Constitutive Models for Active Skeletal Muscle: Review, Comparison, and Application in a Novel Continuum Shoulder Model.

The shoulder joint is one of the functionally and anatomically most sophisticated articular systems in the human body. Both complex movement patterns and the stabilization of the highly mobile joint rely on intricate three-dimensional interactions among various components. Continuum-based finite element models can capture such complexity and are thus particularly relevant in shoulder biomechanics. Considering their role as active joint stabilizers and force generators, skeletal muscles require special attention regarding their constitutive description. In this contribution, we propose a constitutive description to model active skeletal muscle within complex musculoskeletal systems, focusing on a novel continuum shoulder model. Based on a thorough review of existing material models, we select an active stress, an active strain, and a generalized active strain approach and combine the most promising and relevant features in a novel material model. We discuss the four models considering physiological, mathematical, and computational aspects, including the applied activation concepts, biophysical principles of force generation, and arising numerical challenges. To establish a basis for numerical comparison, we identify the material parameters based on experimental stress-strain data obtained under multiple active and passive loading conditions. Using the example of a fusiform muscle, we investigate force generation, deformation, and kinematics during active isometric and free contractions. Eventually, we demonstrate the applicability of the proposed material model in a novel continuum mechanical model of the human shoulder, exploring the role of rotator cuff contraction in joint stabilization.