matlab mcmc package  (MathWorks Inc)

Journal: Journal of NeuroEngineering and Rehabilitation

Article Title: Using Bayesian inference to estimate plausible muscle forces in musculoskeletal models

doi: 10.1186/s12984-022-01008-4

Figure Lengend Snippet: Elbow Musculoskeletal Model and Reference Data: A OpenSim elbow model with the elbow posed at 90 degrees (mid-point position). Red lines represent the paths for each of the six muscles in the model. The reference position ( B) and velocity ( C) trajectories used as input into the MCMC log likelihood function

Article Snippet: Therefore, further developments for MCMC search algorithms which specifically are usable for common musculoskeletal simulation tools (or other problems without easy access to model derivatives) should be at the forefront of future research, since these kinds of mechanics problems are difficult to sample from using the relatively simple techniques in the MATLAB MCMC package.

Techniques:

Journal: Journal of NeuroEngineering and Rehabilitation

Article Title: Using Bayesian inference to estimate plausible muscle forces in musculoskeletal models

doi: 10.1186/s12984-022-01008-4

Figure Lengend Snippet: Flow Chart for MCMC and Elbow Flexion System: A The starting proposal for each parameter is drawn from a uniform distribution between [− 15,-5]. There are 60 parameters total representing amplitudes of the compact radial basis functions (CRBFs), 10 parameters for every muscle, where A 1,1 is the amplitude of the first node of the first muscle, and A 6,10 is the amplitude of the tenth node of the sixth muscle. B The proposal is converted from the set of CRBFs into a muscle excitations (Eqs. – ), which are given to OpenSim to generate a reference motion. C The posterior log-probability is calculated from the log likelihood (sum of square errors to the reference motion) and the log prior (the sum of muscle excitations ( u ) cubed). D The current proposal is accepted or rejected based on the change in posterior log probability from the original proposal to the new proposal (initial proposal is always accepted). E If the current iteration is equal to the pre-defined maximum iterations, the MCMC exits, otherwise it generates a new proposal in F by perturbing the current proposal by a value drawn from a normal distribution and continue to loop through the steps within the green box. Further details on the algorithm and acceptance criteria are given in [ , ]

Article Snippet: Therefore, further developments for MCMC search algorithms which specifically are usable for common musculoskeletal simulation tools (or other problems without easy access to model derivatives) should be at the forefront of future research, since these kinds of mechanics problems are difficult to sample from using the relatively simple techniques in the MATLAB MCMC package.

Techniques:

Journal: Journal of NeuroEngineering and Rehabilitation

Article Title: Using Bayesian inference to estimate plausible muscle forces in musculoskeletal models

doi: 10.1186/s12984-022-01008-4

Figure Lengend Snippet: MCMC Results and Analysis: The position ( A) and velocity ( B) trajectories matched closely with the reference (red dashed line). C The prior (blue dashed) and posterior (post.) density (blue solid) on sum of muscle excitations cubed. The mean (black solid line) and 1 standard deviation (gray shaded region) of muscle force trajectories for triceps long head ( D ), triceps lateralis ( E ), triceps medialis ( F ), biceps long head ( G ), biceps short head ( H ), and brachialis ( I) compared with the forces from the reference trajectory (red). For each of the muscle force subplot, the maximum value on the y-axis represents the peak isometric muscle force of the muscle

Article Snippet: Therefore, further developments for MCMC search algorithms which specifically are usable for common musculoskeletal simulation tools (or other problems without easy access to model derivatives) should be at the forefront of future research, since these kinds of mechanics problems are difficult to sample from using the relatively simple techniques in the MATLAB MCMC package.

Techniques: Standard Deviation

Journal: Journal of NeuroEngineering and Rehabilitation

Article Title: Using Bayesian inference to estimate plausible muscle forces in musculoskeletal models

doi: 10.1186/s12984-022-01008-4

Figure Lengend Snippet: Likelihood, prior, and posterior for the first 150,000 iterations: This figure demonstrates that each of the seven parallel chains reach an equilibrium point in their output by the end of the 150,000th iteration, during the burn-in phase of the MCMC analysis. The raw output for the likelihood function shows a rapid decrease in sum of squared error within the first 50,000 iterations for each chain, eventually reaching an equilibrium point ( A ). The sum of integrated muscle excitations (Prior) has some early peaks during the MCMC chain, but also reaches equilibrium by 150,000 iterations ( B ). Finally, the sum of the likelihood and prior gives the posterior output ( C ). Note that the MCMC algorithm continues after the end of the plotted data to reach 500,000 iterations total

Article Snippet: Therefore, further developments for MCMC search algorithms which specifically are usable for common musculoskeletal simulation tools (or other problems without easy access to model derivatives) should be at the forefront of future research, since these kinds of mechanics problems are difficult to sample from using the relatively simple techniques in the MATLAB MCMC package.

Techniques: