Variability of successive contractions subtracted from unfused tetanus of fast and slow motor units

Stimulation of motor units (MUs) with repeated pulses evokes tetanic contractions, which consist of overlapping mechanical responses. The summation of these responses into tetanus is a nonlinear process due to the dynamic changes in the amplitudes and time parameters of the successive components. In order to study these changes, two MUs (one fast and one slow) of rat medial gastrocnemius muscle were stimulated with a progressively increasing number of pulses, from one (i = 1) to sixteen (i = 16) at a frequency of 15 Hz for the slow MU and 60 Hz for the fast MU. The individual responses were calculated by subtracting the (i)th from the (i + 1)th tetanus recording. The contractions obtained following subtraction were modeled using a novel 6-parameter analytical function. The main conclusions of this study are (1) the newly presented analytical function is able to precisely describe the variable shape of all subtracted experimental contractions; (2) the shapes of successive contractions are variable and the subtracted contractions differ from the individual twitches; (3) as the pulse number increases, the parameters of the subtracted contractions change in a different manner for the slow and fast MUs: for the slow MU, the maximal forces and the time parameters increase considerably up to the 4th response, after which they remain nearly constant or show only a slight increase; for the fast MU, the maximal forces and durations also increase, whereas the remaining time parameters initially increase and then maintain a constant level or decrease, which explains the sag phenomenon visible in the unfused tetanus of fast MUs.     

Motor unit action potential field — Modelling results

The theoretical field of a motor unit (MU) action potential (MUP) was considered. It has been proved that in normal muscles the shape of a smooth threephasic MUP curve is determined mostly by the spatial distribution of MU muscle fibres. Phenomena called time dispersion are of prime importance in pathology, where they complicate normal threephasic MUP.Amplitudes and time parameters of model three-phasic MUP were analyzed as a function of the radial distance R from the geometrical centre of the motor unit territory (MUT) and approximated by mathematical expressions. It appeared that analysis of radial variability of MUP curve allows conclusions to be made about the MUT size and the spatial distribution of MU muscle fibres. These anatomical features of a MU are often changed in pathological muscles, thus the proposed methods of their evaluation could be helpful in diagnosis of neuromuscular diseases.     

Spectral properties of electromyographic and mechanomyographic signals during dynamic concentric and eccentric contractions of the human biceps brachii muscle

The purpose of this study was to describe and examine the variations in recruitment patterns of motor units (MUs) in biceps brachii (BB) through a range of joint motion during dynamic eccentric and concentric contractions. Twelve healthy participants (6 females, 6 males, age = 30 ± 8.5 years) performed concentric and eccentric contractions with constant external loading at different levels. Surface electromyography (EMG) and mechanomyography (MMG) were recorded from BB. The EMGs and MMGs were decomposed into their intensities in time–frequency space using a wavelet technique. The EMG and MMG spectra were then compared using principal component analysis. Variations in total intensity, first principal component (PCI), and the angle θ formed by first component (PCI) and second component (PCII) loading scores were explained in terms of MU recruitment patterns and elbow angles. Elbow angle had a significant effect on dynamic concentric and eccentric contractions. The EMG total intensity was greater for concentric than for eccentric contractions in the present study. MMG total intensity, however, was lower during concentric than during eccentric contractions. In addition, there was no significant difference in θ between concentric and eccentric contractions for both EMG and MMG. Selective recruitment of fast MUs from BB muscle during eccentric muscle contractions was not found in the present study.     

Modelling motor units in 3D: influence on muscle contraction and joint force via a proof of concept simulation

Functional heterogeneity is a skeletal muscle’s ability to generate diverse force vectors through localised motor unit (MU) recruitment. Existing 3D macroscopic continuum-mechanical finite element (FE) muscle models neglect MU anatomy and recruit muscle volume simultaneously, making them unsuitable for studying functional heterogeneity. Here, we develop a method to incorporate MU anatomy and information in 3D models. Virtual fibres in the muscle are grouped into MUs via a novel “virtual innervation” technique, which can control the units’ size, shape, position, and overlap. The discrete MU anatomy is then mapped to the FE mesh via statistical averaging, resulting in a volumetric MU distribution. Mesh dependency is investigated using a 2D idealised model and revealed that the amount of MU overlap is inversely proportional to mesh dependency. Simultaneous recruitment of a MU’s volume implies that action potentials (AP) propagate instantaneously. A 3D idealised model is used to verify this assumption, revealing that neglecting AP propagation results in a slightly less-steady force, advanced in time by approximately 20 ms, at the tendons. Lastly, the method is applied to a 3D, anatomically realistic model of the masticatory system to demonstrate the functional heterogeneity of masseter muscles in producing bite force. We found that the MU anatomy significantly affected bite force direction compared to bite force magnitude. MU position was much more efficacious in bringing about bite force changes than MU overlap. These results highlight the relevance of MU anatomy to muscle function and joint force, particularly for muscles with complex neuromuscular architecture.

