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.     

Predicting optimal electrical stimulation for repetitive human muscle activation.

Functional electrical stimulation is the use of electrical currents to activate paralyzed muscles to produce functional movements. Muscle force output must meet or exceed the external load to maintain a posture or produce movements. A mathematical force-fatigue modeling system that predicts muscle force responses during repetitive electrical stimulation has been developed in our laboratory to help identify stimulation patterns that optimize force output for individual subjects. This study tests how well this model predicts the number of contractions that can be maintained above a required force level (successful contractions) during repetitive activation of a muscle. Healthy human quadriceps muscles were tested isometrically on 12 subjects. Data were first collected and used to parameterize the model. Next, the model was used to predict the number of successful contractions that were produced by trains with frequencies ranging from 5 to 100 Hz while the pulse durations and amplitudes were held constant. Finally, three clinically relevant stimulation frequencies were selected and tested to verify the model's predictions. Under these conditions, the model accurately predicted the number of successful contractions for clinically relevant stimulation frequencies. Furthermore, the model appears to have the potential to identify the stimulation frequency that maximizes muscle force output and minimizes fatigue for each subject.     

Two-step, predictive, isometric force model tested on data from human and rat muscles

Functionalelectrical stimulation can assist paralyzed individuals to performfunctional movements, but muscle fatigue is a major limitation to itspractical use. An accurate and predictive mathematical model canfacilitate the design of stimulation patterns that optimize aspects ofthe force transient while minimizing fatigue. Solution nonuniqueness, amajor shortcoming in previous work, was overcome with a simpler model.The model was tested on data collected during isometric contractions ofrat gastrocnemius muscles and human quadriceps femoris muscles undervarious physiological conditions. For each condition tested, parametervalues were identified using the force response to one or twostimulation trains. The parameterized model was then used to predictforces in response to other stimulation patterns. The predicted forcesclosely matched the measured forces. The model was not sensitive toinitial parameter estimates, demonstrating solution uniqueness. Bypredicting the force that develops in response to an arbitrary patternof stimulation, we envision the present model helping identify optimalstimulation patterns for activation of skeletal muscle duringfunctional electrical stimulation.

     

A predictive model of fatigue in human skeletal muscles.

Fatigue is a major limitation to the clinical application of functional electrical stimulation. The activation pattern used during electrical stimulation affects force and fatigue. Identifying the activation pattern that produces the greatest force and least fatigue for each patient is, therefore, of great importance. Mathematical models that predict muscle forces and fatigue produced by a wide range of stimulation patterns would facilitate the search for optimal patterns. Previously, we developed a mathematical isometric force model that successfully identified the stimulation patterns that produced the greatest forces from healthy subjects under nonfatigue and fatigue conditions. The present study introduces a four-parameter fatigue model, coupled with the force model that predicts the fatigue induced by different stimulation patterns on different days during isometric contractions. This fatigue model accounted for 90% of the variability in forces produced by different fatigue tests. The predicted forces at the end of fatigue testing differed from those observed by only 9%. This model demonstrates the potential for predicting muscle fatigue in response to a wide range of stimulation patterns.     

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

Chronic spinal cord injury (SCI) induces detrimental musculoskeletal adaptations that adversely affect health status, ranging from muscle paralysis and skin ulcerations to osteoporosis. SCI rehabilitative efforts may increasingly focus on preserving the integrity of paralyzed extremities to maximize health quality using electrical stimulation for isometric training and/or functional activities. Subject-specific mathematical muscle models could prove valuable for predicting the forces necessary to achieve therapeutic loading conditions in individuals with paralyzed limbs. Although numerous muscle models are available, three modeling approaches were chosen that can accommodate a variety of stimulation input patterns. To our knowledge, no direct comparisons between models using paralyzed muscle have been reported. The three models include 1) a simple second-order linear model with three parameters and 2) two six-parameter nonlinear models (a second-order nonlinear model and a Hill-derived nonlinear model). Soleus muscle forces from four individuals with complete, chronic SCI were used to optimize each model's parameters (using an increasing and decreasing frequency ramp) and to assess the models' predictive accuracies for constant and variable (doublet) stimulation trains at 5, 10, and 20 Hz in each individual. Despite the large differences in modeling approaches, the mean predicted force errors differed only moderately (8-15% error; P=0.0042), suggesting physiological force can be adequately represented by multiple mathematical constructs. The two nonlinear models predicted specific force characteristics better than the linear model in nearly all stimulation conditions, with minimal differences between the two nonlinear models. Either nonlinear mathematical model can provide reasonable force estimates; individual application needs may dictate the preferred modeling strategy.     

