An approximate stochastic optimal control framework to simulate nonlinear neuro-musculoskeletal models in the presence of noise

Abstract

Optimal control simulations have shown that both musculoskeletal dynamics and physiological noise are important determinants of movement. However, due to the limited efficiency of available computational tools, deterministic simulations of movement focus on accurately modelling the musculoskeletal system while neglecting physiological noise, and stochastic simulations account for noise while simplifying the dynamics. We took advantage of recent approaches where stochastic optimal control problems are approximated using deterministic optimal control problems, which can be solved efficiently using direct collocation. We were thus able to extend predictions of stochastic optimal control as a theory of motor coordination to include muscle coordination and movement patterns emerging from non-linear musculoskeletal dynamics. In stochastic optimal control simulations of human standing balance, we demonstrated that the inclusion of muscle dynamics can predict muscle co-contraction as minimal effort strategy that complements sensorimotor feedback control in the presence of sensory noise. In simulations of reaching, we demonstrated that nonlinear multi-segment musculoskeletal dynamics enables complex perturbed and unperturbed reach trajectories under a variety of task conditions to be predicted. In both behaviors, we demonstrated how interactions between task constraint, sensory noise, and the intrinsic properties of muscle influence optimal muscle coordination patterns, including muscle co-contraction, and the resulting movement trajectories. Our approach enables a true minimum effort solution to be identified as task constraints, such as movement accuracy, can be explicitly imposed, rather than being approximated using penalty terms in the cost function. Our approximate stochastic optimal control framework predicts complex features, not captured by previous simulation approaches, providing a generalizable and valuable tool to study how musculoskeletal dynamics and physiological noise may alter neural control of movement in both healthy and pathological movements.

Evaluation of musculoskeletal models, scaling methods, and performance criteria for estimating muscle excitations and fiber lengths across walking speeds

“…A high exponent in the performance criterion increased co-activation ( Supplementary Figure S1 ) but resulted in excitation estimates that agreed poorly for all models and scaling variants ( Figures 3 , 5 ). Modeling approaches in which MTU controls are solved by minimizing muscle effort and including feedforward and feedback control to account for sensory and motor noise ( Van Wouwe et al, 2022 ) or by regulating mechanical impedance at the joints ( Shourijeh and Fregly, 2020 ), better represent intrinsic motor coordination characteristics; these approaches are more likely to better estimate co-activation than minimizing muscle effort with a high exponent.…”

Assisting walking balance using a bio-inspired exoskeleton controller

“…In our model, mechanical impedance originates from the force-length-velocity relationship in the virtual Hill-type muscle ( 31 ). Mechanical impedance has been shown to be important to reduce the need for active control through delayed feedback ( 30 , 32 , 33 ). However, mechanical impedance and local reflexes alone cannot explain observed changes in ankle torque after perturbations (Fig.…”

Computationally Efficient Personalized EMG-Driven Musculoskeletal Model of Wrist Joint

“…In addition, the personalised MSK model can be obtained through the direct collocation (DC) method. The DC method becomes a powerful approach paired with MSK models for predictive simulation [25], human movement analysing [26], and prosthesis control [27]. Falisse et al employed the direct collocation method to estimate the subject-specific parameters for a lower limb MSK model which results in a short optimisation time and 30% improvement of the estimation performance, compared with the linear scaled method [28].…”