     

Effect of synchronization of firings of different motor unit types on the force variability in a model of the rat medial gastrocnemius muscle

The synchronized firings of active motor units (MUs) increase the oscillations of muscle force, observed as physiological tremor. This study aimed to investigate the effects of synchronizing the firings within three types of MUs (slow—S, fast resistant to fatigue–FR, and fast fatigable–FF) on the muscle force production using a mathematical model of the rat medial gastrocnemius muscle. The model was designed based on the actual proportion and physiological properties of MUs and motoneurons innervating the muscle. The isometric muscle and MU forces were simulated by a model predicting non-synchronized firing of a pool of 57 MUs (including 8 S, 23 FR, and 26 FF) to ascertain a maximum excitatory signal when all MUs were recruited into the contraction. The mean firing frequency of each MU depended upon the twitch contraction time, whereas the recruitment order was determined according to increasing forces (the size principle). The synchronization of firings of individual MUs was simulated using four different modes and inducing the synchronization of firings within three time windows (± 2, ± 4, and ± 6 ms) for four different combinations of MUs. The synchronization was estimated using two parameters, the correlation coefficient and the cross-interval synchronization index. The four scenarios of synchronization increased the values of the root-mean-square, range, and maximum force in correlation with the increase of the time window. Greater synchronization index values resulted in higher root-mean-square, range, and maximum of force outcomes for all MU types as well as for the whole muscle output; however, the mean spectral frequency of the forces decreased, whereas the mean force remained nearly unchanged. The range of variability and the root-mean-square of forces were higher for fast MUs than for slow MUs; meanwhile, the relative values of these parameters were highest for slow MUs, indicating their important contribution to muscle tremor, especially during weak contractions.     

A model for semi-quantitative studies of muscle actions

A determinate scheme for modeling the mechanical effects of muscle contractions in a musculoskeletal system, using the direct-stiffness method of structural analysis, is described. Data concerning skeletal geometries, connective tissue passive mechanical properties, and muscle lines-of-action and cross-sectional areas are incorporated to make the model specific for studies of muscle actions in the human trunk. Several illustrative examples of model trunk responses to muscle contractions are presented and discussed.     

Physiological characteristics of motor units in the brachioradialis muscle across fatiguing low-level isometric contractions.

The purpose of this study was to determine (i) if decomposition-based quantitative electromyography (DQEMG) could detect changes in motor unit potential (MUP) morphology and motor unit (MU) firing pattern statistics associated with muscle fatigue, (ii) if any detected changes are correlated with surface electromyographic (SEMG) signs of fatigue, and (iii) if significant fatigue-dependent changes are repeatable within individuals. Mean MU firing rates and the morphology of MUPs detected using needle and surface electrodes during constant-torque isometric contractions held until exhaustion were investigated in the brachioradialis (BR) muscle in 10 healthy volunteers (mean age=28.6 yr, SD+/-3.9). Time dependant changes were investigated using an analysis of variance with normalized time as a main effect. Partial correlation coefficients were computed using a repeated measures analysis of covariance to determine if changes in MU firing rates, needle-detected MUPs and surface-detected MUPs (SMUPs) were related to changes in SEMG signal amplitude and frequency parameters. Intraclass correlation coefficients (ICCs) were used to determine the within-subject repeatability of changes in MU firing rates, and MUP and SMUP parameters. Significant decreases in mean MU firing rates were found along with significant increases in various duration and area related parameters in both MUPs and SMUPs across the fatiguing contraction. The SEMG signal demonstrated the expected changes with fatigue: an increase in amplitude and a decrease in frequency content. SEMG amplitude was significantly positively correlated with SMUP peak-to-peak voltage (r=0.85, p<0.05), and SMUP area (r=0.86, p<0.05). Mean power frequency was significantly negatively correlated with SMUP negative peak duration (r=-0.74, p<0.05). The significant time-dependent changes were reliably observed (ICCs were 0.94 for MUP peak to peak amplitude, 0.97 for MUP area and 0.95 for MUP area to amplitude ratio, 0.95 for SMUP peak-to-peak voltage, 0.83 for SMUP area, 0.99 for SMUP negative peak amplitude and 0.88 for SMUP negative peak area). The decreases in mean MU firing rates measured along with the increases in amplitude, duration and area parameters of MUPs and SMUPs and their partial correlation with SEMG amplitude during submaximal fatiguing contractions of the BR, suggest that recruitment is a main cause of increased SEMG amplitude parameters with fatigue. We conclude that DQEMG can be effectively and reliably used to detect changes in physiological characteristics of MUs that accompany fatigue.     

