The development of localized muscle fatigue has classically been described by the nonlinear intensity – endurance time (ET) curve (Rohmert, 1960; El Ahrache et al., 2006). These empirical intensity-ET relationships have been well-documented and vary between joint regions. We previously proposed a three-compartment biophysical fatigue model, consisting of compartments (i.e. states) for active (MA), fatigued (MF), and resting (MR) muscle, to predict the decay and recovery of muscle force (Xia and Frey Law, 2008). The purpose of this investigation was to determine optimal model parameter values, fatigue (F) and recovery (R), which define the “flow rate” between muscle states and to evaluate the model’s accuracy for estimating expected intensity – ET curves. Using a grid-search approach with modified Monte Carlo simulations, over 1 million F and R permutations were used to predict the maximum ET for sustained isometric tasks at 9 intensities ranging from 10 – 90% of maximum in 10% increments (over 9 million simulations total). Optimal F and R values ranged from 0.00589 (Fankle) and 0.0182 (Rankle) to 0.00058 (Fshoulder) and 0.00168 (Rshoulder), reproducing the intensity-ET curves with low mean RMS errors: shoulder (2.7s), hand/grip (5.6s), knee (6.7s), trunk (9.3s), elbow (9.9s), and ankle (11.2s). Testing the model at different task intensities (15 – 95% maximum in 10% increments) produced slightly higher errors, but largely within the 95% prediction intervals expected for the intensity-ET curves. We conclude that this three-compartment fatigue model can be used to accurately represent joint-specific intensity-ET curves, which may be useful for ergonomic analyses and/or digital human modeling applications.
This study aimed to test whether adding a rest recovery parameter, r, to the analytical three-compartment controller (3CC) fatigue model (Xia and Frey Law, 2008) will improve fatigue estimates during intermittent contractions. The 3CC muscle fatigue model uses differential equations to predict the flow of muscle between three muscle states: Resting (M), Active (M), and Fatigued (M). This model uses a feedback controller to match the active state to target loads and two joint-specific parameters: F, fatigue rate controlling flow from active to fatigued compartments) and R, the recovery rate controlling flow from the fatigued to the resting compartments. This model does well to predict intensity-endurance time curves for sustained isometric tasks. However, previous studies find when rest intervals are present that the model over predicts fatigue. Intermittent rest periods would allow for the occurrence of subsequent reactive vasodilation and post-contraction hyperemia. We hypothesize a modified 3CC-r fatigue model will improve predictions of force decay during intermittent contractions with the addition of a rest recovery parameter, r, to augment recovery during rest intervals, representing muscle re-perfusion. A meta-analysis compiling intermittent fatigue data from 63 publications reporting decline in peak torque (% torque decline) were used for comparison. The original model over-predicted fatigue development from 19 to 29% torque decline; the addition of a rest multiplier significantly improved fatigue estimates to 6-10% torque decline. We conclude the addition of a rest multiplier to the three-compartment controller fatigue model provides a physiologically consistent modification for tasks involving rest intervals, resulting in improved estimates of muscle fatigue.
Model coefficients for each time point by joint, where intensity (MVC) and duty cycle (DC) are values between 0 and 100 percent, %Decline=a*(DC) b *(MVC) c. .
Background: Ventriculoperitoneal shunting improves gait in patients with normal pressure hydrocephalus. Postural instability is a major concern, but mostly ignored in the evaluation and treatment of these patients. This study quantified postural instability using kinematics via a prospective cohort design. Methods: Seventeen patients with suspected normal pressure hydrocephalus and twenty age-matched, healthy controls underwent quantitative pull test and gait examinations while wearing inertial measurement units at baseline. Patients with suspected normal pressure hydrocephalus who were shunted (n=13) and not shunted (n=4) underwent further testing after a lumbar drain trial and at follow-up visits 6 and 12 months post-operatively. Results: While most gait improvement in patients who were shunted was seen immediately after the lumbar drain trial, measures of their postural response continued to improve after the lumbar drain trial through one year of follow-up. Patients who were not shunted showed no statistically significant changes in gait and postural instability measures. Conclusions: After shunting, postural instability improves continuously over one year. In contrast, a large improvement in gait is seen immediately with minimal change over the subsequent year. This difference in timing may implicate two distinct neurophysiological mechanisms of recovery and provides novel evidence that postural instability improves in response to long-term CSF diversion.
One approach to modelling muscle strength is to represent peak torque as three-dimensional (3D) torque-angle-velocity surfaces at the joint level. These nonlinear relationships have been modelled using polynomial equations. However, we hypothesised logistic equations would better represent 3D peak strength based on known 'S-shaped' relationships between torque and velocity. To compare the two approaches, we modelled eight 3D strength surfaces based on previously published data, elbow and knee strength, using polynomial and logistic equations. Both models fit the strength data well, with median R 2 values of 0.983 and 0.971 for polynomial and logistic equations, respectively. However, when extrapolating the models to a full normal range of motion (0° to 140°) 100% of the polynomial surfaces , but only 25% of the logistic surfaces, displayed non-physiologic strength estimates (i.e., crossed zero). Accordingly, logistic equations may provide equal or better representations of 3D joint strength surfaces for digital human modelling.
Background: Finite element modeling serves as a promising tool for investigating underlying rotator cuff biomechanics and pathology. However, there are currently no concrete guidelines for reporting in finite element model studies. This has compromised the reliability, validity, and reproducibility of literature due to omission of pertinent items within publications. Recently a Finite Element Model Grading Procedure has been proposed as a reporting guideline for model developers. The aim of this study was to conduct a systematic review of rotator cuff focused finite element models and characterize the reporting quality of those articles.Methods: A comprehensive literature search was performed in PubMed, Web of Science, and Embase to find relevant articles. Each article was graded and given a reporting quality ranking based on a score generated from the Finite Element Model Grading Procedure. Findings:We found that only 5/22 articles had scores of 75% or higher and fell within the "exceptional" reporting quality range. Most of the articles (16/22) fell within the "good" reporting quality range with scores between 50% and 75%. However, 9/16 articles within the "good" reporting quality range had scores below 60%.Interpretation: This study indicates that improved guidelines and standards for good reporting practices must be made in the field of finite element modeling. Furthermore, it supports the use of the Finite Element Model Grading Procedure as an objective method for evaluating the quality of finite element model reporting in the literature.
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