Motor Unit Contractions Evoked by Stimulation with Variable Interpulse Intervals

Biocybernetics and Biomedical Engineering 2012, Volume 32, Number 3, pp. 29–42

Motor Unit Contractions Evoked by Stimulation with Variable Interpulse Intervals PIOTR KRUTKI*, JAN CELICHOWSKI, ROSITSA RAIKOVA

Department of Neurobiology, University School of Physical Education, Poznań, Poland

During natural contractions motor units (MUs) are activated by variable frequency discharge patterns of motoneurones. The aim of this review was (1) to discuss differences between tetanic contractions developed at constant and random frequencies of pulses; (2) to show results of mathematical decomposition of these tetani into series of twitch-shaped responses to individual pulses; (3) to indicate that it is possible to predict the tetanic force of a MU with high accuracy by using regression equations derived on a basis of the relationships between the parameters of the decomposed twitches and the force level at which the next response begins. K e y w o r d s: motor unit, tetanic force, decomposition, rat

1. Introduction Numerous studies have revealed that the rate of motoneuronal firing – a major factor regulating the force of motor units (MUs), is not constant during voluntary contractions and the interpulse intervals (IPIs) are variable [1–7]. During usual daily voluntary activity the MUs generate non-uniform unfused tetani, which are characterized by variable force and fusion degree [8–13]. However, only constant frequency contractions have been analyzed in the majority of experimental studies, and development of the MU unfused tetani following a train of pulses at the variable IPIs has so far received little attention. In few reports only small changes in regular stimulation rates have been applied, by linear changes in frequency of stimulation or by adding or deleting individual pulses [14–18]. It has been evidenced that even minimal changes in the stimulation pattern can significantly modify the force generated by the MU. Moreover, it has been revealed that fast the MUs are highly susceptible to modifications of the firing rate in comparison to the slow MUs [17, 19–21]. * Correspondence to: Piotr Krutki, Department of Neurobiology, University School of Physical Education, ul. Królowej Jadwigi 27/39, 61-871 Poznań, Poland, e-mail: [email protected] Received 19 May 2011; accepted 20 April 2012

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In this review we presented results of the three consecutive steps in the analysis of the unfused tetanic contractions of MUs evoked by patterns of stimulation with the variable IPIs, which were based on a series of experiments in the functionally isolated MUs of the rat medial gastrocnemius (MG) muscle [22], and on a recently developed algorithm and computer program for mathematical decomposition of the MU tetanic contractions into a train of individual twitch-shape responses to the successive pulses [23, 24]. Initially we discussed differences between the tetanic contractions evoked by stimulation patterns at constant frequencies and the tetani evoked by respective patterns of random stimuli at the same mean frequencies and the same number of pulses. Subsequently we presented results of the decomposition of tetani evoked by stimulation at the variable IPIs, and we analyzed variability of the time and force properties of the decomposed twitches, either for the fast and slow MUs. Finally, we discussed effects of the previously developed mathematical approach to the prediction of force generated by the MUs stimulated by variable frequency patterns. Our aim was also to demonstrate significance of these findings in understanding physiology of a MU force development during natural contractions.

2. Material and Methods 2.1. Functional Isolation of Motor Units

Electrophysiological experiments were performed on adult female Wistar rats under pentobarbital anesthesia (initial dose of 60 mg/kg, i.p., supplemented as required). The depth of anaesthesia was verified by controlling the withdrawal reflex. All experimental procedures followed the European Union guidelines of animal care as well as the principles of the Polish Law on The Protection of Animals and were approved by the Local Bioethics Committee. After the experiments, the animals were killed with an overdose of pentobarbital (180 mg/kg). The surgical procedures have been previously described in detail [22, 25]. Briefly, the medial gastrocnemius muscle and the respective branch of the sciatic nerve were isolated and other muscles of the hind limb were denervated. Laminectomy over the L2-S1 segments was performed, and dorsal as well as ventral roots of the spinal nerves were cut proximally to the spinal cord. The animals were immobilized in a steel frame and the operated hind limb and the spinal cord were covered with paraffin oil. The muscle was connected to an inductive force transducer by the Achilles tendon to measure the contractile force under isometric conditions and stretched up to the passive force of 100 mN [26]. The functional isolation of MUs was achieved by splitting the L5 or L4 ventral roots into thin filaments, which were electrically stimulated with suprathreshold rectangular pulses (amplitude up to 0.5 V, duration 0.1 ms). A bipolar silver electrode in the muscle served to record evoked action potentials. The “all-ornone” appearance of the twitch contractions and the MU action potentials in response to the stimuli of increasing amplitude indicated the activity of a single MU.