Oxygen availability and motor unit activity in humans.

Six men were studied to determine the interrelationships among blood supply, motor unit (MU) activity and lactate concentrations during intermittent isometric contractions of the hand grip muscles. The subjects performed repeated contractions at 20% of maximal voluntary contraction (MVC) for 2 s followed by 2-s rest for 4 min with either unhindered blood circulation or arterial occlusion given between the 1st and 2nd min. The simultaneously recorded intramuscular MU spikes and surface electromyogram (EMG) data indicated that mean MU spike amplitude, firing frequency and the parameters of surface EMG power spectra (mean power frequency and root mean square amplitude) remained constant during the experiment with unhindered circulation, providing no electrophysiological signs of muscle fatigue. Significant increases in mean MU spike amplitude and frequency were, however, evident during the contractions with arterial occlusion. Similar patterns of significant changes in the surface EMG spectra parameters and venous lactate concentration were also observed, while the integrated force-time curves remained constant. These data would suggest that the metabolic state of the active muscles may have played an important role in the regulation of MU recruitment and rate coding patterns during exercise.     

Activation of human arm muscles during flexion/extension and supination/pronation tasks: A theory on muscle coordination

Generally the number of muscles acting across a joint exceeds the number of degrees of freedom available to the joint. This redundancy raises a problem regarding the ratio in which these muscles are activated during a particular motor task. In this paper we present a theory to explain the activation patterns of muscles used during voluntary and reflex induced contractions. The basic assumptions underlying the theory are that 1) coordination of muscles is based on synergistic muscle activities, 2) the synergisms involved satisfy certain transformations of muscle spindle signals to muscle activation signals and 3) muscle spindle output is proportional to the ratio of muscle stretch and muscle length in lengthening muscles, and is zero in shortening muscles. The theory is used to predict the recruitment threshold of motor units in six arm muscles during voluntary isometric contractions. All theoretical predictions are in reasonable agreement with the experimentally observed behavior of a large population of motor units within each muscle. However, within a single muscle sometimes motor-unit populations have been found to have different types of recruitment behavior. This deviating behavior is discussed in the light of the theory presented here.     

A Modified Hai–Murphy Model of Uterine Smooth Muscle Contraction

We extend and analyze the Wang and Politi modified Hai–Murphy model of smooth muscle cell contractions to capture uterine muscle cell response to variations in intracellular calcium concentrations. This model is used to estimate values of unknown parameters in uterine smooth muscle cell cross-bridging. Uterine motility is responsible for carrying out important processes throughout all phases of the nonpregnant female reproductive cycle, including sperm transport, menstruation, and embryo implantation. The modified Hai–Murphy partial differential equation model accounts for the displacement of myosin cross-bridge heads relative to their binding sites. This model was originally developed for the study of airway contractions; we now extended it for use in modeling nonisometric uterine contractions. Our extended model incorporates cross-bridge position and contractile velocity into the original model, resulting in more accurate modeling of the initial stages of contraction and modeling nonisometric contractions. Numerical simulations show that the contraction rate in our extended model is faster than the original Hai–Murphy model. These simulations provide quantitative estimates for the increased level of responsiveness of our extended model to intracellular calcium concentrations. The extended model and new parameter estimates for the cross-bridging can be coupled with uterine flow models to advance our understanding of embryonic motility and intrauterine flow.     

A comparison of models explaining muscle activation patterns for isometric contractions

One of the main problems in motor-control research is the muscle load sharing problem, which originates from the fact that the number of muscles spanning a joint exceeds the number of degrees of freedom of the joint. As a consequence, many different possibilities exist for the activation of muscles in order to produce a desired joint torque. Several models describing muscle activation have been hypothesized over the last few decades to solve this problem. This study presents theoretical analyses of the various models and compares the predictions of these models with new data on muscle activation patterns for isometric contractions in various directions. None of the existing models fitted the experimental data in all aspects. The best fit was obtained by models based on minimization of the squared sum of muscle forces (∑ _m φ² _m , which is almost equivalent to the Moore-Penrose pseudo-inverse solution), muscle stress σ (∑ _m σ _m ²) or muscle activation α (∑ _m α _m ²). Since muscle activation patterns are different for isometric contractions and for movements, it could well be that other models or optimization criteria are better suited to describe muscle activation patterns for movements. The results of our simulations demonstrate that the predicted muscle activation patterns do not depend critically on the parameters in the model. This may explain why muscle activation patterns are highly stereotyped for all subjects irrespective of differences between subjects in many neuro-anatomical aspects, such as, for example, in the physiological cross-sectional area of muscle. Received: 24 September 1998 / Accepted in revised form: 1 March 1999     

Motor unit activity during long-lasting intermittent muscle contractions in humans

Changes accompanying long-lasting intermittent muscle contractions (30%–50% of the maximal) were investigated by tracing the activity of 38 motor units (MU) of the human biceps brachii muscle recorded from fine-wire branched electrodes. The motor task was a continuous repetition of ramp-and-hold cycles of isometric flexion contractions. During ramp-up phases a significant decline in recruitment thresholds was found with no changes in the discharge pattern. During ramp-down phases the unchanged mean value of derecruitment thresholds during the task was accompanied by increased duration of the last two interspike intervals (ISI). These findings would suggest that during fatigue development the main compensatory mechanism during ramp-up contractions is space coding while for ramp-down contractions it is rate coding. During the steady-state phases the mean value of ISI, as well as the firing variability, had increased by the end of the task in most of the MU investigated . In addition 17 recruited MU were also investigated. These units revealed a lower initial discharge rate and a faster decrease in the mean discharge rate with the development of fatigue. The gradual reduction of the recruitment threshold of already active MU and the recruitment of new units demonstrated an increased excitability of the motorneuron pool during fatigue. A typical recruitment pattern (a first short ISI followed by a long one) was observed during ramp-up contractions in units active from the very beginning of the task, as well as during sustained contractions at the onset of the stable discharge of the additionally recruited MU. Accepted: 23 September 1997     

Estimation of contractile parameters of successive twitches in unfused tetanic contractions of single motor units – A proof-of-concept study using ultrafast ultrasound imaging in vivo

During a voluntary contraction, motor units (MUs) fire a train of action potentials, causing summation of the twitch forces, resulting in fused or unfused tetanus. Twitches have been important in studying whole-muscle contractile properties and differentiation between MU types. However, there are still knowledge gaps concerning the voluntary force generation mechanisms. Current methods rely on the spike-triggered averaging technique, which cannot track changes in successive twitches’ properties in response to individual neural firings. This study proposes a method that estimates successive twitches contractile parameters of single MUs during low force voluntary isometric contractions in human biceps brachii. We used a previously developed ultrafast ultrasound imaging method to estimate unfused tetanic activity signals of single MUs. A twitch decomposition model was used to decompose unfused tetanic activity signals into individual twitches. This study found that the contractile parameters varied within and across MUs. There was an association between the inter-spike interval and the contraction time (r = 0.49, p < 0.001) and the half-relaxation time (r = 0.58, p < 0.001), respectively. The method shows the proof-of-concept to study MU contractile properties of individual twitches in vivo, which can provide further insights into the force generation mechanisms of voluntary contractions and response to individual neural discharges.     

