Auditory system: Peripheral nonlinearity and central additivity, as revealed in the human stapedius-muscle reflex

Abstract

Human stapedius-muscle contractions in response to 3-kHz, 20-msec tone bursts were determined indirectly by measuring the associated acoustic-impedance changes at the tympanic membrane with an acoustic bridge. The measurement was possible because the bridge practically eliminates the effect of the ear-canal air volume interposed between the tympanic membrane and the tip of the measuring tube. By using burst pairs, temporal additivity of the muscle responses was demonstrated both when the stimulus bursts were presented contralaterally to the measured impedance changes and when the first burst was presented ipsilaterally. The summation time constant was on the order of 200 msec, much longer than the twitch time constant of the muscle fibers. Therefore, the summation had to take place in a nucleus preceding the stapedius muscle. The magnitude of the muscle response obeyed a compressive function paralleling the loudness function up to sound pressure levels of at least 120 dB.

It has been known for centuries that the auditory system as well as the visual system compress the enormous range of physical stimulus intensities they are capable of processing to a biologically manageable size. In the 19th century, it was thought that they do this by taking a logarithm of the intensity. Fechner (1), who introduced the idea in 1860, exerted such a powerful influence on the scientific community that, to this day, many psychological and physiological results relating response magnitude to stimulus intensity are plotted on semilogarithmic coordinates, obscuring the true relationships. More recently, scaling experiments of S. S. Stevens (2, 3) and his associates (e.g., refs. 4–6) persuaded many scientists that the compression is achieved by a power-function transformation.

In the auditory system, the compression resides in the periphery. This recognition evolved slowly, moving the site gradually from the auditory nerve (e.g., ref. 7) to the auditory receptor cells (8), and finally, to the mechanical processes in the cochlea, the auditory part of the inner ear (9–11). The mechanism of cochlear compression remained enigmatic for many years. Pioneering intracellular recordings of the receptor potentials of cochlear inner hair cells of Russell and Sellick (12) failed to reveal any response decay during stimulation with tone bursts of constant amplitude. Such a decay would signify a process of adaptation, signaling the possibility of automatic gain control (AGC). As a result, a static nonlinearity was assumed. This proposition implied strong nonlinear distortions of stimulus wave forms. No such distortions were encountered, however, except at very high stimulus intensities. To resolve the paradox, it was suggested that the distortion products may be reduced by cochlear filtering (e.g., ref. 13 for review). The waves that are known to run along the cochlear canal go through an amplitude maximum at a frequency-dependent location, which produces a filter effect. Optimistic calculations were made based on tuning curves (inverse filters) resulting from this effect (14, ‡). However, when the calculations were based on empirically determined forward filtering, the filter sharpness proved insufficient for the required reduction (14, 15). It finally became evident (14, 15) that the adaptation Russell and Sellick (8, 12) failed to see may have been hiding in onset transients, always associated with bandpass filters. The resulting AGC would reduce the amplification in the absence of gradual amplitude reduction. Its presence would only become evident through shortened onset and lengthened offset transients. Such patterns were clearly confirmed experimentally (14, 15).

Placement of stimulus compression in the auditory periphery must have been an important evolutionary adaptation through which the remaining system can operate within a biologically more easily achievable range. Several physiological characteristics consistent with the compression are reproduced in Fig. 1 (16) and compared with the overall intensity characteristic embodied in the loudness function (solid line). The function was measured at a sound frequency of 1 kHz, but similar functions are found at other sound frequencies, especially in the audible mid-frequency range. The crosses in the figure indicate a typical input–output function of a cochlear nerve fiber (domestic cat) (17). Its dynamic range is relatively small, and many fibers with staggered sensitivities are required to produce the integrated whole nerve response, believed to constitute the peripheral code for loudness (e.g., refs. 7 and 18). An example of such a response (guinea pig), derived from data obtained with the help of 1.05-msec impulses (clicks) (7), is shown by the filled circles that coincide approximately with the loudness curve. Note that all of the ordinate values in the figure have been normalized, so that only the slopes are meaningful.

Fig 1.

