Component analysis of the responses of sensory neurons to combined sinusoidal and triangular stimulation

A method for quantitative estimation of sensory neuron sensitivity to small sinusoidal stimuli in the presence of sizable background drift (in the stimulus or response) was developed. The performance of the method was tested by analyzing the responses of 17 muscle spindle primary (Ia) afferent neurons to concomitant sinusoidal and triangular stretching of the soleus muscle. The efficacy and accuracy of several variations of the method were examined. The variations included the use of probability density (PD) and average frequency (AF) histograms as the basis for calculations and two different algorithms for the decomposition of responses to combined sinusoidal and triangular stimulation. One algorithm called the 'inherent-drift' method exploited the inherent half-cycle repeat property of a sine wave to extract the drift component. Another algorithm called the 'forced-drift' method first estimated the drift by linear regression to a response to triangular stimulation alone. The drift estimate (a slope value) was then subtracted from the response to combined sinusoidal and triangular stimulation of the same triangular (background) velocity. A comparison of the performance of the drift correction method applied either to PD or AF histograms revealed no significant differences in the estimates of sinusoidal modulation. The limitations of the AF method were manifest primarily by phase lags at low mean levels of action potential discharge. Calculation of the response parameters using the 'inherent-drift' correction procedure proved straightforward as long as there were at least two pairs of non-empty bins in the sine-cycle histograms on which to base the estimate of drift. The method remained effective in determining sinusoidal sensitivity in the face of distinct non-linearities (harmonic distortions) in the sine-cycle histograms. However, estimates of slope and the extraction of sinusoidal phase by the 'inherent' slope correction method became subject to large errors. Under such circumstances, more reliable estimates could be obtained by using the forced drift-correction method instead. The importance of extracting the drift component prior to estimating the sinusoidal response parameters was evaluated experimentally and theoretically. In general, omission of a drift correction introduced a large bias in the estimates of the phase of sinusoidal response, whereas the estimate of sinusoidal modulation was rather insensitive. Experimental findings were fully accounted for by theoretical considerations. Analytically derived relationships identified low- and high-risk regions more clearly for the estimate of sinusoidal modulation than of phase. The relationship between biased modulation estimate and underlying drift showed minima characteristics with a low-risk region, where absolute errors and dependence on slope variations were small.(ABSTRACT TRUNCATED AT 400 WORDS)