Calcium and the role of motoneuronal doublets in skeletal muscle control

This work presents a novel structural model of skeletal muscle activation, providing a physiologically based account of frequency-dependent muscle responses like the catch-like effect. Numerous Ca²⁺ reservoirs within muscle fibers are considered, and a simplified analysis of the allocation of Ca²⁺ resources and the dynamics of calcium transport is proposed. The model correctly accounts for catch-like effects in slow and fast-twitch fibers during long-train stimulations and force–frequency relations in different muscle types. Results obtained from the model compare favorably to experiments showing that prolonged increases in force characteristic of the catch-like effect are not accompanied by sustained increases in free myoplasmic Ca²⁺. Also, in agreement with early experiments, the interspike interval in catch-inducing doublets is seen to be an important parameter for regulating the precise onset amplitude of the catch-like effect. This suggests that a plausible physiological function for the inclusion of doublets or the exclusion of individual spikes within a regular motor-neuronal spike-train is to rapidly bring skeletal muscles to predefined target forces according to prespecified motor programs in the central nervous system. This is a potentially very useful property directly mediated by the catch-like process modeled here. One further prediction of the model is that the slope of the frequency–tension profile of a given muscle is highly sensitive to changes in the efficiency and temporal characteristics of the dihydropyridine–ryanodine receptor complex. Interestingly, this is consistent with findings made on cardiac muscles, and might incidentally explain some instances of cardiac failure.     

Comparison of contractile function of diaphragm and cardiac muscle in response to paired electrical stimulation

Paired pacing has been shown to potentiate contractile function of cardiac muscle, and it has been suggested that this may enhance contractile function of diaphragmatic muscle. The primary goal of this study was to study the effect of paired pacing on potentiation of contractile function of diaphragmatic muscle compared to atrial and ventricular myocardium. Diaphragmatic muscle was isolated from mouse and rat, and atrial and ventricular myocardium from dogs. Potentiation was induced by isolated extrastimuli (equal in duration and intensity to the pacing stimulus) and by repetitive extrastimuli (i.e. paired pacing) at a paced rate of 12, 30 and 60 beats/min. Baseline studies were performed while preparations were isometrically contracting at L(max) in oxygenated Krebs-Henseleit solution at 28 degrees C. Maximal force generation in response to a premature stimulus was determined at each rate by scanning the coupling interval between paced beats. Under baseline conditions, diaphragmatic muscle contracted faster than atrial and ventricular muscle. In all tissues, maximum potentiation (increase in force above baseline) was approximately 100% of baseline force, and peak potentiation occurred at shorter coupling intervals with increasing rates of stimulation. Single and paired pacing of diaphragm potentiated the contraction during which the extrastimuli were introduced, while in cardiac muscle, extrastimuli potentiated the contraction following the extrastimulus. The maximum potentiated response occurred when the extrastimulus was introduced prior to the development of peak force in diaphragmatic muscle. In contrast, in atrial and ventricular muscle, a single or paired premature stimulus potentiated the subsequent beat when delivered late during relaxation. In cardiac muscle, maximal potentiation gradually occurred following several repetitive stimuli. Following cessation of single and paired pacing, the beat following the potentiated response immediately returned to baseline in diaphragmatic muscle, while a gradual decline was evident over several subsequent beats in cardiac muscle. Increasing the bath temperature from 28 to 37 degrees C resulted in a leftward shift in the peak potentiated force vs. coupling interval curve without a decline in the magnitude of potentiated force in diaphragmatic muscle. In diaphragm muscle, exposure to ryanodine markedly decreased baseline force and maximal potentiation. We conclude that closely timed extrastimuli applied to diaphragmatic muscle can potentiate developed force in a given contraction, while in cardiac tissue a delayed stimulus potentiates the subsequent beat. These differences in contractile responsiveness are not due to differences in loading conditions, but appear to reflect intrinsic differences in calcium handling.     

Dual stable point model of muscle activation and deactivation

Two dynamic models of muscle activation and deactivation based on the concepts of ion transport, reaction rates, and muscle mechanics are proposed. Storage release and uptake of calcium by the sarcoplasmic reticulum, and a two-step chemical reaction of calcium and troponin are included in the first model. This is a concise version of the complex chemical reactions of muscle activation and deactivation in sarcoplasm. The second model is similar to the first, but calcium-troponin reactions are simplified into two nonlinear rates functions. Due to these nonlinear dynamics, the second model can explain the catch-like enhancement of isometric force response. Simulation results which match experimental data are shown. Also, two new phenomena which need further experiment to verify are predicted by the second model.     

