Modeling of summation of individual twitches into unfused tetanus for various types of rat motor units.

Repeated stimulation of motor units (MUs) causes an increase of the force output that cannot be explained by linear summation of equal twitches evoked by the same stimulation pattern. To explain this phenomenon, an algorithm for reconstructing the individual twitches, that summate into an unfused tetanus is described in the paper. The algorithm is based on an analytical function for the twitch course modeling. The input parameters of this twitch model are lead time, contraction and half-relaxation times and maximal force. The measured individual twitches and unfused tetani at 10, 20, 30 and 40 Hz stimulation frequency of three rat motor units (slow, fast resistant to fatigue and fast fatigable) are processed. It is concluded that: (1) the analytical function describes precisely the course of individual twitches; (2) the summation of equal twitches does not follow the results from the experimentally measured unfused tetani, the differences depend on the type of the MU and are bigger for higher values of stimulation frequency and fusion index; (3) the reconstruction of individual twitches from experimental tetanic records can be successful if the tetanus is feebly fused (fusion index up to 0.7); (4) both the maximal forces and time parameters of individual twitches subtracted from unfused tetani change and influence the course of each tetanus. A discrepancy with respect to the relaxation phase was observed between experimental results and model prediction for tetani with fusion index exceeding 0.7. This phase was predicted longer than the experimental one for better fused tetani. Therefore, a separate series of physiological experiments and then, more complex model are necessary for explanation of this distinction.     

Changes in the properties of mechanomyographic signals and in the tension during the fatigue test of rat medial gastrocnemius muscle motor units

The influence of activity-related changes in tension on properties of the mechanomyogram (MMG) was investigated in fast fatigable, fast resistant and slow motor units (MUs). A standard fatigue test was used in which rhythmically repeated unfused tetani were evoked. The amplitudes of the rise in tension of the first and the last contraction within the unfused tetanus and the amplitudes of accompanying signals in MMG were calculated. For fast fatigable MUs a parallel decrease in the amplitudes of both analysed contractions and in the amplitudes of accompanying MMG signals during the fatigue test was observed. For majority of fast resistant MUs at the beginning of the fatigue test a potentiation occurred and this phenomenon increased the tension of the first contraction and of the peak tetanic tension. However, the potentiation coincided also with a decrease of the amplitude of the last contraction in the tension recording of an unfused tetanus. The MMG reflected both, the increase of amplitude of the first contraction and the decrease of the amplitude of the further contractions within the tetanus. The single twitch contraction evoked immediately before and after the fatigue test was additionally recorded. A decrease (fatigue) or an increase (potentiation) of the twitch tension after the fatigue test was reflected by a decrease or an increase in the amplitude of MMG, respectively. However, the fatigue failed to change significantly the time parameters of MMG. To conclude, fatigue and potentiation can occur during activity of fast MUs and both these phenomena involve changes in the amplitude of oscillations in tension of unfused tetani which are reflected in MMG.     

Simulation of post-tetanic potentiation and fatigue in muscle using a visco-elastic model

Post-tetanic potentiation (PTP) in single motor units was simulated using a simple visco-elastic model. Single isometric twitches and unfused tetani were obtained using a wide range of physiological input rates. Values of model parameters were chosen to simulate contraction times close to those of fast and slow muscle fibers. PTP has been attributed either to i) an augmented plateau level of active state or ii) an increase in time constant of active state decay. Our results show that a prolonged decay time of active state can account for most of the experimental data obtained in amphibian and mammalian preparations. In particular, potentiation is more marked in unfused tetani than in single twitches. Moreover the model accounts for PTP even in the case of a reduction of active state plateau due to fatigue.     

