Predicting human chronically paralyzed muscle force: a comparison of three mathematical models

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.

An Energetic Model of Low Frequency Isometric Neuromuscular Electrical Stimulation

The objective of this study was to evaluate whether an adapted Hill-type model of muscle energetics could account for the relatively high energy turnover observed during low frequency isometric Neuromuscular Electrical Stimulation (NMES). A previously validated Hill-based model was adapted to estimate the energy consumption due to muscle activation, force maintenance and internal shortening of the muscle during isometric NMES. Quadriceps muscle model parameters were identified for 10 healthy subjects based on the experimentally measured torque response to isometric stimulation at 8 Hz. Model predictions of torque and energy consumption rates across the stimulation range 1-12 Hz were compared with experimental data recorded from the same subjects. The model provided estimates in close agreement with the experimental values for the group mean energy consumption rate across the frequency range tested, (R adj (2) = 0.98), although prediction of individual data points for all frequencies and all subjects was more variable, (R adj (2) = 0.70). The model suggests that approximately one-third of the energy between 4 and 6 Hz is due to shortening heat. The model provides a means of identifying optimal therapeutic stimulation patterns for sustained incremental oxygen uptake at minimum torque output for a given muscle and provides insight into the energetic components involved.

The effectiveness of FES-evoked EMG potentials to assess muscle force and fatigue in individuals with spinal cord injury

The evoked electromyographic signal (eEMG) potential is the standard index used to monitor both electrical changes within the motor unit during muscular activity and the electrical patterns during evoked contraction. However, technical and physiological limitations often preclude the acquisition and analysis of the signal especially during functional electrical stimulation (FES)-evoked contractions. Hence, an accurate quantification of the relationship between the eEMG potential and FES-evoked muscle response remains elusive and continues to attract the attention of researchers due to its potential application in the fields of biomechanics, muscle physiology, and rehabilitation science. We conducted a systematic review to examine the effectiveness of eEMG potentials to assess muscle force and fatigue, particularly as a biofeedback descriptor of FES-evoked contractions in individuals with spinal cord injury. At the outset, 2867 citations were identified and, finally, fifty-nine trials met the inclusion criteria. Four hypotheses were proposed and evaluated to inform this review. The results showed that eEMG is effective at quantifying muscle force and fatigue during isometric contraction, but may not be effective during dynamic contractions including cycling and stepping. Positive correlation of up to r = 0.90 (p < 0.05) between the decline in the peak-to-peak amplitude of the eEMG and the decline in the force output during fatiguing isometric contractions has been reported. In the available prediction models, the performance index of the eEMG signal to estimate the generated muscle force ranged from 3.8% to 34% for 18 s to 70 s ahead of the actual muscle force generation. The strength and inherent limitations of the eEMG signal to assess muscle force and fatigue were evident from our findings with implications in clinical management of spinal cord injury (SCI) population.

Fatigue and non-fatigue mathematical muscle models during functional electrical stimulation of paralyzed muscle

Electrical muscle stimulation demonstrates potential for preventing muscle atrophy and for restoring functional movement after spinal cord injury (SCI). Control systems used to optimize delivery of electrical stimulation protocols depend upon the algorithms generated using computational models of paralyzed muscle force output. The Hill-Huxley-type model, while being highly accurate, is also very complex, making it difficult for real-time implementation. In this paper, we propose a Wiener-Hammerstein system to model the paralyzed skeletal muscle under electrical stimulus conditions. The proposed model has substantial advantages in identification algorithm analysis and implementation including computational complexity and convergence, which enable it to be used in real-time model implementation. Experimental data sets from the soleus muscles of fourteen subjects with SCI were collected and tested. The simulation results show that the proposed model outperforms the Hill-Huxley-type model not only in peak force prediction, but also in fitting performance for force output of each individual stimulation train.

Coronary blood flow produced by muscle contractions induced by intracardiac electrical CPR during ventricular fibrillation

It has been reported that transthoracic electrical cardiopulmonary resuscitation (ECPR) generates coronary perfusion pressures (CPP) similar to manual chest compressions (MCC). We hypothesized that intracardiac ECPR produces similar CPP.

METHODS

ECPR pulse train protocols were applied for 20 seconds in a porcine model following 10 seconds of ventricular fibrillation (VF), using a defibrillator housing electrode and a right ventricular coil (IC-ECPR). Each protocol consisted of 200-ms electrical pulse trains applied at a rate of 100 pulse trains/min. The protocols were grouped in skeletal-based versus cardiac-based stimulation measurements. CPP was recorded and compared to historical MCC values generated by a similar experimental design. CPP > 15 mm Hg at 30 seconds of VF following the application of an IC-ECPR protocol was defined as successful.