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All recordings were stored on a computer disc using a 12-bit analog-to-digital converter (sampling rates of 1 kHz and 10 kHz for the force and the action potential recordings, respectively). 2.2. Classification of the MUs

All MUs were classified as fast or slow on a basis of a sag effect, visible exclusively in the unfused tetani of fast MUs at 40 Hz stimulation [27, 28]. The fast MUs were divided into fast fatigable (FF) and fast resistant to fatigue (FR) on a basis of the fatigue test (stimulation with trains of 14 stimuli at 40 Hz, repeated each second for 3 minutes). The fatigue index was calculated as the ratio of the force generated after two minutes of the fatigue test to the initial maximum force: the fast units with the fatigue index >0.5 were classified as FR, whereas those with the index of <0.5 were classified as FF [28, 29]. 2.3. Mathematical Approaches

Decomposition of the unfused tetanic contractions into a train of the twitch-shape responses to the successive stimuli was performed according to the algorithm based on a 6-parameter analytical function describing the twitch [23, 30]. The twitch force evoked by one stimulus applied at time Ti had the form Fitw(t) = fi(t,Ti, Tlead(i ),Thc(i ),Tc(i ) ,Thr(i ),Ttw(i ), Fmax(i )), where t is time, Tlead(i ) is the lead time, Thc(i ) is the half-contraction time, Tc(i) is the contraction time, Thr(i ) is the half-relaxation time, Ttw(i ) is the duration of the twitch, and Fmax(i ) is the maximal force of the twitch. The experimental tetanic contraction caused by n stimuli was the sum of n successive twitches. Decomposition of a tetanus consisted of the following steps: (1) a single twitch recorded at the beginning of the experiment was modeled; (2) using this model, the first contraction within the tetanic curve was matched precisely; (3) the modeled twitch was mathematically subtracted from the experimental tetanic force, revealing the mechanical response to the second pulse; (4) the six parameters of the first modeled twitch were modified to match the second mechanical response (the form of the curve). The steps (3) and (4) were repeated until the decomposition of the last contraction. This process allowed us to estimate all 6 parameters for all n decomposed twitches forming the tetanus. Using these parameters, the experimental tetanic curve was then reconstructed by summation of all modeled twitches. Next, the force produced by the same stimulation pattern, but supposing summation of the equal twitches and using 6 parameters from only the first single twitch was calculated. The final step was to predict the tetanic force of the same MU, but obtained by the different stimulation pattern. To achieve this, 6 calculated parameters for each contraction within tetanus were correlated with the respective force level at which these contractions began – Fmintet(i) [24]. The data points were fitted by regression

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curves of form y = a + bx + cx2, where y was the lead time, or the contraction time, or the half-contraction time, or the half-relaxation time, or the duration of the twitch or the maximal force, and x was Fmintet(i). a, b and c are constants; for c = 0, linear regression was tested and for c ≠ 0, quadratic one. The parameters of the successive twitches of the another tetanic force curve, produced by application of the different stimulation patterns, were calculated using the above regression equations and the tetanic curve was then modeled by summation of all twitches. To estimate the error between the experimental curve and the reconstructed force profile, a fit coefficient (FIC) was calculated and expressed in percents [24]. This coefficient is 100% when the two curves match perfectly. The lower the FIC, the greater the differences between the curves under comparison.

