Inverted direction of wave propagation (IDWP) in the cochlea

The "classical" view on wave propagation is that propagating waves are possible in both directions along the length of the basilar membrane and that they have identical properties. Results of several recently executed experiments [T. Ren, Nat. Neurosci. 2, 333-334 (2004) and W. X. He, A. L. Nuttall, and T. Ren, Hear. Res., 228, 112-122 (2007)] appear to contradict this view. In the current work measurements were made of the velocity of the guinea-pig basilar membrane (BM). Distortion products (DPs) were produced by presenting two primary tones, with frequencies below the characteristic frequency f(0) of the BM location at which the BM measurements were made, with a constant frequency ratio. In each experiment the phase of the principal DP, with frequency 2f(1)-f(2), was recorded as a function of the DP frequency. The results indicate that the DP wave going from the two-tone interaction region toward the stapes is not everywhere traveling in the reverse direction, but also in the forward direction. The extent of the region in which the forward wave occurs appears larger than is accounted for by classical theory. This property has been termed "inverted direction of wave propagation." The results of this study confirm the wave propagation findings of other authors. The experimental data are compared to theoretical predictions for a classical three-dimensional model of the cochlea that is based on noise-response data of the same animal. Possible physical mechanisms underlying the findings are discussed.     

Transmission of cochlear distortion products as slow waves: a comparison of experimental and model data

There is a long-lasting question of how distortion products (DPs) arising from nonlinear amplification processes in the cochlea are transmitted from their generation sites to the stapes. Two hypotheses have been proposed: (1) the slow-wave hypothesis whereby transmission is via the transverse pressure difference across the cochlear partition and (2) the fast-wave hypothesis proposing transmission via longitudinal compression waves. Ren with co-workers have addressed this topic experimentally by measuring the spatial vibration pattern of the basilar membrane (BM) in response to two tones of frequency f(1) and f(2). They interpreted the observed negative phase slopes of the stationary BM vibrations at the cubic distortion frequency f(DP) = 2f(1) - f(2) as evidence for the fast-wave hypothesis. Here, using a physically based model, it is shown that their phase data is actually in accordance with the slow-wave hypothesis. The analysis is based on a frequency-domain formulation of the two-dimensional motion equation of a nonlinear hydrodynamic cochlea model. Application of the analysis to their experimental data suggests that the measurement sites of negative phase slope were located at or apical to the DP generation sites. Therefore, current experimental and theoretical evidence supports the slow-wave hypothesis. Nevertheless, the analysis does not allow rejection of the fast-wave hypothesis.     

Wave and place fixed DPOAE maps of the human ear

Human intermodulation distortion product otoacoustic emissions (DPOAE) can be a mixture of low and high latency components. They have different level, phase, and suppression characteristics, which indicate that emissions arise both from the frequency region of the primary tones directly and indirectly via the DP frequency place. Which component dominates the measured DPOAE in the ear canal depends on the stimulus parameters, especially the frequency ratio, f2/f1. Interference between the two emissions adds complexity to measurements of DPOAE. The behavior and even existence of whichever emission route is lower in level often cannot directly be deduced from the raw DPOAE data because the other emission covers it. It is therefore not known whether both emissions are present for all stimulus parameters or whether the trends seen in each emission when they are the dominant emission route continue under stimulus conditions when they are not dominant. In this study, the two DPOAE components are separated by a post-processing method. Previously, maps of raw DPOAE data against f2/f1 and DP frequency have been obtained. To separate the components, sets of data consisting of f2/f1 sweeps were transformed by an inverse Fourier transform into the time domain. The low and high latency components appeared as two distinct peaks because of their different phase gradients. These peaks were separated by windowing in the time domain and two frequency domain maps were reconstructed, representing the low and high latency DPOAEs. It was found that the low latency component of the 2 f1-f2 DP was only emitted strongly with f2/f1 between approximately 1.1 and 1.3. The removal of the high latency component revealed the low ratio edge of this region, at which the level falls sharply. However, the low latency emission has been traced at reduced amplitude over a wide range of stimulus parameters. Although previously only observed at small frequency ratios, the high latency component was found to be present widely in the lower sideband, its level reducing slowly at larger f2/f1. Its phase behavior changes in the lower sideband, being approximately constant with DP frequency at small ratios of f2/f1, but deviating from this at wider ratios. These results support the hypothesis that a DPOAE component which propagates to and is re-emitted from the DP frequency place (place fixed emission) is present across a wide parameter range. However, for all but the close primary condition the lower sideband DPOAE is dominated by direct emission from the region of f2 and f1 wave interaction (wave fixed emission). A simple transmission line model is presented to illustrate how the observed DPOAE maps can arise on the basis of this hypothesis.     

