Optimization based muscle wrapping in biomechanical multibody simulations

Abstract

In musculoskeletal simulations muscle lengths and muscle force directions imply the characteristics of muscles acting around joints. Typically, the anatomical structure of the human body forces muscles to wrap around bones and neighboring tissue, thus most muscle paths cannot be represented adequately as straight lines. Therefore, biomechanical simulations require methods to compute musculotendon paths, their lengths, and their rates of length change to determine the muscle forces. This work focuses on a mechanical analogue to find the shortest path on general smooth surfaces, using a discrete variational principle. In this context, the geodesic path is reinterpreted as the constrained, force-free motion of a particle in n dimensions. The muscle path is then a G1-continuous combination of geodesics on adjacent obstacle surfaces [1,3,4].

Biomechanical simulations with dynamic muscle paths on NURBS surfaces

“…[4,5]. The shortest connection between two points on an obstacle surface is derived using constrained variational dynamics.…”

“…By coupling the control network with the configuration, the NURBS surface moves together with the multibody system, forming a closed wrapping surface for all muscles. On the left hand side, the bone geometry is approximated via a NURBS surface, while the muscles in the centre wrap around several cylinders and spheres with G1-continuous transitions, see [4]. 1 shows the implemented exemplary wrapping surfaces for the biceps and the triceps.…”

“…Assuming that the muscles and tendons are always under tension, their path can be modelled as a locally length minimizing curve that wraps smoothly over adjacent obstacles [2,4,5]. Typically, muscle paths cannot be adequately represented as straight lines because the anatomical structure of the human body forces the muscles to wrap around bones and adjacent tissue.…”

“…The results are compared with muscle paths from a G1-continuous combination of geodesics [2,4,5]. Typically, musculotendon paths, their lengths, and their force directions are modeled as the shortest connection wrapping around obstacles representing bones and adjacent tissue.…”

“…Center: Muscle path of the biceps and the triceps around multiple obstacles with G1-continuous transitions from[4]. Center: Muscle path of the biceps and the triceps around multiple obstacles with G1-continuous transitions from[4].…”