Improved Muscle Wrapping Algorithms Using Explicit Path-Error Jacobians

Muscle wrapping computations are an important feature in musculoskeletal simulations. In this paper we present a novel Jacobian-based method for linebased muscle-path computations over multiple general smooth surfaces allowing for second-order Newton-Raphson iterations. The method is based on the analytical determination of infinitesimal displacements along geodesics using Jacobi fields. It does not share the disadvantages of discretized methods in terms of non-smoothness when using surface discretizations, and high computational costs when using discretized spring-mass approaches. The paper focusses on the technical details of the proposed method, while specific biomechanical applications are left for future contributions. An example with three surfaces involving a surface with a general distribution of curvature shows the general applicability of the method.