Finite element modeling of passive material influence on the deformation and force output of skeletal muscle

The pattern of deformation of different structural components of a muscle-tendon complex when it is activated provides important information about the internal mechanics of the muscle. Recent experimental observations of deformations in contracting muscle have presented inconsistencies with current widely held assumption about muscle behavior. These include negative strain in aponeuroses, non-uniform strain changes in sarcomeres, even of individual muscle fibers and evidence that muscle fiber cross sectional deformations are asymmetrical suggesting a need to readjust current models of contracting muscle. We report here our use of finite element modeling techniques to simulate a simple muscle-tendon complex and investigate the influence of passive intramuscular material properties upon the deformation patterns under isometric and shortening conditions. While phenomenological force-displacement relationships described the muscle fiber properties, the material properties of the passive matrix were varied to simulate a hydrostatic model, compliant and stiff isotropically hyperelastic models and an anisotropic elastic model. The numerical results demonstrate that passive elastic material properties significantly influence the magnitude, heterogeneity and distribution pattern of many measures of deformation in a contracting muscle. Measures included aponeurosis strain, aponeurosis separation, muscle fiber strain and fiber cross-sectional deformation. The force output of our simulations was strongly influenced by passive material properties, changing by as much as ~80% under some conditions. The maximum output was accomplished by introducing anisotropy along axes which were not strained significantly during a muscle length change, suggesting that correct costamere orientation may be a critical factor in the optimal muscle function. Such a model not only fits known physiological data, but also maintains the relatively constant aponeurosis separation observed during in vivo muscle contractions and is easily extrapolated from our plane-strain conditions into a three-dimensional structure. Such modeling approaches have the potential of explaining the reduction of force output consequent to changes in material properties of intramuscular materials arising in the diseased state such as in genetic disorders.