Desynchronizing double-pulse phase resetting and application to deep brain stimulation

 Based on a stochastic phase-resetting approach, three different double-pulse stimulation techniques are presented here which make it possible to effectively desynchronize a population of phase oscillators in the presence of noise. In the three sorts of double pulses the first, stronger pulse restarts the cluster independent of its initial dynamic state. The three methods differ with respect to the mechanism through which the second, weaker pulse desynchronizes the cluster. Both first and second pulses are delivered to the same site. Because of the oscillators' global couplings in the model under consideration, the incoherent state is unstable, so that after the desynchronization the cluster tends to resynchronize. However, resynchronization is effectively blocked by repeated administration of a double pulse. The experimental application of double-pulse stimulation is explained in detail. In particular, demand-controlled deep brain double-pulse stimulation is suggested for the therapy of patients suffering from Parkinson's disease or essential tremor. Received: 22 November 2000 / Accepted in revised form: 26 April 2001     

Post-Activation Potentiation--A Clue for Simplifying Models of Muscle Dynamics

SYNOPSIS. Post-activation potentiation is a phenomena that occursonly in fasttwitch muscle fibers. Its main effect is to enhancemuscle force at sub-maximal activation levels for a short durationof time following previous muscle activation. We characterizedthis phenomenon in feline caudofemoralis (CF) muscle (composedof 100% fast-twitch muscle fibers) to understand its importanceduring physiological patterns of activation. During such patterns(e.g., 43 pps, 8 pulse trains delivered at 1 sec intervals)CF potentiated rapidly and apparently maximally. When CF wasallowed to relax, potentiation decayed slowly with a time constant20–40 x slower than the rise-time. The level of potentiationreached during the potentiating paradigm was stable in responseto a wide range of stimuli, including various stimulation rates(15–120 pps) and various inter-train intervals (up to10 sec). The shape of the twitch force-length curve for potentiatedCF was similar to that of the tetanic force-length curve ineither the potentiated or unpotentiated state. In contrast,the shape of the twitch force-length curve for unpotentiatedCF was shifted markedly to the right accompanied by a narrowingof the curve's peak. We conclude from our observations thatfast-twitch muscle fibers operate and should be modeled in astate of full potentiation, and that modeling the potentiatedstate may actuaUy be simpler than modeling the unpotentiatedstate.     

On the possibility of linear modelling the human arm neuromuscular apparatus

It has been widely claimed that linear models of the neuromuscular apparatus give very inaccurate approximations of human arm reaching movements. The present paper examines this claim by quantifying the contributions of the various non-linear effects of muscle force generation on the accuracy of linear approximation. We performed computer simulations of a model of a two-joint arm with six monarticular and biarticular muscles. The global actions of individual muscles resulted in a linear dependence of the joint torques on the joint angles and angular velocities, despite the great non-linearity of the muscle properties. The effect of time delay in force generation is much more important for model accuracy than all the non-linear effects, while ignoring this time delay in linear approximation results in large errors. Thus, the viscosity coefficients are rather underestimated and some of them can even be paradoxically estimated to be negative. Similarly, our computation showed that ignoring the time delay resulted in large errors in the estimation of the hand equilibrium trajectory. This could explain why experimentally estimated hand equilibrium trajectories may be complex, even during a simple reaching movement. The hand equilibrium trajectory estimated by a linear model becomes simple when the time delay is taken into account, and it is close to that actually used in the non-linear model. The results therefore provide a theoretical basis for estimating the hand equilibrium trajectory during arm reaching movements and hence for estimating the time course of the motor control signals associated with this trajectory, as set out in the equilibrium point hypothesis. Received: 17 February 1999 / Accepted in revised form: 22 October 1999     

Mechanism for the opioid-induced twitch potentiations of frog's skeletal muscle

The twitch-potentiating effects of opioids in the frog's skeletal muscle which are naloxone resistant and nonstereospecific were further studied. The rapid kinetics of the onset and of the offset (following washout) of the opioid effect indicates that the site for this action is the surface membrane of the muscle fibre. On the other hand, the lack of any twitch-potentiating effect by naloxone methylbromide, a quaternary derivative of naloxone, suggests that opioids which potentiate the twitch must enter the lipid phase of the membrane to act. Intracellular microelectrode experiments revealed no relation between the opioid effects on membrane electrical events and twitch potentiation. Blocking slow calcium channels with D-600 did not modify the opioid-induced twitch potentiation. The twitch potentiation was antagonized by increasing the extracellular calcium concentration, [Ca2+]o, to 8.64 mM. The effects of closely spaced multiple electrical pulses revealed that the opioids decreased the summated response relative to predrug controls. The results suggest that opioids facilitate the process of excitation-contraction coupling in the frog's skeletal muscle by the release of an additional amount of "trigger calcium" following a single electrical stimulus, thereby generating a potentiated twitch.     

