Correlation Index: A new metric to quantify temporal coding

Hearing Research

Hearing Research 216–217 (2006) 19–30

www.elsevier.com/locate/heares

Research paper

Correlation Index: A new metric to quantify temporal coding Philip X. Joris *, Dries H. Louage, Liesbeth Cardoen, Marcel van der Heijden Laboratory of Auditory Neurophysiology, K.U. Leuven, Medical School, Campus Gasthuisberg O&N2 bus 1021, Herestraat 49, B-3000 Leuven, Belgium Received 10 November 2005; received in revised form 1 March 2006; accepted 7 March 2006 Available online 27 April 2006

Abstract The standard procedure to study temporal encoding of sound waveforms in the auditory system has been Fourier analysis of responses to periodic stimuli. We introduce a new metric – correlation index (CI) – which is based on a simple counting of spike coincidences. It can be used for responses to aperiodic stimuli and does not require knowledge of the stimulus. Moreover, the basic procedure of comparing spiketimes in spiketrains is more physiological than currently used methods for temporal analysis. The CI is the peak value of the normalized shuffled autocorrelogram (SAC), which provides a quantitative summary of temporal structure in the neural response to arbitrary stimuli. We illustrate the CI and SACs by comparing temporal coding in the auditory nerve and output fibers of the cochlear nucleus. Ó 2006 Elsevier B.V. All rights reserved. Keywords: Phase-locking; Vector strength; Temporal; Correlogram; Fine-structure; Envelope; Revcor

1. Introduction Study of the auditory system at many organizational levels has provided ample evidence that it excels at temporal coding. Correspondingly, auditory neuroscience has often been a breeding ground for new stimuli and analyses that exploit the time dimension. The 1960s and 1970s saw the first computer applications to characterize temporal aspects in the responses of neurons to clicks, tones, modulated tones, broadband noise, and other stimuli (De Boer and Kuyper, 1968; Gerstein and Kiang, 1960; Goldberg and Brown, 1969; Kiang et al., 1965; Møller, 1973; Rose et al., 1967; van Gisbergen et al., 1975). Particularly sophisticated use of this early computing power in auditory nerve Abbreviations: AN, auditory nerve; CF, characteristic frequency; CI, correlation index; CN, cochlear nucleus; CR, coincidence rate; DCN, dorsal cochlear nucleus; ISI, inter-spike interval; SAC, shuffled autocorrelogram; SAM, sinusoidal amplitude modulation; TB, trapezoid body; VS, vector strength; XAC, cross-stimulus autocorrelogram * Corresponding author. Tel.: +32 1634 5741; fax: +32 1634 5993. E-mail addresses: [email protected] (P.X. Joris), Dries. [email protected] (D.H. Louage), Liesbeth.Cardoen@student. kuleuven.ac.be (L. Cardoen), [email protected] (M. van der Heijden). 0378-5955/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.heares.2006.03.010

and cochlear nucleus was evident in series of studies by Aage Møller (reviewed by Rhode, this issue). Several of these temporal characterization techniques have entered mainstream neurophysiology and have been applied to other sensory systems. Generally, simple periodic stimuli and Fourier-based analyses have been favored by most physiologists. Indeed, current knowledge on the coding of fine-structure and envelope is mostly based on the study of phase-locking to pure tones and sinusoidally amplitude-modulated tones, respectively, with vector strength or synchronization index analysis (Goldberg and Brown, 1969; Johnson, 1980) at the stimulus frequencies of interest. The vector strength metric has provided a wealth of data and continues to do so, but it is not fit for all experimental questions (e.g. Cariani and Delgutte, 1996; Greenwood, 1986) and is problematic with aperiodic stimuli. Temporal analyses for such stimuli are available, reverse correlation in particular (Eggermont et al., 1983), but it is not straightforward to quantitatively compare results from these analyses with vector strengths to periodic stimuli. Our focus here is on simple stimuli, but a wealth of studies has addressed temporal coding to complex stimuli, speech in particular (see e.g. Delgutte, 1997; Wong et al., 1998, and references therein).

