Modeling muscle wrapping and mass flow using a mass-variable multibody formulation

Skeletal muscles usually wrap over multiple anatomical features, and their mass moves along the curved muscle paths during human locomotion. However, existing musculoskeletal models simply lump the mass of muscles to the nearby body segments without considering the effect of mass flow, which has been shown to induce non-negligible errors. A mass-variable multibody formulation is proposed here to simultaneously characterize muscle wrapping and mass flow effects. To achieve this goal, a novel cable element of the muscle–tendon unit, which integrates the mass flow feature with a typical Hill-type constitutive relationship, was developed based on an arbitrary Lagrangian–Eulerian description. In addition, sliding joints were used to constrain the elements to move over the underlying bone geometries. After validating the proposed modeling method using two benchmark samples, it was applied to build a large-scale lower limb musculoskeletal model, where knee joint moments were calculated and compared with isokinetic dynamometry measurements of 12 healthy males. The results of the comparison confirm that muscular mass distribution play an important role in the force transmission of muscle wrapping, and the proposed mass-variable formulation provides a better way of predicting and understanding the dynamics of musculoskeletal systems.