Mechanisms of generation of the 2f2-f1 distortion product otoacoustic emission in humans

The 2f1-f2 distortion product otoacoustic emission (DPOAE) is considered to consist of two components in normally hearing ears, one having constant phase with changing DP frequency (wave fixed) and one having an increasing phase lag with increasing frequency (place fixed). The aim was to identify the wave-fixed and place-fixed components of both 2f1-f2 and 2f2-f1 DPs, and, in particular, to show whether a wave-fixed 2f2-f1 DP exists in normally hearing adults. DPOAE recordings were made in 20 ears of normally hearing young adults. Four frequency ratios were used and recording entailed fixed frequency-ratio sweeps. A separation into wave-fixed and place-fixed components was carried out using a time-window separation method. A method for estimating the noise floor after data processing was developed. Results confirmed the presence of wave-fixed and place-fixed components for 2f1-f2, consistent with previous studies. Both components were also present for 2f2-f1 in virtually all subjects. This latter finding conflicts with current models of DPOAE generation, and so a modified model is proposed. Unlike the 2f1-f2 emission, which has a wave-fixed component that is strongly dependent on the frequency ratio, neither component of the 2f2-f1 emission showed such a dependence. The proposed model explains these findings in terms of the overlap of the primary frequency traveling waves.     

Modeling the temporal behavior of distortion product otoacoustic emissions

The temporal behavior of the 2f1-f2 distortion product otoacoustic emission is theoretically investigated for the case in which the lower frequency (f1) primary tone is on continuously, and the higher frequency (f2) one is pulsed on and off [e.g., Talmadge et al., J. Acoust. Soc. Am. 105, 275-292 (1999)]. On physical grounds, this behavior is expected to be characterized by various group delays associated with the propagation of (1) the f2 cochlear primary wave between the cochlear base and the primary distortion product generation region around x2 (the f2 tonotopic place), and (2) the 2f1-f2 cochlear distortion product (DP) waves between the cochlear base, the primary generation region of the distortion product, and the region around the 2f1-f2 tonotopic place where the generated apical moving DP wave is reflected toward the cochlear base [e.g., Talmadge et al., J. Acoust. Soc. Am. 104, 1517-1543 (1998)]. An approximate analytic expression is obtained for this behavior from the analysis of the Fourier integral representation of the auditory peripheral response to the primary stimuli. This expression also approximately describes the transient build-up of the components of different latencies in terms of the damping properties of the cochlear partition. It is shown that considerable caution must be applied in attempting to relate phase derivatives of the distortion product otoacoustic emissions for steady state stimuli and the physical time delays which are associated with the temporal behavior of a distortion product emission in the case of a pulsed primary.     

Evidence for the distortion product frequency place as a source of distortion product otoacoustic emission (DPOAE) fine structure in humans. I. Fine structure and higher-order DPOAE as a function of the frequency ratio f2/f1

Critical experiments were performed in order to validate the two-source hypothesis of distortion product otoacoustic emissions (DPOAE) generation. Measurements of the spectral fine structure of DPOAE in response to stimulation with two sinusoids have been performed with normal-hearing subjects. The dependence of fine-structure patterns on the frequency ratio f2/f1 was investigated by changing f1 or f2 only (fixed f2 or fixed f1 paradigm, respectively), and by changing both primaries at a fixed ratio and looking at different order DPOAE. When f2/f1 is varied in the fixed ratio paradigm, the patterns of 2 f1-f2 fine structure vary considerably more if plotted as a function of f2 than as a function of fDP. Different order distortion products located at the same characteristic place on the basilar membrane (BM) show similar patterns for both, the fixed-f2 and fDP paradigms. Fluctuations in DPOAE level up to 20 dB can be observed. In contrast, the results from a fixed-fDP paradigm do not show any fine structure but only an overall dependence of DP level on the frequency ratio, with a maximum for 2f1-f2 at f2/f1 close to 1.2. Similar stimulus configurations used in the experiments have also been used for computer simulations of DPOAE in a nonlinear and active model of the cochlea. Experimental results and model simulations give strong evidence for a two-source model of DPOAE generation: The first source is the initial nonlinear interaction of the primaries close to the f2 place. The second source is caused by coherent reflection from a re-emission site at the characteristic place of the distortion product frequency. The spectral fine structure of DPOAE observed in the ear canal reflects the interaction of both these sources.     