Pulse charge and not waveform affects M-wave properties during progressive motor unit activation

The aim of this study was to investigate changes in experimentally recorded M-waves with progressive motor unit (MU) activation induced by transcutaneous electrical stimulation with different pulse waveforms. In 10 subjects, surface electromyographic signals were detected with a linear electrode array during electrically elicited contractions of the biceps brachii muscle. Three different monophasic waveforms of 304-μs duration were applied to the stimulation electrode on the main muscle motor point: triangular, square, and sinusoidal. For each waveform, increasing stimulation current intensities were applied in 10 s (frequency: 20 Hz). It was found that: (a) the degree of MU activation, as indicated by M-wave average rectified value, was a function of the injected charge and not of the stimulation waveform, and (b) MUs tended to be recruited in order of increasing conduction velocity with increasing charge of transcutaneous stimulation. Moreover, the subjects reported lower discomfort during the contractions elicited by the triangular waveform with respect to the others. Since subject tolerance to the stimulation protocol must be considered as important as MU recruitment in determining the effectiveness of neuromuscular electrical stimulation (NMES), we suggest that both charge and waveform of the stimulation pulses should be considered relevant parameters for optimizing NMES protocols.     

Effect of temperature on isotonic twitch of white muscle and predicted maximum swimming speeds of skipjack tuna,Katsuwonus pelamis

Synopsis Latent period, rise time, contraction time, and half relaxation time from isotonic contractions of isolated white muscle samples from skipjack tuna, Katsuwonus pelamis, were determined at 20°, 27°, and 34° C. These parameters were found to be inversely proportional to temperature (Q₁₀ = 1.47, 1.67, 1.62, and 1.72, respectively). The data show that contraction time and the effect of temperature on contraction time of skipjack tuna white muscle are not unique when compared to other equal-sized teleosts. Based on contraction time, maximum swimming speeds at each muscle temperature were calculated and found not significantly to exceed the maximum speeds of other equal-sized teleosts, when comparisons are made at the same white muscle temperatures     

A mathematical model for the spontaneous contractions of the isolated uterine smooth muscle from patients receiving progestin treatment

The in vitro spontaneous contractions of human myometrium samples can be described using a phenomenological model involving different cell states and adjustable parameters. In patients not receiving hormone treatment, the dynamic behavior could be described using a three-state model similar to the one we have already used to explain the oscillations of intra-uterine pressure during parturition. However, the shape of the spontaneous contractions of myometrium from patients on progestin treatment was different, due to a two-step relaxation regime including a latched phase which cannot be simulated using the previous model without introducing an ad hoc mechanism to account for the extra energy involved in this sustained contraction. One way to do this is to introduce an anomalous rate of ATP consumption, the biochemical reasons for which have not yet been elucidated and which cannot be mathematically simulated using our experimental data. An alternative explanation is the reduced cycling rate of actin-myosin cross-bridges known to occur during the latch-phase. Our experimental findings suggest a third possibility, namely a sol-gel transition with a specific relaxation time constant, which would maintain a significant part of the cell population in the contracted-state until the intracellular-medium returns to its normal fluid behavior.     

Neuromuscular modulation in Limulus by both octopamine and proctolin

Both octopamine and proctolin potentiate nerve-evoked skeletal muscle contractions in the horseshoe crab, Limulus. The threshold concentration for octopamine was 10^?9 to 10^?8M, while for proctolin it was 3 × 10^?9M. Norepinephrine and dopamine produced effects similar to octopamine but at higher thresholds; tyramine and serotonin were ineffective. Octopamine caused significant increases in amplitudes of excitatory postsynaptic potentials (epsps) of muscle fibers, but had little effect on muscle fiber input resistance or membrane potential. Also, octopamine did not affect depolarization of muscle fibers and subsequent contraction due to the direct action of exogenously applied glutamate. These results suggest that octopamine potentiates nerve-evoked contractions primarily by facilitating release of neuromuscular transmitter. At concentrations above 10^?7M, however, octopamine sometimes caused muscle spikes in response to motoneuron stimulation, a finding that suggests that octopamine may also have some postsynaptic action. Proctolin potentiated the muscle contractions evoked by glutamate but had little effect on glutamate-evoked muscle fiber depolarization, muscle fiber input resistance, or membrane potential. Thus, proctolin appears to act directly on skeletal muscle to enhance contractility. The proctolin-induced potentiations of contraction were sometimes accompanied by modest increases in epsp amplitude, so that unlike lobster skeletal and Limulus cardiac neuromuscular preparations, proctolin may have a secondary direct synaptic effect. Both octopamine and proctolin have been found in Limulus cardiac ganglion. This potential access to the hemolymph and the relatively low threshold concentrations needed for physiological action suggest that octopamine and proctolin could function as hormonal modulators of neuromuscular function in Limulus.     

