Third-order reverse correlation analysis of muscle spindle primary afferent fiber responses to random muscle stretch

Abstract

The response of primary muscle spindle afferent fibers to muscle stretch is nonlinear. Now spindle responses (trains of action potentials) to band-limited Gaussian white noise length perturbations of the gastrocnemius muscles (input signal) are described in cats. The input noise upper cutoff frequency was clearly above the frequency range of physiological length changes in cat hindleg muscles. The input-output relation was analyzed by means of peri-spike averages (PSAs), which could be shown to correspond to the kernels of Wiener's white noise approach to systems identification. The present approach (the reverse correlation analysis) was applied up to the third order. An experiment consisted of two recordings: one (the source recording) to determine PSAs and the other (the test recording) to provide an input signal for predicting responses. The predictions of different orders were compared with the actual neuronal response (the observation) of the test recording. Four different approximation procedures were developed to adapt prediction and observation and to determine weighting factors for the predictions of different orders. The approximations also yielded the value of the power density P of the input noise signal: at a variety of stimulus parameters, P from approximations had the same magnitude as P determined directly from the input signal amplitude spectrum. The prediction of a sequence of action potentials improved the higher the order of components. 37 of 42 action potentials of a test recording (the observation) could be confidently predicted from PSAs or kernels. Compared with the size of the linear first-order prediction curve, the relative sizes of the second and third-order prediction curves were: 1.0∶0.47∶0.26.