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Besides practical problems in relating temporal responses to periodic and aperiodic stimuli, a deeper problem with all these approaches is that they appear unphysiological in their computational complexity and their requirement for independent knowledge of the stimulus, which is not available to the central neural processor. We developed a simple metric, correlation index or CI, which is applicable for all stimuli; for which knowledge of the stimulus is not required; and which is based on a simple counting operation which is physiologically more plausible than any of the above methods. It is inspired on previous autocorrelation work (Cariani and Delgutte, 1996; Rodieck, 1967; Ruggero, 1973) and makes use of a simple manipulation that is a standard procedure in correlation techniques used in the study of the connectivity of neurons (Eggermont, 1990). 2. Materials and methods Our general procedures are described in previous reports (Joris, 1998, 2003; Joris et al., 2005a; Louage et al., 2004) and were approved by the K.U. Leuven Ethics Committee for Animal Experiments. Cats were anesthetised with pentobarbital. Micropipettes filled with 3 M NaCl were used to record from single fibers in the AN or dorsal acoustic stria exposed via a dorsal approach, and in the trapezoid body (TB), using a ventral exposure. Calibrated sounds were delivered with dynamic speakers via earbars placed in the transected ear canal. Spikes were timed at 1 ls resolution. For each fiber encountered, we determined the characteristic frequency (CF: frequency of lowest rate threshold) with an automated tuning curve program. A rate-level function to short tone bursts (25 ms, repeated 200 times every 100 ms) at CF was obtained at increasing SPL in 5 or 10 dB steps. A broadband stimulus (100 Hz–30 kHz) was then delivered at a number of SPLs (the values stated are overall SPLs, compensated for the acoustic calibration). Generally, a single pseudorandom noise token was used throughout an experiment and was played in two polarities, referred to as standard and inverted, typically with the following parameters: 1000 ms duration, repeated 50 times every 1200 or 1500 ms. Stimuli of opposite polarity have been used for response linearization by constructing ‘‘compound histograms’’ (Goblick and Pfeiffer, 1969; Møller, 1977), and they offer other advantages, as described in Section 3. MATLAB (The MathWorks, Natick, MA) routines for calculation of autocorrelograms and testing of statistical significance are provided in the supplementary material. 3. Results We first describe the CI and compare it to vector strength. For illustration we restrict ourselves to only a few auditory nerve (AN) and cochlear nucleus (CN) neurons: more comprehensive population data are found in our recent publications (Joris, 2003; Louage et al., 2004,

2005). We then briefly examine the relationship between shuffled autocorrelograms and revcors. 3.1. Temporal coding of fine-structure measured with the correlation index The top row in Fig. 1 shows responses from a low-frequency auditory nerve fiber (CF = 460 Hz) to a 25 ms tone at CF. The dot raster (panel A) indicates the occurrence of spikes, relative to the stimulus, upon repeated presentations of the same tone. The vertical patterning of the dots indicates that spikes occur at a preferred phase of the stimulus (the difference between red and black dots is explained below). This is more easily seen in the cycle or period histogram (panel B) in which the instantaneous firing rate is plotted as a function of stimulus phase. The inset shows the same data plotted in polar form, with each bin represented by a line with length equalling the number of spikes in the bin, and phase equalling the stimulus phase. Vectorial addition of all bins followed by division by the total number of spikes leads to a resultant referred to as the ‘‘vector strength’’ (Goldberg and Brown, 1969). It takes values between 1 (all spikes occur in 1 bin) and 0 (bin vectors cancel out). The angle / of the resultant (red line in polar plots) gives the average phase of the response. The bottom row in Fig. 1 shows responses from a TB fiber, tuned to the same frequency of 460 Hz. The alignment of spikes is much more precise for this neuron than for the AN fiber, resulting in a higher vector strength (panels D and E). Moreover, while in the AN cycles are often skipped, the CN neuron tends to discharge a spike at every cycle and thus has a higher discharge rate. This phenomenon of ‘‘entrainment’’ is not reflected in the vector strength but markedly influences the distribution of first-order spike intervals, i.e. intervals between successive spike within a spike train, as shown in the right column. In response to low-frequency tones, these interspike interval (ISI) histograms are multimodal in AN fibers (panel C) (Rose et al., 1967), but consist of a single dominating mode in some CN neurons (panel F) (Joris et al., 1994b; Rhode and Smith, 1986). In an earlier study (Joris et al., 1994a,b), enhanced synchronization to short tonebursts was found in the majority of low-CF fibers recorded from the TB. Some of these neurons were labelled intraaxonally and were shown to be CN spherical and globular bushy cells. But tones are unusual stimuli, in that they can induce sustained activity synchronized across a large population of AN fibers (Kim and Molnar, 1979). Does enhanced phase-locking extrapolate to other stimuli, for which synchronization across AN fibers is presumably more limited in spatial extent? We recorded responses of AN and TB fibers to broadband noise. Fig. 2 shows examples for the same two fibers of Fig. 1. The dot rasters (Fig. 2, left column) zoom in on an arbitrary portion of the response (300–400 ms after stimulus onset). They show the same phenomena in the noise responses as were observed in the responses to short tone bursts. There is a tendency to vertical alignment in the

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Fig. 1. Coding of fine-structure in an auditory nerve (AN, top row) and trapezoid body (TB, bottom row) fiber. A and D: Dot rasters to 50 (out of 200) stimulus presentations. The red dots indicate spikes that are coincident (within a 50 ls binwidth) with spikes in response to other presentations of the same stimulus. B and E: Cycle histograms. Magnitude (vector strength, VS) and phase / of the average vector are indicated. Insets are polar plots of the same data. They are at different scales in the two panels. The red line indicates the angle of the resultant. C and F: Interspike interval (ISI) histograms show the distribution of intervals between successive spikes within spiketrains. The dots below the abscissa indicate integer multiples of the stimulus period. All histograms have 100 bins and are based on the response between 10 and 25 ms to 200 stimulus repetitions; they have the same scale within each column. Spontaneous rates were 68 (AN) and 86 (TB) spikes/sec. Stimulus SPL was 50 dB in both cases, at which both fibers had reached rate saturation.