Electromyogram and mechanomyogram changes in fresh and fatigued muscle during sustained contraction in men

In surface electromyogram (EMG) and mechanomyogram (MMG) the electrical and mechanical activities of recruited motor units (MU) are summated. Muscle fatigue influences the electrical and mechanical properties of the active MU. The aim of this study was to evaluate fatigue-induced changes in the electrical and mechanical properties of MU after a short recovery period, using an analysis of force, surface EMG and MMG. In seven subjects the EMG and MMG were recorded from the biceps brachii muscle during sustained isometric effort at 80% of the maximal voluntary contraction (MVC), before (test 1) and 10 min after (test 2) a fatiguing exercise. From the time and frequency domain analysis of the signals, the root mean square (rms) and the mean frequency (fˉ) of the power spectrum were calculated. The results were that the mean MVC was 412 (SEM 90) N and 304 (SEM 85) N in fresh and fatigued muscle, respectively; during tests 1 and 2 the mean EMG rms increased from 0.403 (SEM 0.07) mV to 0.566 (SEM 0.09) mV and from 0.476 (SEM 0.07) mV to 0.63 (SEM 0.09) mV, respectively; during test 1 the mean MMG rms decreased from 9.4 (SEM 0.8) mV to 5.7 (SEM 0.9) mV; in contrast, during test 2 constantly lower values were observed throughout contraction; during tests 1 and 2 the EMG fˉ declined from 122 (SEM 7) Hz to 74 (SEM 7) Hz and from 106 (SEM 8) Hz to 60 (SEM 7) Hz, respectively; during test 1 the MMG fˉ increased in the first 6 s from 19.3 (SEM 1.4) Hz to 23.9 (SEM 2.9) Hz, falling to 13.9 (SEM 1.3) Hz at the end of contraction; in contrast, during test 2 the MMG fˉ declined continuously from 18.7 (SEM 1) Hz to 12.4 (SEM 0.8) Hz. The lower MVC after the fatiguing exercise and the changes in the EMG parameters confirmed that 10 min after the fatiguing exercise, the mechanical and electrical activities of MU were altered. In addition, the MMG results suggested that after a 10-min recovery, some highly fatigable MU might not be recruitable. Accepted: 9 June 1998     

The image of motor units architecture in the mechanomyographic signal during the single motor unit contraction: in vivo and simulation study

The mechanomyographic (MMG) signal analysis has been performed during single motor unit (MU) contractions of the rat medial gastrocnemius muscle. The MMG has been recorded as a muscle surface displacement by using a laser distance sensor. The profiles of the MMG signal let to categorize these signals for particular MUs into three classes. Class MMG-P (positive) comprises MUs with the MMG signal similar to the force signal profile, where the distance between the muscle surface and the laser sensor increases with the force increase. The class MMG-N (negative) has also the MMG profile similar to the force profile, however the MMG is inverted in comparison to the force signal and the distance measured by using laser sensor decreases with the force increase. The third class MMG-M (mixed) characterize the MMG which initially increases with the force increases and when the force exceeds some level it starts to decrease towards the negative values. The semi-pennate muscle model has been proposed, enabling estimation of the MMG generated by a single MU depending on its localization. The analysis have shown that in the semi-pennate muscle the localization of the MU and the relative position of the laser distance sensor determine the MMG profile and amplitude. Thus, proposed classification of the MMG recordings is not related to the physiological types of MUs, but only to the MU localization and mentioned sensor position. When the distance sensor is located over the middle of the muscle belly, a part of the muscle fibers have endings near the location of the sensor beam. For the MU MMG of class MMG-N the deflection of the muscle surface proximal to the sensor mainly influences the MMG recording, whereas for the MU MMG class MMG-P, it is mainly the distal muscle surface deformation. For the MU MMG of MMG-M type the effects of deformation within the proximal and distal muscle surfaces overlap. The model has been verified with experimental recordings, and its responses are consistent and adequate in comparison to the experimental data.