Laser interferometry measurements of middle ear fluid and pressure effects on sound transmission

An otitis media with effusion model in human temporal bones with two laser vibrometers was created in this study. By measuring the displacement of the stapes from the medial side of the footplate, the transfer function of the middle ear, which is defined as the displacement transmission ratio (DTR) of the tympanic membrane to footplate, was derived under different middle ear pressure and fluid in the cavity with a correction factor for cochlear load. The results suggest that the DTR increases with increasing frequency up to 4k Hz when the middle ear pressure was changing from 0 to 20 or -20 cm H20 (e.g., +/-196 daPa) and fluid level was increasing from 0 to a full middle ear cavity. The positive and negative pressures show different effects on the DTR. The effect of fluid on DTR varies between three frequency ranges: f < 1k, between 1k and 4k, and f > 4k Hz. These findings show how the efficiency of the middle ear system for sound transmission changes during the presence of fluid in the cavity and variations of middle ear pressure.     

Experimental study of the Doppler shift generated by a vibrating scatterer

We report an experimental study of the backscattering of a sound wave of frequency f by a surface vibrating harmonically at frequency F (F < f) and amplitude A in the regime where the Doppler effect overcomes bulk nonlinear effects. When the duration to of the analyzed time series of the scattered wave is small compared to the vibration period, the power spectrum of the backscattered wave is proportional to the probability density function of the scatterer velocity, which presents two peaks shifted from f by roughly 2fAomega/c (omega = 2piF). On the contrary, when t0 > F(-1), sidebands at frequencies f +/- nF (n integer) appear in the power spectrum, which are due to the phase modulation of the backscattered wave induced by its reflection on a moving boundary. We use the backscattered power spectrum to validate the phase modulation theory of the Doppler effect in the latter case for 2kA < 1 and 2kA approximately > 1 (k = 2pif/c, where c is the wave velocity) and we test the validity of an acoustic nonintrusive estimator of A as a function of power spectrum bandwidth and of A itself.     

Breaking away: violation of distortion emission phase-frequency invariance at low frequencies

The phase versus frequency function of the distortion product otoacoustic emission (DPOAE) at 2f(1) - f(2) is approximately invariant at frequencies above 1.5 kHz in human subjects when recorded with a constant f(2)/f(1). However, a secular break from this invariance has been observed at lower frequencies where the phase-gradient becomes markedly steeper. Apical DPOAEs, such as 2f(1)?- f(2), are known to contain contributions from multiple sources. This experiment asked whether the phase behavior of the ear canal DPOAE at low frequencies is driven by the phase of the component from the distortion product (DP) region at 2f(1)?- f(2), which exhibits rapid phase accumulation. Placing a suppressor tone close in the frequency to 2f(1)?- f(2) reduced the contribution of this component to the ear canal DPOAE in normal-hearing adult human ears. When the contribution of this component was reduced, the phase behavior of the ear canal DPOAE was not altered, suggesting that the breaking from DPOAE phase invariance at low frequencies is an outcome of apical-basal differences in cochlear mechanics. The deviation from DPOAE phase invariance appears to be a manifestation of the breaking from approximate scaling symmetry in the human cochlear apex.     

Evidence for the distortion product frequency place as a source of distortion product otoacoustic emission (DPOAE) fine structure in humans. II. Fine structure for different shapes of cochlear hearing loss

Distortion product otoacoustic emissions (DPOAE) were recorded from eight human subjects with mild to moderate cochlear hearing loss, using a frequency spacing of 48 primary pairs per octave and at a level L1 = L2 = 60 dBSPL and with a fixed ratio f2/f1. Subjects with different shapes of hearing thresholds were selected. They included subjects with near-normal hearing within only a limited frequency range, subjects with a notch in the audiogram, and subjects with a mild to moderate high-frequency loss. If the primaries were located in a region of normal or near-normal hearing, but DP frequencies were located in a region of raised thresholds, the distortion product 2 f1-f2 was still observable, but the DP fine structure disappeared. If the DP frequencies fell into a region of normal thresholds, fine structure was preserved as long as DPOAE were generated, even in cases of mild hearing loss in the region of the primaries. These experimental results give further strong evidence that, in addition to the initial source in the primary region, there is a second source at the characteristic place of fDP. Simulations in a nonlinear and active computer model for DPOAE generation indicate different generation mechanisms for the two components. The disappearance of DPOAE fine structure might serve as a more sensitive indicator of hearing impairment than the consideration of DP level alone.     