3. Tetanic Contractions Evoked by a Constant Frequency and Random Stimulation Patterns Irregular stimulation patterns of motoneuronal firing are typical for muscle activity during the natural voluntary contractions. Therefore, in the study of the functionally isolated fast-twitch MUs, the random stimulation patterns were used to simulate, as closely as possible, conditions of the voluntary contractions [22]. The unfused tetanic contractions evoked by two trains of stimuli with 41 pulses were compared: the first with the constant 50 ms interpulse interval (IPI), and the second with the variable random IPI at respective mean frequency (for comparison of the respective tetanic profiles for the particular MU types see Fig.1–3 A). This procedure was used for the mean frequencies 20, 25, 33, 40 and 50 Hz, i.e., with the mean interpulse intervals 40, 30, 25, and 20 ms, respectively. The mean frequencies of the irregular stimulation patterns corresponded to the respective regular patterns, but the intervals between individual pulses were randomly set at values in the range of the mean IPI ± 50%. These values (IPIs between 10 and 75 ms, a range of instantaneous frequencies of the tetanic contractions between 13 and 100 Hz) cover the natural range of the preferred firing rates of the MG motoneurones from the unfused to the nearly fused tetanic contractions [9, 31]. The analysis concerned changes in the force and differences in the relative force increase during the subsequent components of unfused tetanic contractions and measurement of the force-time area (FTA) which is an expression of the MU contraction effectiveness. Numerous reports have emphasized that the discharge rate of the motoneurones positively correlates to the absolute force of tetanus during centrally evoked or voluntary contractions of the MUs [8, 32, 33]. For the constant-frequency tetanic contractions, the relationship between the force level and the stimulation frequency has been widely described by analysis of the force-frequency curves. These studies have indicated that the MUs have ability to increase the tetanic force in response

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to even small changes in the stimulation frequency in the relatively wide range of frequencies that evoke the unfused tetanic contractions [13, 29, 32, 34]. Analysis of the force variability in the tetani evoked by the random stimulation patterns revealed that the force variability (measured as standard deviation of the mean tetanic force) is the highest (more than 20%, and in many cases exceeding 30%) at frequencies that produce the contractions of moderate fusion degree, i.e. at the mean frequencies between 24 and 35 Hz [22]. Instantaneous changes of the force are much smaller for the low-fused contractions evoked with the mean IPIs of 50 ms (fusion index < 0.2) as well as for the high-fused tetani with the mean IPIs of 20 and 25 ms (fusion index > 0.8). The instantaneous force developed by the MU during the unfused tetanic contraction evoked by the random stimulation pattern depended both on the IPI and on the initial force level (Fmin). The longer IPIs and the lower Fmin resulted in the higher force increase during responses to the next stimulus within the tetanic contractions. Moreover, these relations were stronger for the tetani evoked with the relatively low mean stimulation frequencies (the longer IPIs) generating the lower forces, than for the high-frequency tetani (the shorter IPIs) generating the higher levels of force. The question arises, whether the IPI or the Fmin could be used for a prediction of the force developed by the successive contractions within this tetanus? To date, the IPI has mainly been described in studies dealing with the decomposition of EMG signals into a series of the MU action potentials [35–39]. The force-time area under the tetanic curve also depends on frequency of the MU stimulation [19, 20, 40, 41] and its analysis is important in view of the economy of the MU contraction. In view of classical mechanics, the FTA reflects the potential to develop changes in the momentum of an object on which the force acts for a given time [42]. Zajac and Young [43] have suggested that the FTA represents the total amount of activated and bound Ca2+ during an isometric contraction. Modifications of the contractile force and/or the time of its increase by changes in interpulse intervals influence the FTA during the various stimulation patterns that allows determining parameters of the optimal tetanus, i.e., the maximal generated FTA per pulse. In our study [22] values of the FTA for the tetani evoked by the constant stimulation patterns were higher or lower than for the tetanic contractions evoked by the random stimulation patterns. Differences between the FTA of the respective tetani were in favor to the tetani evoked by the constant stimulation rates (ratios of the FTA for the constant-frequency tetanic contraction to the FTA of the random pattern tetanus of the same mean IPI > 1.0) at relatively high fusion degrees (fusion index 0.68–0.92, the mean IPIs between 20 and 30 ms). However, the FTAs in the tetani of low and moderate levels of the fusion (fusion index 0.23–0.35, and the mean IPIs of 40 and 50 ms) were higher at the random stimulation patterns than at the constantfrequency (ratios < 1.0). Force of the tetanic contractions with the fusion index exceeding 0.8 is relatively high, but variability of the force is considerably lower in comparison to the weaker,

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less fused contractions. Therefore, one may conclude that higher output of the MUs and higher economy of the contractions evoked by the random stimulation pattern (in comparison to the respective constant frequency tetani) can be observed during the relatively weak tetanic contractions. Moreover, the force of the MU can be more precisely regulated by changing intervals between pulses during motor tasks requiring the low or moderate level of force.

