Correlation Index: A new metric to quantify temporal coding

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.

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 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).

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).