Mathematical model that predicts lower leg motion in response to electrical stimulation

Dynamic optimization of stimulation frequency to reduce isometric muscle fatigue using a modified Hill-Huxley model

INTRODUCTION

Optimal frequency modulation during functional electrical stimulation (FES) may minimize or delay the onset of FES-induced muscle fatigue.

METHODS

An offline dynamic optimization method, constrained to a modified Hill-Huxley model, was used to determine the minimum number of pulses that would maintain a constant desired isometric contraction force.

RESULTS

Six able-bodied participants were recruited for the experiments, and their quadriceps muscles were stimulated while they sat on a leg extension machine. The force-time (F-T) integrals and peak forces after the pulse train was delivered were found to be statistically significantly greater than the force-time integrals and peak forces obtained after a constant frequency train was delivered.

DISCUSSION

Experimental results indicated that the optimized pulse trains induced lower levels of muscle fatigue compared with constant frequency pulse trains. This could have a potential advantage over current FES methods that often choose a constant frequency stimulation train. Muscle Nerve 57: 634-641, 2018.

Validation of empirical mode decomposition combined with notch filtering to extract electrical stimulation artifact from surface electromyograms during functional electrical stimulation

This paper presents the validity of Empirical Mode Decomposition (EMD) combined with Notch filtering to remove the electrical stimulation (ES) artifact from surface electromyogram (EMG) data for interpretation of muscle responses during Functional Electrical Stimulation (FES) experiments. We hypothesized that the EMD algorithm provides a suitable platform for decomposing the EMG signal into physically meaningful intrinsic mode functions (IMFs) which can be further used to isolate electrical stimulation (ES) artifact. The basic EMD algorithm was used to decompose the ES induced EMG signals into IMFs. IMFs most contaminated by ES were identified based on the standard deviation (SD) criterion. An IMF with the maximum signal to noise ratio (SNR) was Notch filtered and added to IMFs containing pure EMG data to get the filtered EMG signal. The method was tested on 5 able bodied (AB) and 2 spinal cord injured (SCI) participants. The validity of the filtered signal was assessed by normalized root mean squared error (NRMSE) and signal to noise (SNR) ratio values obtained by comparing a clean EMG collected during maximum volitional contraction (MVC) and EMD-Notch filtered signal from the combination of a clean EMG with i) simulated ES and, ii) real ES with no activation generated at different ES amplitudes. The results showed that the EMD-Notch filtering approach was successful, reliable and repeatable in extracting pure muscle responses during ES showing improved values for NRMSE and SNR in both AB and SCI individuals.

Prediction of kinematic and kinetic performance in a drop vertical jump with individual anthropometric factors in adolescent female athletes: implications for cadaveric investigations

Anterior cruciate ligament injuries are common, expensive to repair, and often debilitate athletic careers. Robotic manipulators have evaluated knee ligament biomechanics in cadaveric specimens, but face limitations such as accounting for variation in bony geometry between specimens that may influence dynamic motion pathways. This study examined individual anthropometric measures for significant linear relationships with in vivo kinematic and kinetic performance and determined their implications for robotic studies. Anthropometrics and 3D motion during a 31 cm drop vertical jump task were collected in high school female basketball players. Anthropometric measures demonstrated differential statistical significance in linear regression models relative to kinematic variables (p-range <0.01-0.95). However, none of the anthropometric relationships accounted for clinical variance or provided substantive univariate accuracy needed for clinical prediction algorithms (r(2) < 0.20). Mass and BMI demonstrated models that were significant (p < 0.05) and predictive (r(2) > 0.20) relative to peak flexion moment, peak adduction moment, flexion moment range, abduction moment range, and internal rotation moment range. The current findings indicate that anthropometric measures are less associated with kinematics than with kinetics. Relative to the robotic manipulation of cadaveric limbs, the results do not support the need to normalize kinematic rotations relative to specimen dimensions.

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 stochastic model of knee angle in response to electrical stimulation of the quadriceps and hamstrings muscles

A novel stochastic model of knee angle in response to stimulation of the quadriceps and hamstrings muscle groups is presented. This model includes uncertainty due to fatigue and day-to-day changes in the stimulated muscles. The model consists of a normally distributed random variable whose mean and standard deviation vary with time and is characterized using data from a complete spinal cord injuries subject. The experimental data show a significant difference between the left and right legs under certain conditions, and suggest that fatigue-related and day-to-day variation may also be important. The purpose of this model is to generate more realistic electrically stimulated knee movements. This stochastic modeling technique could be incorporated into a comprehensive model of a joint actuated with electrical stimulation, and has great potential as a tool for analyzing closed-loop performance of electrically stimulated systems.

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.

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.

Modeling age-related neuromuscular changes in humans

With aging, motoneurons and muscle tissue undergo significant changes, which influence function in terms of strength, mobility, and overall independence. Mathematical modeling provides a practical method of studying the relationships among recruitment, rate-coding, and force output in motor units, and may be used to predict functional neuromuscular changes related to aging. For this study, the Heckman-Binder model was used to examine changes in human quadriceps motor units. Relationships among current input, firing frequency, and force output were defined for both a younger and an older individual. Included in the model were age-related effects associated with reduced muscle contractile speed; reduced muscle-fibre number, size, and specific tension; reduced gain of the frequency-current relationship; decreased size of motoneurons; and altered motor unit remodeling. Adjustment of this model to reflect age-related changes resulted in a leftward shift of the force-frequency function, lower firing frequency for any given current injected into the motoneuron, and a reduction in maximal force output. The model suggests that older individuals are capable of reaching force levels up to approximately 50% of those attained by younger individuals, with relatively similar or even slightly lower levels of current input. This could mean that the sense of effort and the contribution of factors other than degree of effort from afferent inputs to the pool, including conscious supraspinal centres, might be different in the older adult.