4. Decomposition of Tetanic Contractions The tetanic force of the MU represents a sum of the forces of individual contractions (twitches) [44–46]. In compliance with this assumption, we studied the development of the unfused tetani by a method of decomposition of the unfused tetanic contractions by subtraction of successive force curves evoked by a progressively increasing number of pulses. Initially contrthe actions at constant stimulation frequencies were studied [47–48] and the results unequivocally proved that individual responses were not equal to the single twitch and were not uniform. The bell-shaped twitch-form the extracted components had highly variable parameters (amplitudes, contraction and relaxation times) with the variable force and duration. It was concluded that a linear summation of the equal twitches used in muscle models to calculate the force of the MUs caused by many impulses is a simplification and is far from the reality. As discussed in the previous chapter, the standard method used to study the MU properties by the application of the electrical stimuli to the motor axons at constant frequencies does not reflect conditions of the natural activity of motoneurones [27, 49–54]. Therefore, in the subsequent study we performed a decomposition of the tetani of the fast MUs, evoked by stimulation at the variable IPIs and analyzed the variability of the time and force properties of the responses to successive pulses [23]. The applied frequencies (20–50 Hz) and variability in the IPIs (20–50 ms) simulated the motoneuronal firing rates observed during the natural voluntary contractions of muscles [8, 9, 31, 32]. It was demonstrated that the parameters of the decomposed twitches varied considerably and that an increase in the force amplitude and the time parameters in relation to the first twitch were typical for the most of the contractions (Fig. 1–2 B, C). It is worth noticing that the first twitch had the smallest FTA in comparison to the remaining twitches. The ratio between the highest calculated FTA for the decomposed twitches and the FTA of the first twitch ranged between 1.84 and 3.53. This parameter seems to be the best estimator of the biomechanical value of the twitch [18, 40], so the observed variability of the FTA in decomposed twitches indicated that the mechanical effectiveness of successive action potentials generated by the motoneurones is not identical and they have variable biological value. Our recent experiments performed on 30 type-identified MUs (unpublished observations) confirmed the great variability of the decomposed twitch-type responses

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to individual pulses in all types of MUs. Moreover, there were striking differences between the FF, FR and S MUs (Fig. 1–3 B, C ). The force of the strongest subtracted twitch from the unfused tetanus of the FF MUs was 1.00-2.35 times higher than the amplitude of the first single twitch force, and in many cases, this first twitch was the strongest one. For the FR MUs, the forces of the strongest twitch responses were 1.38–3.33 times higher than the initial twitch force, but the largest differences were found for the S MUs: the force of the strongest subtracted twitch was 3.46–7.35 times higher than the initial one. Even bigger differences were observed for the FTA values. Mean ratios of the maximum FTA and the FTA of the first twitch were 1.00–3.04, 1.50–4.67, 6.01–14.26 for the FF, FR and S units, respectively. These observations are in line with the fact that the slow MUs show considerably higher effectiveness of summation of responses to subsequent stimuli into the tetanic contraction that corresponds to the lower twitch-to-tetanus ratio for these units [18, 55].

Fig.1. The FF MU. A – the superimposed unfused tetanic contractions evoked by two patterns of stimulation, with a constant frequency (grey trace) and with the IPI randomly varying (black trace). B – the twitch responses to successive pulses decomposed from the unfused tetanus evoked at the random stimulation pattern. C – the same twitches as in B, superimposed on each other. The first twitch is depicted by the thick line. Note differences in the amplitude, the contraction and relaxation times between the individual twitch responses. D – the experimental tetanic contraction evoked at the random stimulation pattern (as in A, black trace) versus the tetanic force reconstructed by summation of the equal twitches (as the response to a single pulse), when the same random pattern was applied (grey trace)

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Fig. 2. The FR MU. A – the superimposed unfused tetanic contractions evoked by two patterns of stimulation, with a constant frequency (grey trace) and with the IPI randomly varying (black trace). B – the twitch responses to successive pulses decomposed from the unfused tetanus evoked at the random stimulation pattern. C – the same twitches as in B, superimposed on each other. The first twitch is depicted by the thick line. Note differences in the amplitude, the contraction and relaxation times between the individual twitch responses. D – the experimental tetanic contraction evoked at the random stimulation pattern (as in A, black trace) versus the tetanic force reconstructed by summation of the equal twitches (as the response to a single pulse), when the same random pattern was applied (grey trace)

