Surface-based modeling of muscles: Functional simulation of the shoulder.

Musculoskeletal simulations are an essential tool for studying functional implications of pathologies and of potential surgical outcomes, e.g., for the complex shoulder anatomy. Most shoulder models rely on line-segment approximation of muscles with potential limitations. Comprehensive shoulder models based on continuum-mechanics are scarce due to their complexity in both modeling and computation. In this paper, we present a surface-based modeling approach for muscles, which simplifies the modeling process and is efficient for computation. We propose to use surface geometries for modeling muscles, and devise an automatic approach to generate such models, given the locations of the origin and insertion of tendons. The surfaces are expressed as higher-order tensor B-splines, which ensure smoothness of the geometrical representation. They are simulated as membrane elements within a finite element simulation. This is demonstrated on a comprehensive model of the upper limb, where muscle activations needed to perform desired motions are obtained by using inverse dynamics. In synthetic examples, we demonstrate our proposed surface elements both to be easy to customize (e.g., with spatially varying material properties) and to be substantially (up to 12 times) faster in simulation compared to their volumetric counterpart. With our presented automatic approach of muscle wrapping around bones, the humeral head is exemplified to be wrapped physiologically consistently with surface elements. Our functional simulation is shown to successfully replicate a tracked shoulder motion during activities of daily living. We demonstrate surface-based models to be a numerically stable and computationally efficient compromise between line-segment and volumetric models, enabling anatomical correctness, subject-specific customization, and fast simulations, for a comprehensive simulation of musculoskeletal motion.