ARO, FEB Nonlinear canal impedance Abstract It has been known for some time that the ear canal impedance is nonlinear at low levels. This was r

Transcription

1 ARO, FEB Nonlinear canal impedance Characterization of the nonlinear ear canal impedance at low sound levels Jont B. Allen Acoustics Research Dept. AT&T Bell Labs, Murray Hill, NJ and Greg Shaw and Barry P. Kimberley Department of Ear, Noise, and Throat University of Calgary, Alberta CA ORAL PRESENTATION 757 February 28, 1997

2 ARO, FEB Nonlinear canal impedance Abstract It has been known for some time that the ear canal impedance is nonlinear at low levels. This was rst shown by Kemp (Kemp 1978) who demonstrated nonlinear reectance to low level acoustic clicks in the ear canal. When Kemp reviewed these nonlinear eects (Kemp 1979; Kemp 198), he speculated that it is active (i.e., more energy coming out of the cochlea than going in). We have measured this power ratio and have found that the power transfer function of the eardrum is less than one. This has been shown by measuring the real part of the canal impedance at low levels where the nonlinearity is well developed. An alternative, but equivalent measure, is the power reectance (Voss and Allen 1994), which we nd is always less than 1, even near spontaneous emissions. In this talk we compare the measured cochlear power ow to the hearing thresholds and the spontaneous emissions, as a function of frequency. We have also measured the DPOAE in some ears. We have found that near an SOAE frequency the hearing thresholds improve and the power reectance decreases. We show that there is a strong correlation between all of these measures, and that all three measures are related to the nonlinear properties of the cochlea. No instance of a power reectance greater than 1 has yet been found. We conclude that there is no evidence, based on ear canal impedance measurements, for a cochlear amplier.

3 ARO, FEB Nonlinear canal impedance GOALS Measure the nonlinear power ow in the ear canal to determine if the cochlea is active. { Can we distinguish a low{loss cochlea from an active cochlea? Characterize the OAEs after removing the eects of the source transducers. { Determine if the OAE standing waves are caused by reections from the ear canal transducer system. Establish relations between SOAEs, SFOAEs, and HLs.

4 ARO, FEB Nonlinear canal impedance Denitions: NONLINEAR SYSTEM: a system whose output does not scale with the input level or which generates distortion. LINEAR SYSTEM: a system that is not nonlinear. ACTIVE SYSTEM: a system having power amplication (i.e., more power coming out than going in). PASSIVE SYSTEM: a system that is not active. ACOUSTIC IMPEDANCE Z(!): pressure/volume velocity. OTOACOUSTIC EMISSIONS (OAE): retrograde ear canal signals (signals coming from the cochlea). REFLECTANCE R(!): the transfer function between retrograde (OAE) pressure (or velocity) response and the incident pressure (or velocity). POWER REFLECTANCE R(!): square{magnitude of the re- ectance (R = jrj 2 ). TEOAE: Transient{evoked OAE with click input. SFOAE: Stimulus{frequency OAE with single{tone input. DPOAE: Distortion product OAE with two{tone input. SOAE: Spontaneous OAE with a thermal stimulus but no signal input.

5 ARO, FEB Nonlinear canal impedance THE EXPERIMENT Measure the ear canal acoustic impedance. { This removes the eects of the source transducer. Measure SOAEs Measure hearing thresholds (HL) in 6 Hz steps Measure DPOAEs

6 ARO, FEB Nonlinear canal impedance Acoustic Impedance RETAINER SLEEVE Lr RED RESISTORS ER-1C FOAM PLUG Lw WHITE L4 C4 L1 C1 TO PREAMP CAVITIES L2 C2 L3 C3 This gure shows the experimental setup for measurement of ear canal acoustic impedance (Voss and Allen 1994). The source transducer is calibrated using 4 cavities and 2 acoustic resistors, resulting in the open circuit pressure P s (!) and source impedance Z s (!). The transducer is then placed in the subjects ear. The ear canal pressure P ec (!) then gives Z ec Z ec = Z s P ec =(P s? P ec ):

7 ARO, FEB Nonlinear canal impedance Acoustic reectance R(!) From the canal impedance Z(!), and the canal characteristic impedance z = c=a, we may calculate the reectance R(!) R(!) P? P + = Z=z? 1 Z=z + 1 The reectance allows us to separate P +, the linear incident component, and P?, the delayed linear and nonlinear retrograde (OAE) components Reflectance Frequency (Hz) Wide band linear reectance magnitude jr(!)j for subject 3 measured at high levels using a chirp. Between 1.5 and 3.5 khz, 25% of the power is returned by the middle ear{cochlea interface.

