Beyond Muscles Stiffness: Importance of State-Estimation to Account for Very Fast Motor Corrections

Abstract

Feedback delays are a major challenge for any controlled process, and yet we are able to easily control limb movements with speed and grace. A popular hypothesis suggests that the brain largely mitigates the impact of feedback delays (∼50 ms) by regulating the limb intrinsic visco-elastic properties (or impedance) with muscle co-contraction, which generates forces proportional to changes in joint angle and velocity with zero delay. Although attractive, this hypothesis is often based on estimates of limb impedance that include neural feedback, and therefore describe the entire motor system. In addition, this approach does not systematically take into account that muscles exhibit high intrinsic impedance only for small perturbations (short-range impedance). As a consequence, it remains unclear how the nervous system handles large perturbations, as well as disturbances encountered during movement when short-range impedance cannot contribute. We address this issue by comparing feedback responses to load pulses applied to the elbow of human subjects with theoretical simulations. After validating the model parameters, we show that the ability of humans to generate fast and accurate corrective movements is compatible with a control strategy based on state estimation. We also highlight the merits of delay-uncompensated robust control, which can mitigate the impact of internal model errors, but at the cost of slowing feedback corrections. We speculate that the puzzling observation of presynaptic inhibition of peripheral afferents in the spinal cord at movement onset helps to counter the destabilizing transition from high muscle impedance during posture to low muscle impedance during movement.

Author Summary

Recent studies have investigated how the brain generates purposeful feedback responses to perturbations during motor control. One hypothesis suggests that the brain exploits the spring-like properties of muscles to counter perturbations. However, muscles exhibit high mechanical impedance only against small perturbations during posture, which questions the general contribution of intrinsic muscle impedance for feedback control. Alternatively, the brain may directly map sensory data into motor commands without compensating for sensorimotor delays, which is known to limit control performance. A third hypothesis suggests that neural activity following an external disturbance estimates the current state of the limb to generate a motor response. We used a perturbation paradigm where healthy participants were instructed to respond to perturbations within an extremely short time window. Comparing participants' performances with a model considering intrinsic joint impedance and conduction delays revealed that the case of state estimation was the best candidate control model to explain very fast corrective response of humans. This study emphasizes that model-based control can generate human-like rapid and stable feedback responses given low muscle stiffness and sensorimotor delays.