Luminous intensity (emitted power)/(unit solid angle) candela (cd) basic SI unit 2) Luminous flux emitted energy/time lumen (lm) 3) Illumination (incident power)/(unit area) lux (lx) lm = cd*sr lx = lm/m 2 Recommended illumination levels Task or location Level (lx) Auditorium 150 Laboratory 500 Classroom 700 Office 1500 Operating table Example Sem5/1 Determination of illumination lux-meter Remark: Daylight 10 4 lx, Very dark day 10 2 lx Full moon 0.2 lx, Moonless night 10-4 lx S5 15

16 Minimal image size physical considerations physics of the light waves diffraction limit Diffraction-limited spot size lens A lens of diameter d and focal length F can focus a light beam of wavelength λ to a diameter no smaller than a diameter D D 2.44 (F/d) λ Minimal image size anatomy of the retina minimal vision angle Minimal image size ~5 µm S5 16

17 Standard eye model Object size depends on distance Image distance Q = 17 mm Image size I = ~5 µm Visual acuity = Angle = I Q O = P S5 17

18 Visual acuity determination Standard value L = 5 m or 6 m S5 18

19 Snellen chart (1862) S5 19

20 Summary of various defective vision problems Focusing problem Myopia Hyperopia Common name Nearsightedness Farsightedness Usual cause Long eyeball or cornea too curved Short eyeball or cornea not curved enough Presbyopia Old-age vision Lack of accommodation Astigmatism Astigmatism Unequal curvature of cornea S5 20

21 Corrective lenses (eyeglasses or contact lenses) Vision correction physical background Two connected lenses F1 and F2 1 F tot = 1 F F 2 FPtot = FP1 + FP2 Far-sightedness (hyperopia) Remark: Converging lens FP > 0 Diverging lens FP < 0 S5 21

22 Correction of astigmatism cylindrical lens is added to the spherical lens The cylinder may be converging (plus cylinder) or diverging (minus cylinder) S5 22

23 Vision correction eye surgery the laser procedure alters the shape of the cornea LASIK laser assisted in situ keratomileusis using a laser underneath a corneal flap (in situ) to reshape the cornea (keratomileusis) Correction for near-sightedness (myopia) more flat Correction for far-sightedness (hyperopia) more curved LASIK procedure surgeon first creates a thin hinged corneal flap using a micro-keratome the surgeon then pulls back the flap to expose the underlying corneal tissue the laser ablates (reshapes) the cornea in a unique prespecified pattern for each patient the flap is then gently repositioned onto the underlying cornea S5 23

24 Colour vision Colour is psychophysical property of light If one of the colour sets is gone a person is colour blind certain colours are confused 8% of men and 0.5% of women Color blindness test S5 24

25 Young and Helmholtz tri-chromatic theory Three independent colours red, green, blue any colour C of intensity c is a linear sum of three primaries c*c = r*r + g*g + b*b c = r + g + b total light flux is the sum of components Remark: The intensities of colours (c, r, g, b) can be measured in any standard photometric units (lm) S5 25

26 Differences in the opsin proteins in the rods and the three cones cause the different wavelength responses for photoreceptors Blue cones (S short wavelength) 4% Green cones (M middle wavelength) 32% Red cones (L long wavelength) 64% Detection of colours by the human eye Remark: Intensities are normalized in the figure cones are less sensitive than rods. S5 26

27 Physics of sound waves Sound wave propagation of particle oscillations in the medium (gas, fluid, solid) ` Wavelength λ, period T, frequency f or ν λ = ct = c f c velocity of the sound wave Human ear frequency range from ~20 Hz to ~20 khz S5 27

28 Medium characteristics ρ density c velocity of the sound wave Z acoustic impedance = ρ*c Values of ρ, c and Z for various substances Substance ρ(kg/m 3 ) c (m/s) Z (kg/s*m 2 ) Air *10 2 Water *10 6 Fat *10 6 Muscle *10 6 S5 28

29 Intensity of the sound wave energy carried by the wave per unit area per unit time [W/m 2 ] description of the sound source Sound intensity level I2 1 decibel (db) = 10* log( ) I For hearing tests the reference sound intensity I1 is the threshold of perception I1 = W/m 2 Intensity Intensity (db) (W/m 2 ) Threshold Whisper Business office Speech at 1 m Busy street Subway Sound that produces pain Jet aircraft on takeoff Example Sem5/2 Determination of sound intensity level sound level meter S5 29

30 Theories of hearing Model of the human ear S5 30

31 Outer ear External canal pipe closed at one end (eardrum) diameter = ~6 mm, length = ~(25 30) mm Eardrum thickness = ~0.1 mm, area = ~60 mm 2 External canal resonant cavity (resonator) A resonator is a device or system that exhibits resonance or resonant behavior it naturally oscillates at some frequencies, called its resonance frequencies, with greater amplitude than at others Resonators are used to either generate waves of specific frequencies or to select specific frequencies from a signal S5 31

32 1D resonant cavity (resonator) Possible pressure distribution in the tube closed at one end L length of the tube c velocity of sound in air Biggest amplitude of oscillation L = λ/4 = c/4ν ν = c/4*l General formula νn = (2n - 1)*c/4*L S5 32