Acetaldehyde alters Ca2+-release channel gating and muscle contraction in a dose-dependent manner

We studied whether acetaldehyde, which is produced by alcohol consumption, impacts ryanodine receptor (RyR) activity and muscle force. Exposure to 50–200 µM acetaldehyde enhanced channel activity of frog RyR and rabbit RyR1 incorporated into lipid bilayers. An increase in acetaldehyde to 1 mM modified channel activity in a time-dependent manner, with a brief activation and then inhibition. Application of 200 µM acetaldehyde to frog fibers increased twitch tension. The maximum rate of rise of tetanus tension was accelerated to 1.5 and 1.74 times the control rate on exposure of fibers to 50 and 200 µM acetaldehyde, respectively. Fluorescence monitoring with fluo 3 demonstrated that 200–400 µM acetaldehyde induced Ca²⁺ release from the sarcoplasmic reticulum (SR) in frog muscles. Acetaldehyde at 1 mM inhibited twitch tension by 12%, with an increased relaxation time after a small, transient twitch potentiation. These results suggest that moderate concentrations of acetaldehyde can elicit Ca²⁺ release from the SR by increasing the open probability of the RyR channel, resulting in increased tension. However, the effects of acetaldehyde at clinical doses (1–30 µM) are unlikely to mediate alcohol-induced acute muscle dysfunction. ryanodine receptor; single-channel current; fluo 3 fluorescence; calcium ion release; calcium ion uptake     

The role of energy substrates in the regulation of force-frequency relationship in the rat myocardium: the influence of ambiocor

The effect of ambiocor (15 mg/100 ml), which contains natural substrates of energy metabolism, on the contractility of papillary muscle of the right ventricle of rat heart was studied at stimulation frequencies from 0.1 to 3.0 Hz at a temperature of 30 ± 1°C (n = 7). The effect was recorded 20 min after the addition of the preparation. It was demonstrated that ambiocor causes a significant (about 70%), independent of stimulation frequency, suppression of the amplitude of isometric contractions (negative inotropic effect), which is coupled with an increase in the relative value of the rest potentiation effect (a qualitative index of calcium content in SR). The influence of the mixture leads to significant alterations in the time parameters of the “contraction-relaxation” cycle: an increase in the duration of latent period; and a decrease in the time to peak tension and half-relaxation time. The effect of the mixture is partially reversible. During washing off the preparation with the control solution, the qualitative indicators of the contractile activity of papillary muscle are substantially improved in comparison with the initial ones. The character of alterations allows one to assume that the effect of ambiocor in the papillary muscle of the rat heart is realized partly through the suppression of the activity of sarcolemmal calcium channels.     

Muscle contraction history: modified Hill versus an exponential decay model

In recent years, it has been recognised that improvements to classic models of muscle mechanical behaviour are often necessary for properly modelling co-ordinated multi-joint actions. In this respect, the purpose of the present study was to improve on modelling stretch-induced force enhancement and shortening-induced force depression of muscle contraction. For this purpose, two models were used: a modified Hill model and a model based loosely on mechano-chemistry of the cross-bridge cycle (exponential decay model). The models were compared with a classic Hill model and experimental data. Parameter values were based, as much as possible, on experimental findings in the literature, and tested with new experiments on the gastrocnemius of the rat. Both models describe many features of slow-ramp movements well during short contractions (300–500 ms), but long-duration behaviour is described only partly. The exponential decay model does not incorporate a force–velocity curve. Therefore, its good performance indicates that the status of the classic force–velocity characteristic may have to be reconsidered. Like movement-induced force depression and enhancement, it seems a particular manifestation of time-dependent force behaviour of muscle, rather than a fundamental property of muscle (like the length–tension curve). It is argued that a combination of the exponential decay model (or other models based on the mechano-chemistry of contraction) and structurally based models may be fruitful in explaining this time-dependent contraction behaviour. Furthermore, not in the least because of its relative simplicity, the exponential decay model may prove more suitable for modelling multi-joint movements than the Hill model. Received: 19 March 1999 / Accepted in revised form: 9 June 2000     