Initial force production before sag is enhanced by prior contraction followed by a 3-minute rest period in fast motor units of the rat medial gastrocnemius

Unfused tetanic contractions evoked in fast motor units exhibit extra-efficient force production at the onset of contraction, an effect called “boost”. Boost is diminished in subsequent contractions if there is a short rest period between contractions, but can be re-established with a longer period of rest. We tested the hypothesis that contractile activity and rest could enhance boost-related metrics. Two sets of 3 unfused tetani were evoked 3 min apart in fast fatigable (FF) and fast fatigue-resistant (FR) motor units of the rat medial gastrocnemius. The greatest changes occurred in the first unfused tetanic contractions. Relative to the first contraction in the first set, the first contraction in the second set exhibited higher peak force during boost in a subset of motor units (76% of FF and 48% of FR). Enhanced force during boost was influenced by interaction of slowing of twitch contraction time (up to 20% and 25%, for FF and FR motor units, respectively), half-relaxation time (up to 37% and 49% for FF and FR motor units, respectively), and potentiation of the first twitch (up to 13% and 5% for FF and FR motor units, respectively). Examination of twitches evoked between sets suggested opportunity for greater enhancement of boost with shorter intervening rest periods. The phenomenon of enhanced boost following motor unit activity may interest sports scientists.     

Model-generated decomposition of unfused tetani of motor units evoked by random stimulation

Unfused tetani of motor units (MUs) evoked by stimulation at variable interpulse intervals at mean frequencies of 20, 25, 33, 40 and 50 Hz were studied using ten functionally isolated fast-type MUs from the medial gastrocnemius muscle of adult Wistar rats. A previously proposed algorithm and computer program for mathematical decomposition of unfused tetani into a series of twitches, representing responses to individual pulses, were used. Analysis of the parameters of the decomposed twitches showed considerable variability in force of successive contractions. These twitches were extremely variable with up to 2-fold higher forces and longer contraction times than a single twitch evoked by one stimulus. However, when the stimulation frequency was decreased, the decomposed twitches became similar to the single twitch with respect to amplitude and contraction time. It was found that the basic contractile parameters of decomposed twitches could be predicted with high accuracy on the basis of the tetanus force level at which the next contraction begins. This analysis of the parameters of decomposed twitches demonstrated that the contractile responses of the muscle fibers to successive action potentials generated by motoneurons are highly variable and depend on the previous MU state.     

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.     

Analysis of the unfused tetanus course in fast motor units of the rat medial gastrocnemius muscle

The course of unfused tetani with the sag effect in fast motor units of rat medial gastrocnemius was studied. The analysis of the course of successive contractions within these tetani showed that the high peak force at the beginning of tetanus before the sag resulted from temporary, very efficient sum mation of contractions at this phase, both in FF (fast fatigable) and FR (fast resistant to fatigue) units. The process of summation developed in spite of parallel shortening of the contraction and relaxation. The peak of tetanus force was visible on the average at the 2nd contraction in FF units and at the 5th contraction in FR units. After the tetanus peak the process of the efficient summation was completed and the force decreased what was visible as a sag. In the following part of the tetanus, mainly in FF units, the potentiation occurred and the force of successive contractions increased. The rise of force was visible in spite of shortening of the contraction time and was due to prolongation of the relaxation in this part of the tetanus. These observations indicated that the processes of the summation of successive contractions before sag and during the potentiation underwent different mechanisms discussed in this paper. Considerable release of Ca2+ ions from the sarcoplasmic reticulum was proposed as a possible mechanism responsible for a very efficient summation at the beginning of the tetanus whereas phosphorylation of regulatory light chain of myosin (RLC) in muscle fibers was considered as the reason of potentiation. Moreover, the present analysis revealed that previously found differences in tetani profiles between FF and FR units resulted from faster development of described changes in the course of contractions summating into the tetanus in FF motor units.     

Summation of slow motor unit forces at constant and variable interpulse intervals in rat soleus muscle

Effects of the summation of forces generated by functionally isolated slow-twitch motor units (MU) of the rat soleus muscle were examined in this study. Initially, the twitch, fused tetanic and unfused tetanic contractions evoked by trains of stimuli at variable interpulse intervals were recorded for each MU. Then, two, three or four MUs were co-activated, and the recorded forces were compared to the algebraic sum of the forces of individual MUs. The mean cumulative force of twitches and the mean cumulative force of fused tetani were not statistically different from the respective algebraic sums of forces, which revealed a high degree of linearity in the summation. However, relaxation of the recorded tetanic contractions (either fused or unfused) was faster than that predicted by the linear summation of individual contractions. Moreover, for twitch and tetanic contractions, a tendency to shorten relaxation with an increasing number of co-active MUs was noted. The results indicate that forces of rat soleus slow MUs sum up more linearly than in the respective cat muscle as well as more linearly than for fast MUs in the medial gastrocnemius muscle.     