RESULTS

Mean CPP for all intracardiac ECPR pulse train protocols at 30 seconds of VF was 14.8 +/- 3.8 mm Hg (n = 39). Mean CPP in seven successful skeletal-based IC-ECPR protocols was 19.4 +/- 3.2 mm Hg, and mean CPP in 10 successful cardiac-based IC-ECPR protocols was 17.4 +/- 2.1 mm Hg. Reported CPP for 15 MCC experiments at 30 seconds of VF was 22.9 +/- 9.4 mm Hg (P = 0.35 compared to skeletal-based IC-ECPR, P = 0.08 compared to cardiac-based IC-ECPR).

CONCLUSIONS

Intracardiac applied electrical CPR produced observable skeletal muscle contractions, measurable pressure pulses, and coronary perfusion pressures similar to MCC during a brief episode of untreated VF.

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.

Objective assessment of the fusion frequency in functional electrical stimulation using the fast Fourier transform

In functional electrical stimulation (FES) the dynamics of tetanic muscle contractions is often described by the fusion frequency (FF), as determined by palpation: contractions elicited by stimulation frequencies above the FF appear smooth. To contribute to a more objective assessment of this important FES parameter, we have developed a dedicated signal analysis method based on fast Fourier transformation (FFT). The ripple to peak ratio (R(rpFFT)) - the relation between ripple amplitude and peak force value of a recorded tetanic muscle force in relation to the applied stimulation frequency - was determined automatically by analysing a 0.2-s interval in the steady state of a stimulation burst. The method was tested on simulated data and on force recordings from isolated tibialis anterior muscles of six rabbits. The results were compared to manual estimates. The robustness of the method was tested by adding noise and hum. Simulated noise at 100% of the ripple force increased R(rpFFT) by 4%. Hum at 20 Hz away from the stimulation frequency caused changes of less than 0.5%. The results of the automated analysis of recorded signals matched the manual estimates sufficiently well, especially for stimulation frequencies near or above FF. R(rpFFT) therefore seems suitable for automated, objective and robust assessment of the ripple and the FF of electrically stimulated muscle.

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.

Impact of varying pulse frequency and duration on muscle torque production and fatigue

Neuromuscular electrical stimulation (NMES) involves the use of electrical current to facilitate contraction of skeletal muscle. However, little is known concerning the effects of varying stimulation parameters on muscle function in humans. The purpose of this study was to determine the extent to which varying pulse duration and frequency altered torque production and fatigability of human skeletal muscle in vivo. Ten subjects underwent NMES-elicited contractions of varying pulse frequencies and durations as well as fatigue tests using stimulation trains of equal total charge, yet differing parametric settings at a constant voltage. Total charge was a strong predictor of torque production, and pulse trains with equal total charge elicited identical torque output. Despite similar torque output, higher- frequency trains caused greater fatigue. These data demonstrate the ability to predictably control torque output by simultaneously controlling pulse frequency and duration and suggest the need to minimize stimulation frequency to control fatigue.

Mathematical models of human paralyzed muscle after long-term training

Spinal cord injury (SCI) results in major musculoskeletal adaptations, including muscle atrophy, faster contractile properties, increased fatigability, and bone loss. The use of functional electrical stimulation (FES) provides a method to prevent paralyzed muscle adaptations in order to sustain force-generating capacity. Mathematical muscle models may be able to predict optimal activation strategies during FES, however muscle properties further adapt with long-term training. The purpose of this study was to compare the accuracy of three muscle models, one linear and two nonlinear, for predicting paralyzed soleus muscle force after exposure to long-term FES training. Further, we contrasted the findings between the trained and untrained limbs. The three models' parameters were best fit to a single force train in the trained soleus muscle (N=4). Nine additional force trains (test trains) were predicted for each subject using the developed models. Model errors between predicted and experimental force trains were determined, including specific muscle force properties. The mean overall error was greatest for the linear model (15.8%) and least for the nonlinear Hill Huxley type model (7.8%). No significant error differences were observed between the trained versus untrained limbs, although model parameter values were significantly altered with training. This study confirmed that nonlinear models most accurately predict both trained and untrained paralyzed muscle force properties. Moreover, the optimized model parameter values were responsive to the relative physiological state of the paralyzed muscle (trained versus untrained). These findings are relevant for the design and control of neuro-prosthetic devices for those with SCI.

Neuromuscular electrical stimulation in neurorehabilitation

This review provides a comprehensive overview of the clinical uses of neuromuscular electrical stimulation (NMES) for functional and therapeutic applications in subjects with spinal cord injury or stroke. Functional applications refer to the use of NMES to activate paralyzed muscles in precise sequence and magnitude to directly accomplish functional tasks. In therapeutic applications, NMES may lead to a specific effect that enhances function, but does not directly provide function. The specific neuroprosthetic or "functional" applications reviewed in this article include upper- and lower-limb motor movement for self-care tasks and mobility, respectively, bladder function, and respiratory control. Specific therapeutic applications include motor relearning, reduction of hemiplegic shoulder pain, muscle strengthening, prevention of muscle atrophy, prophylaxis of deep venous thrombosis, improvement of tissue oxygenation and peripheral hemodynamic functioning, and cardiopulmonary conditioning. Perspectives on future developments and clinical applications of NMES are presented.

