Basilar Membrane Motion Research Articles

Physical Basis of Interference Effects in Hearing

To capture faint sounds, the ear uses an active system of amplification. We and our colleagues have put forward the idea that the amplifier comprises a set of ‘self-tuned critical oscillators’: each hair cell contains a force-generating dynamical system which is maintained at the threshold of an oscillatory instability, or Hopf bifurcation. The active response to a pure tone is perfectly suited to the ear’s needs, since it provides frequency selectivity, exquisite sensitivity and wide dynamic range. However, the intrinsic nonlinearity of the mechanism causes tones of different frequency to interfere with one another in the cochlea. In order to provide a framework for understanding how the ear processes the more complex sounds of speech and music, we have examined the response of a critical Hopf oscillator to two tones. Our calculations indicate how the response to one tone is suppressed by the presence of a second tone of similar frequency. They also show how a characteristic spectrum of distortion products is generated. The results are in accord with experimental observations of basilar membrane motion. Given the complexity of the nonlinear response, how does the ear distinguish the frequency components of a sound source? We propose a simple model of pitch extraction based on the timings of neural spikes, and investigate to what extent psychophysical phenomena such as the sensation of dissonance and auditory illusions can be attributed to the physical nature of the peripheral detection apparatus.

Input-output functions for stimulus-frequency otoacoustic emissions in normal-hearing adult ears.

Input-output (I/O) functions for stimulus-frequency (SFOAE) and distortion-product (DPOAE) otoacoustic emissions were recorded in 30 normal-hearing adult ears using a nonlinear residual method. SFOAEs were recorded at half octaves from 500-8000 Hz in an L1=L2 paradigm with L2=0 to 85 dB SPL, and in a paradigm with L1 fixed and L2 varied. DPOAEs were elicited with primary levels of Kummer et al. [J. Acoust. Soc. Am. 103, 3431-3444 (1998)] at f2 frequencies of 2000 and 4000 Hz. Interpretable SFOAE responses were obtained from 1000-6000 Hz in the equal-level paradigm. SFOAE levels were larger than DPOAEs levels, signal-to-noise ratios were smaller, and I/O functions were less compressive. A two-slope model of SFOAE I/O functions predicted the low-level round-trip attenuation, the breakpoint between linearity and compression, and compressive slope. In ear but not coupler recordings, the noise at the SFOAE frequency increased with increasing level (above 60 dB SPL), whereas noise at adjacent frequencies did not. This suggests the existence of a source of signal-dependent noise producing cochlear variability, which is predicted to influence basilar-membrane motion and neural responses. A repeatable pattern of notched SFOAE I/O functions was present in some ears, and explained using a two-source mechanism of SFOAE generation.

Maturation of cochlear nonlinearity as measured by distortion product otoacoustic emission suppression growth in humans.

The growth of distortion product otoacoustic emission (DPOAE) suppression follows a systematic, frequency-dependent pattern. The pattern is consistent with direct measures of basilar-membrane response growth, psychoacoustic measures of masking growth, and measures of neural rate growth. This pattern has its basis in the recognized nonlinear properties of basilar-membrane motion and, as such, the DPOAE suppression growth paradigm can be applied to human neonates to study the maturation of cochlear nonlinearity. The objective of this experiment was to investigate the maturation of human cochlear nonlinearity and define the time course for this maturational process. Normal-hearing adults, children, term-born neonates, and premature neonates, plus a small number of children with sensorineural hearing loss, were included in this experiment. DPOAE suppression growth was measured at two f2 frequencies (1500 and 6000 Hz) and three primary tone levels (55-45, 65-55, and 75-65 dB SPL). Slope of DPOAE suppression growth, as well as an asymmetry ratio (to compare slope for suppressor tones below and above f2 frequency), were generated. Suppression threshold was also measured in all subjects. Findings indicate that both term-born neonates and premature neonates who have attained term-like age, show non-adult-like DPOAE suppression growth for low-frequency suppressor tones. These age effects are most evident at f2 = 6000 Hz. In neonates, suppression growth is shallower and suppression thresholds are elevated for suppressor tones lower in frequency than f2. Additionally, the asymmetry ratio is smaller in neonates, indicating that the typical frequency-dependent pattern of suppression growth is not present. These findings suggest that an immaturity of cochlear nonlinearity persists into the first months of postnatal life. DPOAE suppression growth examined for a small group of hearing-impaired children also showed abnormalities.

