High-Frequency Dynamics of Regularly Discharging Canal Afferents Provide a Linear Signal for Angular Vestibuloocular Reflexes

Timothy E. Hullar1 and Lloyd B. Minor1,2,3

Departments of  1Otolaryngology-Head and Neck Surgery,  2Biomedical Engineering, and  3Neuroscience, The Johns Hopkins University, Baltimore, Maryland 21287-0910


    ABSTRACT
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ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Hullar, Timothy E. and Lloyd B. Minor. High-Frequency Dynamics of Regularly Discharging Canal Afferents Provide a Linear Signal for Angular Vestibuloocular Reflexes. J. Neurophysiol. 82: 2000-2005, 1999. Regularly discharging vestibular-nerve afferents innervating the semicircular canals were recorded extracellularly in anesthetized chinchillas undergoing high-frequency, high-velocity sinusoidal rotations. In the range from 2 to 20 Hz, with peak velocities of 151°/s at 6 Hz and 52°/s at 20 Hz, 67/70 (96%) maintained modulated discharge throughout the sinusoidal stimulus cycle without inhibitory cutoff or excitatory saturation. These afferents showed little harmonic distortion, no dependence of sensitivity on peak amplitude of stimulation, and no measurable half-cycle asymmetry. A transfer function fitting the data predicts no change in sensitivity (gain) of regularly discharging afferents over the frequencies tested but shows a phase lead with regard to head velocity increasing from 0° at 2 Hz to 30° at 20 Hz. These results indicate that regularly discharging afferents provide a plausible signal to drive the angular vestibuloocular reflex (VOR) even during high-frequency head motion but are not a likely source for nonlinearities present in the VOR.


    INTRODUCTION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Information about angular motion of the head is transmitted by vestibular-nerve afferents innervating the semicircular canals. These neurons traditionally have been divided into regular and irregular populations based on the coefficient of variation of interspike interval of their background discharge rate (Goldberg and Fernández 1971a) and the observation that regular afferents respond with significantly less phase difference with regard to head velocity than irregularly discharging afferents (Fernández and Goldberg 1971). In the squirrel monkey, regular afferents have been shown to be principally responsible for the control of the angular vestibuloocular reflex (VOR) over the middle range of frequencies and velocities (up to 4 Hz, ±20°/s) of rotational head movements (Minor and Goldberg 1991).

The frequencies in the power spectrum of human head movements for which compensatory function of the VOR is needed during activities such as running extend above this range to >= 15 Hz (Grossman et al. 1988, 1989). The phase and gain of the VOR at high frequencies are close to compensatory (Keller 1976; Minor et al. 1999) despite a delay in the reflex, measured from responses to steps of acceleration, of ~7 ms in humans (Tabak et al. 1997a,b) and squirrel monkeys (Minor et al. 1999), an interval that would cause a phase lag of ~36° at 15 Hz. The signal that is needed to drive the VOR requires a phase lead that increases with frequency (to compensate for the phase lag arising from the delay) and a gain that remains constant with respect to frequency.

The transfer functions representing data from regular afferents obtained over the range of 0.01-4 Hz do not predict such a compensatory phase in the chinchilla (Baird et al. 1988) or squirrel monkey (Fernández and Goldberg 1971) above the middle range of frequencies. These higher frequencies have been studied using mechanical indentation techniques in fenestrated canals of the toadfish (Highstein et al. 1996) and pigeon (Dickman and Correia 1989a,b). In the toadfish, a decreasing gain and increasing phase lead with increasing frequency between 1 and 10 Hz is noted in low-gain fibers. In the pigeon, gain increased in some regularly discharging afferents and decreased in others; there was a progressive phase lag with increasing frequency in all regular afferents. As pointed out by Rabbitt et al. (1995), the analyses of these experiments must take into account the difference in canal dynamics between rotation and indentation at high frequencies.

We show that the rotational sensitivity of regular afferents in chinchillas remains remarkably constant across frequencies from 2 to 20 Hz and velocities from 6 to 151°/s. These afferents show little change in sensitivity and a phase lead increasing with frequency, providing a signal needed to compensate for the central delays in the VOR. We incorporated these findings into a transfer function that describes the relationship between head velocity and afferent dynamics.