8 ARO, FEB Nonlinear canal impedance Example Take the case of a lossless tube with a hard endcap. The normalized impedance is Z=z = cot(!t =2): If we compute R(!) we nd that the resulting OAE is a pure delay of T seconds, R(!) Z=z? 1 Z=z + 1 cot(!t =2)? 1 = cot(!t =2) + 1 = e?i!t : The inverse Fourier transform of R(!) is r(t) = (t? T ): Thus a very simple OAE having a pure delay leads to pressure and velocity standing waves (i.e., cot(!t =2)).

9 ARO, FEB Nonlinear canal impedance Evoked OAE properties The driven OAEs (TEOAE, SFOAE, DPOAE) are completely and properly characterized by the (time domain) nonlinear ear drum reectance (or impedance). By use of the reectance, we may separate interactions between the cochlea and the complex linear properties of the measurement transducers. The eardrum impedance, reectance, and the hearing thresholds, all have a quasiperiodic 8 Hz structure over frequency (Elliot 1958; Zwicker and Schloth 1984; Shera and Zweig 1993; He and Schmiedt 1993). { The 8 Hz periodic structure appears to be due to a nonlinear cochlear standing wave within the cochlea having a 12.5 ms round trip delay (Kemp 1979; Kemp 198). 2 Normalized Resistance Frequency (Hz) Normalized Reactance Frequency (Hz)

10 ARO, FEB Nonlinear canal impedance SOAE properties 1 Spontaneous Emission 5 Pressure (db re 2e-6 Pa) Frequency (Hz) SOAE for subject 3. The basic periodic structure is approximately 8 Hz, but as is typical, many lines are missing, as may be seen in the region between 1 and 1.5 khz. Do these emissions represent an a) active system in free oscillation, or are they b) standing waves in a (very) low{loss cochlea, driven by cilia Brownian (thermal) motion?

11 ARO, FEB Nonlinear canal impedance Comparison of SFOAEs and SOAEs Normalized Pressure Frequency (Hz) Reflectance Pressure (db re 2e-6 Pa) Frequency (Hz) Spontaneous Emission Frequency (Hz) a) The normalized microphone pressure ratio P (f; SP L) P (f; 5) V in(5) V in (SP L) was measured with a pure tone stepped in frequency. The input voltage level V in (SP L) was dropped by 1 db for each sweep giving a nominal stimulus level of 4, 3, 2, and 1 db SPL. b) The reectance magnitude at 5, 4, 3, 2, and 1 db SPL. c) The SOAE. The transducer was not removed from the ear for the various measures. All measures are for subject 3.

12 ARO, FEB Nonlinear canal impedance Conclusions: The cochlea is nonlinear starting at 5 and down to the lowest levels we measured, at 1 db SPL Based on ear canal measurements, there is no indication that the cochlea is active, since jrj < 1. The period of the SOAEs is identical (or at least close) to that of the evoked SFOAEs The SOAE frequency occurs at (or close to) where jrj is minimum. The pressure standing wave ratio (SWR) depends on level SWR(P ec ) < 1 + max f(jr(f; P ec )j) 1? max f (jr(f; P ec )j) The SWR is a measure of the Q(R 1 R 2 ) which is determined by the product of the two reection coecients at the boundaries. Since the SWR is increasing with decreasing P ec, we need to look at lower levels to nd where R(P ec ) becomes linear.

13 ARO, FEB Nonlinear canal impedance Relation between SOAE and HL The frequency where the hearing level is best is close to an emission frequency (Subject BO at 23 Hz). Pressure (db re 2e-6 Pa) Spontaneous Emission Frequency (Hz) Hearing Thresholds 2 HT (db SPL) Frequency (Hz) Hearing levels measured every 6 Hz between 225 and 235 Hz. Dierent transducers were used for the HL and SOAE measurements, and the 6 Hz dierence between the SOAE and the minimum in HL could be due to this dierence. HL varies by a factor of 4.5.