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Fig. 2. Broadband (0.1–30 kHz) noise responses of the same AN (top) and TB (bottom) fiber as in Fig. 1. Left column: dot rasters for part of the response to the 1 s noise burst. Right column: ISI histograms for the entire stimulus duration (1 s, overall SPL of 60 dB).

AN response, but this is much clearer in the TB response. Both neurons tend to fire a spike at the same temporal position upon repeated presentation of the same noise

stimulus, but the precision and consistency of firing are larger for the CN neuron than for the AN fiber. How can one quantitatively express these tendencies?

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The right column of Fig. 2 shows ISI histograms taken over the entire stimulus duration (1000 ms). The overall shape differs strongly for the two neurons, due to the higher firing rate and preponderance of short intervals in the responses of the TB fiber. There is a periodicity in the envelope of the histograms, be it more subtle than in Fig. 1C. Ruggero (1973) showed in the AN of the squirrel monkey that these periodicities are correlated with fiber CF. In that and later studies (e.g. Cariani and Delgutte, 1996; ten Kate and van Bekkum, 1988), higher-order interval histograms, also referred to as autocorrelograms, were computed by counting the intervals not only between successive spikes but for any two spikes within a spike train (Fig. 3A). Although such histograms provide much information, they have the disadvantage of an absence of small intervals, due to the refractory period. Thus, such autocor-

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Fig. 3. Construction of (A) a regular autocorrelogram and (B–D) a shuffled autocorrelogram (SAC) using 3 hypothetical spike trains. A: The regular autocorrelogram consists of all intervals between spikes within a spiketrain. B–D: SACs are calculated for spikes across spiketrains. In each panel, one spike is selected (asterisk). All forward intervals between this spike and all other spikes in non-identical spike trains are measured and tallied in a histogram (solid squares). Empty squares: histogram entries from intervals with other reference spikes.

relograms are suited to examine serial correlations at delays of several ms, but they do not provide information on the consistency with which neurons fire spikes at a particular time of a repeated stimulus. Also, they do not provide a straightforward metric to compare timing across neurons or across stimuli. Our quantification of the tendency of neurons to fire a well-timed spike at a consistent point of the stimulus waveform is based on counting coincident spikes across spiketrains (indicated by red dots in Figs. 1 and 2), and is inspired by an operation known to occur in coincidence detectors in the auditory system (Goldberg and Brown, 1969; Yin and Chan, 1990). Spike trains to repeated presentations of a single stimulus are obtained from a neuron, as in Figs. 1 and 2, and these spike trains are compared pairwise by counting the number of instances Nc that spikes are fired at the same instant in time. All permutations of spike trains are compared but a spike train is never compared with itself. In counting the number of coincidences, a window has to be defined over which two spikes are regarded as being coincident. We standardly use a 50 ls window: we will return to this choice below. The count of coincident spike times is akin to the output rate that a coincidence detector would show if it received two inputs with the properties of the neuron under study, and the procedure of counting can thus be neurally implemented without an external timing signal. Of course, the presence of coincident spikes does not in itself indicate temporal coding in the spiketrain. As an example, Fig. 5C shows dot rasters for spontaneous activity of the TB neuron also illustrated in previous figures. There is no temporal relationship between the spikes in the different spiketrains, but chance coincidences occur. To statistically test whether the number of coincidences Nc differs from that expected by chance, we use a bootstrap method. By random permutation of the interspike intervals, the measured spike trains are converted into ‘‘random spike trains’’ having the same spike-rate statistics. Nc is then computed for the scrambled data in the usual way. By computing Nc values for many (e.g. 1000) different scrambled versions, all obtained from the same response, the statistical distribution of Nc is examined. The confidence level p is the percentage of Nc values from scrambled data not exceeding the Nc value from the original data. To obtain a metric which quantifies temporal coupling of the spiketrain to the stimulus, we scale Nc to be independent of average firing rate (r), number of presentations (M), coincidence window (x) and stimulus duration (D), by dividing by M(M 1)r2xD (see Louage et al., 2004 for further details). This dimensionless quantity Nc /(M(M 1)r2xD) is the correlation index (CI). A CI of 1 indicates a total lack of stimulus-induced temporal structure; larger values indicate that spike times tend to be correlated between the different spike trains, and lower values indicate anticorrelation. If Nc is not normalized for average rate but only divided by M(M 1)xD, we refer to the metric as ‘‘coincidence rate’’ (CR, dimension s 2).