Approximate expressions for viscous attenuation in marine sediments: relating Biot's "critical" and "peak" frequencies

Simple approximate relations are proposed for the viscous attenuation per cycle of the fast compressional and shear waves in the low-to-intermediate frequency range. Corresponding closed-form formulas are derived for frequencies at which maximum viscous attenuation per cycle occurs according to the Biot-Stoll theory of elastic wave propagation in marine sediments. In the new formulas, Biot's approximation [M. A. Biot, J. Acoust. Soc. Am. 34, 1254-1264 (1962)] for the frequency-dependent viscosity correction factor F(f) and the assumption of relatively low specific loss (Q(-1)<(0.2) [J. Geertsma and D. C. Smith, Geophysics 26(2), 169-181 (1962)] are used to provide an accurate representation of the fast compressional and shear wave attenuation from low frequencies through a transition region extending to two or three times Biot's critical frequency f(c). The approximate viscodynamic behavior of marine sediments for the fast compressional and shear waves shows similarities to that of a "homogeneous relaxation" process for an anelastic linear element [A. M. Freudenthal and H. Geiringer, Encyclopedia of Physics (Springer-Verlag. 1958), Vol. 6].     

Supporting evidence for reverse cochlear traveling waves

As a result of the cochlea's nonlinear mechanics, stimulation by two tones results in the generation of distortion products (DPs) at frequencies flanking the primary tones. DPs are measurable in the ear canal as oto-acoustic emissions, and are used to noninvasively explore cochlear mechanics and diagnose hearing loss. Theories of DP emissions generally include both forward and reverse cochlear traveling waves. However, a recent experiment failed to detect the reverse-traveling wave and concluded that the dominant emission path was directly through the fluid as a compression pressure [Ren, 2004, Nat. Neurosc.7, 333-334]. To explore this further, we measured intracochlear DPs simultaneously with emissions over a wide frequency range, both close to and remote from the basilar membrane. Our results support the existence of the reverse-traveling wave: (1) They show spatial variation in DPs that is at odds with a compression pressure. (2) Although they confirm a forward-traveling character of intraocochlear DPs in a broad frequency region of the best frequency, this behavior does not refute the existence of reverse-traveling waves. (3) Finally, the results show that, in cases in which it can be expected, the DP emission is delayed relative to the DP in a way that supports reverse-traveling-wave theory.     

Sources of DPOAEs revealed by suppression experiments,inverse fast Fourier transforms,and SFOAEs in impaired ears

DPOAE sources are modeled by intermodulation distortion generated near the f2 place and a reflection of this distortion near the DP place. In a previous paper, inverse fast Fourier transforms (IFFTs) of DPOAE filter functions in normal ears were consistent with this model [Konrad-Martin et al., J. Acoust. Soc. Am. 109, 2862-2879 (2001)]. In the present article, similar measurements were made in ears with specific hearing-loss configurations. It was hypothesized that hearing loss at f2 or DP frequencies would influence the relative contributions to the DPOAE from the corresponding basilar membrane places, and would affect the relative magnitudes of SFOAEs at frequencies equal to f2 and fDP. DPOAEs were measured with f2 = 4 kHz, f1 varied, and a suppressor near fDP. L2 was 25-55 dB SPL (L1 = L2 + 10 dB). SFOAEs were measured at f2 and at 2.7 kHz (the average fDP produced by the f1 sweep) for stimulus levels of 20-60 dB SPL. SFOAE results supported predictions of the pattern of amplitude differences between SFOAEs at 4 and 2.7 kHz for sloping losses, but did not support predictions for the rising- and flat-loss categories. Unsuppressed IFFTs for rising losses typically had one peak. IFFTs for flat or sloping losses typically have two or more peaks; later peaks were more prominent in ears with sloping losses compared to normal ears. Specific predictions were unambiguously supported by the results for only four of ten cases, and were generally supported in two additional cases. Therefore, the relative contributions of the two DPOAE sources often were abnormal in impaired ears, but not always in the predicted manner.     