    METHODS
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ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Surgical procedures and recording techniques

Data were obtained from 20 adult chinchillas weighing 500-750 g. Each animal was anesthetized with 0.3 ml/kg Dial injected intraperitoneally as in previous studies (Fernández et al. 1988). Once anesthetized, the animals were maintained with a core body temperature of 36-38°C via an external servomechanism (FHC, model 40-90-8B). A tracheotomy was performed in most animals. After placement in a stereotaxic frame, the superior bulla was opened and the middle ear entered. The paraflocculus and adjacent flocculus overlying the vestibular nerve were aspirated through a window made anterior to the superior semicircular canal. The eighth nerve identified as it emerged from the internal acoustic meatus.

A three-dimensional minimanipulator (You, model US-3F) was held by a microdrive (Narishige International USA, model MO-22) mounted on the stereotaxic frame. Glass micropipettes (WPI, model M1B100F-4) with impedances of 10-30 MOmega were filled with 3 N NaCl and adjusted into position over the nerve using the minimanipulator. The microdrive was advanced until the pipette entered the eighth nerve and the extra-axonal activity of neurons identified. Signals from the nerve were amplified (Dagan, model 2400A) at gains from 500 to 5,000 and band-pass filtered from 100 Hz to 5 kHz. All surgical and recording procedures were in compliance with a protocol approved by the Johns Hopkins University School of Medicine.

Rotational stimulation

The stereotaxic frame was mounted on a gimballed superstructure, allowing the animal to be tilted to bring any semicircular canal into the plane of rotation. In the neutral position, the horizontal canal was in the earth-horizontal plane of rotation. The superstructure was bolted to a servo-controlled rate table (Acutronic USA, model 130-80/ACT2000) programmed to supply rotations in the range of 2-20 Hz.

Once a unit was found, it was checked for sensitivity to rotation. The canal innervated by each rotation-sensitive afferent was determined by monitoring responses during rotations in the pitch and roll combinations that brought the horizontal, superior, and posterior canals into the plane of rotation. The superstructure then was secured in the plane of the canal to which the afferent was related. It was not always possible to record from a superior or posterior canal afferent with its canal precisely in the plane of rotation; slight deviations were noted and sensitivities of afferents tested under these conditions corrected trigonometrically according to the formula: Gc = Gm · [1/cos(90°-roll)] · [1/cos(45°-pitch)] where Gc is corrected gain and Gm is measured gain; roll and pitch are the absolute value of tilt relative to the neutral position. For anterior canal afferents, gain was maximal when the animal the animal was rolled 90° contralaterally and 45° nose down, whereas for posterior canal afferents gain was maximal when the animal was rolled 90° contralaterally and pitched 45° nose up.

Potential uncoupling in the mechanical linkages of the apparatus was assessed using an accelerometer (ICSensors, model 3140) attached to the stereotaxic frame securing the animal's head to the superstructure. Acceleration and position were sampled at 2 kHz while rotating the animal at experimental frequencies and peak velocities. At all frequencies and intensities, the harmonic distortion, measured as the sum of the powers of the 2nd through 10th harmonics divided by the power of the 1st harmonic, was <1.0% for the position of the table. The phase difference between the accelerometer and the table position was 180 ± 3° (mean ± SD) at all frequencies.

Each unit was recorded for 10-20 s at rest before beginning sinusoidal stimulation. Every afferent was recorded at 2 or 4 Hz before testing higher frequencies. The range of amplitudes at each frequency tested was as follows: 2 Hz, 7-139°/s; 4 Hz, 7-145°/s; 6 Hz, 10-151°/s; 8 Hz, 5-105°/s; 10 Hz, 13-54°/s; 12 Hz, 10-81°/s; 14 Hz, 13-52°/s; 16 Hz, 18-40°/s; 18 Hz, 16-35°/s; 20 Hz, 14-52°/s.

