Inverting a model of neuromuscular control to estimate descending activation patterns that generate fast-reaching movements.

Reaching movements generally show smooth kinematic profiles that are invariant across varying movement speeds even as interaction torques and muscle properties vary nonlinearly with speed. How the brain brings about these invariant profiles is an open question. We developed an analytical inverse dynamics method to estimate descending activation patterns directly from observed joint angle trajectories based on a simple model of the stretch reflex, and of muscle and biomechanical dynamics. We estimated descending activation patterns for experimental data from eight different planar two-joint movements performed at two movement times (fast: 400 ms; slow: 800 ms). The temporal structure of descending activation differed qualitatively across speeds, consistent with the idea that the nervous system uses an internal model to generate anticipatory torques during fast movement. This temporal structure also depended on the cocontraction level of antagonistic muscle groups. Comparing estimated muscle activation and descending activation revealed the contribution of the stretch reflex to movement generation that was found to set in after about 20% of movement time.NEW & NOTEWORTHY By estimating descending activation patterns directly from observed movement kinematics based on a model of the dynamics of the stretch reflex, of muscle force generation, and of the biomechanics of the limb, we observed how brain signals must be temporally structured to enable fast movement.

Estimating the time structure of descending activation that generates movements at different speeds.

In targeted movements of the hand, descending activation patterns must not only generate muscle activation but also adjust spinal reflexes from stabilizing the initial to stabilizing the final postural state. We estimate descending activation patterns that change minimally while generating a targeted movement within a given movement time based on a model of the biomechanics, the muscle dynamics, and the stretch reflex. The estimated descending activation patterns predict human movement trajectories quite well. Their temporal structure varies across workspace and with movement speed, from monotonic profiles for slow movements to nonmonotonic profiles for fast movements. Descending activation patterns at different speeds thus do not result from a mere rescaling of invariant templates but reflect varying needs to compensate for interaction torques and muscle dynamics. The virtual attractor trajectories, on which active muscle torques are zero, lie within reachable workspace and are largely invariant when represented in end-effector coordinates. Their temporal structure along movement direction changes from linear ramps to "N-shaped" profiles with increasing movement speed.NEW & NOTEWORTHY The descending activation patterns driving movement must be integrated with spinal reflexes, which would resist movement if left unchanged. We estimate the descending activation patterns at different movement speeds using a model of the stretch reflex and of muscle and limb dynamics. The descending activation patterns we find are temporally structured to compensate for interaction torques as predicted by internal models but also shift the reflex threshold, solving the posture-movement problem.