14 ARO, FEB Nonlinear canal impedance GOAL I: IS THE COCHLEA ACTIVE? Kemp (1978) hypothesized that more power was coming out than going in (jr(!)j > 1) based on the presence of SOAEs. Kemp (1978) concluded that the cochlea must be \active" based on SOAEs. SOAEs are commonly given as a justication for the active cochlea hypothesis. Conclusions: { Based on ear canal power ow measurements, there is no indication that the cochlea is active. { We have never seen jr(!)j > 1. { SOAEs occur at frequencies where jr(!)j is minimum (not maximum).

15 ARO, FEB Nonlinear canal impedance GOAL II: Reectance level dependence The reectance has a low level nonlinear component R(f; P ) = Z(SP L)? Z(5) Z(SP L) + Z(5).15 2,3,4 db SPL Mean Delay (ms) Frequency (khz).15 R 1 angle(r) R.1.5 angle(r) Frequency (khz) Frequency (khz) If the cochlea was connected to an impedance equal to its 5 db SPL value, and the reectance were measured as a function of level, we would see a level dependent reection having 12.5 ms of delay.

16 ARO, FEB Nonlinear canal impedance A Model of OAEs Rec(f) Z c MIDDLE EAR CANAL mode 1: Tme Rst(f) COCHLEA mode 2: Tc(x,f) NONLINEAR REEMISSION Rc(x,f,Pec) Z t mode 3: Tme + Tc(x,f) Two delays, 1) between the ear canal and stapes T me (!) and, 2) within the cochlea T c (x;!), where x is the frequency dependent emission \place". Three reection sites: 1) in the ear canal at the site of the source transducer R ec (!), 2) at the stapes{cochlear interface R st (!), 3) and at the reemission place x on the basilar membrane R c (x;!; P ec ). This latter response is assumed to dependent on ear canal pressure P ec. This model gives three possible sets of modes. Two modes are important corresponding to the 1) round trip dened by the cochlear delay T c (x;!), and the 2) round trip dened by the middle ear plus cochlear delay T me + T c. The shorter delay gives slightly higher frequency modes, with Q's determined R c R st. The longer delay gives lower frequency modes with Q's determined by R c R ec.

17 ARO, FEB Nonlinear canal impedance Relation between the transducer's reectance jr t (!)j and the SOAEs for Subject 3. 1 R for source FREQ (Hz) 1 SOAE FREQ (Hz) There seems to be a correlation between the magnitude of the source transducer reectance and the presences of SOAEs. The reectance is not close enough to 1 to account for the high Q of the SOAEs.

18 ARO, FEB Nonlinear canal impedance References Elliot, E. (1958). \A ripple eect in the audiogram," Nature 181:176. He, N.-j. and Schmiedt, R. A. (1993). \Fine structure of the 2f 1? f 2 acoustic distortion product: changes with primary level," Journal of the Acoustical Society of America 94(5):2659{2669. Kemp, D. (1978). \Stimulated acoustic emissions from within the human auditory system," Journal of the Acoustical Society of America 64:1386{1391. Kemp, D. (1979). \Evidence of mechanical nonlinearity and frequency selective wave ampli- cation in the cochlea," Archives of Oto-Rhino-Laryngology 224. Kemp, D. (198). \Towards a model for the origin of cochlear echoes," Hearing Research 2:533{548. Shera, C. and Zweig, G. (1993). \Noninvasive measurement of the cochlear traveling{wave ratio," Journal of the Acoustical Society of America 93(6):3333{3352. Voss, S. E. and Allen, J. B. (1994). \Measurement of acoustic impedance and reectance in the human ear canal," J. Acoust. Soc. Am. 95(1):372{384. Zwicker, E. and Schloth, E. (1984). \Interrelation of dierent otoacoustic emissions," Journal of the Acoustical Society of America 75:1148{1154. /doc/papers/sfoae/aro 95.tex