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.     

Isometric force and endurance in soleus muscle of thyroid hormone receptor-alpha(1)- or -beta-deficient mice

The specific role of each subtype of thyroid hormone receptor (TR) on skeletal muscle function is unclear. We have therefore studied kinetics of isometric twitches and tetani as well as fatigue resistance in isolated soleus muscles of R-alpha(1)- or -beta-deficient mice. The results show 20-40% longer contraction and relaxation times of twitches and tetani in soleus muscles from TR-alpha(1)-deficient mice compared with their wild-type controls. TR-beta-deficient mice, which have high thyroid hormone levels, were less fatigue resistant than their wild-type controls, but contraction and relaxation times were not different. Western blot analyses showed a reduced concentration of the fast-type sarcoplasmic reticulum Ca(2+)-ATPase (SERCa1) in TR-alpha(1)-deficient mice, but no changes were observed in TR-beta-deficient mice compared with their respective controls. We conclude that in skeletal muscle, both TR-alpha(1) and TR-beta are required to get a normal thyroid hormone response.     

Monophasic and biphasic relaxation during motor unit tetanic contractions of variable fusion degree

The phenomenon of transition of the monophasic relaxation into biphasic course in the unfused tetanic contractions was studied on functionally isolated motor units of the rat medial gastrocnemius muscle. The sample consisted of 16 FF, 16 FR and 10 S MUs which were stimulated with the same, digitally controlled patterns. The new parameter--QRT/HRT ratio, was introduced as a convenient tool for the classification of the relaxation into monophasic or biphasic. Analysis of tetani evoked at increasing stimulation frequencies revealed similar relationships between the tetanic fusion degree and the shape of relaxation for all three types of motor units investigated. In each MU, the QRT/HRT ratio fell into two distinct ranges related to either monophasic (lower values) or biphasic (higher values) relaxation. The relationship was also found between the shape of relaxation and degree of tetanic fusion--the biphasic course appeared for better fused tetani when fusion index was over the mean of 0.8. Mechanisms of development of the biphasic relaxation were discussed with respect to importance of this parameter in force development and summation of successive contractions into tetanus. Moreover, it was pointed out that adequacy of mathematical modeling of motor unit contractions should benefit from the precise analysis of the mono- or biphasic course of relaxation.     

A comparison of contractile properties in human arm and leg muscles

Isometric twitch properties have been compared in two pairs of opposing human limb muscles; these were the brachial biceps and triceps, and the anterior tibial and plantarflexor muscles. All four muscles were examined in each of 24 healthy subjects (16 men and 8 women). The brachial triceps had the shortest contraction and half-relaxation times and the greatest twitch potentiation, while the plantarflexors had the most prolonged twitches and least potentiation; the anterior tibial and brachial biceps muscles had similar characteristics. Susceptibility to fatigue was less in the plantarflexors than in the other three muscles. When muscles were assessed without reference to their anatomical sites, a significant relationship was noted between contraction time and potentiation, but not between either of these features and fatiguability. There was no evidence that muscles were uniformly 'faster' or 'slower' in some subjects than in others.     