Effects of activation frequency and force on low-frequency fatigue in human skeletal muscle.

No comparison of the amount of low-frequency fatigue (LFF) produced by different activation frequencies exists, although frequencies ranging from 10 to 100 Hz have been used to induce LFF. The quadriceps femoris of 11 healthy subjects were tested in 5 separate sessions. In each session, the force-generating ability of the muscle was tested before and after fatigue and at 2, approximately 13, and approximately 38 min of recovery. Brief (6-pulse), constant-frequency trains of 9.1, 14.3, 33.3, and 100 Hz and a 6-pulse, variable-frequency train with a mean frequency of 14.3 Hz were delivered at 1 train/s to induce fatigue. Immediately postfatigue, there was a significant effect of fatiguing protocol frequency. Muscles exhibited greater LFF after stimulation with the 9.1-, 14.3-, and variable-frequency trains. These three trains also produced the greatest mean force-time integrals during the fatigue test. At 2, approximately 13, and approximately 38 min of recovery, however, the LFF produced was independent of the fatiguing protocol frequency. The findings are consistent with theories suggesting two independent mechanisms behind LFF and may help identify the optimal activation pattern when functional electrical stimulation is used.     

Development of a mathematical model that predicts optimal muscle activation patterns by using brief trains.

Because muscles must be repetitively activated during functional electrical stimulation, it is desirable to identify the stimulation pattern that produces the most force. Previous experimental work has shown that the optimal pattern contains an initial high-frequency burst of pulses (i.e., an initial doublet or triplet) followed by a low, constant-frequency portion. Pattern optimization is particularly challenging, because a muscle's contractile characteristics and, therefore, the optimal pattern change under different physiological conditions and are different for each person. This work describes the continued development and testing of a mathematical model that predicts isometric forces from fresh and fatigued muscles in response to brief trains of electrical pulses. By use of this model and an optimization algorithm, stimulation patterns that produced maximum forces from each subject were identified.     

Effects of stimulation frequency versus pulse duration modulation on muscle fatigue.

During functional electrical stimulation (FES), both the frequency and intensity can be increased to increase muscle force output and counteract the effects of muscle fatigue. Most current FES systems, however, deliver a constant frequency and only vary the stimulation intensity to control muscle force. This study compared muscle performance and fatigue produced during repetitive electrical stimulation using three different strategies: (1) constant pulse-duration and stepwise increases in frequency (frequency-modulation); (2) constant frequency and stepwise increases in pulse-duration (pulse-duration-modulation); and (3) constant frequency and pulse-duration (no-modulation). Surface electrical stimulation was delivered to the quadriceps femoris muscles of 12 healthy individuals and isometric forces were recorded. Muscle performance was assessed by measuring the percent changes in the peak forces and force-time integrals between the first and the last fatiguing trains. Muscle fatigue was assessed by measuring percent declines in peak force between the 60Hz pre- and post-fatigue testing trains. The results showed that frequency-modulation showed better performance for both peak forces and force-time integrals in response to the fatiguing trains than pulse-duration-modulation, while producing similar levels of muscle fatigue. Although frequency-modulation is not commonly used during FES, clinicians should consider this strategy to improve muscle performance.     

Catchlike-inducing train activation of human muscle during isotonic contractions: burst modulation.

Stimulation trains that exploit the catchlike property [catchlike-inducing trains (CITs)] produce greater forces and rates of rise of force than do constant-frequency trains (CFTs) during isometric contractions and isovelocity movements. This study examined the effect of CITs during isotonic contractions in healthy subjects. Knee extension was electrically elicited against a load of 10% of maximum voluntary isometric contraction. The stimulation intensity was set to produce 20% of maximum voluntary isometric contraction. The muscle was tested before and after fatigue with a 6-pulse CFT and 6-pulse CITs that contained an initial doublet, triplet, or quadruplet. For prefatigue responses, the greatest isotonic performance was produced by CITs with initial doublets. When the muscles were fatigued, triplet CITs were best. CITs produce greater excursion, work, peak power, and average power than do CFTs, because CITs produced more rapid rates of rise of force. Faster rates of rise of force enabled the preload on the muscle to be exceeded earlier during the stimulation train.     