Multiple internal reflections in the cochlea and their effect on DPOAE fine structure

In recent years, evidence has accumulated in support of a two-source model of distortion product otoacoustic emissions (DPOAEs). According to such models DPOAEs recorded in the ear canal are associated with two separate sources of cochlear origin. It is the interference between the contributions from the two sources that gives rise to the DPOAE fine structure (a pseudoperiodic change in DPOAE level or group delay with frequency). Multiple internal reflections between the base of the cochlea (oval window) and the DP tonotopic place can add additional significant components for certain stimulus conditions and thus modify the DPOAE fine structure. DPOAEs, at frequency increments between 4 and 8 Hz, were recorded at fixed f2/f1 ratios of 1.053, 1.065, 1.08, 1.11, 1.14, 1.18, 1.22, 1.26, 1.30, 1.32, 1.34, and 1.36 from four subjects. The resulting patterns of DPOAE amplitude and group delay (the negative of the slope of phase) revealed several previously unreported patterns in addition to the commonly reported log sine variation with frequency. These observed "exotic" patterns are predicted in computational simulations when multiple internal reflections are included. An inverse FFT algorithm was used to convert DPOAE data from the frequency to the "time" domain. Comparison of data in the time and frequency domains confirmed the occurrence of these "exotic" patterns in conjunction with the presence of multiple internal reflections. Multiple internal reflections were observed more commonly for high primary ratios (f2/f1 > or = 1.3). These results indicate that a full interpretation of the DPOAE level and phase (group delay) must include not only the two generation sources, but also multiple internal reflections.     

Sources of distortion product otoacoustic emissions revealed by suppression experiments and inverse fast Fourier transforms in normal ears.

Primary and secondary sources combine to produce the 2f1-f2 distortion product otoacoustic emission (DPOAE) measured in the ear canals of humans. DPOAEs were obtained in nine normal-hearing subjects using a fixed-f2 paradigm in which f1 was varied. The f2 was 2 or 4 kHz, and absolute and relative primary levels were varied. Data were obtained with and without a third tone (f3) placed 15.6 Hz below 2f1-f2. The level of f3 was varied in order to suppress the stimulus frequency otoacoustic emission (SFOAE) coming from the 2f1-f2 place. These data were converted from the complex frequency domain into an equivalent time representation using an inverse fast Fourier transform (IFFT). IFFTs of unsuppressed DPOAE data were characterized by two or more peaks. Relative amplitudes of these peaks depended on overall primary level and on primary-level differences. The suppressor eliminated later peaks, but early peaks remained relatively unaltered. Results are interpreted to mean that the DPOAE measured in humans includes components from the f2 place (intermodulation distortion) and DP place (in the form of a SFOAE). These findings build on previous work by providing evidence that multiple peaks in the IFFT are due to a secondary source at the DP place.     

双层非线性耦合反应扩散系统中复杂Turing斑图

采用双层耦合的Brusselator模型, 研究了两个子系统非线性耦合时Turing 模对斑图的影响, 发现两子系统Turing 模的波数比和耦合系数的大小对斑图的形成起着重要作用. 模拟结果表明: 斑图类型随波数比值的增加, 从简单斑图发展到复杂斑图; 非线性耦合项系数在0–0.1时, 系统1中短波模在系统2失稳模的影响下不仅可形成简单六边形、四边形和条纹斑图, 两模共振耦合还可以形成蜂窝六边形、超六边形和复杂的黑眼斑图等超点阵图形, 首次在一定范围内调整控制参量观察到由简单正四边形向超六边形斑图的转化过程; 耦合系数在0.1–1时, 系统1中短波模与系统2失稳模未发生共振耦合仅观察到与系统2相同形状的简单六边形、四边形和条纹斑图. 关键词： Brusselator模型 非线性耦合 Turing模     

Distortion product otoacoustic emission test performance when both 2f1-f2 and 2f2-f1 are used to predict auditory status

