Gradient-based optimization with B-splines on sparse grids for solving forward-dynamics simulations of...

Area of Science:

• Biomechanics
• Computational modeling
• Musculoskeletal system analysis

Background:

• Understanding musculoskeletal systems relies on analyzing muscle activity and motion.
• Existing multibody simulation frameworks have limitations due to modeling assumptions.
• Continuum-mechanical models offer improvements but are computationally intensive.

Purpose of the Study:

• To present the first activation-driven musculoskeletal system model.
• To compute skeletal muscle forces using 3D continuum-mechanical models.
• To determine muscle activations via constraint optimization.

Main Methods:

• Developed a novel framework integrating continuum-mechanical muscle models with activation-driven simulations.
• Employed sparse grid surrogates with hierarchical B-splines for numerical feasibility.
• Utilized adaptive sparse grid refinement to reduce computational load.
• Applied gradient-based optimization techniques enabled by B-splines.

Main Results:

• Achieved low relative errors (less than 0.76%) in computed surrogates.
• Demonstrated the framework's utility in forward simulations with constraint optimization.
• Successfully modeled an upper limb system with two muscles and an external load.

Conclusions:

• The proposed framework offers a computationally feasible approach for activation-driven musculoskeletal modeling.
• The method is adaptable for more complex musculoskeletal systems with multiple muscles.
• This advancement aids in understanding healthy and diseased musculoskeletal function.