Effects of muscle activation on fatigue and metabolism in human skeletal muscle.

Increasing stimulation frequency has been shown to increase fatigue but not when the changes in force associated with changes in frequency have been controlled. An effect of frequency, independent of force, may be associated with the metabolic cost resulting from the additional activations. Here, two separate experiments were performed on human medial gastrocnemius muscles. The first experiment (n = 8) was designed to test the effect of the number of pulses on fatigue. The declines in force during two repetitive, 150-train stimulation protocols that produced equal initial forces, one using 80-Hz trains and the other using 100-Hz trains, were compared. Despite a difference of 600 pulses (23.5%), the protocols produced similar rates and amounts of fatigue. In the second experiment, designed to test the effect of the number of pulses on the metabolic cost of contraction, 31P-NMR spectra were collected (n = 6) during two ischemic, eight-train stimulation protocols (80- and 100-Hz) that produced comparable forces despite a difference of 320 pulses (24.8%). No differences were found in the changes in P(i) concentration, phosphocreatine concentration, and intracellular pH or in the ATP turnover produced by the two trains. These results suggest that the effect of stimulation frequency on fatigue is related to the force produced, rather than to the number of activations. In addition, within the range of frequencies tested, increasing total activations did not increase metabolic cost.     

Experimentally verified mathematical approach for the prediction of force developed by motor units at variable frequency stimulation patterns

During normal daily activity, muscle motor units (MUs) develop unfused tetanic contractions evoked by trains of motoneuronal firings at variable interpulse intervals (IPIs). The mechanical responses of a MU to successive impulses are not identical. The aim of this study was to develop a mathematical approach for the prediction of each response within the tetanus as well as the tetanic force itself. Experimental unfused tetani of fast and slow rat MUs, evoked by trains of stimuli at variable IPIs, were decomposed into series of twitch-shaped responses to successive stimuli using a previously described algorithm. The relationships between the parameters of the modeled twitches and the tetanic force level at which the next response begins were examined and regression equations were derived. Using these equations, profiles of force for the same and different stimulation patterns were mathematically predicted by summating modeled twitches. For comparison, force predictions were made by the summation of twitches equal to the first one. The recorded and the predicted tetanic forces were compared. The results revealed that it is possible to predict tetanic force with high accuracy by using regression equations. The force predicted in this way was much closer to the experimental record than the force obtained by the summation of equal twitches, especially for slow MUs. These findings are likely to have an impact on the development of realistic muscle models composed of MUs, and will assist our understanding of the significance of the neuronal code in motor control and the role of biophysical processes during MU contractions.     

Development and validation of a 3-D model to predict knee joint loading during dynamic movement

The purpose of this study was to develop a subject-specific 3-D model of the lower extremity to predict neuromuscular control effects on 3-D knee joint loading during movements that can potentially cause injury to the anterior cruciate ligament (ACL) in the knee. The simulation consisted of a forward dynamic 3-D musculoskeletal model of the lower extremity, scaled to represent a specific subject. Inputs of the model were the initial position and velocity of the skeletal elements, and the muscle stimulation patterns. Outputs of the model were movement and ground reaction forces, as well as resultant 3-D forces and moments acting across the knee joint. An optimization method was established to find muscle stimulation patterns that best reproduced the subject's movement and ground reaction forces during a sidestepping task. The optimized model produced movements and forces that were generally within one standard deviation of the measured subject data. Resultant knee joint loading variables extracted from the optimized model were comparable to those reported in the literature. The ability of the model to successfully predict the subject's response to altered initial conditions was quantified and found acceptable for use of the model to investigate the effect of altered neuromuscular control on knee joint loading during sidestepping. Monte Carlo simulations (N = 100,000) using randomly perturbed initial kinematic conditions, based on the subject's variability, resulted in peak anterior force, valgus torque and internal torque values of 378 N, 94 Nm and 71 Nm, respectively, large enough to cause ACL rupture. We conclude that the procedures described in this paper were successful in creating valid simulations of normal movement, and in simulating injuries that are caused by perturbed neuromuscular control.     