During the reconstruction of the MU tetanic contractions, it was once again confirmed that summation of equal twitches resulted in the different force profiles than in the experimental tetani (Fig. 1–2 D), and only summation of the variable twitch-form responses to individual pulses could result in a good match between the experimental and the modeled tetanus. Considerably lower tetanic forces in the model of summation of the equal twitch responses, in comparison to the experimental results, was especially visible in the slow MUs (Fig. 3D). Parameters of the decomposed twitches were correlated to the Fmin and to the IPI so it was possible to answer the previously asked question which of these parameters could be used for a prediction of the force developed following successive pulses within this tetanus. It was revealed that the Fmin closely correlated with the analyzed parameters of the decomposed twitches composing the tetanus:

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the force amplitude, the twitch contraction time and the force-time area (correlation coefficients r = 0.9388, r = 0.9237, and r = 0.8918, respectively, p < 0.001). Correlation coefficients for the relationships between the IPI and the contractile twitch parameters were lower and frequently non-significant (the respective values r = 0.5771, r = 0.7396, r = 0.4734, p < 0.01). Significance of these observations was confirmed by comparison of variability of the force of the decomposed twitches generated at similar levels of the Fmin or at the identical IPIs [23]. It was shown that the decomposed twitches evoked at almost identical values of the Fmin had similar amplitudes (differences up to 18% between the weakest and the strongest twitch), although the preceding IPIs varied considerably. On the other hand, the force differences of the decomposed twitches evoked at the same IPI were con-

Fig. 3. The S MU. A – the superimposed unfused tetanic contractions evoked by two patterns of stimulation, with a constant frequency (grey trace) and with the IPI randomly varying (black trace). B – the twitch responses to successive pulses decomposed from the unfused tetanus evoked at the random stimulation pattern. C – the same twitches as in B, superimposed on each other. The first twitch is depicted by the thick line. Note differences in the amplitude, the contraction and relaxation times between the individual twitch responses. D – the experimental tetanic contraction evoked at the random stimulation pattern (as in A, black trace) versus the tetanic force reconstructed by summation of the equal twitches (as the response to a single pulse), when the same random pattern was applied (grey trace)

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siderably greater (differences between the weakest and the strongest twitches up to 48%). One may conclude from the observed dependencies that the force of the unfused tetanus can be predicted with high accuracy on the basis of the force level at which the next contraction begins.

5. Prediction of the Tetanic Force A majority of the previously proposed models of the motor unit pools and their control from the nervous system have resulted in simplifications and unrealistic force predictions. It is due to several reasons: constant firing frequencies have been commonly used [56], equal twitches have been summed [57], a gain in the MU force has been provided for higher firing rate frequencies [58] and only two parameters (the contraction time and the maximal force) have often been used to distinguish the different MUs. As described in the previous chapters of this review, considerable nonlinearities in summation of the successive contractions into the unfused tetani appear when the IPIs are variable [22, 23]. Therefore, in order to understand the mechanisms of muscle force regulation, the respective model should be more complex and realistic. In our recent study [24] we used such a more realistic model – a previously verified 6 parameters’ analytical function for decomposition and reconstruction of the tetanus, described in detail in the Material and Methods section. The specific aim was to predict the tetanic profiles of the fast and slow MU contractions on the basis of regression equations describing relationships between the twitch parameters and the initial level of force (Fmin), and to use the same equations for the prediction of tetani evoked by the different random stimulation patterns for the same MU. The parameters of the decomposed twitches for the processed MU tetanic contractions were different and the regression analysis of the decomposed twitch parameters and the Fmin did not show stable linear dependencies, so a better approximation of these relationships could be done with quadratic functions. The highest correlation coefficients were calculated for the twitch contraction and the half-contraction times (mean values 0.8284 and 0.7258, respectively), for the half-relaxation time this coefficient was significantly lower (the mean 0.5997), and the most variable results were obtained for the relationship between the twitch force and the Fmin (the correlation coefficients ranged from 0.1839 to 0.9388). One should also notice that the fitting curves were different (varying in slope and curvature) for the different stimulation patterns and for the different MUs. This should be expected because the twitch parameters of MUs are highly variable (even within one MU type) and continuously distributed within a muscle [47]. Despite these difficulties, the reconstruction of the tetanic profiles within the same MU on the basis of Fmin and regression equations appeared to be quite precise

