Using Perturbations to Probe the Neural Control of Rhythmic Movements

Small continuous sensory and mechanical perturbations are often used to identify properties of the closed-loop neural control of posture and other systems that are approximately linear time invariant. Here we extend this approach to study the neural control of rhythmic behaviors such as walking. Our method is based on the theory of linear time periodic systems, with modifications to account for ability of perturbations to reset the phase of a rhythmic behavior. We characterize responses to perturbations in the frequency domain using harmonic transfer functions and then convert to the time domain to obtain phase-dependent impulse response functions (φIRFs) that describe the response to a small brief perturbation at any phase of the rhythmic behavior. The φIRFs describing responses of kinematic variables and muscle activations (measured by electromyography) to sensory and mechanical perturbations can be used to infer properties of the plant, the mapping from muscle activation to movement, and of neural feedback, the mapping from movement to muscle activation. We illustrate our method by applying it to simulated data from a model and experimental data of subjects walking on a treadmill perturbed by movement of the visual scene.