The objective of this study was to determine whether distortion product otoacoustic emission (DPOAE) test performance, defined as its ability to distinguish normal-hearing ears from those with hearing loss, can be improved by examining response and noise amplitudes at 2 f1-f2 and 2f2-f1 simultaneously. In addition, there was interest in knowing whether measurements at both DPs and for several primary frequency pairs can be used in a multivariate analysis to further optimize test performance. DPOAE and noise amplitudes were measured at 2f1-f2 and 2 f2-f1 for 12 primary levels (L2 from 10 to 65 dB SPL in 5-dB steps) and 9 pairs of primary frequencies (0.5 to 8 kHz in 1/2-octave steps). All data were collected in a sound-treated room from 70 subjects with normal hearing and 80 subjects with hearing loss. Subjects had normal middle-ear function at the time of the DPOAE test, based on standard tympanometric measurements. Measurement-based stopping rules were used such that the test terminated when the noise floor around the 2 f1-f2 DP was < or = -30 dB SPL or after 32 s of artifact-free averaging, whichever occurred first. Data were analyzed using clinical decision theory in which relative operating characteristics (ROC) curves were constructed and areas under the ROC curves were estimated. In addition, test performance was assessed by selecting the criterion value that resulted in a sensitivity of 90% and determining the specificity at that criterion value. Data were analyzed using traditional univariate comparisons, in which predictions about auditory status were based only on data obtained when f2 = audiometric frequency. In addition, multivariate analysis techniques were used to determine whether test performance can be optimized by using many variables to predict auditory status. As expected, DPOAEs were larger for 2f1-f2 compared to 2 f2-f1 in subjects with normal hearing. However, noise amplitudes were smaller for 2f2-f1, but this effect was restricted to the lowest f2 frequencies. A comparison of signal-to-noise ratios (SNR) within normal-hearing ears showed that the 2f1-f2 DP was more frequently characterized by larger SNRs compared to 2f2-f1. However, there were several subjects in whom 2f2-f1 produced a larger SNR. ROC curve areas and specificities for a fixed sensitivity increased only slightly when data from both DPs were used to predict auditory status. Multivariate analyses, in which the inputs included both DPs for several primary frequency pairs surrounding each audiometric frequency, produced the highest areas and specificities. Thus, DPOAE test performance was improved slightly by examining data at two DP frequencies simultaneously. This improvement was achieved at no additional cost in terms of test time. When measurements at both DPs were combined with data obtained for several primary frequency pairs and then analyzed in a multivariate context, the best test performance was achieved. Excellent test performance (ROC) curve areas >0.95% and specificities >92% at all frequencies, including 500 Hz, were achieved for these conditions. Although the results described should be validated on an independent set of data, they suggest that the accuracy with which DPOAE measurements identify auditory status can be improved with multivariate analyses and measurements at multiple DPs.     

Gerbil middle-ear sound transmission from 100 Hz to 60 kHz

Middle-ear sound transmission was evaluated as the middle-ear transfer admittance H(MY) (the ratio of stapes velocity to ear-canal sound pressure near the umbo) in gerbils during closed-field sound stimulation at frequencies from 0.1 to 60 kHz, a range that spans the gerbil's audiometric range. Similar measurements were performed in two laboratories. The H(MY) magnitude (a) increased with frequency below 1 kHz, (b) remained approximately constant with frequency from 5 to 35 kHz, and (c) decreased substantially from 35 to 50 kHz. The H(MY) phase increased linearly with frequency from 5 to 35 kHz, consistent with a 20-29 micros delay, and flattened at higher frequencies. Measurements from different directions showed that stapes motion is predominantly pistonlike except in a narrow frequency band around 10 kHz. Cochlear input impedance was estimated from H(MY) and previously-measured cochlear sound pressure. Results do not support the idea that the middle ear is a lossless matched transmission line. Results support the ideas that (1) middle-ear transmission is consistent with a mechanical transmission line or multiresonant network between 5 and 35 kHz and decreases at higher frequencies, (2) stapes motion is pistonlike over most of the gerbil auditory range, and (3) middle-ear transmission properties are a determinant of the audiogram.     

The "inverse problem" solved for a three-dimensional model of the cochlea. III. Brushing-up the solution method.

In two earlier papers [de Boer, J. Acoust. Soc. Am. 98, 896-903 and 904-910 (1995)] the inherent problems of the inverse-solution method in cochlear mechanics were described. The present paper shows results obtained with a more universal solution method. With the new method it is possible to construct a three-dimensional model of the cochlea producing a response that accurately simulates a measured mechanical basilar-membrane response. With earlier methods this could not be done. The inverse solution invariably yields that, with low stimulus levels, the model simulating a viable cochlea must be locally active. For the response of a dead animal a passive model is sufficient. Once more the inherent intricacies and problems of the inverse-solution method are discussed. Conservation of fluid volume leads to the concept of the "virtual stapes velocity." For best results, the input signal to the inverse-solution procedure should be acquired in the form of a "composite cross-correlation spectrum." Inverse analysis can, under certain circumstances, produce aberrant results. In this paper it is shown why the resulting impedance function is the most accurate in the region of the response peak. Therefore, it is unlikely that a passive model would exist of which the response simulates the data obtained from a healthy animal.