Basilar membrane and osseous spiral lamina motion in human cadavers with air and bone conduction stimuli

It is generally accepted that bone conduction (BC) stimuli yield a traveling wave on the basilar membrane (BM) and hence stimulate the cochlea by the same mechanisms as normal air conduction (AC). The basis for this is the ability to cancel or mask a BC tone with an AC tone and the ability to generate two tone distortion products with a BC tone and an AC tone. The hypothesis is proposed that BC stimulates the BM not only through the hydrodynamics of the scala vestibuli and scala tympani, but also through osseous spiral lamina (OSL) vibrations. To test this hypothesis the BM and OSL response with AC as well as BC stimulation was measured with a laser Doppler vibrometer. Human temporal bones mounted on a shaker were used to record the velocities of the bone per se, the BM and the OSL. The measurements were then converted to relative BM and OSL velocities. The results from the basal turn of the cochlea show similar behavior with AC and BC stimulation. The motion of the OSL at the edge where it connects to the BM is in phase and is typically 6 dB lower than the BM motion. With BC stimulation, there is less phase accumulation in the OSL after the cochlea is drained; the OSL moves due to inertial forces and resonates at approximately 7 kHz. Inertial vibration of the OSL may partially contribute to the total response of BC sound, especially at the high frequencies, although current models of the cochlea assume a rigid OSL. The measurements reported here can be used to include a flexible OSL in cochlear models.

Organ of Corti kinematics.

The internal workings of the organ of Corti and their relation to basilar membrane motion are examined with the aid of a simple kinematic model. It is shown that, due to the lever system embodied in the organ of Corti, there is a significant transformer gain between basilar membrane and cilia displacements. While this transformation is nonlinear, linear response prevails in the narrow physiologically relevant operating range of the ciliary transducer. The model also simulates cilia deflection when the mechanical stimulus is the length change of outer hair cells.

Microsecond temporal resolution in monaural hearing without spectral cues?

The auditory system encodes the timing of peaks in basilar-membrane motion with exquisite precision, and perceptual models of binaural processing indicate that the limit of temporal resolution in humans is as little as 10-20 microseconds. In these binaural studies, pairs of continuous sounds with microsecond differences are presented simultaneously, one sound to each ear. In this paper, a monaural masking experiment is described in which pairs of continuous sounds with microsecond time differences were combined and presented to both ears. The stimuli were matched in terms of the excitation patterns they produced, and a perceptual model of monaural processing indicates that the limit of temporal resolution in this case is similar to that in the binaural system.

Separate mechanical processes underlie fast and slow effects of medial olivocochlear efferent activity

Sound-evoked vibrations of the basilar membrane (BM) in anaesthetised guinea-pigs are shown to be affected over two distinct time scales by electrical stimulation of the medial olivocochlear efferent system: one is fast (10–100 ms), the other much slower (10–100 s). For low and moderate level tones near the BM's characteristic frequency, both fast and slow effects inhibited BM motion. However, fast inhibition was accompanied by phase leads, while slow inhibition was accompanied by phase lags. These findings are consistent with a hypothesis that both fast and slow effects decrease sound amplification in the cochlea. However, the opposing directions of the phase changes indicate that separate mechanical processes must underlie fast and slow effects. One plausible interpretation of these findings is that efferent slow effects are caused by outer-hair-cell stiffness decreases, while efferent fast effects are caused by reductions in ‘negative damping’.

Dynamic material properties of the tectorial membrane: a summary

Dynamic material properties of the tectorial membrane (TM) have been measured at audio frequencies in TMs excised from the apical portions of mouse cochleae. We review, integrate, and interpret recent findings. The mechanical point impedance of the TM in the radial, longitudinal, and transverse directions is viscoelastic and has a frequency dependence of the form 1/( K(j2π f) α ) for 10≤ f≤4000 Hz, where f is frequency, K is a constant, j= −1 , and α≈0.66. Comparison with other connective tissues shows that the TM is a relatively lossy viscoelastic material. The median magnitudes of the point impedance at 10 Hz in the radial, longitudinal, and transverse directions are 4.6×10 −3 N·s/m, 1.8×10 −3 N·s/m, and 2.7×10 −3 N·s/m. Consistent with osmotic responses (Freeman et al., 2003), the TM point impedance is anisotropic – the TM is stiffer in the radial than in the longitudinal and transverse directions. The mechanical space constant of the TM is approximately 20 μm. Comparisons reveal that in the apical region of the mouse cochlea, the TM dynamic stiffness at 10 Hz is 10 times larger than the static stiffness of the aggregate hair cells in a mechanical space constant and roughly comparable to the stiffness of the basilar membrane. We conclude that the TM provides a mechanical load on the basilar membrane and that the lability of the TM to changes in endolymph composition may well be reflected in changes in basilar membrane motion.

Separate mechanical processes underlie fast and slow effects of medial olivocochlear efferent activity.

Sound-evoked vibrations of the basilar membrane (BM) in anaesthetised guinea-pigs are shown to be affected over two distinct time scales by electrical stimulation of the medial olivocochlear efferent system: one is fast (10-100 ms), the other much slower (10-100 s). For low and moderate level tones near the BM's characteristic frequency, both fast and slow effects inhibited BM motion. However, fast inhibition was accompanied by phase leads, while slow inhibition was accompanied by phase lags. These findings are consistent with a hypothesis that both fast and slow effects decrease sound amplification in the cochlea. However, the opposing directions of the phase changes indicate that separate mechanical processes must underlie fast and slow effects. One plausible interpretation of these findings is that efferent slow effects are caused by outer-hair-cell stiffness decreases, while efferent fast effects are caused by reductions in 'negative damping'.

Physiopathological significance of distortion-product otoacoustic emissions at 2f1-f2 produced by high- versus low-level stimuli.

Distortion product otoacoustic emissions emitted by the cochlea at 2f1-f2 in response to pairs of pure tones at f1 and f2 (DPOAE) form a class of otoacoustic emissions and as such, are viewed as a reliable tool for screening outer hair cell (OHC) dysfunctions on a pass/fail basis. However, the persistence of residual DPOAEs from impaired cochleae at high stimulus levels has suggested that above 60-70 dB SPL, instead of reflecting "active" cochlear motion, DPOAEs might represent another "passive" modality: they would thus become unsuitable for analyzing cochlear function. The present work reports the consequences on high- vs low-level DPOAEs of three types of cochlear impairments involving OHCs: progressive OHC degeneration of genetic origin in CD1 mice, complete cochlear ischemia in gerbils, and furosemide injection vs ischemia-reperfusion in gerbils. An alternative to the "active-passive" model was used wherein regardless of stimulus level, cubic DPOAEs are produced by N (probably OHC-borne) nonlinear elements driven by input I and modulated by a function F3 of their operating point o; thus, DPOAE proportional to NI3F3(o). When OHCs degenerated, thereby implying a decrease of N, DPOAE levels also decreased regardless of the stimulus level up to 80 dB SPL, in line with the previous formula but at variance with the prediction of the active-passive concept. Instead of affecting N, the other two experiments impaired the efficiency of the cochlear feedback loop as a result of its electrical drive being decreased by strial dysfunction. As it is well accepted that the impaired basilar-membrane motion, although greatly reduced at low levels, tends to catch up with a normal one at higher levels, it was assumed the same was true with I so that DPOAE levels had to be, and indeed were little affected at high levels while plummeting at low levels, without any need for invoking two modalities for DPOAE generation. Finally, comparisons of furosemide vs ischemia effects revealed additional influences on DPOAEs, possibly accounted for by function F3(o). These results lead to the proposal that although high-level DPOAEs are expected to be poor audiometric indicators, they seem well adapted to assessing the functional integrity of nonlinear elements in OHCs, i.e., presumably their mechanoelectrical transduction channels.

Effect of click intensity on click-evoked otoacoustic emission waveforms: implications for the origin of emissions

The rather shallow growth of click-evoked otoacoustic emissions (CEOAE) with click intensity, namely <1 dB/dB, distinguishes genuine CEOAEs from stimulus artifacts, thereby providing the rationale for the popular ‘derived nonlinear recording’ method. However, other CEOAE nonlinearities regarding phase or envelope dependence on stimulus intensity have been barely acknowledged so far. The present work used CEOAEs from 20 normal ears recorded in response to 50–86 dB peak equivalent SPL clicks. The phases of CEOAE spectral components varied considerably with click intensity (sometimes more than 120°), mostly in a monotonic manner and in such a way that in the majority of ears, phase lagged with increasing intensity. When present, synchronized spontaneous otoacoustic emissions exhibited the same behavior. In a few instances, conspicuous frequency shifts of CEOAE spectral peaks were seen. In contrast to CEOAE phases, envelopes were almost intensity-invariant. This behavior contrasts with that of basilar membrane motion at the place tuned to the stimulus frequency, as consistently disclosed by several recent publications, i.e., no phase shift and large envelope shift with stimulus intensity. It is thought that the phase invariance of basilar membrane motion implies that whatever they do, outer hair cells cannot alter the resonance frequency of the cochlear partition. If one elaborates along this line of reasoning, the large phase shift of CEOAEs with click intensity implies that CEOAEs at frequency f cannot come from the place tuned to f and that instead, they may be intermodulation distortion products produced by nonlinear interactions between spectral components of the click stimulus over a significant length of the basilar membrane.

Thyroid hormone is not necessary for the development of outer hair cell electromotility

The outer hair cell (OHC), one of two receptor cell types in the organ of Corti, plays a critical role in mammalian hearing. OHCs enhance basilar membrane motion through a local mechanical feedback process within the cochlea, termed the ‘cochlear amplifier’. It is generally believed that the basis of cochlear amplification is a voltage-dependent electromotile response of OHCs. Measurements of electromotility in developing animals indicate that the onset of motility normally occurs around 7 days after birth in altricial rodents such as gerbils and rats. Thyroid hormone (TH) plays a crucial role in the development of the auditory system. Deficiency of the hormone between the late embryonic stage and the second postnatal week can cause severe hearing loss. Several studies suggest that TH deficiency might also affect the development of the cochlear amplifier. The goal of this study was therefore to examine whether TH was necessary for the development of OHC motility. The organ of Corti of gerbils was dissected out at birth and grown in culture with defined concentration of triiodothyronine (T3), the active ligand for the TH receptor. Motility was measured from OHCs isolated from 7-, 11- and 14-day-old cultures. Motility did indeed develop in OHCs deprived of normal concentration of T3. This suggests that the defective auditory function seen in TH-deficient animals is most likely due to morphological and physiological changes in the cochlea, rather than the motor function of the OHCs.