Some intensity characteristics (input/output functions) of the mammalian auditory system. Solid line, loudness function (human); crosses, firing rate of a typical auditory-nerve fiber (cat); filled circles, integrated auditory-nerve response (guinea pig); unfilled circles, contralateral stapedius-muscle contraction as measured by the acoustic impedance change at the tympanic membrane (human). [Reproduced with permission from ref. 16 (Copyright 1974, Kluwer Academic/Plenum Publishers).]

Determination of the whole-nerve response was possible up to a sound pressure level (SPL) of about 100 dB, whereas useful hearing extends to at least 120 dB. The acoustic reflex of the stapedius muscle, a small middle-ear muscle that does not show a clear contraction below an SPL of 90 dB and has a dynamic range of about 30 dB (e.g., ref. 19), allowed us to bridge the gap. The muscle contraction reduces sound transmission at low sound frequencies, and is believed to protect the auditory system against excessively intense sound as well as to improve speech intelligibility (e.g., ref. 19). The muscle contracts bilaterally, but only the intensity characteristic of the contralateral reflex seems to parallel the loudness function and is considered here. The contraction stiffens the ossicular chain of the middle ear and is reflected in a change of the acoustic impedance measured at the tympanic membrane. The impedance change is directly proportional to the strength of the muscle contraction (e.g., ref. 19). The unfilled circles of Fig. 1 show that the contraction strength parallels the compressive course of the loudness function at least up to 130 dB SPL.

The hypothesis that, for substantial parts of the auditory system, the compressive nonlinearity is limited to the periphery is supported by the experiments on the stapedius reflex and related theory described in the following sections. This support is provided in two ways. First, it is shown that the superposition theorem holds for the muscle contractions, in other words, responses to multiple stimuli are additive; second, that the peripheral nonlinearity is maintained unchanged throughout the contralateral reflex arc, as is already evident in Fig. 1.

Measurement of the Stapedius Muscle Response

The stapedius reflex arc begins at the cochlear inner hair cells and proceeds through the auditory nerve fibers to the ventral cochlear nucleus; from there to the vicinity of the ipsilateral medial superior olive for the ipsilateral reflex and to that of the contralateral one for the contralateral reflex. On both sides, the path leads from the neighborhood of the medial superior olive to the muscle fibers through the seventh cranial nerve (e.g., refs. 20 and 21). According to McCue and Guinan (21), the ipsilateral and contralateral reflex arcs are almost entirely separated between the auditory nerve and the muscle itself.

Contractions of the stapedius muscle were measured indirectly through changes of the acoustic impedance encountered at the tympanic membrane by sound waves in the ear canal. As already mentioned, these changes are directly proportional to changes in muscle tension, which in turn are directly proportional to the neural potentials measured at the muscle (e.g., ref. 20). Numerous measurements of the stapedius reflex were performed in the past by means of the impedance changes (e.g., ref. 22). Unfortunately, they resulted in great variability due mainly to inadequate instrumentation. The acoustic impedance at the tympanic membrane cannot be measured directly because of the column of air interposed between the tip of the measuring instrument and the tympanic membrane. The direct measurement usually includes the impedance of this column, which must be eliminated by calculation. This is possible only approximately and, depending on the method, substantial errors may be introduced. In the measurements described here, an acoustic bridge (Zwislocki Bridge, Grason & Stadler, Madison, WI, Model 3) was used, in which the effect of the air column in the ear canal is counterbalanced by a column of air with a similar geometry. The acoustic bridge is shown schematically in Fig. 2 (23). It consists essentially of two equal tubes, A and B, disposed symmetrically on both sides of a bilateral electroacoustic transducer, E, that served in the experiments described here as a microphone whose diaphragm was exposed to sound in both tubes. When the sound delivered to the two tubes from a second electroacoustic transducer through the tube arrangement, Y, was bilaterally equal in magnitude and phase, the net sound pressure effect on the diaphragm was zero, and there was no electrical microphone output. This nulling of the bridge occurred through manipulation of a variable acoustic impedance arrangement consisting of a variable volume of air, V₂, acting as an acoustic reactance, and a narrow slit, R_A, acting as an acoustic resistance. The volume of air, V₁, mimicked the ear canal volume and was preset according to a separate measurement (23). Because of the compensation of the column of air in the ear canal by volume V₁, the variable impedance elements of the bridge were equal to the elements of the acoustic impedance at the tympanic membrane, when the bridge was balanced. For the measurement of reactance changes produced by stapedius muscle contractions, the compliance of the bridge was set slightly off balance, so that the bridge microphone generated a small signal. Muscle contraction increased the signal. The voltage output of the bridge was amplified and displayed on the calibrated screen of an oscilloscope for direct measurement. This method proved to be sufficiently accurate and provided visual information on the time course of the muscle contraction without introducing nonnegligible time delays. In the absence of muscle contraction, the voltage output produced a trace whose width depended on the mistuning of the bridge. Muscle contraction increased the width of the trace, and the difference served as an indirect measure of muscle tension. The measurement did not depend on the reference trace width (bridge mistuning). Examples of arising oscilloscope patterns can be seen in Fig. 3.

