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Department of Psychology, Monash University, Clayton, Victoria 3168, Australia
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ABSTRACT |
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 Abstract
 Introduction
Methods
Results
Discussion
References
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Heil, Peter. Auditory cortical onset responses revisited. I. First-spike timing. J. Neurophysiol. 77: 2616-2641, 1997. Sound onsets are salient and behaviorally relevant, and most auditory neurons discharge spikes locked to such transients. The acoustic parameters of sound onsets that shape such onset responses are unknown. In this paper is analyzed the timing of spikes of single neurons in the primary auditory cortex of barbiturate-anesthetized cats to the onsets of tone bursts. By parametric variation of sound pressure level, rise time, and rise function (linear or cosine-squared), the time courses of peak pressure, rate of change of peak pressure, and acceleration of peak pressure during the tones' onsets were systematically varied. For cosine-squared rise function tones of a given frequency and laterality, any neuron's mean first-spike latency was an invariant and inverse function of the maximum acceleration of peak pressure occurring at tone onset. For linear rise function tones, latency was an invariant and inverse function of the rate of change of peak pressure. Thus latency is independent of rise time or sound pressure level per se. Latency-acceleration functions, obtained with cosine-squared rise function tones under different stimulus conditions (frequency, laterality) from any given neuron and across the neuronal pool, were of strikingly similar shape. The same was true for latency-rate of change of peak pressure functions obtained with linear rise function tones. Latency-acceleration/rate of change of peak pressure functions could differ in their extent and in their position within the coordinate system. The positional differences reflect neuronal differences in minimum latency Lmin and in a sensitivity S to acceleration and rate of change of peak pressure (transient sensitivity), a hitherto unrecognized neuronal property that is distinctly different from firing threshold. Estimates of Lmin and S, which were derived by fitting a simple function to the neuronal latency-acceleration/rate of change of peak pressure functions, were independent of rise function. On average, Lmin decreased with increasing characteristic frequency (CF), but varied widely for neurons with the same CF. S varied with CF in a fashion similar to the cat's audiogram and, for a given neuron, varied with frequency. SD of first-spike latency was roughly proportional to the slope of the functions relating latency to acceleration/rate of change of peak pressure. Thus SD increased exponentially, rather than linearly, with mean latency, and did so at about twice the rate for linear than for cosine-squared rise function tones. The proportionality coefficients were quite similar across the neuronal pool and similar for both rise functions. Minimum SD increased nonlinearly with increasing Lmin. These findings suggest a peripheral origin of S and a peripheral establishment of latency-acceleration/rate of change of peak pressure functions. Because of the striking similarity in the shapes of such functions across the neuronal pool, sound onsets will produce orderly and predictable spatiotemporal patterns of first-spike timing, which could be used to instantaneously track rapid transients and to represent transient features by partly scale-invariant temporal codes.
Natural acoustic signals, including many of those used by animals and humans for auditory communication, are spectrally and temporally complex. A recent study has emphasized the importance of the temporal structure of the envelope by showing that it can convey an unexpected amount of information needed for speech recognition (Shannon et al. 1995 Animal preparation
Seven adult cats (3 females and 4 males, weighing between 2.6 and 3.8 kg) contributed data to this study. All had healthy ears as judged by otoscopic inspections of the tympani and middle ears and by the shapes and sensitivities of the N1 audiogram. Each cat was deeply anesthetized with pentobarbitone sodium (40 mg/kg ip). Atropine (0.3 ml im) was administered to reduce tracheal mucous secretion. A broad-spectrum antibiotic (Amoxil; 0.5 ml im) was also given. The trachea and the radial vein were cannulated and anesthesia was maintained throughout surgery and recordings (up to 30 h) by intravenous injections of pentobarbitone in a physiological saline solution that also contained a few drops of heparin. The electrocardiogram was continuously monitored and rectal temperature was held near 38°C by a thermostatically controlled DC blanket. Surgical procedures have been described in detail elsewhere (Heil et al. 1992b Acoustic stimulation and recording procedures
The cat was located in a sound-attenuating chamber. Stimuli were digitally produced (Tucker Davis Technology) and presented to the cat's ears via precalibrated sealed sound delivery systems. Each system consisted of a STAX SRS-MK3 transducer in a coupler. The sound delivery tube of the coupler fitted snugly into the meatal stub.
Data analysis
Spikes in response to the 20 presentations of a given stimulus were displayed off-line as a poststimulus time histogram. The histogram was used to select analysis windows that would comprise only onset responses and would discard late discharges, offset responses, and occasionally presumed spontaneous spikes. Spontaneous activity was generally very low (<3 spikes/s) and late discharges, if they occurred at all, were clearly separated in time from onset responses by marked intervals of no activity. Thus the selection of an appropriate onset window was generally straightforward. In most cases, analysis windows used for a given neuron were the same for all rise times and amplitudes studied (e.g., from 5 to 100 ms after tone burst onset). In some instances, however, different windows had to be selected. In these cases, windows for tones of long rise times and low amplitudes were longer or delayed relative to windows for tones of short rise times and high amplitudes, because otherwise onset responses would have been missed or late responses would have been included, respectively. In the present paper aspects of spike timing are analyzed, whereas in the companion report the focus is on response magnitudes. Only the timing of the first (and in many neurons the only) spike will be considered because the interspike intervals of the onset responses of auditory cortex neurons, which discharge more than one spike per stimulus, are very regular and independent of stimulus level (Phillips and Sark 1991 The results on mean first-spike latency are presented first, and then those on the variability of first-spike latency. In each section, data recorded with cosine-squared rise function tones are presented before those recorded with linear rise function tones, followed by a comparison of the results obtained with the two different rise functions.
Data base
This study is based on 74 well-isolated single neurons, recorded in the left AI, as inferred from the locations of the recording sites with respect to the sulcal pattern, the tonotopic sequence, and the presence of a short-latency strong evoked potential to tone bursts. In only one penetration in one cat did we not see an AI-like evoked potential. The twoneurons recorded in this penetration (95-87/03 and 95-87/04)had very long minimum latencies (>30 ms). A few isolated AI neurons, which were spontaneously active, appeared not to be driven by tone bursts. Sixty-five neurons were studied with tones shaped with cosine-squared rise functions, 39 neurons were studied with tone bursts shaped with linear rise functions, and 30 neurons were studied with both types of tones. Tones were presented with the neuron's preferred stimulus laterality, which was binaural for 31 neurons, contralateral for 40 neurons, and ipsilateral for 3 neurons. Four neurons were in addition studied with several stimulus lateralities. The neurons in the sample had CFs ranging from 1.5 to 35.2 kHz, with most CFs in the octave band from 12 to 24 kHz. Three neurons were also studied at multiple frequencies other than their CFs.
Mean first-spike timing
ASPECTS OF COSINE-SQUARED RISE FUNCTION TONES.
Figure 1, left, schematically illustrates the time courses of the envelopes of the onsets of cosine-squared rise function signals. During the rise time the peak pressure (in Pa), but not the SPL (in dB SPL), of the signal changes according to the rise function (Fig. 1, top left). The rate of change of peak pressure also changes gradually during the rise time (Fig. 1, top middle). It is zero at the beginning and at the end of the rise time and reaches a maximum halfway through the rise time. Acceleration of peak pressure is maximal at the beginning of the rise time and decreases smoothly with time. It is zero halfway through the rise time. From then on acceleration becomes increasingly negative (deceleration) and reaches a negative maximum at the end of the rise time (Fig. 1, top right). Thereafter acceleration is zero. Alterations of both plateau peak pressure and rise time effect the onset of stimuli shaped with cosine-squared rise functions, but in different fashions. A 6-dB increase in the plateau SPL of stimuli with a given rise time will lead to a twofold increase in the maximum rate of change of peak pressure and in the maximum acceleration of peak pressure. Shortening the rise time by a factor of 2 for any given plateau SPL also leads to a twofold increase in the maximum rate of change of peak pressure (Fig. 1, 2nd row, middle), but maximum acceleration of peak pressure increases fourfold (Fig. 1, 2nd row, right). Therefore signals can be grouped to match in rise time, plateau peak pressure, maximum rate of change of peak pressure, or maximum acceleration of peak pressure (Fig. 1, 1st-4th rows, respectively). Signals that share the same value of maximum acceleration of peak pressure differ in rise time and in plateau peak pressure (Fig. 1, bottom row).
MEAN FIRST-SPIKE LATENCY TO COSINE-SQUARED RISE FUNCTION TONES.
Figure 2a shows the mean first spike latencies of one AI neuron (95-95/04) to contralateral CF tone bursts of 22 kHz, all shaped with cosine-squared rise functions. The data are plotted as a function of plateau peak pressure (in Pa). The longest mean first-spike latency of ~100 ms was measured in response to tones with 170-ms rise times and plateau peak pressures of 0.00028 Pa, equivalent to 20 dB SPL. For each rise time, latency declines nonlinearly with increasing plateau peak pressure. For tones of any given plateau peak pressure, latency increases systematically with rise time, although the different functions appear to converge on a single minimum at ~12.3 ms.
