We need this for stroke survivors so we can objectively determine what our muscle problems are. Knowing that we can objectively assign EXACT STROKE PROTOCOLS to fix those problems. At least that is what smart competent people would be doing. But no one in stroke leadership or the stroke medical world seems to be smart or competent.
Using Bayesian inference to estimate plausible muscle forces in musculoskeletal models
Journal of NeuroEngineering and Rehabilitation volume 19, Article number: 34 (2022)
Abstract
Background
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.
Methods
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.
Results
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.
Conclusions
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.
Background
Movement scientists are often interested in quantifying the timing and magnitude of muscle forces during motions like walking or reaching to understand causal links between muscle mechanics and movement. Accurately and reliably estimating individual muscle forces has implications for how well researchers can evaluate muscle function to help guide surgical interventions, inform the design of prosthetics and orthotics, and estimate other clinically relevant outputs (e.g., joint contact forces) [1,2,3,4,5,6]. Measuring muscle forces in vivo is difficult to do, except on a limited scale (e.g., triceps surae forces [7]), but most often the methodology is far too invasive to use with human participants. Instead, researchers often use experimental data combined with musculoskeletal modeling to estimate muscle forces during a movement [8,9,10,11]. Several methods have been developed to estimate individual muscle forces during a motion, including static optimization, computed muscle control, as well as direct collocation or simulated annealing methods to solve for muscle forces [e.g., [12,13,14,15]]. Typically, these methods result in a single force trajectory for each muscle that optimizes a chosen objective function for a given musculoskeletal model and experimental motion. However, accurately solving for muscle forces remains difficult because the musculoskeletal system is redundant (an infinite combination of muscle forces can often give rise to the same joint moment) [16], and simulations of movement depend on experimental data and a variety of parameters that are prone to uncertainties [17, 18].
The uncertainty associated with muscle force estimation can arise from the uncertainty with which we mathematically represent how the central nervous system distributes muscle forces amongst agonist muscles [8, 12], errors in marker placement and skin movement relative to anatomical landmarks [19, 20], and modeling assumptions related to muscle parameters [21, 22]. Typical representations of motor control assume that the central nervous system attempts to minimize some objective function (e.g., minimize muscle fatigue or metabolic energy cost [8, 17, 23]). Choosing an appropriate objective function for a particular motion is difficult because it is not known exactly how the nervous system distributes forces across muscles. In reality, the nervous system is unlikely to generate an “optimal” motion under any hypothesis represented by a simple objective function, as biological systems may find “good-enough” solutions to movement objectives, but these may not necessarily be optimal behavior as defined in trajectory optimization problems [24]. The unknowns associated with choosing an appropriate objective function for musculoskeletal simulations are problematic because muscle force estimates are sensitive to the objective function chosen [17, 23, 25,26,27]. There are other aspects of musculoskeletal modeling that can lead to uncertainty in muscle force estimation, such as variability in marker placement, movement artifact, and unknown model parameters which can also play a role in impacting the computed muscle forces [18,19,20,21, 28,29,30]. With uncertainties in the motor control model, the measured data, and the musculoskeletal model, the single solutions typically obtained from standard optimizations conceal the inherent uncertainty we have about the predicted muscle forces. By better quantifying the uncertainty in muscle force estimation, researchers can evaluate experimental design approaches capable of reducing uncertainty and better predict whether a designed intervention would lead to meaningful changes in muscle force production.
One approach to quantifying uncertainty in musculoskeletal modeling is to treat the objective function as unknown while keeping the other model parameters fixed. There have been a few different methods developed to try to capture some of the uncertainty associated with choosing an objective function and how it would affect the estimated muscle forces for a given model or motion [31,32,33]. These approaches have used mathematical mappings between joint torques and muscle activations to compute upper and lower bounds on the muscle forces for each muscle over time. Instead of choosing an explicit objective function to solve the muscle redundancy problem, these methods instead solve for the upper and lower bounds then assume the muscle forces lie somewhere in between. However, these ranges include solutions that would only be possible with extreme co-activation of agonist and antagonist muscles. Extreme co-activation is unlikely to occur in most healthy human sub-maximal movements, especially if muscle forces are distributed in a way that is sensitive to the physiological load (or effort) across individual muscles [23] or reduces metabolic cost. One previous study used EMG data as a way to provide some bounds on the range of possible muscle forces [31], however the remaining muscles without EMG data were left unbounded and therefore still had vast ranges of possible muscle forces. Additionally, there are other limitations to directly using EMG data for this approach, such as uncertainty about how to normalize EMG, resolving forces from EMG, and collecting EMG from deep muscles [34,35,36,37]. Therefore, there is a critical gap in the field of musculoskeletal modeling and simulation between (a) solving for muscle forces with an explicit, but uncertain, objective function (or subset of them) and (b) solving for the broad range of possible muscle forces that include muscle force combinations that are not realistic without extreme co-activation of agonist muscle groups.
Bayesian inference methods are well suited for problems where we want to constrain the set of plausible solutions based on prior evidence and knowledge of the musculoskeletal system. This evidence could include information about physiology, measurement errors, and model-based uncertainties. Bayesian inference problems are defined with a prior function (a set of plausible assumptions about the problem), a likelihood function (provided by observed data about a set of parameters), and a posterior function (a quantification of the plausible values of a set of parameters) [38]. The logarithmic forms of these functions (log Prior, log Likelihood, and log Posterior) are preferred for a Bayesian inference problem because it is computationally more stable and effective.
One common way to sample from the solution space is to use a Markov Chain Monte Carlo (MCMC), which is a computer-driven sampling method that allows us to characterize a posterior distribution without knowing all of the distribution’s properties. The MCMC analysis generates the random samples (or proposals) from a multi-dimensional parameter space via a sequential process according to rules that compare consecutive proposals, and this generates a ‘chain’ of proposals [39, 40]. One unique property of a MCMC chain is that new proposals are based on the previous proposal, but do not depend on any proposal prior to the previous one [38]. Then, as the MCMC algorithm is iterated, the set of visited locations is used as a sample from the Bayesian posterior distribution of the unknown parameters [40, 41], which numerically represents a set of equally plausible parameter vectors that could produce a result that is similar to the observed data.
Our aim is to evaluate the feasibility of using Bayesian inference methods to quantify the plausible range of muscle forces for human motion. For this initial feasibility assessment, we developed a prior based on a commonly used objective function (integrated muscle excitation cubed), while keeping other musculoskeletal model parameters constant throughout the study (e.g., peak isometric muscle forces, tendon slack lengths). Our prior was based on physiological hypotheses that muscle forces are distributed amongst agonist muscles and that co-activation of agonist and antagonist muscles is typically low for healthy human motions [23, 42]. We used an MCMC sampling algorithm in MATLAB and simulated an elbow flexion–extension task (reference motion) using OpenSim to explore the plausible excitations that could give rise to the reference joint trajectory. We then compared the excitations from MCMC to the known original simulation that generated the reference motion. Our aim for this paper is to present a workflow for building a Bayesian model and performing MCMC analysis to sample plausible muscle forces for a measured motion with a musculoskeletal model. Ultimately, we hope that this workflow will allow movement scientists to appropriately account for uncertainties in measurement, model structure, model parameters, and assumed cost functions in musculoskeletal simulations.
More at link.
No comments:
Post a Comment