Predicting fatigue during electrically stimulated non-isometric contractions

Exhaustion of Skeletal Muscle Fibers Within Seconds: Incorporating Phosphate Kinetics Into a Hill-Type Model

Initiated by neural impulses and subsequent calcium release, skeletal muscle fibers contract (actively generate force) as a result of repetitive power strokes of acto-myosin cross-bridges. The energy required for performing these cross-bridge cycles is provided by the hydrolysis of adenosine triphosphate (ATP). The reaction products, adenosine diphosphate (ADP) and inorganic phosphate (P i ), are then used-among other reactants, such as creatine phosphate-to refuel the ATP energy storage. However, similar to yeasts that perish at the hands of their own waste, the hydrolysis reaction products diminish the chemical potential of ATP and thus inhibit the muscle's force generation as their concentration rises. We suggest to use the term "exhaustion" for force reduction (fatigue) that is caused by combined P i and ADP accumulation along with a possible reduction in ATP concentration. On the basis of bio-chemical kinetics, we present a model of muscle fiber exhaustion based on hydrolytic ATP-ADP-P i dynamics, which are assumed to be length- and calcium activity-dependent. Written in terms of differential-algebraic equations, the new sub-model allows to enhance existing Hill-type excitation-contraction models in a straightforward way. Measured time courses of force decay during isometric contractions of rabbit M. gastrocnemius and M. plantaris were employed for model verification, with the finding that our suggested model enhancement proved eminently promising. We discuss implications of our model approach for enhancing muscle models in general, as well as a few aspects regarding the significance of phosphate kinetics as one contributor to muscle fatigue.

Predictive Neuromuscular Fatigue of the Lower Extremity Utilizing Computer Modeling

This paper studies the modeling of lower extremity muscle forces and their correlation to neuromuscular fatigue. Two analytical fatigue models were combined with a musculoskeletal model to estimate the effects of hamstrings fatigue on lower extremity muscle forces during a side step cut. One of the fatigue models (Tang) used subject-specific knee flexor muscle fatigue and recovery data while the second model (Xia) used previously established fatigue and recovery parameters. Both fatigue models were able to predict hamstrings fatigue within 20% of the experimental data, with the semimembranosus and semitendinosus muscles demonstrating the largest (11%) and smallest (1%) differences, respectively. In addition, various hamstrings fatigue levels (10-90%) on lower extremity muscle force production were assessed using one of the analytical fatigue models. As hamstrings fatigue levels increased, the quadriceps muscle forces decreased by 21% (p < 0.01), while gastrocnemius muscle forces increased by 36% (p < 0.01). The results of this study validate the use of two analytical fatigue models in determining the effects of neuromuscular fatigue during a side step cut, and therefore, this model can be used to assess fatigue effects on risk of lower extremity injury during athletic maneuvers. Understanding the effects of fatigue on muscle force production may provide insight on muscle group compensations that may lead to altered lower extremity motion patterns as seen in noncontact anterior cruciate ligament (ACL) injuries.

A new method for muscle fatigue assessment: Online model identification techniques

INTRODUCTION

The purpose of this study was to propose a method that allows extraction of the current muscle state under electrically induced fatigue.

METHODS

The triceps surae muscle of 5 subjects paralyzed by spinal cord injury was fatigued by intermittent electrical stimulation (5 × 5 trains at 30 Hz). Classical fatigue indices representing muscle contractile properties [peak twitch (Pt) and half-relaxation time (HRT)] were assessed before and after each 5-train series and were used to identify 2 relevant parameters (Fm , Ur ) of a previously developed mathematical model using the Sigma-Point Kalman Filter.

RESULTS

Pt declined significantly during the protocol, whereas HRT remained unchanged. Identification of the model parameters with experimental data yielded a model-based fatigue assessment that gave a more stable evaluation of fatigue than classical parameters.

CONCLUSIONS

This work reinforces clinical research by providing a tool that clinicians can use to monitor fatigue development during stimulation.

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.

A three-compartment muscle fatigue model accurately predicts joint-specific maximum endurance times for sustained isometric tasks

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 (M(A)), fatigued (M(F)), and resting (M(R)) muscles, 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% to 90% of maximum in 10% increments (over 9 million simulations total). Optimal F and R values ranged from 0.00589 (F(ankle)) and 0.0182 (R(ankle)) to 0.00058 (F(shoulder)) and 0.00168 (R(shoulder)), 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.

A generic model of real-world non-ideal behaviour of FES-induced muscle contractions: simulation tool

Functional electrical stimulation (FES) applications are frequently evaluated in simulation prior to testing in human subjects. Such simulations are usually based on the typical muscle responses to electrical stimulation, which may result in an overly optimistic assessment of likely real-world performance. We propose a novel method for simulating FES applications that includes non-ideal muscle behaviour during electrical stimulation resulting from muscle fatigue, spasms and tremors. A 'non-idealities' block that can be incorporated into existing FES simulations and provides a realistic estimate of real-world performance is described. An implementation example is included, showing how the non-idealities block can be incorporated into a simulation of electrically stimulated knee extension against gravity for both a proportional-integral-derivative controller and a sliding mode controller. The results presented in this paper illustrate that the real-world performance of a FES system may be vastly different from the performance obtained in simulation using nominal muscle models. We believe that our non-idealities block should be included in future simulations that involve muscle response to FES, as this tool will provide neural engineers with a realistic simulation of the real-world performance of FES systems. This simulation strategy will help engineers and organizations save time and money by preventing premature human testing. The non-idealities block will become available free of charge at www.toronto-fes.ca in late 2011.