Fatigue from incompletely fused tetanic contractions in skeletal muscle in situ

The purpose of this study was to investigate the contractile response of skeletal muscle in situ when stimulation results in an unfused tetanic contraction. The left gastrocnemius-plantaris muscle group of anesthetized (pentobarbital sodium) dogs (n = 16) was connected to an isometric lever and stimulated indirectly for 30 min. During 10-Hz stimulation, total tension (the peak of each oscillation in tension) increased during the first 2 min of stimulation (staircase), then decreased during the remaining 28 min of stimulation. Since relaxation was incomplete at this rate of stimulation, the developed tension, the difference between peak tension and the lowest tension between successive contractions, did not follow the same pattern of staircase and fatigue as the peak tension did. Developed tension (delta T) decreased during the staircase response then increased from 2 to 10 min before finally decreasing again during the last 20 min, ending at 56 +/- 15 (mean +/- SE) % of the initial (first contraction) delta T. At 2 min of 10-Hz contractions, half-relaxation time (1/2 RT) was too long to measure (insufficient relaxation between contractions), but later, 1/2 RT decreased from greater than 65 ms to less than 40 ms. Increased 1/2 RT has been associated with reduced energy availability. If an increased 1/2 RT is an indication of insufficient energy, then it can be concluded that fatigue continued in spite of a recovery of energy supplies. This suggests a possible dissociation of fatigue and energy availability.     

Summation of motor unit forces in rat medial gastrocnemius muscle

The summation of contractile forces of motor units (MUs) was analyzed by comparing the recorded force during parallel stimulation of two and four individual MUs or four groups of MUs to the algebraic sum of their individual forces. Contractions of functionally-isolated single MUs of the medial gastrocnemius muscle were evoked by electrical stimulation of thin filaments of the split L5 or L4 ventral roots of spinal nerves. Additionally, contractions of large groups of MUs were evoked by stimuli delivered to four parts of the divided L5 ventral root. Single twitches, 40 Hz unfused tetani, and 150 Hz fused maximum tetani were recorded. In these experimental situations the summation was more effective for unfused tetani than for twitches or maximum tetani. The results obtained for pairs of MUs were highly variable (more- or less-than-linear summation), but coactivation of more units led to progressively weaker effects of summation, which were usually less-than-linear in comparison to the algebraic sums of the individual forces. The variability of the results highlights the importance of the structure of the muscle and the architecture of its MUs. Moreover, the simultaneous activity of fast and slow MUs was considerably more effective than that of two fast units.     

Adaptation of rat lateral gastrocnemius muscle motor units during hindlimb unloading

Contractile and fatigue-resistance properties of 71 lateral gastrocnemius muscle (LG) motor units (MU) following 14 days of hindlimb unloading (HU) were compared to those of 60 LG MU from control rats. The MU properties were assessed from isolated and stimulated individual motor axons. The MU were classified using standard criteria (shape of unfused tetani and fatigue resistance). The HU did not affect LG MU composition, but diminished the maximal tetanic tension (Po) of all MU types: P0 was significantly reduced by about 40% for the slow and fast-resistant MU, and by 18% for the fast-fatigable ones. The speed-related properties of fast-resistant MU became more similar to those of slower MU. The fatigue properties of MU were evaluated during a 5-min exercise test, using two fatigue indexes, FI2 and FI5, which expressed the relative capacity of MU to generate tension after 2 and 5 min, respectively. Results showed that 14 days of HU did not change the fatigue sensitivity of the LG MU. However, when F15 was compared to FI2, a greater decrease was observed after HU than in control conditions for the fast-resistant and fast-intermediate MU. It was concluded that a prolonged fatigue test may show changes in metabolic properties of muscle fibres during 14 days of HU. Specific adaptations of LG MU as well as comparisons with those of the soleus muscle under the same conditions are discussed.     

The dependence of the twitch course of medial gastrocnemius muscle of the rat and its motor units on stretching of the muscle.

The relationship between the force of a single twitch of the medial gastrocnemius muscle of the rat and contraction and half-relaxation times, on one hand, and the load of the muscle on the other, was studied. Twitches of the whole muscle and its individual motor units were induced. The optimal load, at which the majority of motor units reached the greatest twitch force, was 10 G. Mean optimal loads for twitches of different types of motor units were very similar. Slow motor units reached a slightly greater twitch force at greater loads (12.5 G) than at 10 G. However, the optimal load for the twitch of the whole muscle was much greater. It was 47 G on the average. The contraction and half-relaxation times of motor units, as well as of the whole muscle, became longer as the force stretching the muscle increased. Half-relaxation time changed more rapidly than contraction time. Both parameters were undergoing the greatest changes in slow motor units.     

