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.

肌肉骨骼模拟是研究病理和潜在手术结果的功能影响的重要工具，例如复杂的肩部解剖结构。大多数肩部模型依赖于具有潜在限制的肌肉的线段近似。由于建模和计算的复杂性，基于连续介质力学的综合肩部模型很少。

在本文中，我们提出了一种基于表面的肌肉建模方法，它简化了建模过程并且计算效率高。

我们建议使用表面几何形状来模拟肌肉，并设计一种自动方法来生成此类模型，考虑到肌腱的起源和插入的位置。表面表示为高阶张量 B 样条，这确保了几何表示的平滑性。它们在有限元模拟中被模拟为膜单元。这在上肢的综合模型上得到了证明，其中执行所需运动所需的肌肉激活是通过使用逆动力学获得的。

在合成示例中，我们证明了我们提出的表面元素既易于定制（例如，具有空间变化的材料属性），并且与体积对应物相比，模拟速度要快得多（最多 12 倍）。通过我们提出的肌肉包裹骨骼的自动方法，肱骨头被举例说明，以生理上一致地包裹表面元素。我们的功能模拟被证明可以在日常生活活动中成功复制跟踪的肩部运动。

我们展示了基于表面的模型是线段模型和体积模型之间数值稳定且计算效率高的折衷方案，可实现解剖学正确性、特定主题定制和快速模拟，以全面模拟肌肉骨骼运动。