An efficient heterogeneous continuum model to simulate active contraction of facial soft tissue structures

Abstract

A computationally efficient and accurate finite element model of a soft tissue continuum with heterogeneous constitutive properties is presented in this article. Cubic-Hermite interpolation functions were used in formulating nonlinear, finite elasticity finite element equations. The use of Hermite family elements serves two purposes here. Firstly, the topology of the structure can be accurately represented with a fewer number of degrees of freedom and hence shorter computational time. Secondly, Hermite family elements guarantee derivative continuity of the displacement field across element boundaries ensuring that no physical laws are violated in large deformation mechanics. The model was used to simulate the skin/subcutaneous fat deformation of the human face due to contraction of the underlying zygomaticus major muscle. The heterogeneity of the soft tissue continuum representing the skin, subcutaneous fat and muscle was incorporated into the computational model by assigning different constitutive properties at the Gauss (integration) points. Furthermore, anatomically accurate 3-dimensional geometry of the zygomaticus major muscle was embedded in the continuum and fiber directions of the muscle were fitted as a vector field to construct a curvilinear material coordinate system of the continuum. The active stress resulting from muscle contraction in the direction of the fitted fiber field was determined at the integration points that were inside the muscle volume and combined with the passive stress tensor components obtained from the tissue constitutive relationship. A steady state model describing the relationship between the stress, fiber extension ratio and intracellular Ca2+ activation level was used to estimate the active tensile stress in the muscle fibers.