Computer models of the musculoskeletal system generally use simple geometric representations of muscle architecture and geometry. These simplifications limit the ability of models to represent the in vivo behavior of many muscles. This dissertation introduces a mechanics-based formulation for representing the architecture and geometry of skeletal muscles. The formulation includes a constitutive model for muscle, methods for building three-dimensional (3D) finite-element muscle models from image data, and graphics-based techniques to model the 3D trajectories of muscle fibers.

We used the new modeling formulation to identify the features of muscle architecture that cause nonuniform strains along muscle fascicles. Though it is generally assumed that fibers within a muscle shorten uniformly along their length, dynamic magnetic resonance (MR) images of the biceps brachii have shown nonuniform shortening along some fascicles during elbow flexion. We created a 3D model of the biceps to reveal the features of the muscle's architecture that could contribute to nonuniform strains along fascicles. The model predicted strains that were within one standard deviation of the experimentally-measured strains. We found that the variation in fascicle lengths and the curvature of the fascicles were the factors contributing to the nonuniform strains.

We also used the new modeling formulation to characterize muscles with complex geometry. Models generally represent muscle geometry using a series of line segments and assume that all fibers within each muscle have the same length and moment arm. We created 3D models of the psoas, iliacus, gluteus maximus, and gluteus medius from MR images. These muscles have broad attachments, a variety of architectures, and complex paths that wrap around underlying structures. Moment arms from the literature were generally within the range of fiber moment arms predicted by our 3D models. The peak fiber moment arms varied substantially among fibers within each muscle, indicating that the assumption that all fiber lengths and moment arms within a muscle are the same may not be valid.

This dissertation introduces new 3D models of muscle that deepen our understanding of muscle architecture and geometry and can enhance the accuracy of musculoskeletal models used for many applications.