Muscle path predictions using a discrete geodesic Euler–Lagrange model in constrained optimisation: comparison with OpenSim and experimental data

Abstract Accurate and robust modelling of muscle paths is crucial for predicting human movement. Traditional methods often rely on simplified straight-line representations and manual specifications of via-points and wrapping surfaces, which may lead to inconsistent and unrealistic muscle paths The discrete geodesic Euler–Lagrange (DGEL) method identifies geodesics with minimal curvature trajectories that adhere closely to anatomical constraints. Embedding DGEL into an optimisation problem with a specific objective function has the potential to identify muscle paths with smooth changes in muscle length over the course of the motion, thereby avoiding abrupt muscle discontinuities. This study aims to investigate the performance of the DGEL method. We developed multibody models with increasing complexity (i.e. a static arm model, a kinematic elbow model and a kinematic shoulder model) and investigated different scenarios, such as muscle attachment modifications, simulation of diverse motions and extreme ranges of motion. We performed a comparative analysis between the geodesic model and the open-source OpenSim framework, with validation against experimental data to assess physiological plausibility. Our findings reveal that the DGEL method overcomes limitations inherent in traditional approaches, including discontinuities and incorrect wrapping surface interactions. For the static arm model, the DGEL-computed muscle length showed a closer match to ground truth compared to OpenSim. In the elbow model, the DGEL method eliminated unphysiological muscle path discontinuities. In the shoulder model, the DGEL method was validated across three different motions against experimental muscle moment arms, achieving great accuracy and superior robustness in handling complex muscle paths. This method effectively addressed common pitfalls in muscle path modelling, such as bone penetrations and erratic trajectories. Future work will further validate the DGEL method across diverse real-world applications and optimise its performance through advanced objective functions. The DGEL approach represents a significant improvement in the accuracy and robustness of muscle path modelling, advancing the field of biomechanics and musculoskeletal modelling.