Fast and robust path wrapping algorithms for musculoskeletal modelling and simulation

• Applicant: Professor Dr.-Ing. Andreas Scholz
• Subject Area: Mechanics ; Mathematics
• Term: since 2026
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 570021776

In musculoskeletal simulation, muscle paths are often represented by thin taut strings that can wrap frictionlessly across geometric obstacle surfaces. The surfaces are assumed to represent surrounding anatomical structures such as bones, but also the neglected muscle thickness itself. These simplifications allow to reduce the muscle-path computation problem to a purely geometric problem, i.e., to find the locally shortest connection line between muscle origin and insertion, with a series of obstacle surfaces between them. Despite these simplifications, solving the so-called muscle wrapping problem remains a challenging task. This is because there exist no closed-form solutions in the general case so that numerical methods must be applied instead. This potentially leads to high computational costs when simulating musculoskeletal models with multiple muscles that wrap over surfaces. As a result, researchers often neglect muscle wrapping completely, which in turn limits the accuracy of their models. This trade-off between accuracy and speed has prevented musculoskeletal models from providing deeper insights into human and animal movement. The proposed research project aims at improving the “Natural Geodesic Variation Method” (NGVM), which was originally published in 2015, so that it becomes a robust tool for simulating muscle paths in biomechanical simulation software packages. The NGVM can compute muscle paths across an arbitrary number of complex surfaces and is numerically very fast because it uses a root-finding approach with an analytic gradient. However, it is still limited with respect to (1) its numerical robustness and its convergence behavior; (2) the need to manually specify an initial path guess before simulation; and (3) the resulting dynamic path behavior, which is not always physically plausible. The scientific focus of this proposed research project lies in the development of new and more robust mathematical formulations of the NGVM, which also utilize the concept of natural geodesic variations so that explicit derivatives can be computed and the high computational speed can be maintained. This includes deriving the necessary mathematical equations of alternative formulations that are based on root-finding, but also on nonlinear optimization, particularly for improving the path initialization and for preventing physically implausible path dynamics. The project aims developing benchmarks to test and compare the different formulations with respect to their numerical efficiency, robustness and convergence, as well as with respect to their dynamic path behavior. It is an associated goal of the project to implement the NGVM and its improvements into OpenSim so that it becomes available for a worldwide community of users.

• DFG Programme: Research Grants
• International Connection: Netherlands, USA
• Cooperation Partners: Professor Scott Delp, Ph.D.; Professor Ajay Seth, Ph.D.