Data acquisition and analysis

The signal from the microelectrode was passed through a window discriminator (Mentor, model N-750) to identify action potentials. A data acquisition device (CED, model micro1401) interfaced to a Pentium-based microcomputer was used to record spike times, table position (sampled at 2 kHz), and voltage of the microelectrode (sampled at 5 kHz). Accurate identification of action potentials was confirmed off-line by comparing spike times with the recording of the microelectrode voltage. Data were stored on JAZ disks for later analysis.

Each cycle of a particular frequency and velocity stimulation paradigm was divided into 40 equal bins and the average table velocity and afferent discharge rate (calculated by binning spike times) over the entire paradigm were computed for each bin. Using the MATLAB (The Mathworks) environment, Fourier analysis was performed on the results, and the gain and phase of neuronal response with regard to head velocity were calculated. Discharge rates also were calculated by assigning the reciprocal of the interspike interval to the midpoint between every pair of spikes, as previously described by others (Dickman and Correia 1989a,b). Fourier analysis then was performed on the result. This procedure reduces noise, creating a smoother response curve with identical gain to that produced by binning spike times. As the instantaneous discharge rate is assigned arbitrarily to a time at the midpoint between each pair of spikes, this technique can introduce a significant phase shift at high frequencies of stimulation and was not used to calculate the phase relationships described here. Response linearity was measured on this smoothed curve using harmonic analysis as well as linear regression on plots of stimulus versus response after correction for phase. Harmonic distortion was calculated on those spike trains >1,500 spikes in length and was defined as the sum of the powers in the 2nd through 10th harmonics divided by the power in the fundamental.

Normalization of CV based on mean interval

Data were collected from 87 otolith afferents to create curves normalizing the coefficient of variation of interspike intervals (CV) to a uniform discharge rate of 66.7 spikes/s and allow comparisons of discharge regularity among afferents. These curves were identical to those calculated previously for the chinchilla (Baird et al. 1988).


    RESULTS
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ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

We recorded 70 regularly discharging canal afferents (CV* <0.1), 12 intermediate afferents (0.1< CV* < 0.2), and 14 irregular afferents (CV* >0.2). Of the regular afferents, 54 innervated the horizontal canal, 13 the superior canal, and 3 the posterior canal. The resting rate of these regular afferents measured 57.7 ± 17.4 spikes/s with a range from 11.5 to 94.3 spikes/s. CV* for the sample was 0.040 ± 0.016 with a range from 0.022 to 0.088. Three horizontal canal afferents were silenced for at least part of the inhibitory half-cycle (silenced for 50 ms at 4 Hz, 80°/s peak velocity; 162.5 ms at 2 Hz, 151°/s; and 62.5 ms at 2 Hz, 101°/s, respectively). These units tended to have a combination of high CV* (0.06, 0.07, 0.09), high sensitivity (0.39, 0.34, 0.19 spikes · s-1/deg · s-1), and low resting discharge rate (34.5, 45.5, 11.5 spikes/s) and were not included in further analysis.

Response linearity

Figure 1, B and C, shows the sensitivities and phases with regard to head velocity of all afferents in the sample held for testing at more than one frequency. Dark lines indicate the 11 units with resting interspike intervals >20 ms, medium lines the 15 units with resting interspike intervals between 15 and 20 ms, and light lines the 10 with intervals <15 ms. Afferents for which only one frequency was tested were not included in this figure. The most rapidly discharging afferents had sensitivities of 0.23 ± 0.13 spikes · s-1/deg · s-1, intermediate rate fibers had sensitivities of 0.16 ± 0.06 spikes · s-1/deg · s-1, and the most slowly discharging fibers had sensitivities of 0.26 ± 0.22 spikes · s-1/deg · s-1, differences that were not statistically significant (ANOVA, P > 0.2). A power law regression of the form sensitivity = a · (CV*)b gave a value for a = 1.03 (95% confidence intervals, 0.50-2.23) and b = 0.51 (95% confidence intervals, -0.02-1.04). These findings are comparable with those of Baird et al. (1988) when taking into account the difference in mean discharge rate between the two studies.