COMPARISON OF LATENCY-ACCELERATION FUNCTIONS AMONG DIFFERENT NEURONS.
The latencies of neurons 95-95/04 and 95-98/03 in Fig. 2 are plotted with the same resolution, and comparison of Fig. 2, c and f, reveals that their latency-acceleration functions are very similar in shape. In Fig. 3a, latency-acceleration functions obtained from another five neurons are plotted in a single graph, facilitating a comparison of latency-acceleration functions among different neurons. The data illustrated in Fig. 3a were selected to represent neurons recorded in different cats and with widely different CFs (range 2.3-30 kHz), data obtained with different laterality of presentation, and functions covering very different ranges of latency. The latency-acceleration function of neuron 95-98/08 ( MATHEMATICAL DESCRIPTION OF LATENCY-ACCELERATION FUNCTIONS.
To get quantitative measures of the similarity of the latency-acceleration functions of different neurons and of the shifts along the ordinate and abscissa required to obtain congruence, a simple mathematical function was selected that described the form of the latency-acceleration functions, and also allowed quantification of the positional differences along the abscissa and the ordinate
COMPARISON OF TRANSIENT SENSITIVITY AND FIRING THRESHOLD.
S is not to be confused with firing threshold, a measure generally expressed in dB SPL and related to peak pressure. To emphasize this point more clearly, note, for example, that in Fig. 3a, the latency functions of neurons 95-98/08 (
EFFECTS OF STIMULUS LATERALITY ON LATENCY-ACCELERATION FUNCTIONS.
In four neurons latencies to tone bursts were presented with different stimulus lateralities, i.e., binaural, monaural contralateral, and monaural ipsilateral. In general, stimulus laterality had a very small, if any, effect on the shapes of the latency-acceleration functions or their horizontal position within the coordinate systems. In a comparison of stimulus laterality in a given neuron, fitting results yielded differences in S that averaged 0.1 and were all <0.3, ~1/10 of the variation seen across neurons. The largest effect of stimulus laterality was on the estimated Lmin. With monaural ipsilateral stimulation Lmin was consistently 2-3 ms longer than with contralateral or binaural stimulation, whereas differences in Lmin between monaural contralateral and binaural stimulation were <0.9 ms.
EFFECTS OF STIMULUS FREQUENCY ON LATENCY-ACCELERATION FUNCTIONS IN A GIVEN NEURON.
In three neurons latencies were obtained to tone bursts of different frequencies including the CF. Results from two of these neurons (95-95/18 and 95-95/09) are illustrated in Fig. 6. Figure 6, a and d, shows mean latencies plotted against maximum acceleration of peak pressure. The latency-acceleration functions for different frequencies all have similar shape, but are obviously dispersed along the abscissa. The analysis of the fitting results illustrates the systematic nature of this dispersion: in Fig. 6, b and e, the value of S obtained from these fits is plotted against tone burst frequency. For neuron 95-95/18 the highest transient sensitivity is obtained for 26.8 and 24.8 kHz, and S decreases toward higher and lower frequencies, whereas for neuron 95-95/09 the function is more complex.
EFFECTS OF STIMULUS FREQUENCY ON LATENCY-ACCELERATION FUNCTIONS ACROSS NEURONS.
For a comparison of latency-acceleration functions among different neurons, only measures obtained at CF were considered. Figure 7 provides a scatterplot of Lmin, as obtained from the fits, against frequency. In different neurons, Lmin varied between 5.6 and 37 ms, with most values between 9 and 15 ms. On average, Lmin decreased with increasing CF. This decrease is obvious for the shortest Lmin and a similar trend for the entire data set emerged from a regression analysis. Lmin was closely correlated with the shortest measured latency (r2 = 0.894), but on average was 1.8 ms shorter.
ASPECTS OF LINEAR RISE FUNCTION TONES.
With linear rise functions, the rate of change of peak pressure during the rise time is constant (Fig. 9) and, for a given rise time, its magnitude is directly proportional to the plateau peak pressure achieved at the end of the rise time, and, for a given plateau peak pressure, is inversely proportional to rise time. Thus the first derivative of the stimulus envelope has the shape of a rectangle, with its vertical axis proportional to rate of change of peak pressure (expressed in Pa/s) and its horizontal axis equivalent to the rise time (Fig. 9, middle). Signals shaped with linear rise functions can be grouped to match either in rise time (Fig. 9, top), in plateau peak pressure (middle), or in the rate of change of peak pressure (bottom). Acceleration of peak pressure occurs at the beginning of the rise time and deceleration occurs at the end of the rise time. Mathematically, acceleration and deceleration are instantaneous and their magnitudes are infinite.
MEAN FIRST-SPIKE TIMING TO LINEAR RISE FUNCTION TONES.
Figure 10, a and b, shows the mean first-spike latencies of neuron 95-95/04 to linear rise function tones. It is the same neuron for which latencies obtained with cosine-squared rise function tones were illustrated in Fig. 2, a-c. Figure 10a illustrates that for each rise time, latency declines nonlinearly with plateau peak pressure. For tones of a given plateau peak pressure, latency increases with rise time. As was the case with cosine-squared rise function tones, the curves appear to converge on a single minimum and in response to some tones of long rise times the neuron discharges long before the plateau peak pressure is reached.
POST HOC ANALYSIS OF PREVIOUSLY PUBLISHED LATENCY DATA.
There has been one previous report on the effect of varying rise time and level of linear rise function tones on the responses of AI neurons (Phillips 1988
COMPARISON OF LATENCY-RATE OF CHANGE OF PEAK PRESSURE FUNCTIONS AMONG DIFFERENT NEURONS.
As was the case for latency-acceleration functions obtained with cosine-squared rise function tones, the latency-rate of change of peak pressure functions of different neurons obtained with linear rise functions tones could be brought into very close register by allowing shifts along the ordinate and the abscissa (not shown). The common form of these latency-rate of change of peak pressure functions, which differed from that of the latency-acceleration functions, and the shifts along the coordinates were found with fitting procedures analogous to those described above for cosine-squared rise functions and using the same type of formula
COMPARISON OF LATENCY WITH LINEAR AND WITH COSINE-SQUARED RISE FUNCTION TONES.
Thirty neurons were studied with both linear and cosine-squared rise function tones of the same frequency and can therefore be used for a direct comparison of the relevant features of latency functions. Figure 12a shows a scatterplot of the estimated minimum latencies obtained with linear and with cosine-squared rise functions tones. As expected, the two estimates are nearly identical. Note that they lie close to the line of unity slope. A linear regression analysis yielded a slope of 0.87 with r2 = 0.973. Exclusion of only the rightmost point increases the slope to 0.94.
SD of first-spike timing
The data presented so far have been based on the mean first-spike latency derived from up to 20 individual measures of latency on consecutive stimulus repetitions. However, the timing of the first spike varied from trial to trial. In accordance with previous studies (e.g., Aitkin et al. 1970 COSINE-SQUARED RISE FUNCTIONS.
The finding that with cosine-squared rise function tones a neuron's mean first-spike latency is a function of the maximum acceleration of peak pressure suggests the possibility that the SD of the first-spike latency may also be a function of this parameter.
LINEAR RISE FUNCTION TONES.
Comparable results were obtained with linear rise function tones. Data from one neuron (95-92/02) are illustrated in Fig. 17. With linear rise function tones, SD of first-spike latency is an inverse function of the rate of change of peak pressure (Fig. 17b), just as for mean latency (Fig. 17a). The systematic differences in the shapes of the functions relating mean latency and SD to rate of change of peak pressure again suggest that SD may be proportional to the slope of the function relating mean latency to rate of change of peak pressure
COMPARISON OF COSINE-SQUARED AND LINEAR RISE FUNCTION TONES.
Figure 18a shows a scatterplot of the estimated minimum SDs obtained with linear and cosine-squared rise function tones. Both stimuli yielded very similar estimates, the points lying close to the line of unity slope. A linear regression analysis yielded a slope of 0.75 with r2 = 0.912. Exclusion of only the rightmost point increased the slope to 0.98 with r2 = 0.938. In Fig. 19, the estimated minimum SD obtained with linear rise function tones is plotted against the estimated minimum first-spike latency (open circles). This plot also suggests a nonlinear relationship between the two estimates. To emphasize the similarity with the results obtained with cosine-squared rise functions, the data of Fig. 16 are retained in Fig. 19 (solid squares).