A new model for calculating muscle forces from electromyograms

A muscle model is described that uses electromyogram (EMG), muscle length and speed of contraction to predict muscle force. Physiological parameters are the Hill constants and the shape of the twitch response to a single stimulus. The model was incorporated in a jaw model of the rabbit and tested by predicting the bite force produced by the jaw muscles during mastication. The time course of the calculated force appeared to match the bite force, measured in vivo by a strain gauge, applied to the bone below the teeth. The variation in peak strain amplitude from cycle to cycle correlated with the variation predicted by the model. The peak amplitude of the integrated EMGs of individual jaw muscles showed an average correlation with peak strain of 0.41. Use of the sum of the available peak amplitudes, weighted according to their effect upon the bite force increased the correlation to 0.46; the model predicted bite forces showed a correlation of 0.57 with the strain. The increase in correlation was statistically significant. The muscle forces were calculated using a minimum number of easily obtainable constants.     

Catchlike property of rat diaphragm: subsequent train frequency effects in variable-train stimulation.

A high-frequency burst of pulses at the onset of a subtetanic train of stimulation allows skeletal muscle to hold force at a higher level than expected from the extra pulses alone because of the catchlike property of muscle. The present study tested the hypothesis that the presence and degree of force increase induced by a high-frequency burst are strongly modulated by the subsequent train frequency. Rat diaphragm muscle strips (studied in vitro at 37 degrees C) underwent two-, three-, or four-pulse bursts [interpulse interval (IPI) of 5 or 10 ms] at the onset of 10- to 50-Hz subtetanic trains. Force was quantified during the train with respect to its peak value (F(peak)), mean value (F(mean)), and force-time integral (F(area)), and it was compared with that produced during subtetanic trains of an equal number of pulses without preceding pulse bursts (Diff-F(peak), Diff-F(mean), Diff-F(area)). F(peak) and F(mean) increased with two-, three-, and four-pulse bursts, and Diff-F(peak) and Diff-F(mean) increased progressively with decreasing frequency of the subtetanic train. F(area), the best reflection of catchlike force augmentation, was increased mainly by the four-pulse bursts with an IPI of 10 ms, and Diff-F(area) was maximal at subsequent train frequencies of 15-25 Hz. The use of incorrect patterns of burst stimulation could also precipitate F(area) decreases, which were observed with the four-pulse, 5-ms IPI paradigm. The time required to reach 80% of maximal force (T(80%)) became shorter for each of the pulse burst stimulation patterns, with maximal reduction of Diff-T(80%) occurring at a subsequent train frequency of 20 Hz in all cases. These data indicate that extra-pulse burst stimulation paradigms need to incorporate the optimal combinations of extra-pulse number, IPI, and the frequency of the subsequent subtetanic train to take greatest advantage of the catchlike property of muscle.     

Effects of stimulation frequencies and patterns on performance of repetitive, nonisometric tasks.

The purpose of this paper was to determine the effects of stimulation pattern and frequency on repetitive human knee movements. Quadriceps femoris muscles were stimulated against a load equal to 10% of each subject's maximum voluntary isometric force. The main variable of interest was the number of repetitions in which the leg reached a target angle of 40 degrees of knee extension. Sixteen different trains were tested, including 1) six constant-frequency trains with frequencies ranging from 9 to 100 Hz, 2) five variable-frequency trains with an initial 5-ms triplet and mean frequencies ranging from 11 to 35 Hz, and 3) five doublet-frequency trains, which used doublets (2 pulses with a 5-ms interpulse interval) to replace single pulses, with mean frequencies of 17-57 Hz. Testing was stopped when the subject failed to reach the target angle for three consecutive activations. Results showed that no single pattern was best for all subjects. The 33- and 100-Hz constant-frequency trains, 35-Hz variable-frequency trains, and 27- and 36-Hz doublet frequency trains each met the target the most times for some subjects. The results showed that, under our testing conditions, higher frequency trains were better suited for producing repetitive knee movements than lower frequency trains.     

