A sigmoid function is the best fit for the ascending limb of the Hoffmann reflex recruitment curve

Abstract

The Hoffmann (H)-reflex has been studied extensively as a measure of spinal excitability. Often, researchers compare the H-reflex between experimental conditions with values determined from a recruitment curve (RC). An RC is obtained experimentally by varying the stimulus intensity to a nerve and recording the peak-to-peak amplitudes of the evoked H-reflex and direct motor (M)-wave. The values taken from an RC may provide different information with respect to a change in reflex excitability. Therefore, it is important to obtain a number of RC parameters for comparison. RCs can be obtained with a measure of current (HCRC) or without current (HMRC). The ascending limb of the RC is then fit with a mathematical analysis technique in order to determine parameters of interest such as the threshold of activation and the slope of the function. The purpose of this study was to determine an unbiased estimate of the specific parameters of interest in an RC through mathematical analysis. We hypothesized that a standardized analysis technique could be used to ascertain important points on an RC, regardless of data presentation methodology (HCRC or HMRC). For both HCRC and HMRC produced using 40 randomly delivered stimuli, six different methods of mathematical analysis [linear regression, polynomial, smoothing spline, general least squares model with custom logistic (sigmoid) equation, power, and logarithmic] were compared using goodness of fit statistics (r-square, RMSE). Behaviour and robustness of selected curve fits were examined in various applications including RCs generated during movement and somatosensory conditioning from published data. Results show that a sigmoid function is the most reliable estimate of the ascending limb of an H-reflex recruitment curve for both HCRC and HMRC. Further, the parameters of interest change differentially with respect to the presentation methodology and the analysis technique. In conclusion, the sigmoid function is a reliable analysis technique which mimics the physiologically based prediction of the input/output relation of the ascending limb of the recruitment curve. Therefore, the sigmoid function should be considered an acceptable and preferable analytical tool for H-reflex recruitment curves obtained with reference to stimulation current or M-wave amplitude.