The present paper demonstrates that first-spike latency of auditory cortical neurons is an unambiguous function of acceleration of peak pressure at tone onset for cosine-squared rise function tones, and of the (constant) rate of change of peak pressure for linear rise function tones. With linear rise functions, acceleration of peak pressure is mathematically instantaneous and infinite in amplitude. However, the acoustic signal is transformed into a receptor potential, and, as jugded from intracellular recordings of inner hair cells (e.g., Russell and Sellick 1983 Comparison with previous studies
Acceleration of peak pressure has previously not been recognized as a relevant parameter of acoustic signals. But this parameter has been varied, almost certainly without the experimenters' awareness, in a huge number of studies, e.g., in all those in which stimulus manipulations affected the SPL at the eardrum, whereas rise time and rise function were kept constant. In the context of the recent proposal of a temporal code for sound location by cortical neurons (Middlebrooks et al. 1994 Other factors influencing first-spike latency
Although first-spike latency is a function of the acceleration/rate of change of peak pressure at tone onset, this is not to say that a particular acceleration/rate of change in a signal will under all circumstances evoke a response from a neuron with the same latency. The near-threshold effect, as described in this paper (e.g., Fig. 14), is a case in point. The laterality of stimulus presentation is another factor. Laterality does not appear to influence the shape of latency-acceleration/rate of change functions, but it affects the functions' position along the ordinate, i.e., it affects the minimum latency. In the few neurons excited by stimulation of either ear, studied here, minimum latency was systematically longer by 2-3 ms for ipsilateral stimulation than for contralateral or binaural stimulation. This could reflect one or two additional synapses, slower conduction velocities, or longer lengths of the ipsilateral pathways to these neurons.
Common shape of latency-acceleration functions
A comparison of latency-acceleration functions, or of latency-rate of change of peak pressure functions, among different neurons or stimulus conditions revealed that they are all of strikingly similar shape despite differences in the position and in the extent of these functions along the coordinates. The latter observation simply reflects differences in the shape of the spike count functions (see companion paper for a detailed account of these issues).
Possible origin of the latency-acceleration/rate of change of peak pressure relationship
The finding of nearly identical shapes of latency-acceleration/rate of change of peak pressure functions among different neurons and different stimulus conditions is surprising given the enormous degree of convergence and divergence of connections at nuclei peripheral to the cortex, as well as within the cortex itself, and given that cortical cells are likely to differ widely in the number of serial synapses in their afferent pathways. However, the findings that the shortest estimated minimum latencies decrease with increasing CF, that the distribution of estimated transient sensitivities grossly parallels the cat's audiogram, and that the relationship between SD and first-spike latency could possibly be accounted for by jitter in peripheral mechanics, suggest that the common relationship between latency and acceleration/rate of change of peak pressure may have its origin in the peripheral auditory system. The latencies of basilar membrane vibration and of the receptor potential of inner hair cells appear to be independent of the amplitude of acoustic stimuli, such as clicks (Robles et al. 1976 Functional implications
Although a particular acceleration or rate of change of peak pressure at tone onset is transformed into a particular neuronal latency in a smooth analog fashion, the brain has no means of measuring the latency. However, one way for the brain to derive useful information through latency is by means of a comparison of the timing of spikes across a neuronal population, as originally proposed by Hind et al. (1963)
INTRODUCTION
Abstract
Introduction
Methods
Results
Discussion
References
). Animal studies have shown that throughout the auditory pathway neurons can be excited by rapid temporal changes in stimulus envelopes, provided that the stimuli have an adequate spectral content. In many studies researchers have used stimuli with repetitive envelope fluctuations, such as periodically amplitude-modulated sinusoids or noise or click trains, and have demonstrated that neuronal responses can be locked to the individual repetitive envelope fluctuations (e.g., auditory nerve: Joris and Yin 1992; cochlear nucleus: Frisina et al. 1985; Rhode and Greenberg 1994; inferior colliculus: Heil et al. 1995; Langner and Schreiner 1988; Rees and Møller 1983; thalamus: Rouiller et al. 1981; cortex: Eggermont 1993; Schreiner and Urbas 1988).
). This peak reflects the locking of the neuron's initial spike(s) to the tone's onset, and therefore such responses or response components are sometimes referred to as onset responses. Because of the demonstrated phase-locking of spikes to amplitude-modulated signals or click trains, such signals may constitute a rapid series of like onsets for a neuron. In fact, Rhode and Greenberg (1992) have noted that cochlear nucleus neurons, classified as onset units, phase-lock with high precision also to low-frequency signals (sinusoidal carriers and amplitude-modulated sounds) ". . . responding as if each cycle is an effective excitatory stimulus" (p. 100). Onset response components are also evident in the discharge patterns of neurons in locations higher up the pathway, such as the medial geniculate or the auditory cortex (for review see Clarey et al. 1992). Onset responses appear to be least vulnerable to the effects of anesthesia (Zurita et al. 1994), and the responses of neurons in the auditory cortices of chloralose- and barbiturate-anesthetized animals are dominated by discharges locked to the stimulus onset (e.g., Brugge et al. 1969; Phillips 1988; Zurita et al. 1994).
; Pickles 1988) have been of some concern, and to reduce spectral splatter at signal onset, signals are generally shaped with some finite rise time. The neglect of the physical parameters of sound onsets (other than the general concern about spectral splatter), despite the recognition that the initial discharges of most auditory neurons are evoked by stimulus onsets, has an almost paradoxical consequence: it can be seen in innumerable studies that measures of neuronal properties that were extracted from onset responses (or responses that contained an onset component) are reported and analyzed with respect to stimulus parameters that characterize features of the steady-state or plateau portion of the stimulus. An important case in point is the effect of sound pressure level (SPL) on neuronal onset responses. Alterations of the SPL of a stimulus inevitably coalter features of its onset, particularly when the rise function and the rise time are held constant, as is routinely done. When stimuli are shaped with the widely used linear rise function, for example, the most obvious feature is the slope of the envelope, i.e., the rate at which the peak pressure changes until the plateau value is reached. Any 6-dB increase in SPL will double this rate. A second feature that is coaltered with SPL under such conditions is the quasi-instantaneous acceleration of peak pressure, a parameter whose potential relevance has not been recognized at all. Both stimulus onset parameters are also coaltered when the rise time is altered and the SPL is held constant. Thus it is conceivable that neuronal onset responses might be shaped by factors other than the SPL or the short-term frequency spectrum.
; Hall and Feng 1988). In speech sounds, for example, rise time can vary with the manner of articulation (Pickett 1980; Stevens 1980). Rise time can in fact cue perceptual categories in speech (Cutting and Rosner 1974; Stevens 1980), but clearly affects the perception of nonspeech sounds as well (Cutting and Rosner 1974). In humans, the just noticable difference for a change in rise time is ~25% of the duration of the rise time (van Heuven and van den Broecke 1979). Natural signals, including speech sounds, also differ in rise function, but according to our knowledge, in no physiological or psychophysical studies has the potential relevance of this onset feature been investigated. Nevertheless, the auditory system will experience, and may be able to discriminate, a wealth of different sound onsets.
) the question of how auditory onset responses code or represent auditory onsets is investigated. This question is addressed by focusing the analysis on onset parameters such as the rate of change or the acceleration of peak pressure. Onset features were varied by varying SPL, rise time, and rise function. In addition to the widely used linear rise function, which is characterized by a constant rate of change of peak pressure during the rise time, cosine-squared rise functions were used. These have the advantage that peak pressure, rate of change, and acceleration of peak pressure are smooth and assessable functions of time that reach their maxima at different points during the rise time and are differentially affected by manipulations of rise time or SPL. Neurons of the primary auditory cortex (AI) are particularly suited to tackle the issue of onset coding because they preferentially respond to sound onsets, and any later discharges, if they occur, can be readily distinguished (e.g., Brugge et al. 1969). Because auditory cortical neurons have complex frequency filters, we have employed simple tonal stimuli to more easily decipher the effects of carrier frequency. A thorough understanding of coding strategies for isolated onsets will also promote our understanding of the coding of envelope transients that occur periodically or aperiodically during the course of complex auditory signals and that are so critical for speech recognition (Shannon et al. 1995). Preliminary reports of some of the findings have been presented (Heil 1996; Heil and Irvine 1996a).
METHODS
Abstract
Introduction
Methods
Results
Discussion
References
). In brief, the left auditory cortex was exposed by trepanation of the overlying skull and removal of the dura. A specially designed Perspex chamber was mounted to the skull surrounding the opening, filled with warm saline, and sealed with a glass plate on which a small hydraulic microdrive was mounted and that housed the glass-insulated tungsten microelectrode. Each bulla was exposed and a round-window electrode and a length of fine-bore polyethylene tubing, allowing static pressure equalization within the middle ear, were inserted through a small hole. Thereafter the bullae were resealed with dental acrylic. The external meati were also cleared of surrounding tissue and transected to leave only short meatal stubs.
at 1 kHz) was positioned manually close above a chosen point on the cortical surface and was then advanced near-normal to the surface by means of the microdrive. Neural activity was amplified (×1,000) and, for recording of action potentials, also filtered (500-5,000 Hz) and displayed on storage oscilloscopes.
).
where CRT is the cosine-squared rise time (in s).1
(1)
Maximum RCPP is reached halfway through the rise time and is given by
(2)
The acceleration of peak pressure APP (in Pa/s2) varies with time according to
(3)
![− sin<SUP>2</SUP>(<IT>t</IT>/<IT>CRT</IT>*π/2 + π/2)]](/content/vol77/issue5/fulltext/2616/img006.gif)
Maximum APP occurs at the beginning of the rise time and is given by
(4)
With a linear rise function, the peak pressure changes according to
(5)
where LRT is the linear rise time (in s) and PPplateau/LRT identifies the constant rate of change of peak pressure RCPP (in Pa/s). Mathematically, acceleration and deceleration of peak pressure are instantaneous and infinite and occur at the beginning and at the end of the rise time, respectively.
(6)
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FIG. 1.
Schematics of envelope characteristics of the onsets of tone bursts shaped with cosine-squared rise functions. Left: for 3 different stimuli, time courses of the peak pressure during the rise time are shown. Only the top halves of the symmetrical envelopes are illustrated. Middle and right: resulting time courses of the rate of change of peak pressure and the acceleration of peak pressure, respectively. Signals in the rows from top to bottom are of identical rise time, plateau peak pressure, maximum rate of change of peak pressure, and maximum acceleration of peak pressure, respectively. Note that plateau peak pressure, rate of change of peak pressure, and acceleration of peak pressure reach their maxima at different points during the rise time.
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FIG. 9.
Schematics of envelope characteristics of the onsets of tone bursts shaped with linear rise functions. Left and right: for 3 different stimuli (identified by 
, - - -, and · · ·), the time courses of peak pressure and of rate of change of peak pressure, respectively. Signals in the top row are of identical rise time, signals in the middle row are of identical plateau peak pressure, and signals in the bottom row are of identical magnitude of rate of change of peak pressure.
). Mean and SD of first-spike latency, measured from stimulus onset, response probability, and number of discharges in the window were computed. As a rule, only means and SDs based on response probabilities of 
0.15 were considered further.
RESULTS
Abstract
Introduction
Methods
Results
Discussion
References
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FIG. 2.
Effects of rise time and plateau peak pressure of cosine-squared rise function tones on latency. Mean 1st-spike latency of neurons 95-95/04 and 95-98/03 (left and right, respectively) to 20 repetitions of characteristic frequency (CF) tones shaped with cosine-squared rise functions of 5 and 6 different rise times (see key). In a and d, mean latency is plotted as a function of plateau peak pressure (in Pa). The range of 5 orders of magnitude is equivalent to a 100-dB range of sound pressure level (SPL) from about 
10 to 90 dB SPL. In b and e, mean latency is plotted as a function of the maximum rate of change of peak pressure, and in c and f as a function of the maximum acceleration of peak pressure. Note the close congruence of the latency-acceleration functions. For further details see RESULTS.
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FIG. 14.
Comparison of SD and of mean of 1st-spike latency. Data are from neuron 95-98/14, stimulated binaurally with CF tones of 5.5 kHz. Note the pronounced near-threshold effects for both mean and SD of 1st-spike latency. The 7 near-threshold points were discarded for the fits of the functions relating SD to maximum acceleration of peak pressure and to mean latency in b and c, respectively. All other conventions as in Fig. 13.
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FIG. 3.
Comparison of latency-acceleration functions. a: data from neurons from different cats, with different CFs, obtained with different laterality of stimulus presentation are selected to illustrate the similarity in the shapes of the latency-acceleration functions despite differences in their extent. Mean latencies obtained from a given neuron are represented by the same symbols, and latencies obtained from that neuron with tones of the same rise time are connected by solid lines. Note that, as in the cases illustrated in Fig. 2, mean latencies are in close register when plotted as a function of maximum acceleration of peak pressure. b: mean latencies of 2 neurons from a are reproduced. Solid and dashed lines: best fits of Eq. 8 to the data. The 2 fitted functions have identical shape. As can be derived from the differences in the solutions for Lmin and S for the 2 neurons (as specified in the key), the function for neuron 95-98/16 is displaced upward by 8.3 ms and rightward by 0.95 log units of maximum acceleration of peak pressure relative to the function of neuron 95-95/03. For further descriptions see RESULTS.
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FIG. 13.
Comparison of SD and mean of 1st-spike latency. Data from neuron 95-98/11 (a-c), stimulated with contralateral CF tones of 10.3 kHz, and from neuron 95-98/01 (d-f), stimulated binaurally with CF tones of 20.3 kHz, are illustrated. a and c: mean 1st-spike latencies obtained with tones of different cosine-squared rise times (see keys) plotted against maximum acceleration of peak pressure. b and e: corresponding SDs of 1st-spike latency also plotted against maximum acceleration of peak pressure. Note that the functions obtained with different rise times are in close register. Solid lines without symbols: best fits of Eq. 15 to the data sets. The equation assumes that the SD is proportional to the slope of the mean latency-acceleration function. c and f: scatterplots of the SD of 1st-spike latency against the mean. Solid lines: best fits of Eq. 16 to the data sets. Dashed lines: best linear fits. See RESULTS for further explanations.
) covered an extensive range of latency (130-15 ms) and of maximum acceleration of peak pressure (>8 orders of magnitude). Because of higher response thresholds, strongly nonmonotonic spike count functions, or both, the latency-acceleration functions of the other neurons were more restricted along the abscissa, but also along the ordinate. However, an inspection of Fig. 3a suggests that the shapes of these more restricted functions closely resemble sectors of the extensive function of neuron 95-98/08. This is most obvious for neuron 95-95/03 (
), which had a threshold slightly higher than that of neuron 95-98/08. Neuron 95-92/21 (
) had a considerably higher threshold, but also slightly longer mean latencies, than neuron 95-98/08. But even the course of the latency-acceleration function of neuron 95-98/16 (
), which is restricted at each end, resembles the course of the extensive function of neuron 95-98/08 in its intermediate part.
The subscript CRF indicates that the measures were obtained with cosine-squared rise function tones. LCRF is a neuron's mean latency as a function of maximum acceleration of peak pressure APPmax. Lmin is the minimum or asymptotic latency against which LCRF converges for acceleration approaching infinity. Lmin is a constant that would include all the delays that are independent of the stimulus magnitude, such as acoustic delays, delays introduced by the traveling wave in the cochlea, the sum of all axonal travel times, and possibly some synaptic factors. The other term describes the inverse dependence of latency on the magnitude of maximum acceleration of peak pressure, where ACRF is a scaling factor and S is the neuron's transient sensitivity, which codetermines the position of the function along the abscissa. The value of S is the logarithm of an acceleration of peak pressure (in Pa/s2). A larger S places the function more to the left and represents a higher transient sensitivity (see also Fig. 3b). The function does not account for the near-threshold effects observed in some neurons and described above. It also does not account for the finding that in a few neurons with nonmonotonic spike-count functions, mean latency could increase slightly but systematically with very high values of maximum acceleration of peak pressure (e.g., 95-95/03 in Fig. 3, a and b).
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were allowed to vary. Each deviation of the fitted function from the measured mean latency was squared and then weighted by multiplying it with the response probability on which the measured mean was based. The smallest sum of the weighted squared deviations, i.e., the best fit, was generally found with <1,000 iterations. In some cases the fit was found to improve with increasing . The improvement, however, was marginal for > 4, and also pushed ACRF into unwieldy dimensions (e.g., years for = 10). For a second fitting step, we therefore selected = 4, and allowed Lmin, ACRF, and S to vary. For the 93 different functions fitted, ACRF showed a unimodal distribution. Figure 4a shows a scatterplot of ACRF against the number of first spikes that had contributed to the fitted function. The figure shows that the width of the distribution of ACRF diminished rapidly with increasing number of first spikes and converged toward theweighted average of ÃCRF = 12,791 ms (Fig. 4a, - - -).In a third and final fitting procedure, ACRF was also kept constant (at 12,791 ms). In this way, a function with a fixed shape, as determined by and ACRF, but free to be placed within the coordinate system of latency and maximum acceleration of peak pressure, was fitted to the data
Figure 4b provides a scatterplot of the sums of the weighted least-squared deviations of mean latency obtained with the second and third fitting step, i.e., with ACRF variable and ÃCRF fixed at 12,791 ms, respectively. Only few points are considerably above the line of unity slope (dashed line). The three most deviating points were provided by one neuron tested under different stimulus conditions. In general, the most deviating points were based on low numbers of first spikes. Most points are in relatively close proximity to the dashed line, indicating that the latency-acceleration function with the fixed shape provides nearly as good a description of the data as does a function with an additional free variable.
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FIG. 4.
Descriptions of neuronal latency-acceleration functions. a: scatterplot of the scaling factor ACRF obtained from fitting the function
to neuronal latency-acceleration functions against the number of 1st spikes contributing to the fit. Note that the distribution converges against the weighted average of ÃCRF = 12,791 ms (- - -) with increasing number of 1st spikes, thus with presumed increasing reliability of the fit. b: scatterplot of the sums of the weighted least-squared deviations of the above functions, fitted to the relationship between mean latency and maximum acceleration of peak pressure, from the actual data. ACRF was either a free parameter or it was fixed at ÃCRF = 12,791 ms, the value of its weighted average. In only a few instances was the quality of the fit notably reduced when ACRF was fixed. Note that most points are close to the line of unity slope (- - -).