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The CI equals the peak height of the normalized shuffled autocorrelograms (SACs) that we have recently described, which we review before comparing CI and vector strength values.

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3.2. Shuffled autocorrelograms The CI as defined above measures the tendency of spikes to occur at the same poststimulus time: given that a spike occurs at instant t, how likely are spikes to occur at the same instant t when the stimulus is repeated? More generally, we want to pose this question for any other instant t + s. The distribution of coincidences for any delay s is given by the SAC, as illustrated in Fig. 3B– D. In each panel, the same 3 hypothetical spike trains from the same neuron in response to the same stimulus are shown, from which one spike is selected (asterisk). All forward intervals between this spike and all other spikes in non-identical spike trains are measured, and tallied in a histogram. This procedure is repeated for all spikes. Only intervals across spike trains are considered: by excluding intervals within spike trains the obscuring effect of the refractory period on short intervals is avoided. A similar procedure is used in cross-correlation analysis of paired neuronal recordings, be it with a different purpose: to distinguish stimulus–response coupling from neural coupling. This procedure is referred to as ‘‘shuffling’’ or the ‘‘shift predictor’’ (Eggermont, 1990; Gerstein and Perkel, 1972; Perkel et al., 1967a). SACs can be scaled with the same factor M(M 1)r2xD used for the CI: the value at s = 0 then equals the CI. This normalization renders the correlogram independent of stimulus and analysis parameters. Fig. 4 illustrates the SACs and CI for the data shown in Figs. 1 and 2. The SACs of the tonal responses (left column) consist of peaks spaced at the stimulus period. In comparison to the AN fiber (top), the responses of the TB fiber (bottom) yield peaks which are much narrower and have higher amplitude. The SACs to broadband noise (right column) have the shape of a damped oscillation and asymptote to unity at large positive and negative values of delay. The periodicity and shape of this oscillation are not imposed by the stimulus but by the cochlea (for the AN fiber) and further processing in the CN (for the TB fiber). Again, the main peak of the response of the TB neuron is higher and narrower than that of the AN neuron. Note that the presence of temporal structure is much more obvious in the SACs in Fig. 4B and D than in the corresponding ISI histograms (Fig. 2B and D) or all-order interval histograms (not shown, see Louage et al., 2004, Fig. 2 for several examples). This advantage of SACs is even more marked at higher CFs, where the temporal structure of the response can be entirely masked in ISI and all-order histograms because of the refractory period. The SACs are also much smoother than ISI histograms (Fig. 2B and D) of these same responses, even though no smoothing or any other processing was applied. The reason

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Fig. 4. Normalized SACs for the AN (top) and TB (bottom) responses of Figs. 1 and 2. The correlation index (CI) is indicated for each SAC. The tonal responses were analysed over a window of 10–25 ms; the noise responses over the entire stimulus duration (1 s). All SACs have the same scale.

is simply that SACs show many more intervals: from M(M 1) pairs of spiketrains rather than from M spiketrains in the case of standard histograms. An advantage of the CI is that it allows comparison of temporal coding of periodic and non-periodic stimuli by the same neuron. Interestingly, Fig. 4A and B shows that the CI of the AN fiber to noise is larger than that to short tones. This is the case in most low-CF AN fibers and is not dependent on the choice of SPLs (Louage et al., 2004). The CI of the TB fiber is larger to the short tone burst than to noise (Fig. 4C and D), but this reverses when the tone has the same long duration as the noise (Fig. 5A and B). This probably reflects temporal adaptation in TB (but not AN) fibers (Joris et al., 1994b). Note that the decrease in the magnitude of the peaks at non-zero delays in the SAC for tones in Fig. 4A and C is a consequence of the short analysis window (15 ms) and is not informative. Indeed, at a delay of 15 ms the spiketrains being compared no longer overlap so that the number of coincidences at that delay is 0. The decrease in number of coincidences as the delay approaches the analysis or response window gives all SACs a triangular shape, for which we did not correct (see e.g. ten Kate and van Bekkum, 1988). With sustained responses to long stimuli and a large analysis window (1000 ms in Figs. 4 and 5, right column), this triangular shape can be ignored because the delays of interest are small relative to the size of the analysis window. In counting the number of coincidences, a window x has to be defined over which two spikes are regarded as being

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Fig. 5. Responses to long tone bursts at CF, for the TB fiber of Figs. 1, 2 and 4. Left column: dot rasters at 50 dB (A) and 0 dB (C) for an arbitrary part of the response. Right column: SACs for the entire stimulus period (1000 ms). The stimulus at 0 dB was below the rate threshold (13 dB) and the spiketrains lack any temporal structure. CI values are stated in the right column: the value at 0 dB (D) was not significant. VS for the long tone in (A) was 0.92.

