Musculoskeletal simulations are useful in biomechanics to investigate the causes of movement disorders, estimate nonmeasurable physiological quantities, or study the optimality of human movement. We introduce Bioptim, an easy-to-use Python framework for biomechanical optimal control based on both direct multiple shooting and direct collocation, handling musculoskeletal models. Relying on algorithmic differentiation, Bioptim is fast and it interfaces several nonlinear solvers. The software is both computationally efficient (C++ core) and easily customizable, thanks to its Python interface. It allows to quickly define a variety of biomechanical problems, such as motion tracking/prediction, muscle-driven simulations, parameters optimization, multiphase problems, etc. It is also intended for real-time applications, such as moving horizon estimation and model predictive control.

Ensuring the accurate tracking of hand and fingers movements is an ongoing challenge for upper limb rehabilitation assessment, as the high number of degrees of freedom and segments in the limited volume of the hand makes this a difficult task. The objective of this study is to evaluate the performance of two markerless approaches (the Leap Motion Controller and the Google MediaPipe API) in comparison to a marker-based one, and to improve the precision of the markerless methods by introducing additional data processing algorithms fusing multiple recording devices. Fifteen healthy participants were instructed to perform five distinct hand movements while being recorded by the three motion capture methods simultaneously. The captured movement data from each device was analyzed using a skeletal model of the hand through the inverse kinematics method of the OpenSim software. Finally, the root mean square errors of the angles formed by each finger segment were calculated for the markerless and marker-based motion capture methods to compare their accuracy. Our results indicate that the MediaPipe-based setup is more accurate than the Leap Motion Controller-based one (average root mean square error of 10.9° versus 14.7°), showing promising results for the use of markerless-based methods in clinical applications.

Real-time biofeedback of muscle forces should help clinicians adapt their movement recommendations. Because these forces cannot directly be measured, researchers have developed numerical models and methods informed by electromyography (EMG) and body kinematics to estimate them. Among these methods, static optimization is the most computationally efficient and widely used. However, it suffers from limitation, namely: unrealistic joint torques computation, non-physiological muscle forces estimates and inconsistent for motions inducing co-contraction. Forward approaches, relying on numerical optimal control, address some of these issues, providing dynamically consistent estimates of muscle forces. However, they result in a high computational cost increase, apparently disqualifying them for real-time applications. However, this computational cost can be reduced by combining the implementation of a moving horizon estimation (MHE) and advanced optimization tools. Our objective was to assess the feasibility and accuracy of muscle forces estimation in real-time, using a MHE. To this end, a 4-DoFs arm actuated by 19 Hill-type muscle lines of action was modeled for simulating a set of reference motions, with corresponding EMG signals and markers positions. Excitation- and activation-driven models were tested to assess the effects of model complexity. Four levels of co-contraction, EMG noise and marker noise were simulated, to run the estimator under 64 different conditions, 30 times each. The MHE problem was implemented with three cost functions: EMG-markers tracking (high and low weight on markers) and marker-tracking with least-squared muscle excitations. For the excitation-driven model, a 7-frame MHE was selected as it allowed the estimator to run at 24 Hz (faster than biofeedback standard) while ensuring the lowest RMSE on estimates in noiseless conditions. This corresponds to a 3,500-fold speed improvement in comparison to state-of-the-art equivalent approaches. When adding experimental-like noise to the reference data, estimation error on muscle forces ranged from 1 to 30 N when tracking EMG signals and from 8 to 50 N (highly impacted by the co-contraction level) when muscle excitations were minimized. Statistical analysis was conducted to report significant effects of the problem conditions on the estimates. To conclude, the presented MHE implementation proved to be promising for real-time muscle forces estimation in experimental-like noise conditions, such as in biofeedback applications.

Human-robot interaction based on real-time kinematics or electromyography (EMG) feedback improves rehabilitation using assist-as-needed strategies. Muscle forces are expected to provide even more comprehensive information than EMG to control these assistive rehabilitation devices. Measuring in vivo muscle force is challenging, leading to the development of numerical methods to estimate them. Due to their high computational cost, forward dynamics-based optimization algorithms were not viable for real-time estimation until recently. To achieve muscle forces estimation in real time, a moving horizon estimator (MHE) algorithm was used to track experimental biosignals. Two participants were equipped with EMG sensors and skin markers that were streamed in real time and used as targets for the MHE. The upper-limb musculoskeletal (MSK) model was composed of 10 degrees-of-freedom actuated by 31 muscles. The MHE relies on a series of overlapping trajectory optimization subproblems of which the following parameters have been adjusted: the fixed duration and the frame to export. We based this adjustment on the estimation delay, the muscle saturation, the joint kinematic mean power frequency, and errors to experimental data. Our algorithm provided consistent estimates of muscle forces and kinematics with visual feedback at 30 Hz with a 110 ms delay. This method is promising to guide rehabilitation and enrich assistive device control laws with personalized force estimations.