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when compared to the experimental curves. The fit coefficients (FIC) for the original experimental data and the reconstructed MU forces were between 93.3968 and 96.9908 for either fast and slow MUs. When the same regression equations were used in the same MU for reconstructing the tetani curves evoked by the different mean frequencies and the different random stimulation patterns more errors appeared in the predicted curves, but still the fit coefficients were relatively high (86.9811–95.2917). For comparison, values of the FIC for the reconstructed tetani composed of the equal twitches were much lower (37.0475–88.062). The described method appeared to be useful for the tetanic force prediction for various patterns of stimulation, but only within the particular MU. Further research is necessary to determine if there is a possibility to create a general equation for the prediction of the force of various MUs within a muscle.

6. Conclusions It has been demonstrated by comparison of the tetanic contractions evoked at the constant-frequency and at the random patterns of stimuli that application of the constant-frequency stimulation patterns during experimental analysis of the MU properties can lead to several conclusions that do not correspond to activity of the MUs during their natural voluntary movements. This concerns contractile parameters of the successive components of the tetanic contractions, the instantaneous force of the tetanic contraction and the force variability as well as the effectiveness and economy of the MU contraction. Decomposition of the unfused tetanic contractions of the MU evoked by stimulation at the variable IPIs has revealed considerable variability in the twitch responses to successive pulses, what indicates that physiological significance of the successive action potentials generated by the active motoneurones depends on a history of the MU contraction and on the MU type. The most considerable ranges of variability of the parameters of the individual decomposed twitches are characteristic for the slow MUs. These results considerably broaden our understanding of the role of the neuronal code in motor control during the normal muscle activity. Finally, the best predictor of the parameters of the twitches composing the tetanus appeared to be the force level at which the next contraction begins. This parameter can be used in a mathematical model of reconstruction of the tetanic force of the MU, even for different mean frequencies and the random stimulation patterns. High accuracy of such prediction is promising in view of possibility to apply an algorithm to predict the force of natural contractions on a basis of the actual MU activity patterns and to make a mathematical model of recruitment of many MUs for prediction of a whole muscle force.

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40 Acknowledgment

The research summarized in this review was supported by grants from the Ministry of Science and Informatization No. 2P05D10929 and from the Ministry of Higher Education and Science No. N N404 027035 and by the bilateral agreement between the Polish Academy of Sciences and the Bulgarian Academy of Sciences.

References 1. Adam A., DeLuca C., Erim Z.: Hand dominance and motor unit firing behavior. J. Neurophysiol. 1998, 80, 1373–1382. 2. Boe S.G., Stashuk D.W., Brown W.F., Doherty T.J.: Decomposition-based quantitative electromyography: effect of force on motor unit potentials and motor unit number estimates. Muscle Nerve, 2005. 31, 365–373. 3. Convit R.A., Stashuk D., Tracy B., McHugh M., Brown W.F., Metter E.J.: The relationship of motor unit size, firing rate and force. Clin. Neurophysiol. 1999, 110, 1270–1275. 4. Masakado Y., Akaboshi K., Nagata M., Kimura A., Chino N.: Motor unit firing behavior in slow and fast contractions of the first dorsal interosseous muscle of healthy men. Electroencephalogr. Clin. Neurophysiol. 1995, 97, 290–295. 5. Masuda T., DeLuca C.: Recruitment threshold and muscle fiber conduction velocity of single motor units. J. Electromyogr. Kinesiol. 1991, 2, 116–123. 6. Moritz C.T., Barry B.K., Pascoe M.A., Enoka,R.M.: Discharge rate variability influences the variation in force fluctuations across the working range of a hand muscle. J. Neurophysiol. 2005, 93, 2449–2459. 7. Nakamura H., Yoshida M., Kotani M., Akazawa K., Moritani T.: The application of independent component analysis to the multi-channel surface electromyographic signals for separation of motor unit action potential trains: part I – measuring techniques. J. Electromyogr. Kinesiol. 2004, 14, 423–432. 8. Person S., Kudina L.P.: Discharge frequency and discharge pattern of human motor units during voluntary contraction of muscle. Electroencephal. Clin. Neurophysiol. 1972, 32, 471–483. 9. Hennig R., Lømo T.: Gradation of force output in normal fast and slow muscles of the rat. Acta Physiol. Scand. 1987, 130. 133–142. 10. Enoka R.M., Robinson G.A., Kossev A.R.: Task and fatigue effects on low-threshold motor units in human hand muscle. J. Neurophysiol. 1989, 62, 1344–1359. 11. De Luca C.J., Erim Z.: Common drive of motor units in regulation of muscle force. Trends Neurosci. 1994, 17, 299–304. 12. Grimby L., Hannerz J., Hedman B.: Contraction time and voluntary discharge properties of individual short toe extensor motor units in man. J. Physiol. 1979, 289, 159–201. 13. Nordstrom M.A., Miles T.S., Veale J.L.: Effect of motor unit firing pattern on twitches obtained by spike-triggered averaging. Muscle Nerve 1989, 12, 556–567. 14. Binder-Macleod S.A., Clamann P.H.: Force output of cat motor units stimulated with trains of linearly varying frequency. J. Neurophysiol. 1989, 61, 208–217. 15. Powers R.K., Binder M.D.: Effects of low frequency of stimulation on the tension-frequency relations of fast-twitch motor units of the cat. J. Neurophysiol. 1991, 66, 905–918. 16. Binder-Macleod S.A., Barrish W.J.: Force response of rat soleus muscle to variable-frequency train stimulation. J. Neurophysiol. 1992, 68. 1068–1078. 17. Grottel K., Celichowski J.: The influence of changes in the stimulation pattern on force and fusion in motor units of the rat medial gastrocnemius muscle. Exp. Brain Res. 1999, 127, 298–306.

