Using Bayesian inference to estimate plausible muscle forces in musculoskeletal models

Area of Science:

• Biomechanics
• Computational Biology
• Robotics

Background:

• Musculoskeletal modeling is key for estimating muscle forces in observed movements.
• Estimates are sensitive to assumptions and uncertainties, complicating interpretation.
• Bayesian inference offers a method to define plausible muscle force ranges and represent uncertainty.

Purpose of the Study:

• To develop and evaluate a Bayesian inference approach for estimating muscle forces.
• To quantify uncertainty in muscle force estimation for a simple motion.
• To represent uncertainty in motion measurement and objective functions within musculoskeletal simulations.

Main Methods:

• Generated reference elbow flexion-extension motion and forces using OpenSim Moco.
• Employed a Markov Chain Monte Carlo (MCMC) algorithm to sample muscle excitations from a posterior probability distribution.
• Combined position/velocity error (likelihood) with cubed muscle excitations (prior) to compute posterior probability density.

Main Results:

• Estimated muscle forces favorably compared to reference forces.
• Achieved close matches for elbow angle and velocity (RMSE: 2° and 32°/s, respectively).
• MCMC algorithm chains did not fully converge, indicating potential mixing issues.

Conclusions:

• Bayesian inference is a promising approach for characterizing uncertainty in muscle force estimation.
• Computational time and MCMC convergence issues limit current feasibility for large-scale models.
• Further advancements in MCMC algorithms are required for wider application in musculoskeletal modeling.