3.3. Comparison of vector strength and CI To further illustrate the relationship between vector strength and CI, Fig. 7 shows both measures calculated from responses to short CF-tones in a population of TB fibers. The sample was arbitrarily chosen without testing for statistical significance of vector strength or CI, but only responses to stimuli P20 dB SPL, from fibers with CF < 3.5 kHz, are included. Clearly, there is a positive correlation between the two measures, but not all datapoints follow the general trend. For example, TB fibers with ‘‘high-sync’’ responses (vector strength >0.9, (Joris et al.,

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coincident. The choice of this window requires balancing two opposing requirements. On the one hand it should be small enough to reveal the fastest temporal response features. The SACs in Fig. 4 show that a submillisecond window is required to capture the temporal features of this response. For example, integration over x = 1 ms would clearly bring down the central peak (and thus the CI) of the SAC in panel C. On the other hand, a small window results in fewer coincidences and a noisier measurement, which can only be offset with longer recording times. Fig. 6 shows CI values calculated for a range of x values, using noise responses of 5 neurons (1 AN and 4 TB fibers) spanning a range of CFs and SPLs. These functions all show the expected low-pass shape. In our studies of the AN and CN we have standardly used x = 50 ls because it is in the plateau portion of all fibers encountered. This x value is also used for the binwidth of the SACs, i.e. the Ds increments at which the spiketrains are shifted relative to each other.

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1994b)) show a considerable range of CI values. Datapoints that deviate from the general compressive relationship between the two metrics show smaller vector strengths than expected from this relationship. There is thus an asymmetry between the two metrics: responses with high vector strengths also give high CI values, but the

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reverse is not always the case. Neurons can fire spikes that are well-timed but with a small resultant vector. A straightforward example are responses with peak-splitting to acoustic stimuli at high SPLs (Kiang, 1990; Spirou et al., 1990) or to electrical sinewaves (van den Honert and Stypulkowski, 1987). Another example is chopping triggered by the stimulus envelope. 3.4. Temporal coding of envelope Enhancement of phase-locking is not restricted to finestructure but also occurs to envelopes. In fact, enhanceSAC A+

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ment of gain and dynamic range to envelopes were first described in the pioneering studies of Møller (1972, 1974, 1976) and have been confirmed by many authors since (reviewed by Joris et al., 2004). The CI and SAC analysis described above naturally pick up temporal coding of either fine-structure or envelope, or any mixture of these two. This is also the case for binaural neurons, which was partly the motivation for resorting to this analysis (Joris, 2003). SACs of responses synchronized to SAM stimuli are periodic (cf. Fig. 5B), and here too the CI can be used to quantify the alignment of spikes across repetitions, as a function of modulation frequency, SPL, etc. We have not systematically examined responses to SAM but have studied responses to noise for envelope contributions. Using the responses of two CN fibers, we now illustrate how the relative contributions of fine-structure and envelope can be disambiguated and quantified. Fig. 8 (top row) shows correlograms of a low-CF chopper (CF = 880 Hz) recorded in the TB. Panels A and B show SACs to the standard and inverted noise (these noises are henceforth referred to as A+ and A ). Inversion of the noise has no effect on the SAC: both panels show an oscillation which agrees with CF, superimposed on a broader peak. Any Gaussian noise with the same bandwidth and overall level will result in the same SAC: the differences between the two SACs shown are due to slow adaptation in the responsivity of the neuron during data collection (the responses to A were collected after those to A+). Panel C shows a cross-stimulus autocorrelogram (XAC) calculated from the responses to A+ and A . XACs are also all-order interval histograms, but the spike times are compared across responses to different stimuli (here the standard and inverted noise), rather than across responses to the same stimulus. Because here, in contrast to SACs, XAC

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DELAY (ms) Fig. 8. Coding of fine-structure and envelope revealed by correlogram analysis. Correlograms are for responses to broadband noise at an overall SPL of 70 dB, for a low-CF chopper in the TB (top row, noise bandwidth 50–8000 Hz) and a Pauser/Buildup unit recorded in the dorsal acoustic stria (bottom row, noise bandwidth 0.1–30 kHz). CFs were 880 Hz and 18.9 kHz, respectively. Columns 1 and 2 show SACs to standard (A+) and inverted (A ) broadband noise. From the spiketrains to these two stimuli, the cross-stimulus autocorrelogram (XAC, column 3) was calculated. Addition of the XAC to the SAC averaged from columns 1 and 2 results in the sumcor of column 4. In column 5, the XAC is subtracted from the averaged SAC. All graphs within a row have the same scale.