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Fig. 1. A: response of a horizontal canal afferent to 4-Hz, ±26.5°/s sinusoidal stimulation (sensitivity = 0.39 spikes · s-1/deg · s-1; resting discharge rate = 73 spikes/s; CV* = 0.03) Instantaneous firing rate at each spike calculated as the reciprocal of the preceding interspike interval. Sensitivity (B) and phase (C) of 36 semicircular canal afferents recorded at >= 2 frequencies. Dark lines indicate units with a resting discharge interspike interval >20 ms, light lines <15 ms, and medium lines in between. Average normalized sensitivity (D) and average phase with regard to head velocity (E) for 70 afferents tested across the frequency spectrum 2-20 Hz. Bars represent SE.

Figure 1D shows the average sensitivity for all afferents after normalization to the average value at 2 Hz (n = 31units) or at 4 Hz (n = 5 units), and Fig. 1E shows the averaged (nonnormalized) phase of the afferent response with regard to head velocity. The high-frequency dynamics of the sample of afferents presented here were best represented by a transfer function with two poles and one zero, shown as a dashed line in Fig. 1, D and E.

Figure 2 presents a comparison among three previously published transfer functions describing the dynamics of vestibular-nerve afferents. At low frequencies, the response predicted by the transfer function proposed here closely matches that predicted by transfer functions based on previously published data for the squirrel monkey and chinchilla. At higher frequencies, however, the predictions of previously published squirrel monkey and chinchilla transfer functions diverge. The data presented here indicate that the response dynamics of regular afferents actually lie between previous predictions (Baird et al. 1988). A curve representing the phase lag caused by the 7-ms delay in the VOR is included for comparison.



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Fig. 2. Simulations for 4 different transfer functions used to describe vestibular afferent dynamics. Line 1 represents the dynamics of the torsion-pendulum model. Line 2 represents the dynamics of the regularly discharging afferents of the squirrel monkey (Fernández and Goldberg 1971). Line 3 represents the dynamics of regular afferents in the chinchilla based on data collected to 4 Hz (Baird et al. 1988). Line 4 represents the best-fitting transfer function for the data presented in this study collected in the range 2-20 Hz. Line 5 (shown on the phase plot only) represents the phase lag created expected based on the 7-ms delay in the vestibuloocular (VOR).

Analysis of nonlinearities

Responses to rotations of a particular frequency and velocity exceeded 1,500 spikes in length for 71 stimulus records. The average harmonic distortion of these spike trains was 12.8 ± 8.0%, whereas shorter sampling periods sometimes produced spike trains with higher harmonic distortions. Spike trains with high harmonic distortion can be created from long recordings with low distortion simply by truncating the recording; these abbreviated recordings show identical sensitivity and phase as their full-length sources despite higher harmonic distortion.

Three or more peak stimulus velocities at one or more stimulus frequencies were used to test 23 afferents in 10 animals. Ten afferents were tested at multiple frequencies and 13 afferents at a single frequency for a total of 40 trials. Linear regression was performed, and the dependence of sensitivity on stimulus intensity determined to be insignificant (P > 0.05) for all but one of the trials. In unit 24_0018, tested at 4 Hz, the sensitivity decreased slightly from 0.13 spikes · s-1/deg · s-1 at 14.0°/s to 0.12 spikes · s-1/deg · s-1 at 79.2°/s (P = 0.041). Regression of sensitivity versus peak amplitude of stimulation for all afferents at all frequencies yielded a line with a slope of -0.0002 (95% confidence intervals: -0.0004 to -0.0001), indicating a similar independence of sensitivity from the peak stimulus amplitude.

The instantaneous firing rate of a representative afferent (CV* = 0.033, resting rate = 45 spikes/s) is plotted versus stimulus intensity (corrected for phase) in Fig. 3A. Lines fit to data points collected during the excitatory and inhibitory portions of the stimulus are similar in slope and cross the zero-velocity axis at the same point, indicating no half-cycle asymmetry or DC offset in the response. Figure 3B shows the results of 258 stimulus paradigms from 37 regular afferents. The sensitivity of each afferent during the excitatory half-cycle is plotted against its sensitivity during the inhibitory half-cycle. All results lie closely on the unit slope line, indicating that there is no half-cycle asymmetry in the responses of these afferents (2-tailed paired t-test, P = 0.66). A further measure of half-cycle asymmetry is the power in the second harmonic of the neural response. Of 71 recordings >1,500 spikes in length, the third harmonic carried more power than the second harmonic in 41 records (58%), and the difference between the two groups was not significant (paired t-test, P > 0.25), indicating that the small amount of distortion was predominantly symmetric.