Doublet potentiation during eccentric and concentric contractions of cat soleus muscle

Sandercock, Thomas G., and C. J. Heckman. Doubletpotentiation during eccentric and concentric contractions of cat soleusmuscle. J. Appl. Physiol. 82(4):1219-1228, 1997.The addition of an extra stimulus pulse, ordoublet, at the beginning of a low-frequency train has been shown tosubstantially increase isometric force. This study examined the effectsof muscle movement on this doublet potentiation. The soleus muscles ofanesthetized cats were stimulated at 10 Hz for 1 s, with and without anadded doublet (0.01-s interval). Isovelocity releases reduced but didnot eliminate peak and early doublet potentiation (average 0.0-0.5s after the doublet). Large releases, >0.4 s after the doublet,completely abolished sustained doublet potentiation (average0.5-1.0 s after the doublet). In contrast, early isovelocitystretches boosted peak doublet potentiation. Yet, large stretches laterin the stimulus almost completely eliminated sustained doubletpotentiation. This suggests that a different mechanism is responsiblefor early and sustained doublet potentiations. Because peak and averageinitial doublet potentiation were not strongly affected by movement,doublets still offer a viable control strategy to increase force during movement while minimizing the number of stimulus pulses.

     

Posttetanic potentiation and skeletal muscle fatigue: interactions with caffeine

The purpose of this study was to determine the interaction of three factors that modify twitch contraction amplitude in the rat gastrocnemius muscle in situ: posttetanic potentiation, fatigue, and caffeine. Posttetanic (200 Hz for 1 s) twitch responses were observed before and after 15 Hz stimulation for 6 min (group FS), injection of caffeine (75 mg/kg dissolved in saline, group NC), a combination of both repetitive stimulation and caffeine injection (group FC), or no treatment (group NS). Developed tension increased significantly with posttetanic potentiation and caffeine injection and these potentiating factors were additive (group NC). Repetitive stimulation attenuated the twitch response and the fatigued muscle was still responsive to the potentiating factors. Posttetanic potentiation was accomplished primarily by a significant increase in the peak rate of force development whereas caffeine potentiation and fatigue were effected with a proportional change in contraction time. It seems likely that the mechanism of posttetanic potentiation is not the same as the mechanism of caffeine-induced potentiation. Caffeine-induced potentiation is known to be related to increased release of calcium. Because changes in contraction time with fatigue were opposite to those associated with caffeine potentiation, it is proposed that the attenuated twitch response in fatigue results from reduced release of calcium.     

Lower force and impaired performance during high-intensity electrical stimulation in skeletal muscle of GAMT-deficient knockout mice

Force characteristics of skeletal muscle of knockout mice lacking creatine (Cr) due to a deletion of guanidinoacetate methyltransferase (GAMT) were studied in situ. Medial gastrocnemius muscles of anesthetized GAMT-deficient (GAMT^–/–) and control (Con) littermates were stimulated at optimum length via the sciatic nerve at different stimulation frequencies (60–250 Hz). GAMT^–/– mice showed reduced maximal tetanic and twitch force, reduced relative force at 60 Hz, and increased relaxation times. High-intensity fatigue protocols consisting of 30 successive isometric or dynamic contractions showed a strong reduction in force at the beginning of the series in GAMT^–/– mice, followed by a smaller reduction compared with Con littermates toward the end of the series. Cr supplementation for 2 days in GAMT^–/– animals (GAMT) resulted in normalization to Con values for relaxation times, relative force at lower stimulation frequencies, and relative force during 30 isometric contractions. Force per muscle mass, however, remained decreased. Furthermore,GAMT mice showed differences compared with both Con and unsupplemented animals in maximal rates of force rise and relaxation times during the isometric protocol as well as in force during the dynamic protocol. Our results show that the absence of Cr plays a direct role in relaxation times, maximal rate of force rise, and force production during high-intensity fatigue protocols. The lower force per muscle mass, however, is probably caused by other factors; i.e., high intracellular guanidinoacetate concentrations. energy metabolism; creatine; fatigue; force characteristics     

