System identification of human triceps surae stretch reflex dynamics

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Abstract
The interpretation of stretch-evoked reflex responses is complicated by the fact that the pattern of response will depend upon both the underlying reflex mechanisms and the time course of the stretch used to evoke the response. The objective of the present study was to use engineering systems analysis techniques to identify the dynamics of the human triceps surae (TS) stretch reflex in terms of its impulse response by deconvolving the position input from the observed response. Five normal subjects were instructed to maintain a tonic contraction of (TS) while subjected to repeated, computer-generated, stochastic perturbations of ankle position. Position, torque and smoothed, rectified surface EMGs were recorded and ensemble averaged over 25 stimulus presentations. Linear impulse response functions describing the dynamic relation between ankle velocity and TS EMG were found to account for a significant amount of the observed EMG variance (mean 60%). However, the impulse responses were noisy and the predicted EMG was systematically smaller than the observed EMG during the dorsiflexing phases of displacement. These findings suggested that a direction dependent nonlinearity might be present. Consequently, impulse responses relating half-wave rectified velocity to TS EMG were computed and found to be less noisy and to account for significantly more variance (mean 74%) than the purely linear model. The undirectional, velocity-sensitive impulse response functions were dominated by a large peak at about 40 ms followed by a smaller period of reduced activity. This is consistent with its mediation by primary spindle afferents. Although the shape of the impulse response remained unchanged, its amplitude, which provides a measure of relative gain, varied systematically with the level of contraction and the displacement amplitude. Multiple regression analysis demonstrated that most of the variation in the impulse response amplitude could be attributed to proportional increases with level of contraction (measured by average EMG) and proportional decreases with displacement amplitude.