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 met hod was tested by analyzing the responses of 17 muscle spindle primary (Ia) afferent neurons to concomitant sinusoidal and triangular stretc hing of the soleus muscle. The efficacy and accuracy of several variat ions of the method were examined. The variations included the use of p robability density (PD) and average frequency (AF) histograms as the b asis for calculations and two different algorithms for the decompositi on of responses to combined sinusoidal and triangular stimulation. One algorithm called the 'inherent-drift' method exploited the inherent h alf-cycle repeat property of a sine wave to extract the drift componen t. 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 th e response to combined sinusoidal and triangular stimulation of the sa me triangular (background) velocity. A comparison of the performance o f the drift correction method applied either to PD or AF histograms re vealed no significant differences in the estimates of sinusoidal modul ation. The limitations of the AF method were manifest primarily by pha se lags at low mean levels of action potential discharge. Calculation of the response parameters using the 'inherent-drift' correction proce dure proved straightforward as long as there were at least two pairs o f non-empty bins in the sine-cycle histograms on which to base the est imate of drift. The method remained effective in determining sinusoida l sensitivity in the face of distinct non-linearities (harmonic distor tions) in the sine-cycle histograms. However, estimates of slope and t he extraction of sinusoidal phase by the 'inherent' slope correction m ethod became subject to large errors. Under such circumstances, more r eliable estimates could be obtained by using the forced drift-correcti on method instead. The importance of extracting the drift component pr ior to estimating the sinusoidal response parameters was evaluated exp erimentally and theoretically. In general, omission of a drift correct ion introduced a large bias in the estimates of the phase of sinusoida l response, whereas the estimate of sinusoidal modulation was rather i nsensitive. Experimental findings were fully accounted for by theoreti cal considerations. Analytically derived relationships identified low- and high-risk regions more clearly for the estimate of sinusoidal mod ulation than of phase. The relationship between biased modulation esti mate and underlying drift showed minima characteristics with a low-ris k region, where absolute errors and dependence on slope variations wer e small. The precise shape of these characteristic curves depended on the phase value of the sinusoidal response component. This suggests th at in situations where the phase of sinusoidal responses can be estima ted independently, experimental paradigms can be optimized by adjustin g the phase of sinusoidal stimuli, so as to minimize the effects of co mplete omission of drift correction or of inappropriate drift determin ation on the estimates of modulation. In contrast, for phase estimatio n low-risk regions are very narrow, indicating that inappropriate drif t compensation almost invariably leads to significant errors in phase estimates. In its current form, the method is directly applicable to s ensory responses which consist of rate-modulated trains of action pote ntials. Nevertheless, the same principles used to develop the method c ould be applied to sensory responses in the form of receptor or genera tor potentials. The method should therefore be applicable to the analy sis of a wide variety of sensory systems.