Internal Shearing within the Hearing Organ Evoked by Basilar Membrane Motion

The vibration of the hearing organ that occurs during sound stimulation is based on mechanical interactions between different cellular structures inside the organ of Corti. The exact nature of these interactions is unclear and subject to debate. In this study, dynamic structural changes were produced by stepwise alterations of scala tympani pressure in an in vitro preparation of the guinea pig temporal bone. Confocal images were acquired at each level of pressure. In this way, the motion of several structures could be observed simultaneously with high resolution in a nearly intact system. Images were analyzed using a novel wavelet-based optical flow estimation algorithm. Under these conditions, the reticular lamina moved as a stiff plate with a center of rotation in the region of the inner hair cells. Despite being enclosed in several types of supporting cells, the inner hair cells, together with the adjacent inner pillar cells, moved in a manner signifying high compliance. The outer hair cells displayed radial motion indicative of cellular bending. Together, these results show that shearing motion occurs between several parts of the organ, and that structural relationships within the organ change dynamically during displacement of the basilar membrane.

Effects of the finite speed of sound in—and surgical modification of—the cochlea

Most analyses of the mechanics of the cochlear to date have involved the assumption that the cochlea is a rigid chamber filled with incompressible fluids. However, in vivo measurements of the cochlear fluid pressure or basilar membrane motion necessarily must be performed by first surgically modifying the cochlea through removing part of the cochlear bone. This modification violates the assumption of a rigid chamber, and can significantly modify the mechanics of the cochlea. Because of anatomical constraints, many of these measurements are performed near the base of the cochlea. For the species that are used (guinea pig, gerbil, chinchilla, etc.), measurements near the base necessitate the use of stimulus tones with frequencies that are too high for the assumption of an incompressible fluid to be valid. In this paper, we discuss the modifications to the cochlear mechanics necessary to accommodate both the finite speed of sound and the surgical modification of the cochlea. We show that both of these modifications can easily be incorporated into numerical cochlear model codes. Semianalytic solutions based the WKB method are also discussed.

Timing of neural excitation in relation to basilar membrane motion in the basal region of the guinea pig cochlea during the presentation of low-frequency acoustic stimulation

In spite of many studies concerning auditory nerve action potentials, the timing of neural excitation in relation to basilar membrane (BM) motion is still not well understood. In this study, therefore, BM vibrations in the basal region of the guinea pig cochlea were measured using a laser Doppler velocimeter, and action potentials in auditory nerve fibers were recorded by a conventional microelectrode technique. An attempt was then made to determine the relationship between BM motion and neural excitation in auditory nerve fibers. To obtain BM responses in the high-characteristic frequency (CF) region (18–22 kHz) and responses of auditory nerve fibers with high CFs (14–22 kHz), low-frequency stimuli (50–2000 Hz), frequencies of which were well below CFs, were presented at 60–100 dB SPL. The results indicated that neural excitation occurred when the BM was displaced toward the scala vestibuli. Moreover, the neural excitatory phase did not significantly vary with the fiber’s CF between 14 and 22 kHz nor with the stimulus level between 60 and 100 dB SPL.

3-d model of the cochlea and basilar membrane motion

3-d model of the cochlea and basilar membrane motion

In vivo Micromechanical Measurements of the Organ of Corti in the Basal Cochlear Turn

Cochlear mechanical measurements of organ of Corti motion are generally accomplished in the apical or basal turn as in vivo or in vitro studies. In the apex it is possible to observe and measure tectorial membrane vibration as well as vibrations of structures such as the reticular lamina or the basilar membrane (BM). However, compared to the basal turn, cochlear amplification and nonlinearity are not strong in the apex. Basal turn studies have typically been limited to point location measurements of the BM but improved technology for laser interferometry is now making possible the spatial mapping of BM motion. The ‘complexity’ of BM motion in the radial direction (particularly the phase variation) is important to new models of cochlear wave amplification. In future work it may be possible to learn about vibration of structures within the organ of Corti.

The use of distortion product otoacoustic emission suppression as an estimate of response growth.