Biomechanical properties and a kinetic simulation model of the smooth muscle I2 in the buccal mass of Aplysia

The muscle I2 is a smooth muscle from the buccal mass of the marine mollusc Aplysia californica whose neural control, in vivo kinematics, and behavioral role have been extensively analyzed. In this study, we measured the activation and contractile dynamics of the muscle in order to construct a Hill-type kinetic model of the muscle. This is the first study to our knowledge, of Aplysia muscle contractile dynamics. The isometric force-frequency relationship of I2 had a frequency threshold of about 6–8 Hz, and its force output saturated at 20–25 Hz, properties that match the high frequency (20 Hz) bursts generated by the B31/B32 neurons that innervate it. Peak isometric force was generated at about 118% of the in situ relaxed length. These results and I2's estimated in vivo kinematics suggest that it generates maximum force at the onset of protraction. The muscle tension during iso-velocity lengthening and shortening was an asymmetric function of velocity. Short range stiffness and yielding responses were observed in lengthening, whereas muscle tension decreased smoothly in shortening. These visco-elastic properties suggest that the I2 muscle can serve to brake forceful retraction movements. A Hill-type model, parameterized from the measurements, captured many of the mechanical properties of I2. Our results provide a quantitative understanding of the biomechanical significance of the muscle's neural control and provide a basis for simulation studies of the control of feeding behavior. Received: 5 February 1999 / Accepted in revised form: 18 May 1999     

Bifurcations in the decremental propagation of a spike train in the Hodgkin-Huxley model of low excitability

Response of a nerve fiber of low excitability to periodic stimulus pulses is studied with computer simulation of the Hodgkin-Huxley model. The excitability of the Hodgkin-Huxley model is reduced by decreasing the equilibrium potential for the sodium ion and by increasing the temperature, so that the decremental propagation of spikes occurs in the refractory period. It is shown that, as the period of stimulus pulses is decreased, the propagation length of the spikes is continuously changed, and period-doubling bifurcations occur. The response of a nerve fiber of low excitability is then qualitatively different from that of a normal fiber. Received: 6 December 1996 / Accepted in revised form: 12 June 1998     

Computer simulation of the motoneuron pool–muscle complex. I. Input system and motoneuron pool

 The aim of the present study was to simulate the input system and the motoneuron (MN) pool of the MN pool–muscle complex (MNPMC). Input fibers, which can originate from command centers in the central nervous system or from sensory organs, activate the MN pool. They generate sequences of action potentials, the frequency of which is proportional to a time-dependent activation factor (which is an input to the model). Different connection patterns between the input fibers and motor units (MUs) are allowed. For simplicity and since no precise experimental data are available, 70 input fibers and 4 boutons per fiber and MN are simulated (this corresponds approximately to the monosynaptic group-Ia input of the cat medial gastrocnemius muscle). Each bouton generates the same conductance change in the postsynaptic membrane. The MNs are modeled with a single compartment and a homogenous membrane. According to experimental data, the membrane leakage conductance and capacitance are MU dependent. Since the precise relation is unknown: (a) the computed relation between MU contraction force and the MN leakage conductance was taken from a steady-state MNPMC model, and (b) the capacitance was assumed to be proportional to the leakage conductance. The MN membrane includes time- and voltage-dependent ionic channels (fast and slow K⁺ and low- and high-threshold Ca²⁺ channels). The density and time constant of the slow K⁺ channels and the density of the Ca²⁺ channels were fitted to approximate afterhyperpolarization characteristics and frequency-injected current relations of type-identified cat MNs. If the membrane reaches a voltage threshold the MNs generate action potentials, which were simulated by voltage pulses. The activation of the MN pool of the human first dorsal interosseus muscle was simulated with injected and synaptic currents in order to illustrate the size principle, synaptic noise, and other features of muscle activation. It is concluded that the present model reproduces the main properties of the input–output relations of different MN types within a muscle. Together with the simulation of the muscle force and the surface EMG, which will be published in subsequent papers, it will be a powerful tool for reproducing experiments on the motor system and investigating functional mechanisms of motor control. Received: 17 April 2001 / Accepted in revised form: 6 November 2001     

