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.     

Changes in the time course of potentiated and fatigued contractions of fast motor units in rat muscle

The contraction and relaxation times of the twitches and the last contractions within 32 unfused tetani of FF and 27 unfused tetani of FR motor units in the rat medial gastrocnemius muscle were studied during prolonged activity. The pattern of the MU stimulation included single pulses (to evoke twitches) and series of three trains of stimuli at 40, 50 and 60 Hz (to evoke unfused tetani), repeated 30 times. The analysis concerned changes of force and time parameters at the beginning of activity, during the potentiation and then during the fatigue. It was found that changes of force during the potentiation and the fatigue were mainly accompanied by changes in the course of relaxation. The significant prolongation of the half-relaxation time during the potentiation of either twitches or unfused tetani was revealed in both types of fast MU. The twitch contraction time did not change markedly, whereas significantly shortened in the last contractions of unfused tetani during the potentiation. These changes of time parameters correlated to the increase of the fusion degree. During the fatigue, the time parameters shortened, however, changes of the half-relaxation times were remarkably higher. The shortening of relaxation was responsible for the decrease of the fusion degree. Changes of the fusion index exceeding 0.75 during the potentiation or decreasing below this value during the fatigue, were accompanied by respective appearance or disappearance of the biphasic relaxation.     

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.     

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.     

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.     

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.     

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.     

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.     

Sensitivity of the motor unit unfused tetanus to changes in the pattern of motoneuronal firing

The effects of decreasing as well as increasing the interpulse intervals on the tension produced by motor units in the rat medial gastrocnemius muscle were investigated. The increase and decrease in tension, resulting from these changes in interpulse intervals were observed and compared for each motor unit in tetani fused to a various degree. It was found that amplitudes of both changes in tension were the same when the tetanic fusion index was approximately 0.70 and the tension corresponded to 40-50% of the maximal tetanic tension. This observation concerned the all three types of motor units. We also studied the effects of introducing a short interpulse interval ("doublet") at the beginning of the stimulation. The doublet produced an increased tetanic tension with a more fused profile, however the tension was similarly sensitive to an increase as well as a decrease in the interpulse interval when the tetanic fusion index was also about 0.70. Therefore, the extent of tetanic fusion determines the sensitivity of motor unit tetani to changes in a pattern of stimulation. The tetanus of the fusion index about 0.70 can be considered as the most sensitive to changes in the pattern of motoneuronal firing.     

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.     

Effects of electrically induced fatigue on the twitch and tetanus of paralyzed soleus muscle in humans

Shields, Richard K., Laura Frey Law, Brenda Reiling, KellySass, and Jason Wilwert. Effects of electrically induced fatigueon the twitch and tetanus of paralyzed soleus muscle in humans.J. Appl. Physiol. 82(5):1499-1507, 1997.We analyzed the twitch and summated torque(tetanus) during repetitive activation and recovery of the human soleusmuscle in individuals with spinal cord injury. Thirteen individualswith complete paralysis (9 chronic, 4 acute) had the tibial nerveactivated every 1,500 ms with a 20-Hz train (7 stimuli) for 300 ms anda single pulse at 1,100 ms. The stimulation protocol lasted 3 min andincluded 120 twitches and 120 tetani. Minimal changes were found forthe acute group. The chronic group showed a significant reduction inthe torque and a significant slowing of the contractile speeds of boththe twitch and tetanus. The decrease in the peak twitch torque was significantly greater than the decrease in the peak tetanus torque early during the fatigue protocol for the chronic group. The twitch time to peak and half relaxation time were prolonged during fatigue, which was associated with improved fusion of the tetanus torque. At theend of the fatigue protocol, the decrease in the peak twitch torque wasnot significantly different from the decrease in the peak tetanustorque. After 5 min of rest, the contractile speeds recovered causingthe tetanus to become unfused, but the tetanus torque became lessdepressed than the twitch torque. The differential responses for thetwitch and the tetanus suggest an interplay between optimal fusioncreated from contractile speed slowing and excitation contractioncoupling compromise. These issues make the optimal design of functionalelectrical stimulation systems a formidable task.

     

The rate of changes in tension within fused tetani of single motor units in rat medial gastrocnemius muscle.

The time course of fused tetani of three main types of motor units: slow (S), fast resistant (FR) and fast fatigable (FF) was studied in the rat medial gastrocnemius. The rate of tension generation and of the relaxation within a tetanus was measured under isometric conditions. These measurements were performed at three points during both the contraction and relaxation: the beginning, the middle and the end of the phase of changes in tension. Significant differences were found in the rate of tension changes between fast and slow units. Comparison of FF and FR units showed less pronounced differences in their rates of the contraction and the relaxation. Moreover, slow units showed significantly greater slowing of both the contraction and relaxation within a tetanus in relation to the speed of their twitch when compared to fast motor units. The rate of changes in tetanic tension correlated to twitch time parameters and to tension generated during twitch or tetanus. The results point out that the well known difference in the speed of twitch contraction between fast and slow units is also visible in their fused tetani.     

