Division of Biokinesiology and Physical Therapy, University of Southern California, Los Angeles, CA, USA.
Lakeland Applied Sciences, Los Angeles, CA, USA.
J Neuroeng Rehabil. 2022 Mar 23;19(1):34. doi: 10.1186/s12984-022-01008-4.
Musculoskeletal modeling is currently a preferred method for estimating the muscle forces that underlie observed movements. However, these estimates are sensitive to a variety of assumptions and uncertainties, which creates difficulty when trying to interpret the muscle forces from musculoskeletal simulations. Here, we describe an approach that uses Bayesian inference to identify plausible ranges of muscle forces for a simple motion while representing uncertainty in the measurement of the motion and the objective function used to solve the muscle redundancy problem.
We generated a reference elbow flexion-extension motion and computed a set of reference forces that would produce the motion while minimizing muscle excitations cubed via OpenSim Moco. We then used a Markov Chain Monte Carlo (MCMC) algorithm to sample from a posterior probability distribution of muscle excitations that would result in the reference elbow motion. We constructed a prior over the excitation parameters which down-weighted regions of the parameter space with greater muscle excitations. We used muscle excitations to find the corresponding kinematics using OpenSim, where the error in position and velocity trajectories (likelihood function) was combined with the sum of the cubed muscle excitations integrated over time (prior function) to compute the posterior probability density.
We evaluated the muscle forces that resulted from the set of excitations that were visited in the MCMC chain (seven parallel chains, 500,000 iterations per chain). The estimated muscle forces compared favorably with the reference forces generated with OpenSim Moco, while the elbow angle and velocity from MCMC matched closely with the reference (average RMSE for elbow angle = 2°; and angular velocity = 32°/s). However, our rank plot analyses and potential scale reduction statistics, which we used to evaluate convergence of the algorithm, indicated that the chains did not fully mix.
While the results from this process are a promising step towards characterizing uncertainty in muscle force estimation, the computational time required to search the solution space with, and the lack of MCMC convergence indicates that further developments in MCMC algorithms are necessary for this process to become feasible for larger-scale models.
肌肉骨骼建模目前是一种用于估计潜在运动的肌肉力量的首选方法。然而，这些估计对各种假设和不确定性很敏感，这给解释肌肉骨骼模拟中的肌肉力量带来了困难。在这里，我们描述了一种使用贝叶斯推断来识别简单运动中肌肉力量的合理范围的方法，同时代表了运动测量和用于解决肌肉冗余问题的目标函数的不确定性。
我们生成了一个参考的肘部屈伸运动，并计算了一组参考力，这些力在通过 OpenSim Moco 最小化肌肉兴奋的立方时会产生运动。然后，我们使用马尔可夫链蒙特卡罗（MCMC）算法从肌肉兴奋的后验概率分布中进行采样，这些兴奋会导致参考肘部运动。我们构建了一个关于兴奋参数的先验，该先验对肌肉兴奋更大的参数空间进行了加权。我们使用肌肉兴奋来使用 OpenSim 找到相应的运动学，其中位置和速度轨迹的误差（似然函数）与时间积分的立方肌肉兴奋的总和（先验函数）相结合，以计算后验概率密度。
我们评估了 MCMC 链中访问的一组兴奋所产生的肌肉力量（七个并行链，每个链 50 万次迭代）。估计的肌肉力量与使用 OpenSim Moco 生成的参考力相比表现良好，而 MCMC 的肘部角度和速度与参考值非常匹配（肘部角度的平均 RMSE=2°；角速度=32°/s）。然而，我们的秩图分析和潜在规模缩减统计，我们用于评估算法的收敛性，表明链没有完全混合。
虽然这个过程的结果是朝着描述肌肉力量估计不确定性迈出的有希望的一步，但搜索解决方案空间所需的计算时间和 MCMC 收敛的缺乏表明，对于这个过程来说，MCMC 算法的进一步发展是必要的，以便使其在更大规模的模型中变得可行。