) and 95-95/03 () are in nearly perfect register, without requiring any notable shifts to obtain congruence, i.e., the two neurons have the same S. However, the latency functions do not start at the same point along the abscissa, reflecting differences in their firing thresholds. Figure 5 presents, for all neurons in the sample, a scatterplot of the firing thresholds (in dB SPL) against S. Each neuron contributed multiple data points to the plot, because threshold SPL increased with rise time (see companion paper and also Fig. 6). Although a low transient sensitivity seems to exclude low-threshold SPLs, there is only a loose relationship between the two parameters (r2 = 0.123; n = 319). Threshold SPLs can vary over a range of 100 dB for the same S.
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FIG. 5.
Scatterplot of neuronal firing thresholds (expressed in dB SPL) against S extracted from latency-acceleration functions. S is the logarithm of acceleration of peak pressure measured in Pa/s2. Note that the 2 measures are only loosely related.
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FIG. 6.
Effects of tone burst frequency on latency-acceleration functions. Data from 2 neurons (95-95/18, a-c, and 95-95/09, d-f) are shown. In a and d, mean latency is plotted against maximum acceleration of peak pressure and different symbols identify different frequencies. Mean latencies obtained with tones of the same cosine-squared rise time are connected. Note the different resolutions of the abscissas and ordinates in a and d. b and e: measure of S, obtained from fitting Eq. 8 to the latency-acceleration functions for tones of different frequencies. S reflects the size of the lateral displacement of these functions, and a difference in S of 1 is equivalent to 20 dB. c and f: conventional response threshold curves or tuning curves obtained with tones of different cosine-squared rise times. Threshold was defined by a response probability of 0.1. Note the increase in thresholds with rise time throughout the frequency range (see also companion paper). Note that the transient sensitivity vs. frequency functions share features with the classical tuning curves (cf. b with c and e with f).
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FIG. 7.
Estimated minimum latency Lmin obtained from fits of Eq. 8 to the latency-acceleration functions plotted against tone frequency. Data obtained at frequencies other than the CF are omitted. Note that neurons of the same CF can differ widely in their minimum latency and that Lmin tends to decrease with frequency.
for illustrations of audiograms measured under different stimulus conditions). At most frequencies the vertical scatter in the data points of Fig. 8 is in the range of only 0.5, equivalent to 10 dB. Because there may have been differences in hearing sensitivity among the six cats that contributed data to this figure, differences in the sensitivities of the two ears in a given cat, and imprecisions in CF determination (cf. Fig. 6), it is conceivable that some, if not all, of this vertical scatter may be noise due to these factors.
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FIG. 8.
S obtained from fits of Eq. 8 to the latency-acceleration functions plotted against tone frequency. Data obtained at frequencies other than the CF are omitted and fits with the most reliable S are shown with solid squares.
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FIG. 10.
Effects of rise time and plateau peak pressure of linear rise function tones on latency. Mean 1st-spike latency of neurons 95-95/04 and 95-87/13 (left and right, respectively) to linear rise function CF tones of different plateau peak pressure and different rise time. In a and c, mean latency is plotted as a function of plateau peak pressure (in Pa). Different symbols identify different rise times (see key) and latencies to tones of the same rise time are connected. In b and d, mean latency is plotted as a function of rate of change of peak pressure. Note the close match of the latency functions obtained with the 5 different rise times.
). In the following, I present a post hoc analysis of latency data published in that paper, because they showed a behavior that is markedly different from that of all neurons in my sample. Figure 11, left, replots latency of one of the three units (viz., RT206) for which Phillips has presented data, and Fig. 11a does so in the published and conventional form, viz., as a function of plateau peak pressure or tone level (in dB SPL). As noted by Phillips (1988), for each rise time latency declines with increasing level toward asymptotic values, but the functions do not converge on a single minimum.
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FIG. 11.
Analysis of data presented by Phillips (1988) on effects of rise time and plateau peak pressure of linear rise function tones on latency of 2 neurons from cat auditory cortex (RT206, left, and RT209, right). a and f were taken from this study, and show latency to CF tones with different linear rise times (see key) as a function of SPL. In b and g, latency is plotted as a function of rise time for tones of the same plateau peak pressure (in dB SPL, see key). Note that all functions have slopes >1. Dashed lines have unity slope. In c and h, latency is plotted as a function of the rate of change of peak pressure for tones of the same rise time. Note that the functions are not in register, unlike those of the units illustrated in Fig. 10. In d and i, latency is plotted as a function of rise time for tones of the same rate of change of peak pressure. Note that latency increases directly with rise time, and thus increases with plateau peak pressure. Dashed lines have unity slope. In e and j, the rise time was subtracted from the response latency and values were plotted as a function of rate of change of peak pressure. These corrected latency functions are in close register, suggesting that in these units spikes were triggered by the quasi-instantaneous deceleration at the end of the rise time. See text for further discussion.
), all slopes are 1 (for comparison, unity slope is illustrated by the dashed line in Fig. 11b). Linear regression analysis revealed slopes of 2.94 ± 0.05, 1.91 ± 0.02, 1.54 ± 0.04, 1.46 ± 0.05, and 1.05 ± 0.03 for plateau peak pressures equivalent to 22, 34, 46, 58, and 70 dB SPL, respectively. In other words, the differences in response latencies to tone bursts of the same plateau peak pressure are larger than the differences in rise time. In Fig. 11c, the latency data of Fig. 11a are plotted against the rate of change of peak pressure during the rise time. Note that the functions obtained with different rise times are not in register, quite unlike the behavior of all neurons in our sample (cf. Fig. 10, b and d). Instead, latency for tones of the same rate of change of peak pressure still increases systematically with rise time. This is more clearly illustrated in Fig. 11d, where latency is plotted as a function of rise time, and where each function represents latencies obtained from tone bursts characterized by the same rate of change of peak pressure.
has published latency data, and are illustrated for RT209 in Fig. 11, f-j.
The weighted average of the scaling factor ÃLRF found with the 39 neurons studied with linear rise function tones was 1,277 ms.
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FIG. 12.
Comparison of estimates derived from latency to linear and to cosine-squared rise function tones. a: scatterplot of minimum latencies. b: scatterplot of S. Note that both types of stimuli yield nearly identical estimates of minimum latency and of transient sensitivity. Dashed lines have unity slope.
Rearranging terms yields
and
![log<IT>APP</IT><SUB>max</SUB> = (<IT><A><AC>A</AC><AC>˜</AC></A></IT><SUB>CRF</SUB>/<IT><A><AC>A</AC><AC>˜</AC></A></IT><SUB>LRF</SUB>)<SUP>1/4</SUP>*log<IT>RCPP + S</IT>*[(<IT><A><AC>A</AC><AC>˜</AC></A></IT><SUB>CRF</SUB>/<IT><A><AC>A</AC><AC>˜</AC></A></IT><SUB>LRF</SUB>)<SUP>1/4</SUP>* − 1]](/content/vol77/issue5/fulltext/2616/img016.gif)
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; Brugge et al. 1969; Kitzes et al. 1978; Phillips and Hall 1990; Phillips et al. 1989), the SD of the first-spike latency around the mean will be used here as a measure of this variability.
. Instead, the shape differences suggest that SD may be proportional to the slope of the latency-acceleration function. Such a relationship would result from jitter in the effective acceleration of peak pressure, viz., in the term (APPmax + S).
where SDCRF is the SD of the first-spike latency as a function of APPmax and cCRF is the proportionality coefficient. SDmin is a minimum or asymptotic SD that is independent ofAPPmax, as is the estimated minimum latency in Eq. 8, and would include the total jitter in those components thought to add up to the minimum latency, such as cochlear travel time, propagation of action potentials, and some synaptic factors. The term dLCRF/d(log APPmax + S) identifies the slope of the function relating mean first-spike latency to maximum acceleration of peak pressure. This relationship can be described as in Eq. 8
(14)
so that SDCRF should be related to APPmax by
()
and to the mean first-spike latency LCRF by
(15)
Thus, if the SD of the first spike were proportional to the slope of the function relating mean first-spike latency to the logarithm of the maximum acceleration of peak pressure, then the SD should grow in a nonlinear, exponential fashion with mean latency (Eq. 16).
(16)
), linear fits did provide good descriptions of the relationships between SD and mean latency: values of r2 were as high as 0.969 with a weighted average of 0.610. However, the nonlinear fits proposed here (Eq. 16) were in some cases markedly better than linear fits (up to 40%). Averaged over the entire data sample, the nonlinear functions provided a fit that was ~2% better than the linear functions. In a small number of data sets, SD appeared to be independent of maximum acceleration of peak pressure, and thus also independent of mean first-spike latency. This was the case with 10 linear and 8 nonlinear fits. These data sets were all among those with the smallest numbers of first spikes.