Diazepam reveals different rate-limiting processes in rat skeletal muscle contraction

The action of the tranquilizer diazepam on rat skeletal muscle showed that relaxation of isometric twitches is controlled by different processes in extensor digitorum longus (fast-twitch) and soleus (slow-twitch) muscles. Diazepam caused an increase in the amplitude of twitches in fibres from both muscles but increased the twitch duration only in soleus. The amplitude of fused tetani were reduced in both muscles and the rate of relaxation after the tetanus slowed by as much as 34% when the amplitude of the tetanus was reduced by only 11%. The slower tetanic relaxation indicated that calcium uptake by the sarcoplasmic reticulum was slower than normal in slow- and fast-twitch fibres. We conclude therefore that calcium uptake by the sarcoplasmic reticulum is rate limiting for twitch relaxation in slow-twitch but not fast-twitch fibres and suggest that calcium binding to parvalbumin controls relaxation in the fast fibres.     

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.     

Interspecies differences of motor units properties in the medial gastrocnemius muscle of cat and rat

The purpose of the study was to analyze the interspecies differences of motor unit contractile properties in two most frequently studied mammals: cats and rats. A total sample of 166 motor units (79 in cats and 85 in rats) was investigated in the medial gastrocnemius muscle. Considerable differences were found in composition of the studied muscle. In cats, fast fatigable, fast resistant and slow units formed 68, 18 and 14% of the investigated population, whereas in rats 36, 52 and 12%, respectively. The contraction and relaxation times of motor units in the cat muscle were evidently longer than in the rat and the border values for fast/slow motor units division in these species were 44 and 20 ms, respectively. The mean values of twitch and tetanic forces appeared to be 7-8 times lower in rats, for fast, while 2-5 times for slow motor units. Also variability between the strongest and the weakest units within each type revealed differences 10-60 times in cats, whereas only 3.5-14 times in rats. The summation of twitches into tetanus for fast units was comparable in both species, but for S units was evidently more effective in the cat. In fast motor units' tetanic contractions evident interspecies differences concerned sag appearance and profiles of unfused tetani of FF and FR units. Differences in contractile properties described in the study may depend on the size, number and innervation ratio of motor units in the muscle of cat and rat, as well as their biochemical variability. Differences in composition of motor unit types and uneven mechanisms of force development may reflect biological adaptation to variable behaviour of cats and rats.     

Interspecies differences in the force-frequency relationship of the medial gastrocnemius motor units.

Single, functionally isolated motor units were studied in the medial gastrocnemius (MG) muscle of cats and rats. Axons of their motoneurons were stimulated with trains of pulses at frequencies increasing from 1 to 150 Hz and forces developed by muscle fibers were measured and force-frequency curves were compared between species. The following observations were made: (1) the most steep parts of curves (related to unfused tetani of motor units) begun at lower frequencies of stimulations in all types of feline motor units, (2) for fast motor units, the same relative values of force of unfused tetani were achieved at significantly lower frequencies of stimulations in the cat than in the rat. Twitch time parameters of both species influenced the course of force-frequency curves. It was showed that the contraction times of feline units varied in the wide range (21-81 ms), and these units reached 60% of the maximum force at stimulation frequencies between 10 and 38 Hz. On the other hand, contraction times of rat units ranged from 10 to 34 ms, whereas stimulation frequencies necessary to reach 60% of the maximum force varied considerably, from 12 to 65 Hz. The correlations between the above parameters were found for motor units of each species. However, the regression lines drown for the collected population of cat and rat units did not form linear continuity. Thus it seems that interspecies differences in the twitch contraction times do not fully explain different force-frequency relationships in mammalian skeletal muscles.     

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.     

Summation of elementary phonomyograms during isometric twitches in humans

To study its summation principle, the phonomyogram (PMG) from the first interosseus dorsalis muscle was recorded in five subjects during single twitches evoked by electrical stimulation over the motor point. By increasing the current pulse from threshold to maximal intensity, PMG amplitude increased linearly with motor unit recruitment. The twitch amplitude-intensity relationship was also linear. The PMG amplitude was therefore linearly related to the external force. For all these relationships highly significant correlation coefficients were found. These relationships were interpreted as being a consequence of an orderly recruitment, although, contrary to what happens during voluntary contraction, the largest and strongest motor units were recruited before the smallest and weakest ones during axon electrical stimulation. The PMG onset always preceded twitch onsets as indicated by latency measurements [mean 3.2 (SD 1.3) ms versus 11.5 (SD 3.9) ms, respectively]. Moreover, PMG and twitch latencies may have been significantly reduced by recruitment, suggesting that orderly recruitment influenced both PMG amplitude and occurrence. These results were interpreted as being the result of the summation of elementary PMG from every contracting motor unit and the stiffness change of the muscle medium occurring with recruitment. Accepted: 25 August 1997     

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.