Fig 2.

Zwislocki acoustic bridge in schematic representation. A and B sound-transmitting tubes, symmetrically disposed relative to the electroacoustic transducer, E; tube A to be inserted in the ear canal, tube B ending in the variable acoustic impedance ensemble, where V₁ is a cavity simulating the residual volume of the ear canal, R_A is a variable acoustic resistance element, and V₂ is a variable cavity simulating the negative acoustic impedance found at the tympanic membrane at low sound frequencies. Y denotes a tube system serving for symmetrical sound delivery. [Reproduced with permission from ref. 23 (Copyright 1963, American Speech-Language-Hearing Association).]

Fig 3.

Calibration curve relating the bridge output to the difference between the measured reactance and the reactance of the variable bridge cavity, V₂. The reactance difference is expressed in terms of equivalent air volume, and the bridge output is expressed in terms of an oscilloscope trace width proportional to the bridge output voltage.

The direct proportionality between the increments of the microphone signal and the reactance changes was verified with the help of a calibration cavity at the sound frequency of 500 Hz used for the impedance measurements. At this frequency, the impedance of the cavity was practically equal to a pure reactance. The calibration results are shown in Fig. 4, where the difference between the volume of the calibration cavity and volume, V₁, of the bridge is plotted against the output of the bridge microphone, as reflected in the oscilloscope trace. The effect of resistance changes was negligible. The 500-Hz tone emitted by the bridge at ≈60 dB SPL was well below a noticeable reflex response.

Fig 4.

Acoustic-bridge calibration. Stapedius-muscle contractions, as detected by changes of the acoustic reactance at the tympanic membrane (oscilloscope trace width) and recorded as functions of time. In every panel, the upper trace refers to the reflex-eliciting 3-kHz tone bursts, as measured at the input of the electroacoustic transducer, and the lower trace refers to the muscle response. The trace width in the absence of muscle contraction is proportional to the reference mistuning of the bridge. The time interval between the signals in every pair, and the time scales are indicated under every recording.

Summation of Contralateral Muscle Responses

The reflex eliciting stimuli consisted of pairs of equal 3-kHz tone bursts of 20-msec duration with 5-msec on and off transients presented contralaterally to the ear where the impedance changes were measured. At 3 kHz, the sound transmission through the middle ear is practically independent of the muscle tension. The effect of the latter is the strongest at low sound frequencies and fades out near 2 kHz (e.g., ref. 20). As a consequence, the experiments were performed in the open loop condition of the reflex arc. The burst pairs were presented at 3-sec intervals, long enough to prevent mutual interaction.

