Real-Time Calibration-Free Musculotendon Kinematics for Neuromusculoskeletal Models

Neuromusculoskeletal (NMS) models enable non-invasive estimation of clinically important internal biomechanics. A critical part of NMS modelling is the estimation of musculotendon kinematics, which comprise musculotendon unit lengths, moment arms, and lines of action. Musculotendon kinematics, which are partially dependent on joint angles, define the non-linear mapping of muscle forces to joint moments and contact forces. Currently, real-time computation of musculotendon kinematics requires creation of a per-individual surrogate model. The computational speed and accuracy of these surrogates degrade with increasing number of coordinates. We developed a feed-forward neural network that completely encodes musculotendon kinematics of a target model across a wide anthropometric range, enabling accurate real-time estimates of musculotendon kinematics without need for a priori creation of a per-individual surrogate model. Compared to reference, the neural network had median normalized errors ~0.1% for musculotendon lengths, <0.4% for moment arms, and <0.10° for line of action orientations. The neural network was employed within an electromyogram-informed NMS model to calculate hip contact forces, demonstrating little difference (normalized root mean square error $1.23\pm 0.15$ %) compared to using reference musculotendon kinematics. Finally, execution time was <0.04 ms per frame and constant for increasing number of model coordinates. Our approach to musculoskeletal kinematics may facilitate deployment of complex real-time NMS modelling in computer vision or wearable sensors applications to realize biomechanics monitoring, rehabilitation, and disease management outside the research laboratory.