Self-organized dynamics in plastic neural networks: bistability and coherence

 In this paper, we study the combined dynamics of the neural activity and the synaptic efficiency changes in a fully connected network of biologically realistic neurons with simple synaptic plasticity dynamics including both potentiation and depression. Using a mean-field of technique, we analyzed the equilibrium states of neural networks with dynamic synaptic connections and found a class of bistable networks. For this class of networks, one of the stable equilibrium states shows strong connectivity and coherent responses to external input. In the other stable equilibrium, the network is loosely connected and responds non coherently to external input. Transitions between the two states can be achieved by positively or negatively correlated external inputs. Such networks can therefore switch between their phases according to the statistical properties of the external input. Non-coherent input can only “rcad” the state of the network, while a correlated one can change its state. We speculate that this property, specific for plastic neural networks, can give a clue to understand fully unsupervised learning models. Received: 8 August 1999 / Accepted in revised form: 16 March 2000     

The positive force–frequency relationship is maintained in absence of sarcoplasmic reticulum function in rabbit,but not in rat myocardium

Myocardial calcium handling differs between species, mainly in the relative contribution between the sources for activator calcium. To investigate the role of the myofilaments and intracellular calcium decline in governing the relaxation phase of cardiac muscle, and to elucidate additional determinants of relaxation other than the sarcoplasmic reticulum (SR) at various frequencies within the in vivo range, the present study was performed by altering the calcium handling in rat and rabbit. Trabeculae, iontophoretically loaded with bis-fura-2 to monitor cytoplasmic calcium levels, were subjected to ryanodine and cyclopiazonic acid to inhibit SR function. Simultaneous force and [Ca²⁺]_i measurements were obtained at 1–4 Hz in rabbit and at 4–8 Hz in rat before and after SR inhibition. Inhibition of the SR resulted in increased diastolic and peak calcium levels as well as decreased developed force in both species. Calcium transient amplitude decreased in rat, but increased in rabbit after SR inhibition. Time to peak tension, time from peak tension to 50% relaxation, time to peak calcium, and time from peak calcium to 50% calcium decline were all prolonged. Results suggest that L-type calcium channel current is responsible for increases in calcium with increasing frequency, and that the SR amplifies this effect in response to increased L-type current. The response of the myofilaments to alterations in calcium handling plays a critical role in the final determination of force, and may differ between species. These results imply the balance between force relaxation and calcium decline is significantly different in larger mammals, necessitating a critical re-evaluation of how myocardial relaxation is governed, specifically regarding frequency-dependent activation.     

Model study of time‐dependent muscle response to pulsed electrical stimulation

A systems‐level model analysis of neuromuscular response to external electrical stimulation is presented. Action potential (AP) generation, dynamics of voltage‐based calcium release at the motor endplates controlled by the arrival of APs, and muscle force production are all comprehensively included. Numerical predictions exhibit trends that are qualitatively similar to measurements of muscle response in rats from a burst of cortical stimulation and a nanosecond impulse. Modulation of neural membrane conductances (including possible electroporation) that alters the neural impulse generation frequency is hypothesized as a possible mechanism leading to observed changes in muscle force production. Other possibilities such as calcium release at nerve end endings also exist. It is also proposed that multipulsing strategies and changing the electric field direction by using multielectrode systems would be useful. Bioelectromagnetics 31:361–370, 2010. © 2010 Wiley‐Liss, Inc.     

Linear combinations of nonlinear models for predicting human–machine interface forces

 This study presents a computational framework that capitalizes on known human neuromechanical characteristics during limb movements in order to predict human–machine interactions. A parallel–distributed approach, the mixture of nonlinear models, fits the relationship between the measured kinematics and kinetics at the handle of a robot. Each element of the mixture represented the arm and its controller as a feedforward nonlinear model of inverse dynamics plus a linear approximation of musculotendonous impedance. We evaluated this approach with data from experiments where subjects held the handle of a planar manipulandum robot and attempted to make point-to-point reaching movements. We compared the performance to the more conventional approach of a constrained, nonlinear optimization of the parameters. The mixture of nonlinear models accounted for 79±11% (mean ±SD) of the variance in measured force, and force errors were 0.73 ± 0.20% of the maximum exerted force. Solutions were acquired in half the time with a significantly better fit. However, both approaches suffered equally from the simplifying assumptions, namely that the human neuromechanical system consisted of a feedforward controller coupled with linear impedances and a moving state equilibrium. Hence, predictability was best limited to the first half of the movement. The mixture of nonlinear models may be useful in human–machine tasks such as in telerobotics, fly-by-wire vehicles, robotic training, and rehabilitation. Received: 20 October 2000 / Accepted in revised form: 8 May 2001