Event-related cross-correlations between spike trains illustrated on interactions between motor units and muscle spindle afferents.

A method is presented for computing correlation coefficients of two (or more) output spike trains in temporal relation to one (or more) input even trains. These event-related correlation functions are computed by convolving the output spike trains, represented as point processes, with rectangular pulses of selectable width, and by then calculating linear correlation coefficients for the pairs of amplitude values obtained from the two convolved processes in temporal relation to the input events. The merits of this technique are illustrated on stimulus trains delivered to motor units (MUs) and output spike trains recorded from muscle spindle afferents of the same cat hindlimb muscle. The correlation functions obtained show the temporal course of the correlated firings of the two afferents (mostly Ia afferents from primary muscle spindle endings) as a function of time from MU activation; they are compared with the conventional cross-correlation histograms (CCHs) between afferents and with peri-stimulus time histograms (PSTHs) between stimulus and afferent firing patterns. Stimulus-related cross-correlation functions as displayed here can be calculated for any three spike trains. Possible extensions of the method to larger numbers of input and output channels are also discussed.