33 Example Sem5/3 The stethoscope the device to listen to sounds originating inside the body auscultation Open bell accumulates sounds from the contact area skin behaves like a diaphragm resonant frequency is controlled by the diameter of the bell and the pressure with which the bell is held on the skin most effectively transmits low frequencies (heart sounds) Closed bell bell with known resonant frequency lung sound (higher frequencies than heart frequencies) S5 33

34 3D resonator vibrations in the body The body can be the source of many sounds as well as can absorb external signal in the resonant manner Pain symptoms from vibrations S5 34

35 Middle ear model transmission of vibration from the eardrum to the inner ear Hammer malleus Anvil incus Stirrup stapes S5 35

36 Acoustic impedance-matching Intensity of incident wave I0 Intensity of reflected wave IR Intensity of transmitted wave IT Transmission coefficient T = IT/I0 Reflection coefficient R = IR/I0 R + T = 1 T = 1 - R R = (Z (Z Z Z 2 2 ) ) 2 2 S5 36

37 Inner ear multi-chamber cavity Convert mechanical energy presented as a mechanical vibration at the oval window into electrical pulses (nerve firings) transmitted through the auditory nerve into brain S5 37

38 Cross-section of the cochlea Cochlea is a tapered tube ~35 mm in length 3 chambers (vestibular chamber, cochlear duct, tympanic chamber) the membrane separating the tympanic chamber and the cochlear duct is called the basilar membrane inside the cochlear duct and supported on the basilar membrane is the organ of Corti organ of Corti contains hair cells rooted on the basilar membrane which are connected to nerve fibres S5 38

39 Remark: The basilar membrane gradually changes in width, tension and visco-elastic properties each portion of the basilar membrane vibrates with maximum amplitude only ay one resonant frequency S5 39

40 Trigonometric functions are periodic functions sin(x + 2π) = sin(x) The trigonometric functions are commonly used in biophysics to describe periodic phenomena Periodic phenomenon is a function of time and is characterize by the period (T) or the frequency (f = 1/T) Trigonometric function period = 2π angle Recalculation sin(angle) = sin(2π*t/t) = sin(2π*f*t) A(t) = A0*sin(2π*f*t) = A0*sin(ω*t) ω angular (circular) frequency ω = 2π*f A0 amplitude (maximum value) S5 40

41 Time domain representation and frequency domain presentation Amplitude [a.u.] Amplitude [a.u.] y 1 =2sin(2πx) time [s] y 2 =3sin(4πx) time [s] 10 Amplirude [a.u.] Amplitude [a.u] frequency [Hz] frequncy [Hz] Amplitude [a.u.] Amplitude [a.u.] y 3 =4sin(6πx) time [s] y 4 =y 1 +y 2 +y time [s] Amplitude [a.u.] Amplitude [a.u.] frequnecy [Hz] frequency [Hz] Summation of waves A(t) = A1(t) + A2(t) + A2(t) Remark: It is important to recognize that the frequency domain gives an equivalent representation of the sine function of interest in a simplified format. The identification of the frequency components is called spectral (Fourier, harmonic) analysis. Fourier (harmonic) analysis of this pattern can be performed without previous knowledge of these individualized components and yields the frequency spectrum. The magnitude at each frequency describes the relative contribution of that frequency to the original waveform. S5 41

42 Fourier (harmonic) analysis mathematical formula Fun(t) = 1 2 A N 0 + Ansin(2π *n * f * t) n= 1 N B n = B1 + B2 + B3 + + BN n= 1 f1 = 1*f fundamental frequency (1 st harmonic) f2 = 2*f 2 nd harmonic f3 = 3*f 3 rd harmonic fn = n*f n th harmonic 20 Amplitude [a.u.] ,500 1,505 1,510 1,515 1,520 time [s] Amplitude [a.u.] "A" frequency [Hz] Harmonic analysis very useful in the interpretation of different function S5 42

43 Theories of hearing how the inner ear codes the frequency of sound Place theory basilar membrane is stimulated at different places along its length according to the frequency components in the input sound Temporal theory detailed nature of the actual waveform exciting the different places along the length of the basilar membrane is considered Place theory (G. von Bekesy) Place theory is a theory of hearing which states that our perception of sound depends on where each component frequency produces vibrations along the basilar membrane Cochlea is a critically damped mechanical system motion of the basilar membrane is in the form of a wave moving from the oval window the amplitude of vibration of the basilar membrane varies along its length position of maximum amplitude is a function of frequency basilar membrane is treated as a bank of many resonant cavities At very high frequency (~10 khz) peak amplitude near the oval window at low frequency (~100 Hz) peak amplitude near the apex S5 43

44 Basic measurements of ear function Perception of sound the sensitivity of the ear depends on frequency Threshold for young person 0 db occurs at (2 3) khz Sensitivity of the ear 1) sensitivity depends of frequency 2) the best sensitivity is in the region of 2 to 4 khz (about) 3) sensitivity changes with age S5 44

45 Basic measurement of ear function 1) Pure tone audiometry The normal hearing threshold (average of the population) at each frequency is taken to be 0 db Sounds of ~10 different frequencies (64, 128, 256, 512, 724, 1024, 1448, 2048, 2896, 4096, 5792, 8192, Hz) are used in the examination Left and right ear is examined separately 2) Recognition of speech Example Sem5/4 Hearing test S5 45

46 Hearing defects The simplest aid to cup hand behind ear Electronic device amplifies the incoming sounds for hearing losses of 40 db to 85 db In the ear S5 46