The muscle response patterns, as seen on the oscilloscope screen, are shown in the 6 panels of Fig. 3 by the lower trace. The upper trace shows the electric input to the sound-generating transducer. In the top left panel, the bursts were presented simultaneously. Subsequently, the time interval between them was increased gradually, as indicated in the remaining panels. The width of the lower trace is directly proportional to the bridge output. The effect of the muscle contractions is clearly visible. The contractions persisted for relatively long durations compatible with a time constant of τ₁ = 200 msec encountered in psychophysical threshold experiments (24, 25). The greatest contraction magnitude did not occur during simultaneous burst presentation but at an interburst time interval of about 80 msec, probably, for the following reasons. During simultaneous burst presentation, their combined input amplitude was doubled, but, because of the peripheral compression, the neural output was increased only by roughly a square root of 2. At short time intervals, a well known desensitization of single nerve fibers takes place, whose recovery can be grossly approximated by an exponential function with a time constant on the order of τ₂ = 50 msec (26). The desensitization very likely decreased the response to the second burst. Note that the maximum magnitude increment due to the burst summation exceeded the response to single bursts (lowest right panel) by more than a factor of two. The seeming paradox can be accounted for by a reflex threshold that follows the summation effect. This order is consistent with the observation that the time constants of the muscle fiber responses are much shorter than 200 msec (27), so that the temporal summation effect evident in Fig. 3 must take place at a neural location preceding the muscle. The threshold effect is detectable in the right bottom panel of the figure, where it truncates the decay of the muscle responses.

The relationships described above can be expressed mathematically as

where η is the peak response, B, the peak response to a single burst, D, a desensitization constant, T, the muscle response threshold, τ₁ = 200 msec, and τ₂ = 50 msec are the time constants already mentioned, and Δt is the time interval between the bursts. By normalizing to the one-burst response,

we obtain

In this equation, only the constants, T = 0.65, and D = 0.84, not being known empirically, had to be chosen ad hoc. The time constants were derived from independent experiments mentioned above.

The theoretical values obeying Eq. 3 are shown in Fig. 5 by the intermittent line and compared with individual empirical data marked by solid symbols and having median values joined by the solid line. The empirical data were obtained on four subjects with normal hearing and were derived from response patterns, like those shown in Fig. 3. The intrasubject variability was small compared with the intersubject variability. In view of the latter and the independently obtained time constants, the agreement of the theory with the experimental data can be considered as satisfactory. The theoretical time pattern certainly has the same characteristics as the empirical one.

Fig 5.

Change of tympanic-membrane reactance produced by stapedius-muscle contraction as a function of time interval between contraction-eliciting contralateral pairs of tone bursts. The various symbols indicate individual data (4 subjects); the solid line connects their medians. The dashed line is theoretical.

Summation of Muscle Responses Produced by Dichotic Stimuli

To avoid the effect of poststimulatory desensitization, the first burst was transmitted to the ear in which the acoustic impedance change was measured, and the second, to the contralateral ear. The ipsilateral burst was delivered through the bridge transducer, and its magnitude was adjusted to produce the same reactance change as produced by the second burst individually. On the assumption that the response to the ipsilateral stimulus undergoes the same temporal summation as that to the contralateral one, the expression of Eq. 3 can be simplified in the absence of neural desensitization to

With the same numerical values of the constants as for the contralateral reflex, the equation produces the time pattern indicated by the intermittent line in Fig. 6. It agrees well with the empirical data obtained on the same subjects as the data of the preceding figure. The solid line connecting the medians of these data nearly coincides with the theoretical curve. The agreement is significant in at least four respects. It confirms the process of linear summation, the similarity of the contralateral and ipsilateral summation processes, the existence of a postsummation threshold, and the peripheral nature of the desensitization. Because the muscle reflex seems to have a relatively high threshold, only part of the neural input becomes effective, as illustrated schematically in Fig. 7 for the dichotic burst pair. The continuous lines indicate the superposed inputs from the summation stage, and the intermittent line schematizes the threshold. Of course, in more precise terms, the threshold must be expected to have a noisy nature. The drawing illustrates how the input produced by the first burst is decreased relative to that produced by the second burst, and how the summated maximum response can be increased by more than a factor of two relative to the response to the first burst. For monotic contralateral bursts, similar relationships are evident in the oscilloscope traces of Fig. 3.

Fig 6.

Similar to Fig. 5 but for dichotic pairs of tone bursts, the ipsilateral one being presented first.

Fig 7.

Schematic representation of the stapedius-muscle response threshold (dashed line) on the hypothetical neural input to the muscle (solid lines).