Fatigue and recovery contractile properties of young and elderly men

The 24 h recovery pattern of contractile properties of the triceps surae muscle, following a period of muscle fatigue, was compared in physically active young (25 years, n = 10) and elderly (66 years, n = 7) men. The fatigue test protocol consisted of 10 min of intermittent submaximal 20 Hz tetani. The maximal twitch (Pt) and tetanic force at 3 frequencies (10, 20 and 50 Hz) were determined at baseline and at 15 min, 1, 4 and 24 h after fatiguing the muscle. Maximal voluntary contraction (MVC) and vertical jump (MVJ) were also assessed. The loss of force during the fatigue test was not significantly different between the young (18 +/- 13%) and elderly (22 +/- 15%). Both groups showed similar and significant reductions of Pt (15%), tetanic force (10 to 35%) and rate of force development (dp/dt) (20%) 15 min and 1 h into recovery. The loss of force was greater at the lower stimulation frequencies of 10 and 20 Hz. Time-to-peak tension was unchanged from baseline during recovery in either group. The average rate of relaxation of twitch force (-dPt/dt) was decreased (p less than 0.05) and half-relaxation time significantly increased at 15 min and 1 h in the elderly but not the young. The findings indicate that after fatiguing contractions, elderly muscle demonstrates a slower return to resting levels of the rate and time course of twitch relaxation compared to the young.     

Mechanical behavior of skeletal muscle during intermittent voluntary isometric contractions in humans

Vøllestad, N. K., I. Sejersted, and E. Saugen. Mechanical behavior of skeletal muscle duringintermittent voluntary isometric contractions in humans.J. Appl. Physiol. 83(5):1557-1565, 1997.Changes in contractile speed and force-fusionproperties were examined during repetitive isometric contractions withthe knee extensors at three different target force levels. Sevenhealthy subjects were studied at target force levels of 30, 45, and60% of their maximal voluntary contraction (MVC) force. Repeated 6-s contractions followed by 4-s rest were continued until exhaustion. Contractile speed was determined for contractions elicited by electrical stimulation at 1-50 Hz given during exercise and a subsequent 27-min recovery period. Contraction time remained unchanged during exercise and recovery, except for an initial rapid shift in thetwitch properties. Half relaxation time(RT_1/2) decreased gradually by 20-40% during exercise at 30 and 45% of MVC. In the recovery period, RT_1/2 values werenot fully restored to preexercise levels. During exercise at 60% MVC,the RT_1/2 decreased for twitches and increased for the 50-Hz stimulation. In the recovery period after60% MVC, RT_1/2 values declinedtoward those seen after the 30 and 45% MVC exercise. The forceoscillation amplitude in unfused tetani relative to the mean forceincreased during exercise at 30 and 45% MVC but remained unalteredduring the 60% MVC exercise. This altered force-fusion was closelyassociated with the changes inRT_1/2. The faster relaxation mayat least partly explain the increased energy cost of contractionreported previously for the same type of exercise.

     

Twitch potentiation during fatiguing exercise in the elderly: the effects of training.

Twitch potentiation was studied during a fatigue paradigm involving intermittent maximum voluntary contractions (MVCs) of the tibialis anterior muscle in the elderly and in young adults. Resting twitch torques were similar between groups, but twitch potentiation was significantly greater (241% vs 166%) in the young; the recovery of the twitch after fatigue was similar between groups. Contraction time, time to peak torque and half-relaxation time were all significantly slower in the elderly. Following 12 weeks of resistance training in the elderly, there was no significant change in the twitch contractile properties at rest, but there was a significant main effect of training on the degree of twitch potentiation during the same fatigue protocol (peak potentiation 192% post-training vs 165% pretraining). These data suggest that the mechanism(s) responsible for twitch potentiation following MVCs may be influenced by both aging and training.     

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.