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Fig. 3. A: horizontal canal afferent (CV* = 0.033, resting rate = 45 spikes/s) undergoing 4-Hz, 144°/s peak velocity sinusoidal head rotations shown with the rate of discharge plotted vs. the stimulus amplitude (after adjustment for phase). Average responses during the excitatory half-cycle (ipsilateral head rotations) and during the inhibitory half-cycle (contralateral head rotations) were fit with separate lines. Slopes of the lines are statistically indistinguishable. B: half-cycle asymmetries of 37 afferents (258 stimulus paradigms in total) plotted as sensitivity of each afferent during the inhibitory half-cycle vs. during the excitatory half-cycle. Close adherence to the unit slope (2-tailed t-test, P = 0.66) indicates no significant difference in sensitivity of the afferents to excitatory or inhibitory rotations.


    DISCUSSION
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ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

These results demonstrate that across the frequency range of 2-20 Hz, most regularly discharging afferents (CV* <0.10) have a constant sensitivity that is independent of peak stimulus velocity or resting discharge rate. These afferents respond in phase with head velocity at 2 Hz but have a steadily increasing phase lead re head velocity that reaches 30° at 20 Hz.

These findings differ from those predicted by previously published transfer functions, shown in Fig. 2, describing responses of mammalian vestibular-nerve afferents to lower- and middle-frequency stimuli (0.01-4 Hz). Those transfer functions, first derived for data obtained in squirrel monkeys, consist of two poles and two zeroes. The poles describe the dynamics of the torsion pendulum, which serves as the mechanical analogue of a toroidal canal. One of the two zeroes is at the origin, with its coefficient specifying the rotational sensitivity of the afferent, whereas the second zero confers the phase lead and putative gain enhancement of the afferent with rising rotational frequency. In a previous study of vestibular-nerve afferents in the chinchilla (Baird et al. 1988), a fractional exponent was used with this second term largely in an effort to improve the fit of the transfer function to data collected from irregularly discharging afferents. Because the response dynamics of irregularly discharging afferents vary much more than regularly discharging afferents, regular afferents could have been nearly as well represented without it.

Over the lower and middle range of frequencies tested in previous studies of squirrel monkeys and chinchillas, these transfer functions provide similar predictions for regular afferent physiology (Baird et al. 1988; Fernández and Goldberg 1971). They give rise to substantially different predictions, however, at the higher frequencies used in this study (Fig. 2). Our data resolve this discrepancy with a transfer function, derived to represent the experimental findings in this study, consisting of a single pole and two zeroes (Eq. 1). This transfer function also provides a good fit to data previously obtained at lower frequencies from regularly discharging afferents in the chinchilla (Baird et al. 1988).
<IT>H</IT>(<IT>s</IT>)<IT>= </IT><FR><NU><IT>s</IT>(<IT>0.0042</IT><IT>s</IT><IT>+1.0072</IT>)</NU><DE>(<IT>4.4</IT><IT>s</IT><IT>+1</IT>)</DE></FR> (1)
The coefficients were determined from a least-squares optimization fit to the data. The second pole of the torsion pendulum transfer function was not included because its effect, given its previously assumed time constant of 3-7 ms, would have been to cause a phase lag and gain decrease at the higher rotational frequencies used here. A second pole with a time constant shorter than that previously proposed must be present to prevent the gain of the linear system from growing toward infinity as the frequency increases, but the exact determination of its value would require rotational frequencies higher than could be obtained in this study. Because this second pole produces a negligible change in gain and phase in the responses described here, its time constant is likely to correspond to a frequency at least one decade above the range studied here (tau  = 8 × 10-4s). This second pole may be a manifestation of dynamics inherent in the mechanics of the canal and the transduction processes of the hair cell and afferent.

