Modeling of anatomically accurate skeletal muscle models is still a challenging area of research to date. In general, muscles have complex architectures with spatially varying fiber orientations. Using the conventional Finite Element analysis, the generated mesh needs to be conformed to the muscle geometry and material interfaces to obtain accurate simulation models. Poorly built meshes can also lead to significant errors in analysis. To alleviate these issues and to provide effective transformation from images to simulation models, this work introduces the meshfree strong form Reproducing Kernel Collocation Method (RKCM) in context of nonlinear hyperelasticity. Further, Reduced Order Modeling (ROM) for nonlinear RKCM is developed to achieve simultaneous computational efficiency and controllable accuracy for large scale problems. The proposed methods are applied for modeling of skeletal muscles.
A segmentation framework is first developed for three dimensional model construction from Magnetic Resonance (MR) images using level set based technique, which incorporates multiple materials and muscle fiber orientations specified from Diffusion Tensor (DT) images. Further, a semi-automatic method of segmentation is proposed for segmenting individual muscles from images. A strong form RKCM is proposed to allow discretization of problem domain using MR and DT imaging data directly for effective image-based modeling, and to avoid the issues associated with domain integration and essential boundary imposition that typically exist in the Galerkin meshfree methods. In this work, nonlinear solution procedures and algorithms for RKCM analysis of hyperelasticity problems is formulated. It is shown that RKCM for nonlinear analysis provides more accurate results compared to Galerkin meshfree methods with quadratic bases using Gauss integration.
ROM for RKCM is further developed for nonlinear analysis, where a Least Squares Galerkin projection is introduced to project the over-determined system onto a discrete system with relatively lower dimension. For nonlinear analysis using RKCM, the construction of the stiffness matrix and force vector in each iteration is relatively less time consuming than that for Galerkin meshfree method using Gauss integration, making it a robust method for nonlinear model reduction. Sufficient accuracy can be achieved in the proposed method even by using only 1-2% of degrees of freedom of the full model in skeletal muscle modeling.