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there are no identical spike trains to be excluded, the normalization factor is MA+MA rA+rA xD. The XAC again shows a fast oscillatory component, which is however inverted in polarity compared to the SACs, as well as a slower component which is not inverted. These two components are better illustrated by summing (panel D, ‘‘sumcor’’) and subtracting (panel E, ‘‘difcor’’) SAC and XAC. They reflect spike timing coupled to fine-structure and envelope, respectively (Joris, 2003). Indeed, whereas inverting the stimulus waveform corresponds to a p phase shift of all stimulus components and thus also of all response components locked to the fine-structure, inversion does not affect the phase relationship between components, which determines the envelope phase (Hartmann, 1997). The temporal response of this low-CF chopper to noise is clearly affected by both fine-structure and envelope, to an about equal degree. The bottom panels illustrated correlograms for a highCF Pauser/Buildup neuron recorded from the dorsal acoustic stria (likely the axon of a DCN fusiform cell). Here the SACs and XAC are virtually indistinguishable. They show a single large central peak which lacks an oscillation coupled to stimulus fine-structure, and when subtracted from each other only noise remains (panel J). Note that in the difcor a value of 0 indicates the number of coincidences expected from chance (rather than a value of 1 as in the other correlograms).

Interestingly, some correlograms of high-CF neurons in the CN (but not in the AN) show a mild degree of envelope-induced oscillation (e.g. Fig. 8I), visible as shallow troughs surrounding the peak. This suggests bandpass-filtering of envelope components – a well-described phenomenon in the some CN types (Frisina et al., 1990; Møller, 1973, 1974; Rhode and Greenberg, 1994). However, the relationship between modulation transfer functions obtained with SAM stimuli and autocorrelograms has not been studied directly. Note that the broadband noise stimuli used here have no envelope modulation: the envelope components in the neural responses arise from processes in the cochlea (bandpass filtering, rectification, compression) and neuronal interactions in the CN. 3.5. Comparison of SACs and revcors From the response to broadband noise, both autocorrelograms and revcors (De Boer and Kuyper, 1968) can be calculated. Revcor analysis has proven its merits as a powerful tool (Eggermont et al., 1983) and, compared to the autocorrelogram analysis proposed here, it has the advantage of providing phase information. However, it is a linear analysis and it is therefore interesting to examine how its results may differ from an analysis based on autocorrelograms. Fig. 9 gives a first indication of such differences, again taking the AN and TB responses illustrated earlier

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Fig. 9. Comparison of difcor and revcor for AN (top row) and TB (bottom row) fiber of Fig. 2. Panels A and C: difcor (red) and revcor autocorrelation (blue), normalized to their maxima. Panels B and D: corresponding power spectra. Overall stimulus level was 60 dB.

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(Fig. 2). Revcors were calculated for both the response to the standard (A+) and the inverted (A ) broadband noise. Rather than autocorrelating each revcor with itself, which gives rise to a narrow artifactual peak at 0 delay due to the presence of high-frequency noise in the revcor, we cross-correlated the two revcors. Because the two revcors are obtained from the same neuron to the same stimulus (be it of opposite polarity), we refer to this product as the revcor autocorrelation, which we compare with the difcor obtained from these same responses. We choose to compare the revcor autocorrelation to the difcor rather than to the SAC, because difcors, like revcors, reflect fine-structure coding and lack envelope coding. For the AN fiber, the revcor autocorrelation and its power spectrum (Fig. 9, top row) are rather similar to the difcor and its spectrum (red), obtained from the same responses. The ordinate dimension differs for the two analyses and in this figure all functions have been normalized to their maximum. Note however that the dimension of the difcor (number of coincidences, normalized for average rate) is easier to interpret in physiological terms. The magnitude of the difcor can be used to compare the strength of phase-locking to fine-structure e.g. in low- versus highspontaneous AN fibers or in AN versus TB fibers. In principle revcors should be suited for that purpose as well, but we are not aware of such use, possibly because the magnitude of the revcor is a stimulus dimension rather than a neural dimension. For the TB fiber (Fig. 9, bottom row), there is less agreement between revcor and difcor. The difcor shows considerable distortion, reflected in a peak of harmonics slightly above 1 kHz which is absent in the revcors. A similar but smaller peak is also present in the difcor of the AN response (Fig. 9B). The presence of these harmonics is not surprising: strong distortion is present in all the TB responses shown earlier and to less an extent in the AN responses (Figs. 1, 4 and 5). The important point here is that simple autocorrelation analysis captures neuronal response properties that are interesting but which are lost when using a linear analysis like revcor. The distortion that stands out in Fig. 9D is a cubic distortion. In the autocorrelation function of the output of a system, the linear portion of the system’s response does not play a preferred role. More specifically, in a model system whose output is determined by a series of Wiener Kernels of increasing order, the output correlation function depends on kernels of all orders (including h0, the mean response rate). The 3rd-order contribution stands out in Fig. 9D because of the ‘‘symmetrization’’ procedure underlying the computation of difcors. The symmetrization (subtraction of XACs from SACs) cancels all even-order distortions, rendering the 3rd-order distortion the lowestorder distortion present. The sharpened peaks in the SACs (and difcors) are directly related to enhanced synchrony in the CN compared to the AN. Clearly, such sharpening requires non-linear processing; conversely, any expansive non-linearity will do the sharpening job. In that respect