Two-Burst Summation in Terms of Equivalent SPL

To demonstrate that, except for the reflex threshold, no nonlinearity intervened between the peripheral compression (e.g., ref. 18) and the stapedius muscle response, two additional experiments were performed on 6 subjects with normal hearing. In the first, single 3-kHz bursts of 20-msec duration were presented at 3-sec intervals, and the reactance change was measured as a function of the burst SPL. The individual results and their medians (filled circles) approximated by a least-squares straight line are shown in Fig. 8. The line follows closely (R = 0.9961) a power function (straight line on double-log coordinates) with an exponent of 0.585 approximating the exponent of the loudness function of Fig. 1.

Fig 8.

Growth of the stapedius-muscle contraction reflected in the reactance change at the tympanic membrane, as a function of SPL relative to the median reflex threshold. The various unfilled symbols indicate individual data (6 subjects), the filled symbols indicate their medians, and the solid straight line indicates the least-squares approximation of the medians.

In the second experiment, a comparison tone burst was added to the contralateral burst pair whose additivity was studied. The third burst was presented with a time delay of 700 msec from the second burst to avoid interburst interaction. The SPL of this burst was adjusted by the experimenter so that the reactance change it produced matched the maximum reactance change produced by the burst pair. The time interval between the bursts in the burst pair served as the independent variable, as in the initial experiment with the contralateral burst pair. The median SPL changes obtained on the same 6 subjects who served in the preceding experiment are shown in Fig. 9 by the filled circles. Because the scatter of the individual data were similar to that in Fig. 8, these data have been omitted to avoid cluttering the plot.

Fig 9.

Magnitude of the stapedius muscle response to contralateral pairs of tone bursts, as measured in terms of the equivalent change in SPL of a single burst, plotted as a function of the interburst time interval (filled circles). Crosses indicate the results of theoretical calculation.

If the summation process is independent of the peripheral nonlinearity, it should be possible to obtain the matching SPLs from the measurements of the impedance changes of Fig. 5 by converting them to decibels and dividing the result by the slope of the magnitude function of Fig. 8, obtained with single bursts. The data so produced are shown by the crosses in Fig. 9. They are in close agreement with the directly obtained dB values indicated by the filled circles. Thus, the requirement of independence, or orthogonality, between the summation process in the contralateral stapedius muscle reflex arc and the peripheral nonlinearity of the auditory system is satisfied. Restriction to the contralateral process has to be emphasized because of empirical evidence that the independence does not hold for the ipsilateral reflex (unpublished data).

Conclusions

Stapedius muscle contractions, as determined indirectly by changes of the acoustic impedance at the tympanic membrane, revealed a linear process of temporal summation in a nucleus preceding the 7th cranial nerve that innervates the muscle (28). The linearity was tested by means of pairs of tone bursts presented either contralaterally or dichotically with the first burst appearing in the ipsilateral ear. The time course of the temporal summation was examined by varying the time interval between the bursts. It was consistent with a linear summation having a time constant of about 200 msec. When both bursts were presented to the same ear, the summation was decreased at small interburst time intervals, apparently, because of peripheral neural desensitization. When the first burst was presented to a different ear than the second, the effect disappeared. In addition, the summation characteristic was distorted by an effect that was ascribed to the response threshold of the muscle. The distortion produced an apparent shortening of the integration decay function and an apparent enhancement of the summation effect.

In the intensity domain, the muscle response was found to obey the same compressive nonlinearity as the integrated response of the auditory nerve. This result is significant in that it shows that no additional global nonlinearity intervened through several synaptic relays up to the muscle itself. It is in harmony with the finding that the loudness function also parallels the peripheral nonlinearity. These conclusions should not be interpreted to mean that the whole auditory system beyond the periphery functions linearly. An exception was mentioned concerning the ipsilateral stapedius muscle reflex. Many experiments show nonlinear effects in responses of single neurons. If central linearity is found in global auditory functions based on large neural populations, such as loudness and the contralateral stapedius muscle reflex, this should not necessarily imply that neural units belonging to these populations function linearly on an individual basis. That their aggregates sometimes do can probably be ascribed to evolutionary adaptations. As was already mentioned, it makes sense from the engineering point of view to place a compressive nonlinearity at the periphery of a system to reduce the dynamic range required of the remaining parts of the system.

Abbreviations

• SPL, sound pressure level