Feedback-controlled stimulation enhances human paralyzed muscle performance

Chronically paralyzed muscle requires extensive training before it can deliver a therapeutic dose of repetitive stress to the musculoskeletal system. Neuromuscular electrical stimulation, under feedback control, may subvert the effects of fatigue, yielding more rapid and extensive adaptations to training. The purposes of this investigation were to 1) compare the effectiveness of torque feedback-controlled (FDBCK) electrical stimulation with classic open-loop constant-frequency (CONST) stimulation, and 2) ascertain which of three stimulation strategies best maintains soleus torque during repetitive stimulation. When torque declined by 10%, the FDBCK protocol modulated the base stimulation frequency in three ways: by a fixed increase, by a paired pulse (doublet) at the beginning of the stimulation train, and by a fixed decrease. The stimulation strategy that most effectively restored torque continued for successive contractions. This process repeated each time torque declined by 10%. In fresh muscle, FDBCK stimulation offered minimal advantage in maintaining peak torque or mean torque over CONST stimulation. As long-duration fatigue developed in subsequent bouts, FDBCK stimulation became most effective ( approximately 40% higher final normalized torque than CONST). The high-frequency strategy was selected approximately 90% of the time, supporting that excitation-contraction coupling compromise and not neuromuscular transmission failure contributed to fatigue of paralyzed muscle. Ideal stimulation strategies may vary according to the site of fatigue; this stimulation approach offered the advantage of online modulation of stimulation strategies in response to fatigue conditions. Based on stress-adaptation principles, FDBCK-controlled stimulation may enhance training effects in chronically paralyzed muscle.

Peripheral quantitative computed tomography: measurement sensitivity in persons with and without spinal cord injury

OBJECTIVES

To determine (1) the error attributable to external tibia-length measurements by using peripheral quantitative computed tomography (pQCT) and (2) the effect these errors have on scan location and tibia trabecular bone mineral density (BMD) after spinal cord injury (SCI).

DESIGN

Blinded comparison and criterion standard in matched cohorts.

SETTING

Primary care university hospital.

PARTICIPANTS

Eight able-bodied subjects underwent tibia length measurement. A separate cohort of 7 men with SCI and 7 able-bodied age-matched male controls underwent pQCT analysis.

INTERVENTIONS

Not applicable.

MAIN OUTCOME MEASURES

The projected worst-case tibia-length-measurement error translated into a pQCT slice placement error of +/-3 mm. We collected pQCT slices at the distal 4% tibia site, 3 mm proximal and 3 mm distal to that site, and then quantified BMD error attributable to slice placement.

RESULTS

Absolute BMD error was greater for able-bodied than for SCI subjects (5.87 mg/cm(3) vs 4.5 mg/cm(3)). However, the percentage error in BMD was larger for SCI than able-bodied subjects (4.56% vs 2.23%).

CONCLUSIONS

During cross-sectional studies of various populations, BMD differences up to 5% may be attributable to variation in limb-length-measurement error.

Postfatigue potentiation of the paralyzed soleus muscle: evidence for adaptation with long-term electrical stimulation training

Understanding the torque output behavior of paralyzed muscle has important implications for the use of functional neuromuscular electrical stimulation systems. Postfatigue potentiation is an augmentation of peak muscle torque during repetitive activation after a fatigue protocol. The purposes of this study were 1) to quantify postfatigue potentiation in the acutely and chronically paralyzed soleus and 2) to determine the effect of long-term soleus electrical stimulation training on the potentiation characteristics of recently paralyzed soleus muscle. Five subjects with chronic paralysis (>2 yr) demonstrated significant postfatigue potentiation during a repetitive soleus activation protocol that induced low-frequency fatigue. Ten subjects with acute paralysis (<6 mo) demonstrated no torque potentiation in response to repetitive stimulation. Seven of these acute subjects completed 2 yr of home-based isometric soleus electrical stimulation training of one limb (compliance = 83%; 8,300 contractions/wk). With the early implementation of electrically stimulated training, potentiation characteristics of trained soleus muscles were preserved as in the acute postinjury state. In contrast, untrained limbs showed marked postfatigue potentiation at 2 yr after spinal cord injury (SCI). A single acute SCI subject who was followed longitudinally developed potentiation characteristics very similar to the untrained limbs of the training subjects. The results of the present investigation support that postfatigue potentiation is a characteristic of fast-fatigable muscle and can be prevented by timely neuromuscular electrical stimulation training. Potentiation is an important consideration in the design of functional electrical stimulation control systems for people with SCI.