Predicting non-isometric fatigue induced by electrical stimulation pulse trains as a function of pulse duration.

BACKGROUND: Our previous model of the non-isometric muscle fatigue that occurs during repetitive functional electrical stimulation included models of force, motion, and fatigue and accounted for applied load but not stimulation pulse duration. Our objectives were to: 1) further develop, 2) validate, and 3) present outcome measures for a non-isometric fatigue model that can predict the effect of a range of pulse durations on muscle fatigue. METHODS: A computer-controlled stimulator sent electrical pulses to electrodes on the thighs of 25 able-bodied human subjects. Isometric and non-isometric non-fatiguing and fatiguing knee torques and/or angles were measured. Pulse duration (170-600 µs) was the independent variable. Measurements were divided into parameter identification and model validation subsets. RESULTS: The fatigue model was simplified by removing two of three non-isometric parameters. The third remained a function of other model parameters. Between 66% and 77% of the variability in the angle measurements was explained by the new model. CONCLUSION: Muscle fatigue in response to different stimulation pulse durations can be predicted during non-isometric repetitive contractions.

Modelling of individual subject ozone exposure response kinetics.

CONTEXT: A better understanding of individual subject ozone (O(3)) exposure response kinetics will provide insight into how to improve models used in the risk assessment of ambient ozone exposure. OBJECTIVE: To develop a simple two compartment exposure-response model that describes individual subject decrements in forced expiratory volume in one second (FEV(1)) induced by the acute inhalation of O(3) lasting up to 8 h. METHODS: FEV(1) measurements of 220 subjects who participated in 14 previously completed studies were fit to the model using both particle swarm and nonlinear least squares optimization techniques to identify three subject-specific coefficients producing minimum "global" and local errors, respectively. Observed and predicted decrements in FEV(1) of the 220 subjects were used for validation of the model. Further validation was provided by comparing the observed O(3)-induced FEV(1) decrements in an additional eight studies with predicted values obtained using model coefficients estimated from the 220 subjects used in cross validation. RESULTS: Overall the individual subject measured and modeled FEV(1) decrements were highly correlated (mean R(2) of 0.69 ± 0.24). In addition, it was shown that a matrix of individual subject model coefficients can be used to predict the mean and variance of group decrements in FEV(1). CONCLUSION: This modeling approach provides insight into individual subject O(3) exposure response kinetics and provides a potential starting point for improving the risk assessment of environmental O(3) exposure.

Predicting fatigue during electrically stimulated non-isometric contractions.

Mathematical prediction of power loss during electrically stimulated contractions is of value to those trying to minimize fatigue and to those trying to decipher the relative contributions of force and velocity. Our objectives were to: (1) develop a model of non-isometric fatigue for electrical stimulation-induced, open-chain, repeated extensions of the leg at the knee; and (2) experimentally validate the model. A computer-controlled stimulator sent electrical pulses to surface electrodes on the thighs of 17 able-bodied subjects. Isometric and non-isometric non-fatiguing and fatiguing leg extension torque and/or angle at the knee were measured. Two existing mathematical models, one of non-isometric force and the other of isometric fatigue, were combined to develop the non-isometric force-fatigue model. Angular velocity and 3 new parameters were added to the isometric fatigue model. The new parameters are functions of parameters within the force model, and therefore additional measurements from the subject are not needed. More than 60% of the variability in the measurements was explained by the new force-fatigue model. This model can help scientists investigate the etiology of non-isometric fatigue and help engineers to improve the task performance of functional electrical stimulation systems.

Predicting the effect of muscle length on fatigue during electrical stimulation.

Mathematical models have been developed to predict fatigue during functional electrical stimulation, but the predictive accuracy at different muscle lengths is unknown. The objectives of our study were to: (1) experimentally determine the relationship between knee extension angle (20 degrees, 40 degrees, 65 degrees, and 90 degrees) and fatigue of the quadriceps muscles, and (2) predict that relationship using a mathematical model. A computer-controlled stimulator sent trains of pulses to surface electrodes on the thighs of five subjects while forces were measured at the ankle. A two-component mathematical model was developed. One component accounted for force, and the other accounted for fatigue. The model was fit to the data, and parameters were identified at 90 degrees . The fitted subject-averaged r(2) value was 0.89. The model was used to predict fatigue at the remaining angles, and the subject-averaged r(2) values were >0.75. Therefore, at least 75% of the variability in the measurements was explained by the model. The force model is explicitly dependent on angle, and the fatigue model is explicitly dependent on force; therefore, the dependence of fatigue on knee angle was implicit.