0.102. This observation is reminiscent of the one made above for the scaling factor A (Fig. 4a), used in the description of the latency-acceleration functions. Thus cCRF between SD and slope of the latency-acceleration function may in fact be very similar across the neuronal pool and the range of stimulus conditions used here. For a description of the average relationship between SD and acceleration of peak pressure, Eq. 15 may therefore be written as
and Eq. 16 as
(17)
Figure 16 provides a scatterplot of the estimated SDmin against the estimated Lmin. SDmin increases continuously with Lmin, but note that the distribution of the points does not suggest a linear but rather a power relationship between the two parameters. With Lmin approaching zero, SDmin converges against zero (Fig. 16, - - -).
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FIG. 15.
Scatterplot of the proportionality coefficient cCRF, relating the SD of the 1st-spike latency to the slope of the latency-acceleration function (Eq. 15), plotted against the number of 1st spikes having contributed to the fit. Note that with increasing number of 1st spikes the distribution rapidly converges against the weighted average of cCRF = 0.1016 (- - -).
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FIG. 16.
Scatterplot of the estimated SDmin of 1st-spike latency against the estimated Lmin. SDmin approaches 0 (- - -) with Lmin approaching 0. Also note that SDmin grows in a distinctly nonlinear fashion with Lmin.
and therefore
(19)
And the relationship with the mean latency is then given by
(20)
The solid lines in Fig. 17, b and c, represent the best fits of Eq. 20 and 21 to the data, whereas the dashed line in Fig. 17c represents the best linear fit. Again, although linear fits provided a good description of the relationship between SD and mean latency, Eq. 21 provided yet a better fit, both for the neuron illustrated in Fig. 17 and, on average, for the entire data sample (not shown). The width of the distribution of the cLRF also decreased with the number of first spikes that contributed to the fit (not shown), with a weighted average of cLRF =
(21)
0.119. This number is close to the one obtained with cosine-squared rise functions signals, viz., 0.102 (see above).
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FIG. 17.
Comparison of SD and of mean of 1st-spike latency obtained with linear rise function tones. Data are from neuron 95-92/02, stimulated with contralateral CF tones of 18.5 kHz. Other conventions as in Fig. 13.
and Eq. 21 as
(22)
(23)
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FIG. 18.
Comparison of estimates derived from SD to linear and to cosine-squared rise function tones. a: scatterplot of the estimated minimum SDs. b: scatterplot of the proportionality coefficient between SD and slope of the functions relating mean latency to rate of change (cLRF) and to acceleration of peak pressure (cCRF), respectively. Note that both types of stimuli yield nearly identical estimates of minimum SD and similar estimates of the proportionality coefficients. Dashed lines have unity slope. Dot-dashed line in b has a slope of 1.78. This slope would have been expected if there were a fixed exponential relationship between SD and mean latency, irrespective of the rise function. Note that nearly all points fall well below this line. See RESULTS for further explanation.
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FIG. 19.
Scatterplot of the estimated SDmin of 1st-spike latency against the estimated Lmin. Data obtained with linear and with cosine-squared rise function tones are shown by open circles and solid squares, respectively. Other conventions as in Fig. 16.
Figure 20 shows, for three neurons, scatterplots of the SD against the mean first-spike latency to CF tones shaped with linear and with cosine-squared rise functions. Note that SD above the estimated minimum SD grows with mean latency at a higher rate for linear rise function tones than for cosine-squared rise function tones.
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FIG. 20.
Comparison of the growth of SD with mean latency for linear and for cosine-squared rise function tones. Data for 3 neurons are shown. Neuron 95-91/02 was stimulated with binaural tones of 15.5 kHz, neuron 95-92/02 with contralateral tones of 18.5 kHz, and neuron 95-95/04 with contralateral tones of 22 kHz. Solid and dashed lines: best fit of Eq. 16 and 21, respectively. Note that SD grows with mean latency at a higher rate for linear rise function tones than for cosine-squared rise function tones.
DISCUSSION
Abstract
Introduction
Methods
Results
Discussion
References
), the rise of the DC receptor potential to high-frequency tones shaped with linear rise functions is no longer precisely linear, but rather somewhat curvilinear. Consequently, the rate of rise of the DC receptor potential is no longer constant, and its acceleration is no longer instantaneous and infinite. Acceleration of the DC receptor potential may rather be a rapidly decaying function of time (in principle similar to the course of acceleration of peak pressure in cosine-squared rise function tones; Fig. 1). Thus, with linear rise function tones, latency may also be a function of the (transformed) acceleration at tone onset, a view also favored by the finding that latency to such tones could be determined very early during the rise time (i.e., within <1 ms). For both cosine-squared and linear rise functions, acceleration is maximal at the beginning of the rise time. The present study therefore cannot resolve the question of whether it is the magnitude of the initial or the maximum acceleration occurring during the rise time that is the critical value.
). Furthermore, as is shown in the companion paper, the first spike can be triggered at very different signal amplitudes, even for signals that share the same acceleration or, with linear rise functions, the same rate of change of peak pressure.
), it is worth emphasizing that the SPL is also affected by changes in a sound source's position in three-dimensional space (azimuth, elevation, and distance) given the frequency-dependent shadowing effect of the head and the frequency-dependent pressure transformations performed by the pinna (for review see Carlile 1996). The neglect of acceleration in onsets has likely been due to the focus of attention on features characteristic of the steady-state parts of signals, such as the SPL or, in binaural studies, interaural intensity differences. Thus, in previous studies, latency was usually plotted as a function of SPL, and was found to be inversely related to it (e.g., Aitkin et al. 1970; Brugge et al. 1969; Hind et al. 1963; Kitzes et al. 1978; Phillips 1985, 1988; Phillips and Hall 1990; Phillips et al. 1989). Rise functions of artificial auditory signals have mainly been introduced with the purpose of reducing spectral splatter at signal onsets. However, even in studies specifically designed to investigate the effects of the shape of tone onsets on neuronal responses by altering rise times, neuronal response properties were plotted with respect to SPL (Phillips 1988; Phillips et al. 1995).
showed that for these neurons the first spike is triggered at the end of the rise time, i.e., at the instant of deceleration of peak pressure (see Fig. 11). A consequence of this behavior is that when signals are grouped according to the same rate of change of peak pressure during the rise time, latency increases with rise time, and thus increases with tone level, a phenomenon that at first glance seems paradoxical. Phillips (1988) did not measure first-spike latency, but instead latency was defined as the interval between stimulus onset and the peak bin of the poststimulus time histogram. Although this methodological difference is highly unlikely to account for the observed differences in response latency between the present data and those of Phillips, there may be further, undetected, methodological differences between the two studies. On the other hand, it cannot be excluded that there might be two classes of cells in auditory cortex, in one of which the latencies are a function of acceleration and in the other a function of deceleration of peak pressure. The latter neurons might be either very rare, or located in areas that were not surveyed in the present study, although we probably did study a representative sample of AI neurons, as judged by their distributions of CF and minimum latency, their frequency tuning and binaural characteristics (see Data base), and the shapes of their spike count functions (see companion paper).
; Brugge et al. 1969; Kitzes et al. 1978; Phillips 1985, 1988; Phillips and Hall 1990; Phillips et al. 1989), and in two studies as a function of mean first-spike latency (e.g., Phillips and Hall 1990; Phillips et al. 1989). Although Phillips and Hall proposed a linear relationship between SD and mean latency, several observations in the present study are incompatible with a linear relationship. The different growth rates of SD with mean latency for cosine-squared and linear rise function tones (Fig. 20) and the finding that SD declined more rapidly than latency with acceleration (or rate of change) of peak pressure for low values of this parameter and less rapidly for higher values are difficult to reconcile with a linear relationship. Careful inspection of previous publications (e.g., Aitkin et al. 1970; Brugge et al. 1969; Kitzes et al. 1978; Phillips and Hall 1990) reveals that the latter result was also obtained by these authors. The nature of the differences in the shapes of the functions relating mean latency and SD to maximum acceleration (or rate of change) of peak pressure suggested that SD is proportional to the slope of the functions relating mean latency to acceleration (or rate of change) of peak pressure, and this relationship described the data somewhat better than a linear one. Jitter in the effective acceleration of peak pressure, i.e., in the term (log APPmax + S) of Eq. 8 or, for linear rise function tones, jitter in the effective rate of change of peak pressure, i.e., in the term (log RCPP + S) of Eq. 12, would cause or closely approach such a relationship. Thus jitter in the neuronal S or jitter in the way in which a given acceleration or rate of change of peak pressure is represented in the motion of the basilar membrane, i.e., jitter in peripheral mechanics and cochlear amplifiers, might underlie the SD of first-spike timing. The finding that the proportionality coefficient between SD and the slope of the latency functions is so similar across the neuronal population, and similar for the two rise functions, also favors this notion.
) by some factor in the postsynaptic neuron. Thus a nonlinear relationship between minimum SD and minimum latency should be expected, in line with the finding of the nonlinear growth of the minimum SD with the minimum mean latency (Figs. 16 and 19).
; Brugge et al. 1969; Heil et al. 1992a; Hind et al. 1963; Kitzes et al. 1978). The present study shows in addition that the forms of the functions relating latency to acceleration are very similar for different frequencies, and that it is their position along the acceleration axis that differs systematically with frequency. Latency to a tone burst has also been shown to increase by up to 3 ms when the tone burst is preceded by a masking tone (Calford and Semple 1995). Similarly, latency also increases with the repetition rate of tone bursts (Phillips and Hall 1990; Phillips et al. 1989), a parameter that was not varied in the present study. Close inspection of the figures provided by Phillips and coworkers (Figs. 1c, 2c, and 8b in Phillips et al. 1989; Fig. 3a in Phillips and Hall 1990) reveals that the effect of repetition rate on latency seems to be a systematic displacement of the latency functions (i.e., latency-level functions) along the ordinate. This suggests that the effects of repetition rate and frequency on latency are different in origin. And finally, latency to tone bursts is prolonged when the tone bursts are presented after the onset of a long-duration broadband noise masker (Phillips 1985). Inspection of the relevant figures (Figs. 2, c and f, 6, and 7, c and f) suggests that background noise has a similar effect as frequency, i.e., brings about a displacement of the latency functions along the abscissa.
; Ruggero and Rich 1987), axonal travel times, and possibly some synaptic components, simply add up and yield a minimum latency.
; Heil et al. 1995; Kitzes et al. 1978; Langner et al. 1987), although latency was measured either at some fixed tone level or at some level above firing threshold (30-60 dB in different studies).
; but see companion paper). The distribution of transient sensitivities at CF for different neurons is also a function of frequency, and appears to be grossly similar to the cat's audiogram. For comparison, the reader is referred to a study by Rajan et al. (1991) that summarizes a range of N1 audiograms measured under various experimental conditions in barbiturate-anesthetized cats. Although N1 thresholds depend critically on stimulus paradigms, such as rise time, and other conditions, audiogram shapes are fairly similar, particularly for frequencies >3 kHz.
), whereas in response to similar stimuli the latencies of auditory nerve fibers are a sensitive function of amplitude (e.g., Pfeiffer and Kim 1972). If these findings can be extrapolated to stimuli with longer rise times, it then appears that the relationship between latency and acceleration/rate of change of peak pressure originates in the synapses between inner hair cells and afferent fibers. This proposal requires that the same relationship between latency and acceleration as seen in cortical cells must exist in the auditory nerve.
. It has long been recognized, for example, that differences in the timing of inputs from the two ears provide an important cue for sound localization, and that the differences are extracted via appropriate delays and coincidence detection mechanisms in brain stem auditory nuclei (e.g., Goldberg and Brown 1969; Overholt et al. 1992; Yin and Chan 1990). Likewise, interaural intensity differences of otherwise identical signals will lead to interaural latency differences from the two ears, and thus interaural intensity differences could be processed in a similar way as neural time differences ("latency hypothesis"; Jeffress 1948). However, as suggested by the present study, such latency differences would not be brought about by the intensity differences per se, but rather by the associated differences in acceleration or rate of change of peak pressure, urging a reinterpretation of observations made on time-intensity trading (see, e.g., Irvine et al. 1995).
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FIG. 21.
Schematic latency-acceleration functions of 6 hypothetical auditory neurons. Neurons 1-3 have identical transient sensitivity, but differ in minimum latency. Neurons 4-6 have identical minimum latency (the same as neuron 2), but differ in transient sensitivity, both from each other and from neurons 1-3. Note that the relative timing of the 1st spikes is independent of the magnitude of the acceleration of peak pressure for neurons with the same transient sensitivity, i.e., neurons 1-3 (middle), whereas the 1st spikes disperse with decreasing acceleration for neurons with the same minimum latency but with different transient sensitivity, i.e., neurons 2 and 4-6 (bottom).
). These neurons are best excited by a particular delay between a component of the pulse emitted by the bat and a component of the returning echo (e.g., O'Neill and Suga 1982). Interestingly, these neurons are tuned to combinations of an echo component with the highest amplitude preceded by the pulse component with the lowest amplitude, and thus likely with the lowest acceleration of peak pressure. This particular selection of pulse and echo components for target range computation is ideal with respect to minimizing the delay requirements of spikes triggered by the pulse so that they coincide at some comparator neuron with the spikes triggered by the echo.
). Consequently, the temporal relationships between the first spikes in such a population of neurons are constant and independent of the magnitude of acceleration of peak pressure (Fig. 21, middle). Such a temporal pattern could therefore constitute a scale-invariant representation, as recently suggested by Hopfield (1995), of this stimulus parameter. Minimum latencies seem to be laid out in orderly topographic fashions within isofrequency domains of various auditory nuclei (e.g., Heil and Scheich 1991; Heil et al. 1992a; Park and Pollak 1993; Schreiner and Langner 1988). It is therefore conceivable that the detection of such temporal patterns might be mediated through neurons receiving coincident inputs from neurons with some range of minimum latencies. Discharges from the higher-order neurons could then decode the presence of acceleration of peak pressure in a scale-invariant fashion, i.e., such neurons would signal the presence of a transient.
).
; Vos and Rasch 1981) may have its origin in differences in acceleration of peak pressure, rather than in ". . . adaptation of the hearing mechanism to a certain relative stimulus level . . ." (Vos and Rasch 1981, p. 323).
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ACKNOWLEDGEMENTS |
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I am grateful to Drs. D.R.F. Irvine and R. Rajan for help with the experiments; to J. F. Cassell, M. Farrington, V. N. Park, and R. Williams for technical support; to Drs. M. B. Calford, D.R.F. Irvine, and G. K. Yates and two anonymous reviewers for comments on the manuscript; and to many colleagues for critical discussions.
This study was supported by the National Health and Medical Research Council of Australia.
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FOOTNOTES |
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1 Tucker Davis Technologies utilizes a fudge factor of 0.5903 in their built-in cosine-squared rise function so that the actual rise time is 1.69 times as long as the one specified by the experimenter.
Received 5 August 1996; accepted in final form 26 December 1996.
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REFERENCES |
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Abstract
Introduction
Methods
Results
Discussion
References
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C. Huetz, B. Philibert, and J.-M. Edeline A Spike-Timing Code for Discriminating Conspecific Vocalizations in the Thalamocortical System of Anesthetized and Awake Guinea Pigs J. Neurosci., January 14, 2009; 29(2): 334 - 350. [Abstract] [Full Text] [PDF]
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W.-X. Pan, R. Schmidt, J. R. Wickens, and B. I. Hyland Tripartite Mechanism of Extinction Suggested by Dopamine Neuron Activity and Temporal Difference Model J. Neurosci., September 24, 2008; 28(39): 9619 - 9631. [Abstract] [Full Text] [PDF]
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 H. Luo, Y. Wang, D. Poeppel, and J. Z. Simon Concurrent Encoding of Frequency and Amplitude Modulation in Human Auditory Cortex: Encoding Transition J Neurophysiol, December 1, 2007; 98(6): 3473 - 3485. [Abstract] [Full Text] [PDF]
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S. C. Furtak, T. A. Allen, and T. H. Brown Single-Unit Firing in Rat Perirhinal Cortex Caused by Fear Conditioning to Arbitrary and Ecological Stimuli J. Neurosci., November 7, 2007; 27(45): 12277 - 12291. [Abstract] [Full Text] [PDF]
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H. H. Lim and D. J. Anderson Spatially Distinct Functional Output Regions within the Central Nucleus of the Inferior Colliculus: Implications for an Auditory Midbrain Implant J. Neurosci., August 8, 2007; 27(32): 8733 - 8743. [Abstract] [Full Text] [PDF]
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L. Qin, S. Chimoto, M. Sakai, J. Wang, and Y. Sato Comparison Between Offset and Onset Responses of Primary Auditory Cortex ON-OFF Neurons in Awake Cats J Neurophysiol, May 1, 2007; 97(5): 3421 - 3431. [Abstract] [Full Text] [PDF]