Predicting muscle forces of individuals with hemiparesis following stroke

Background

Functional electrical stimulation (FES) has been used to improve function in individuals with hemiparesis following stroke. An ideal functional electrical stimulation (FES) system needs an accurate mathematical model capable of designing subject and task-specific stimulation patterns. Such a model was previously developed in our laboratory and shown to predict the isometric forces produced by the quadriceps femoris muscles of able-bodied individuals and individuals with spinal cord injury in response to a wide range of clinically relevant stimulation frequencies and patterns. The aim of this study was to test our isometric muscle force model on the quadriceps femoris, ankle dorsiflexor, and ankle plantar-flexor muscles of individuals with post-stroke hemiparesis.

Methods

Subjects were seated on a force dynamometer and isometric forces were measured in response to a range of stimulation frequencies (10 to 80-Hz) and 3 different patterns. Subject-specific model parameter values were obtained by fitting the measured force responses from 2 stimulation trains. The model parameters thus obtained were then used to obtain predicted forces for a range of frequencies and patterns. Predicted and measured forces were compared using intra-class correlation coefficients, r² values, and model error relative to the physiological error (variability of measured forces).

Results

Results showed excellent agreement between measured and predicted force-time responses (r² >0.80), peak forces (ICCs>0.84), and force-time integrals (ICCs>0.82) for the quadriceps, dorsiflexor, and plantar-fexor muscles. The model error was within or below the +95% confidence interval of the physiological error for >88% comparisons between measured and predicted forces.

Conclusion

Our results show that the model has potential to be incorporated as a feed-forward controller for predicting subject-specific stimulation patterns during FES.

Mathematical model that predicts the force-intensity and force-frequency relationships after spinal cord injuries

We have previously developed and tested a muscle model that predicts the effect of stimulation frequency on muscle force responses. The aim of this study was to enhance our isometric mathematical model to predict muscle forces in response to stimulation trains with a wide range of frequencies and intensities for the quadriceps femoris muscles of individuals with spinal cord injuries. Isometric forces were obtained experimentally from 10 individuals with spinal cord injuries (time after injury, 1.5-8 years) and then compared to forces predicted by the model. Our model predicted accurately the force-time integrals (FTI) and peak forces (PF) for stimulation trains of a wide range of frequencies (12.5-80 HZ) and intensities (150-600-mus pulse duration), and two different stimulation patterns (constant-frequency trains and doublet-frequency trains). The accurate predictions of our model indicate that our model, which now incorporates the effects of stimulation frequency, intensity, and pattern on muscle forces, can be used to design optimal customized stimulation strategies for spinal cord-injured patients.

Relationship between stimulation train characteristics and dynamic human skeletal muscle performance

AIM

The purpose of the present study was to investigate the effect of activation frequency on dynamic human muscle performance for a range of train durations and number of pulses during free limb movement.

METHODS

The quadriceps femoris muscles of 10 subjects were activated with stimulation trains with different activation frequency, train durations and number of pulses. The peak excursion produced in response to each train was the dependent measure of muscle performance.

RESULTS

The excursion-frequency (for a 300-ms train duration) and excursion-train duration (for trains with frequencies of 10, 30 or 59 Hz) relationships could each be fit with a two-parameter exponential equation (R(2) values > 0.97). Because the number of pulses in a stimulation train is a function of both train duration and frequency, the excursion produced as a function of the number of pulses was characterized by a three-parameter exponential equation that represented this combined relationship. The relationship between the measured and predicted excursions in response to a wide range of stimulation trains had a R(2) = 0.96. In addition, one-way repeated measures analyses of variance (anovas) showed that the frequency at which the maximum excursion was produced increased with an increase in the number of pulses in the trains tested.

CONCLUSION

These results show the importance of train duration and the number of pulses contained within a train on the relationship between activation frequency and human skeletal muscle performance.

Effects of activation pattern on nonisometric human skeletal muscle performance

During volitional muscle activation, motor units often fire with varying discharge patterns that include brief, high-frequency bursts of activity. These variations in the activation rate allow the central nervous system to precisely control the forces produced by the muscle. The present study explores how varying the instantaneous frequency of stimulation pulses within a train affects nonisometric muscle performance. The peak excursion produced in response to each stimulation train was considered as the primary measure of muscle performance. The results showed that at each frequency tested between 10 and 50 Hz, variable-frequency trains that took advantage of the catchlike property of skeletal muscle produced greater excursions than constant-frequency trains. In addition, variable-frequency trains that could achieve targeted trajectories with fewer pulses than constant-frequency trains were identified. These findings suggest that similar to voluntary muscle activation patterns, varying the instantaneous frequency within a train of pulses can be used to improve muscle performance during functional electrical stimulation.