A mass-length scaling law for modeling muscle strength in the lower limb

Musculoskeletal computer models are often used to study muscle function in children with and without impaired mobility. Calculations of muscle forces depend in part on the assumed strength of each muscle, represented by the peak isometric force parameter, which is usually based on measurements obtained from cadavers of adult donors. The aim of the present study was twofold: first, to develop a method for scaling lower-limb peak isometric muscle forces in typically-developing children; and second, to determine the effect of this scaling method on model calculations of muscle forces obtained for normal gait. Muscle volumes were determined from magnetic resonance (MR) images obtained from ten children aged from 7 to 13yr. A new mass-length scaling law was developed based on the assumption that muscle volume and body mass are linearly related, which was confirmed by the obtained volume and body mass data. Two musculoskeletal models were developed for each subject: one in which peak isometric muscle forces were estimated using the mass-length scaling law; and another in which these parameters were determined directly from the MR-derived muscle volumes. Musculoskeletal modeling and quantitative gait analysis were then used to calculate lower-limb muscle forces in normal walking. The patterns of muscle forces predicted by the model with scaled peak isometric force values were similar to those predicted by the MR-based model, implying that assessments of muscle function obtained from these two methods are practically equivalent. These results support the use of mass-length scaling in the development of subject-specific musculoskeletal models of children.     

Photoresponses of Halobacterium salinarum to repetitive pulse stimuli.

Halobacterium salinarum cells from 3-day-old cultures have been stimulated with different patterns of repetitive pulse stimuli. A short train of 0.6-s orange light pulses with a 4-s period resulted in reversal peaks of increasing intensity. The reverse occurred when blue light pulses were delivered as a finite train: with a 3-s period, the response declined in sequence from the first to the last pulse. To evaluate the response of the system under steady-state conditions of stimulation, continuous trains of pulses were also applied; whereas blue light always produced a sharply peaked response immediately after each pulse, orange pulses resulted in a declining peak of reversals that lasted until the subsequent pulse. An attempt to account for these results in terms of current excitation/adaptation models shows that additional mechanisms appear to be at work in this transduction chain.     

In silico chaperonin-like cycle helps folding of proteins for structure prediction

Currently, one of the most serious problems in protein-folding simulations for de novo structure prediction is conformational sampling of medium-to-large proteins. In vivo, folding of these proteins is mediated by molecular chaperones. Inspired by the functions of chaperonins, we designed a simple chaperonin-like simulation protocol within the framework of the standard fragment assembly method: in our protocol, the strength of the hydrophobic interaction is periodically modulated to help the protein escape from misfolded structures. We tested this protocol for 38 proteins and found that, using a certain defined criterion of success, our method could successfully predict the native structures of 14 targets, whereas only those of 10 targets were successfully predicted using the standard protocol. In particular, for non-α-helical proteins, our method yielded significantly better predictions than the standard approach. This chaperonin-inspired protocol that enhanced de novo structure prediction using folding simulations may, in turn, provide new insights into the working principles underlying the chaperonin system.     

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

Electrical stimulation of skeletal muscles of patients with upper motor neuron lesions can be used to restore functional movements such as standing or walking. Mathematical muscle models can assist in designing stimulation patterns that will enable patients to perform particular tasks more efficiently. In this study we extend our previous model to allow us to predict changes in knee joint angle in response to electrical stimulation of the human quadriceps femoris muscle. The model was tested both with and without inertial loads placed around the ankle joints of healthy subjects. Results showed that the model predicted the knee extensions with a RMS angle error that was generally 相似文献   

Estimation of the error between experimental tetanic force curves of MUs of rat medial gastrocnemius muscle and their models by summation of equal successive contractions

More accurate muscle models require appropriate modelling of individual twitches of motor units (MUs) and their unfused tetanic contractions. It was shown in our previous papers, using a few MUs, that modelling of unfused tetanic force curves by summation of equal twitches is not accurate, especially for slow MUs. The aim of this study was to evaluate this inaccuracy using a statistical number of MUs of the rat medial gastrocnemius muscle (15 of slow, 15 of fast resistant and 15 of fast fatigable type). Tetanic contractions were evoked by trains of 41 stimuli at random interpulse intervals and different mean frequencies, resembling discharge patterns observed during natural muscle activity. The tetanic curves were calculated by the summation of equal twitches according to the respective experimental patterns. The previously described 6-parameter analytical function for twitch modelling was used. Comparisons between the experimental and the modelled curves were made using two coefficients: the fit coefficient and the area coefficient. The errors between modelled and experimental tetanic forces were substantially different between the three MU types. The error was the most significant for slow MUs, which develop much higher forces in real contractions than could be predicted based on the summation of equal twitches, while the smallest error was observed for FF MUs – their recorded tetanic forces were similar to those predicted by modelling. The obtained results indicate the importance of the inclusion of the type-specific non-linearity in the summation of successive twitch-like contractions of MUs in order to increase the reliability of modelling skeletal muscle force.