The high-frequency dynamics of this transfer function are consistent with the requirements of the angular VOR. To keep an image steady on the retina, the VOR must move the eyes to compensate for head motion. Inherent delays in the three-neuron reflex arc have been measured at 7 ms (Minor et al. 1999; Tabak et al. 1997a,b), which is equivalent to a lag of 10° at 4 Hz and 50° at 20 Hz. The phase lag between spike detection in the afferent and eye movement is actually slightly shorter, as the minimum delay between hair cell transduction and detection of a spike in the afferent has been measured as 0.7 ms (Highstein et al. 1996) or 5° at 20 Hz. Thus the phase lead with regard to head velocity demonstrated by the transfer function described here provides a signal that is close to the signal requirements for a compensatory VOR. The previously published transfer function describing regular afferent dynamics in the chinchilla predicts their sensitivity to decrease by 15% over the range 2-20 Hz, and their phase re velocity to change from 0° to a 36° lag over the same range (Baird et al. 1988). Although the present study of the dynamics of regular discharging afferents in response to higher frequency rotations was performed in chinchillas, the same groups of afferents and similar innervation patterns in the sensory epithelia of the canal ampullae have been demonstrated in squirrel monkeys and chinchillas (Lysakowski et al. 1995).

Although the regular afferents provide a linear signal to the VOR, recent studies have shown that the reflex has significant nonlinearities, particularly at high frequencies and velocities (Das et al. 1995; Minor et al. 1999). Several methods were used in this study to examine the possibility that regularly discharging afferents could be the source of some of these effects. The most general measure of response nonlinearity used here is harmonic distortion. Previous work (Baird et al. 1988) has reported harmonic distortions of ~10% in the responses of chinchilla afferents to sinusoidal rotational stimuli having a duration of a minute or more, a figure matched at the higher frequencies used here.

Another potential nonlinearity is a dependence of the sensitivity of afferents on the peak amplitude of stimulation at a particular frequency. In the chinchilla, Baird et al. (1988) found no change in sensitivity at stimulus amplitudes ranging between 160°/s (at 0.01 Hz) and 10°/s (at 4 Hz). The data presented here show that this conclusion is valid even at much higher stimulus amplitudes and frequencies.

A final potential nonlinearity examined is half-cycle asymmetry between responses of a sinusoidally stimulated afferent to inhibitory and excitatory rotations. Previous work in the squirrel monkey has shown that the responses of vestibular-nerve afferents to constant excitatory and inhibitory accelerations (Goldberg and Fernández 1971a) and sinusoidal rotation (Fernández and Goldberg 1971) may not always be equal. In regularly firing units in the chinchilla, over the frequency range studied here, no such asymmetry was noted either by analysis of stimulus-response plots or by comparing the second and third harmonics of the neural response.

The signals provided by regularly discharging afferents are thus remarkably linear even at the highest peak velocities and accelerations tested. Although a small proportion are silenced in response to the most intense stimuli, the bulk of regular afferents provide information faithful enough to drive the VOR over the physiological range of sinusoidal head movements. This finding is supported by and extends the conclusions of previous work (Minor and Goldberg 1991) that showed, using galvanic ablation of irregularly discharging afferents, that signals from the regular afferents are sufficient to drive the VOR at frequencies <= 4 Hz for stimuli with a peak velocity of 20°/s.

Because the regular afferents maintain their linearity well into the range over which nonlinearities in the VOR have been identified (Das et al. 1995; Minor et al. 1999), other mechanisms must be responsible for creating these nonlinearities observed in the normal physiology of the reflex and after unilateral loss of vestibular function (Aw et al. 1996). Whether these mechanisms originate in signals carried by irregular afferent fibers or in central vestibular processes remains to be determined.


    ACKNOWLEDGMENTS

This work was supported by National Institute on Deafness and Other Communication Disorders Grants R01 DC-02390 and T32 DC-00027, and by National Aeronautics and Space Administration Cooperative Agreement NCC 9-58 with the National Space Biomedical Research Institute.


    FOOTNOTES

Address for reprint requests: L. B. Minor, Department of Otolaryngology- Head and Neck Surgery, Johns Hopkins University School of Medicine, 601 N. Caroline St., Rm. 6253, Baltimore, MD 21287-0910.

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

Received 14 April 1999; accepted in final form 22 June 1999.


    REFERENCES
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

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