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the distortions in Fig. 9 are both expected and consistent with enhanced synchrony. Given the distortion revealed by the autocorrelograms, one may wonder whether it is appropriate to speak of ‘‘synchronization enhancement’’ to fine-structure or envelope. One criticism that has been raised against vector strength (and that would equally apply to CI) is that higher values do not indicate a more ‘‘faithful’’ coding of the stimulus. Can a distribution of spikes that resembles a click train more than the stimulus sinewave be considered an enhanced representation? This likely depends on how this representation is used in the neural system and for what purpose. We have found lower thresholds in simple binaural detection tasks when an ideal observer uses TB inputs rather than AN inputs (Louage et al., 2006), confirming the intuition that the bushy cell output is an ‘‘enhanced’’ representation. It remains to be seen whether this also applies to other, e.g. monaural, detection tasks. 3.6. From autocorrelograms to cross-correlograms So far, we have restricted ourselves to the analysis of responses from single neurons to single stimuli (i.e. one stimulus at one SPL) or pairs of closely related stimuli (standard and inverted noise at one SPL). In this final section, we briefly touch on other uses of correlograms, which have been barely explored but which yield much promise in the study of the auditory brainstem. One of the attractions of the correlogram approach is indeed that it easily and naturally extends to compare temporal coding to different stimuli in the same neuron, or of different neurons to the same stimulus. A disadvantage of the autocorrelograms is the loss of phase information. SACs are perfectly symmetric around delay 0 and have their highest peak and CI around 0 delay. Thus, in contrast to vector strength, absolute estimates of the delay between the stimulus and the response can not be obtained. However, it is straightforward to measure delays between different responses, either from the same cell to different stimuli (e.g. responses at different SPLs), or from different cells to the same stimulus. A preliminary report of such analysis is found in (Joris et al., 2005b). Fig. 10 shows an example for 2 AN fibers. Cross-correlograms rather than autocorrelograms are calculated, i.e. the responses are from different fibers to the same A+ and A stimuli, but otherwise the logic in the construction of the correlograms is the same as in Fig. 8. All correlograms are with reference to the response at 70 dB of one fiber with CF of 1060 Hz. The other responses are from a second fiber (CF of 1720 Hz) at SPLs from 30 to 90 dB. The main peaks in the correlograms are at positive delays. Thus, with the convention used here, the responses of the higher-CF fiber need to be delayed relative to the reference (lower CF fiber) to reach maximal correlation, consistent with traveling wave delay. The thick line is the difcor between responses from both fibers at 70 dB; the line at 80 dB is the difcor between the reference fiber at 70 dB

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SPL (dB)

80

60

40

-5

-4

-3

-2

-1

0

1

2

3

4

5

DELAY (ms) Fig. 10. Difcors between two AN fibers. The response of one fiber with CF of 1070 Hz at 70 dB was crosscorrelated with responses of a fiber with CF of 1720 Hz at 30–90 dB, in all cases both to a standard and inverted broadband noise. The large and small dots indicate the largest peak and its neighbors. All curves are difcors from unnormalized crosscorrelograms, at the same scale.

and the higher-CF fiber at 80 dB, etc. The correlograms show that the response of the lower-CF fiber is delayed relative to that of the higher-CF fiber, and that the delay is remarkably constant despite large changes in stimulus level to one of the fibers. If these two nerve fibers were from different ears and would be fed to a binaural coincidence detector, the mismatch in CF would result in a large ‘‘internal delay’’ that would be little affected by interaural level differences. 4. Discussion Techniques to study temporal coding in the auditory system are mostly stimulus-based. Often simple (e.g. sinusoidal) stimuli are used whose temporal structure is compared with that of the neuronal response. Since it involves reference to the stimulus, the comparison of temporal properties of different neurons afforded by these techniques is indirect. For example, one can measure vector strengths to the envelope signal of SAM stimuli in neurons of different physiological classes or in different nuclei, and then compare the magnitude and phase of these responses. These techniques yield much information but give a view that is biased towards the experimenter. In contrast, analyses based on counting coincidences afford a view that is closer to that of the brain. The brain can only compare timings between neurons, not between neurons and the stimulus. Coincidence analysis is also direct: it does not involve the extra step of referencing to the stimulus. Moreover it