Distortion product otoacoustic emission (DPOAE) levels in response to primary pairs (f2 = 2 or 4 kHz, L2 ranging from 20 to 60 dB SPL, L1 = 0.4L2 + 39 dB) were measured with and without suppressor tones (f3), which varied from 1 octave below to 1/2 octave above f2, in normal-hearing subjects. Suppressor level (L3) varied from -5 to 85 dB SPL. DPOAE levels were converted into decrements by subtracting the level in the presence of the suppressor from the level in the absence of a suppressor. DPOAE decrement vs L3 functions showed steeper slopes when f3 < f2 and shallower slopes when f3 > f2. This pattern is similar to other measurements of response growth, such as direct measures of basilar-membrane motion, single-unit rate-level functions, suppression of basilar-membrane motion, and discharge-rate suppression from lower animals. As L2 increased, the L3 necessary to maintain 3 dB of suppression increased at a rate of about 1 dB/dB when f3 was approximately equal to f2, but increased more slowly when f3 < f2. Functions relating L3 to L2 in order to maintain a constant 3-dB reduction in DPOAE level were compared for f3 < f2 and for f3 approximately = f2 in order to derive an estimate related to "cochlear-amplifier gain." These results were consistent with the view that "cochlear gain" is greater at lower input levels, decreasing as level increases.

Physical basis of two-tone interference in hearing.

The cochlea uses active amplification to capture faint sounds. It has been proposed that the amplifier comprises a set of self-tuned critical oscillators: each hair cell contains a force-generating dynamical system that is maintained at the threshold of an oscillatory instability, or Hopf bifurcation. While the active response to a pure tone provides frequency selectivity, exquisite sensitivity, and wide dynamic range, its intrinsic nonlinearity causes tones of different frequency to interfere with one another in the cochlea. Here we determine the response to two tones, which provides a framework for understanding how the ear processes the more complex sounds of speech and music. Our calculations of two-tone suppression and the spectrum of distortion products generated by a critical oscillator accord with experimental observations of basilar membrane motion and the nervous response. We discuss how the response of a set of self-tuned oscillators, covering a range of characteristic frequencies, represents the structure of a complex sound. The frequency components of the stimulus can be inferred from the timing of neural spikes elicited by the vibrating hair cells. Passive prefiltering by the basilar membrane improves pitch discrimination by reducing interference between tones. Our analysis provides a general framework for examining the relation between the physical nature of the peripheral detection apparatus and psychophysical phenomena such as the sensation of dissonance and auditory illusions.

Mechanics of the mammalian cochlea.

In mammals, environmental sounds stimulate the auditory receptor, the cochlea, via vibrations of the stapes, the innermost of the middle ear ossicles. These vibrations produce displacement waves that travel on the elongated and spirally wound basilar membrane (BM). As they travel, waves grow in amplitude, reaching a maximum and then dying out. The location of maximum BM motion is a function of stimulus frequency, with high-frequency waves being localized to the "base" of the cochlea (near the stapes) and low-frequency waves approaching the "apex" of the cochlea. Thus each cochlear site has a characteristic frequency (CF), to which it responds maximally. BM vibrations produce motion of hair cell stereocilia, which gates stereociliar transduction channels leading to the generation of hair cell receptor potentials and the excitation of afferent auditory nerve fibers. At the base of the cochlea, BM motion exhibits a CF-specific and level-dependent compressive nonlinearity such that responses to low-level, near-CF stimuli are sensitive and sharply frequency-tuned and responses to intense stimuli are insensitive and poorly tuned. The high sensitivity and sharp-frequency tuning, as well as compression and other nonlinearities (two-tone suppression and intermodulation distortion), are highly labile, indicating the presence in normal cochleae of a positive feedback from the organ of Corti, the "cochlear amplifier." This mechanism involves forces generated by the outer hair cells and controlled, directly or indirectly, by their transduction currents. At the apex of the cochlea, nonlinearities appear to be less prominent than at the base, perhaps implying that the cochlear amplifier plays a lesser role in determining apical mechanical responses to sound. Whether at the base or the apex, the properties of BM vibration adequately account for most frequency-specific properties of the responses to sound of auditory nerve fibers.