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B. Gourevitch and J. J. Eggermont Spatial Representation of Neural Responses to Natural and Altered Conspecific Vocalizations in Cat Auditory Cortex J Neurophysiol, January 1, 2007; 97(1): 144 - 158. [Abstract] [Full Text] [PDF]
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R. Narayan, G. Grana, and K. Sen Distinct Time Scales in Cortical Discrimination of Natural Sounds in Songbirds J Neurophysiol, July 1, 2006; 96(1): 252 - 258. [Abstract] [Full Text] [PDF]
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C. P. Billimoria, R. A. DiCaprio, J. T. Birmingham, L. F. Abbott, and E. Marder Neuromodulation of spike-timing precision in sensory neurons. J. Neurosci., May 31, 2006; 26(22): 5910 - 5919. [Abstract] [Full Text] [PDF]
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R. Narayan, A. Ergun, and K. Sen Delayed Inhibition in Cortical Receptive Fields and the Discrimination of Complex Stimuli J Neurophysiol, October 1, 2005; 94(4): 2970 - 2975. [Abstract] [Full Text] [PDF]
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A. V. Galazyuk, W. Lin, D. Llano, and A. S. Feng Leading Inhibition to Neural Oscillation Is Important for Time-Domain Processing in the Auditory Midbrain J Neurophysiol, July 1, 2005; 94(1): 314 - 326. [Abstract] [Full Text] [PDF]
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S. W. Cheung, S. S. Nagarajan, C. E. Schreiner, P. H. Bedenbaugh, and A. Wong Plasticity in Primary Auditory Cortex of Monkeys with Altered Vocal Production J. Neurosci., March 9, 2005; 25(10): 2490 - 2503. [Abstract] [Full Text] [PDF]
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 M. Steinschneider, I. O. Volkov, Y. I. Fishman, H. Oya, J. C. Arezzo, and M. A. Howard III Intracortical Responses in Human and Monkey Primary Auditory Cortex Support a Temporal Processing Mechanism for Encoding of the Voice Onset Time Phonetic Parameter Cereb Cortex, February 1, 2005; 15(2): 170 - 186. [Abstract] [Full Text] [PDF]
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Y. Kajikawa, L. de La Mothe, S. Blumell, and T. A. Hackett A Comparison of Neuron Response Properties in Areas A1 and CM of the Marmoset Monkey Auditory Cortex: Tones and Broadband Noise J Neurophysiol, January 1, 2005; 93(1): 22 - 34. [Abstract] [Full Text] [PDF]
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K. Imaizumi, N. J. Priebe, P. A. C. Crum, P. H. Bedenbaugh, S. W. Cheung, and C. E. Schreiner Modular Functional Organization of Cat Anterior Auditory Field J Neurophysiol, July 1, 2004; 92(1): 444 - 457. [Abstract] [Full Text] [PDF]
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A. Y. Y. Tan, L. I. Zhang, M. M. Merzenich, and C. E. Schreiner Tone-Evoked Excitatory and Inhibitory Synaptic Conductances of Primary Auditory Cortex Neurons J Neurophysiol, July 1, 2004; 92(1): 630 - 643. [Abstract] [Full Text] [PDF]
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M. Elhilali, J. B. Fritz, D. J. Klein, J. Z. Simon, and S. A. Shamma Dynamics of Precise Spike Timing in Primary Auditory Cortex J. Neurosci., February 4, 2004; 24(5): 1159 - 1172. [Abstract] [Full Text] [PDF]
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T. Lu and X. Wang Information Content of Auditory Cortical Responses to Time-Varying Acoustic Stimuli J Neurophysiol, January 1, 2004; 91(1): 301 - 313. [Abstract] [Full Text]
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M. A. Escabi, L. M. Miller, H. L. Read, and C. E. Schreiner Naturalistic Auditory Contrast Improves Spectrotemporal Coding in the Cat Inferior Colliculus J. Neurosci., December 17, 2003; 23(37): 11489 - 11504. [Abstract] [Full Text] [PDF]
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A. Fishbach, Y. Yeshurun, and I. Nelken Neural Model for Physiological Responses to Frequency and Amplitude Transitions Uncovers Topographical Order in the Auditory Cortex J Neurophysiol, December 1, 2003; 90(6): 3663 - 3678. [Abstract] [Full Text] [PDF]
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M. R. DeWeese, M. Wehr, and A. M. Zador Binary Spiking in Auditory Cortex J. Neurosci., August 27, 2003; 23(21): 7940 - 7949. [Abstract] [Full Text] [PDF]
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D. L. Barbour and X. Wang Auditory Cortical Responses Elicited in Awake Primates by Random Spectrum Stimuli J. Neurosci., August 6, 2003; 23(18): 7194 - 7206. [Abstract] [Full Text] [PDF]
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M. W. Raggio and C. E. Schreiner Neuronal Responses in Cat Primary Auditory Cortex to Electrical Cochlear Stimulation: IV. Activation Pattern for Sinusoidal Stimulation J Neurophysiol, June 1, 2003; 89(6): 3190 - 3204. [Abstract] [Full Text] [PDF]
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 P. Heil and H. Neubauer A unifying basis of auditory thresholds based on temporal summation PNAS, May 13, 2003; 100(10): 6151 - 6156. [Abstract] [Full Text] [PDF]
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D. Zoccolan, G. Pinato, and V. Torre Highly Variable Spike Trains Underlie Reproducible Sensorimotor Responses in the Medicinal Leech J. Neurosci., December 15, 2002; 22(24): 10790 - 10800. [Abstract] [Full Text] [PDF]
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O. Bar-Yosef, Y. Rotman, and I. Nelken Responses of Neurons in Cat Primary Auditory Cortex to Bird Chirps: Effects of Temporal and Spectral Context J. Neurosci., October 1, 2002; 22(19): 8619 - 8632. [Abstract] [Full Text] [PDF]
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J. P. Walton, H. Simon, and R. D. Frisina Age-Related Alterations in the Neural Coding of Envelope Periodicities J Neurophysiol, August 1, 2002; 88(2): 565 - 578. [Abstract] [Full Text] [PDF]
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L. Liang, T. Lu, and X. Wang Neural Representations of Sinusoidal Amplitude and Frequency Modulations in the Primary Auditory Cortex of Awake Primates J Neurophysiol, May 1, 2002; 87(5): 2237 - 2261. [Abstract] [Full Text] [PDF]
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J. J. Eggermont Temporal Modulation Transfer Functions in Cat Primary Auditory Cortex: Separating Stimulus Effects From Neural Mechanisms J Neurophysiol, January 1, 2002; 87(1): 305 - 321. [Abstract] [Full Text] [PDF]
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D.R.F. Irvine, V. N. Park, and L. McCormick Mechanisms Underlying the Sensitivity of Neurons in the Lateral Superior Olive to Interaural Intensity Differences J Neurophysiol, December 1, 2001; 86(6): 2647 - 2666. [Abstract] [Full Text] [PDF]
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P. Heil and H. Neubauer Temporal Integration of Sound Pressure Determines Thresholds of Auditory-Nerve Fibers J. Neurosci., September 15, 2001; 21(18): 7404 - 7415. [Abstract] [Full Text] [PDF]
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A. Fishbach, I. Nelken, and Y. Yeshurun Auditory Edge Detection: A Neural Model for Physiological and Psychoacoustical Responses to Amplitude Transients J Neurophysiol, June 1, 2001; 85(6): 2303 - 2323. [Abstract] [Full Text] [PDF]
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T. Lu, L. Liang, and X. Wang Neural Representations of Temporally Asymmetric Stimuli in the Auditory Cortex of Awake Primates J Neurophysiol, June 1, 2001; 85(6): 2364 - 2380. [Abstract] [Full Text] [PDF]
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S. W. Cheung, P. H. Bedenbaugh, S. S. Nagarajan, and C. E. Schreiner Functional Organization of Squirrel Monkey Primary Auditory Cortex: Responses to Pure Tones J Neurophysiol, April 1, 2001; 85(4): 1732 - 1749. [Abstract] [Full Text] [PDF]
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M. Brosch and C. E. Schreiner Sequence Sensitivity of Neurons in Cat Primary Auditory Cortex Cereb Cortex, December 1, 2000; 10(12): 1155 - 1167. [Abstract] [Full Text] [PDF]
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S. Biermann and P. Heil Parallels Between Timing of Onset Responses of Single Neurons in Cat and of Evoked Magnetic Fields in Human Auditory Cortex J Neurophysiol, November 1, 2000; 84(5): 2426 - 2439. [Abstract] [Full Text] [PDF]
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M. I. Sanderson and J. A. Simmons Neural Responses to Overlapping FM Sounds in the Inferior Colliculus of Echolocating Bats J Neurophysiol, April 1, 2000; 83(4): 1840 - 1855. [Abstract] [Full Text] [PDF]
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J. J. Eggermont Azimuth Coding in Primary Auditory Cortex of the Cat. II. Relative Latency and Interspike Interval Representation J Neurophysiol, October 1, 1998; 80(4): 2151 - 2161. [Abstract] [Full Text] [PDF]
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P. Heil and D. R. F. Irvine Functional Specialization in Auditory Cortex: Responses to Frequency-Modulated Stimuli in the Cat's Posterior Auditory Field J Neurophysiol, June 1, 1998; 79(6): 3041 - 3059. [Abstract] [Full Text] [PDF]
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P. Heil and D. R. F. Irvine First-Spike Timing of Auditory-Nerve Fibers and Comparison With Auditory Cortex J Neurophysiol, November 1, 1997; 78(5): 2438 - 2454. [Abstract] [Full Text] [PDF]
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P. Heil Auditory Cortical Onset Responses Revisited. II. Response Strength J Neurophysiol, May 1, 1997; 77(5): 2642 - 2660. [Abstract] [Full Text] [PDF]
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