brings out temporal information as it is actually present in the system, without requiring assumptions or models. Of course, to what extent the brain actually makes use of this temporal information is another issue. Coincidence detection is certainly important in binaural processing of interaural time differences (Goldberg and Brown, 1969; Yin and Chan, 1990), but may also be important in monaural processing (Carney et al., 2002; Deng and Geisler, 1987; Heinz et al., 2001; Joris et al., 1994b; Shamma, 1985). In this paper we have focussed on one metric, the CI, which provides a simple means to measure temporal information in a single neuron to a single stimulus. It is a purely temporal measure which quantifies the degree to which spikes are generated at the same instant of poststimulus time upon repeated presentation of the stimulus. Precision and consistency or reliability of spiking are both required to obtain large CI values. The CI is normalized for average firing rate. For some experimental questions, the unnormalized metric (CR, e.g. Louage et al., 2005) is more relevant because both timing and rate affect the impact of neurons on their postsynaptic targets. This is analogous to vector strength, which has also been combined in various ways with spike rate (e.g. Kim et al., 1990; Liang et al., 2002; Rees and Palmer, 1989; Sachs et al., 1983; Shofner et al., 1996). Technically, the CI and correlograms are easier to measure than vector strength or revcors because reference to the stimulus is not needed. They do not require long recording times (roughly 15 s of data usually suffice, but this is obviously dependent on response rate). There are also some disadvantages to these techniques. Perhaps the largest disadvantage, already noted in Section 3, is the absence of phase information (in contrast to e.g. the revcor). Another disadvantage is that several (at least two) repetitions to an identical stimulus are needed, while this is not essential for any of the other traditionally used analyses (vector strength, ISI histograms, all-order histograms, revcor). One difficulty, which actually reflects the precision of these measurements and of the neurons studied, is that the spike triggering needs to be at a consistent point of the spike waveform throughout the recording. In our early experiments we used a level detector (DIS-1, BAK Electronics, Germantown, MD) to convert spikes to standard pulses, and found that changes in the voltage level of triggering relative to the spike maximum could produce noticeable shifts effects in the correlograms (an example is the small remaining ‘‘signal’’ in the difcor of Fig. 8J). This problem is eliminated by using a peak-detection circuit rather than a Schmitt trigger and by interleaving different stimuli to the extent possible. The CI is only one point of the correlogram. The shape of the correlogram contains much additional information, e.g. in its envelope, spectrum, width of the central peak, etc. The definition of the CI can actually be broadened to indicate the amplitude of the largest peak in normalized correlograms, whether obtained from a single neuron to a single stimulus, a single neuron to multiple stimuli, multi-

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ple neurons to a single stimulus, or multiple neurons to multiple stimuli. As illustrated in Fig. 10, the largest peak does not necessarily occur at s = 0: its delay provides interesting information on the relative timing between spiketrains. The use of correlograms to examine temporal relationships between fibers is somewhat closer to the original use of coincidence analyses, which were pioneered in the 1960s mainly to study relationships between simultaneously recorded spiketrains (Gerstein and Perkel, 1972; Perkel et al., 1967b,c). There is a vast literature on these techniques (reviewed by Eggermont, 1990), but it is mostly concerned with the study of correlated multiple-neuron activity and connectivity rather than stimulus-response coupling per se. To our knowledge, the only study that used these correlation techniques for purposes similar to ours is that by Aertsen et al. (1979). They calculated ‘‘cross coincidence histograms’’ for 2 or more repetitions of a vast ensemble of stimuli (the ‘‘Acoustic Biotope’’) to obtain a quantitative measure for the existence of a stimulus– response relationship. Acknowledgements Supported by the Fund for Scientific Research – Flanders (G.0083.02 and G.0392.05), and Research Fund K.U. Leuven (OT/01/42 and OT/05/57). We thank Bram Van de Sande for programming, and Eli Nelken for drawing our attention to the study of Aertsen et al. (1979). Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.heares. 2006.03.010. References Aertsen, A.M.H.J., Smolders, J.W.T., Johannesma, P.I.M., 1979. Neural representation of the acoustic biotope: on the existence of stimulusevent relations for sensory neurons. Biol. Cybern. 32, 175–185. Cariani, P., Delgutte, B., 1996. Neural correlates of the pitch of complex tones. I. Pitch and pitch salience. J. Neurophysiol. 76, 1698–1716. Carney, L.H., Heinz, M.G., Evilsizer, M.E., Gilkey, R.H., Colburn, H.S., 2002. Auditory phase opponency: a temporal model for masked detection at low frequencies. Acta Acustica united with Acustica 88, 334–346. De Boer, E., Kuyper, P., 1968. Triggered correlation. IEEE T BIO-MED ENG 15, 169–179. Delgutte, B., 1997. Auditory neural processing of speech. In: Hardcastle, W.J., Laver, J. (Eds.), The Handbook of Phonetic Sciences. Blackwell, Oxford, pp. 507–538. Deng, L., Geisler, C.D., 1987. A composite auditory model for processing speech sounds. J. Acoust. Soc. Am. 82, 2001–2012. Eggermont, J.J., 1990. The Correlative Brain. Springer Verlag, Berlin. Eggermont, J.J., Johannesma, P.I.M., Aertsen, A.M.H.J., 1983. Reversecorrelation methods in auditory research. Quart. Rev. Biophys. 16, 341–414. Frisina, R.D., Smith, R.L., Chamberlain, S.C., 1990. Encoding of amplitude modulation in the gerbil cochlear nucleus: I. A hierarchy of enhancement. Hear. Res. 44, 99–122.

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