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18. Celichowski J., Bichler E.: The influence of increasing and decreasing frequency of stimulation on the contraction of motor units in rat medial gastrocnemius muscle. J. Physiol. Pharmacol. 2000, 514, 847–855. 19. Burke R.E., Rudomin P., Zajac F.E.: Catch property in single mammalian motor units. Science 1970, 168, 122–124. 20. Burke R.E., Rudomin P., Zajac F.E.: The effect of activation history on the tension production by the individual muscle units. Brain Res. 1976, 109, 515–529. 21. De Ruiter C.J., De Haan A., Sargeant A.J.: Fast-twitch muscle unit properties in different rat medial gastrocnemius muscle compartments. J. Neurophysiol. 1996, 75, 2243–2254. 22. Krutki P., Pogrzebna M., Drzymała H., Raikova R. T., Celichowski J.: Force generated by fast motor units of the rat medial gastrocnemius muscle during stimulation with pulses at variable intervals. J. Physiol. Pharmacol. 2008, 59, 85–100. 23. Celichowski J., Raikova R.T., Drzymała-Celichowska H., Ciechanowicz-Kowalczyk I., Krutki P.: Model-generated decomposition of unfused tetani of motor units evoked by random stimulation. J. Biomech. 2008, 41, 3448–3454. 24. Raikova R., Rusev R., Drzymała-Celichowska H., Krutki P., Aladjov H., Celichowski J.: Experimentally verified mathematical approach for the prediction of force developed by motor units at variable frequency stimulation patterns. J. Biomech. 2010, 43, 1546–1552. 25. Celichowski J., Pogrzebna M., Raikova R.T.: Analysis of the unfused tetanus course in fast motor units of the rat medial gastrocnemius muscle. Archiv. Ital. Biol. 2005, 143, 51–63. 26. Celichowski J., Grottel K.: The dependence of the twitch course of medial gastrocnemius muscle of the rat and its motor units on stretching of the muscle. Arch. Ital. Biol. 1992;, 130, 315–325. 27. Burke R.E., Levine D.N., Tsairis P., Zajac F.E.: Physiological types and histochemical profiles in motor units of the cat gastrocnemius. J. Physiol. 1973, 234, 723–748. 28. Grottel K., Celichowski J.: Division of motor units in medial gastrocnemius muscle of the rat in the light of variability of their principal properties. Acta Neurobiol. Exp. 1990, 50. 571:588. 29. Kernell D., Eerbeek O., Verhey B.A.: Relation between isometric force and stimulus rate in cat’s hindlimb motor units of different twitch contraction time. Exp. Brain Res. 1983, 50, 220–227. 30. Raikova R.T., Pogrzebna M., Drzymała H., Celichowski J., Aladjov H.: Variability of successive contractions subtracted from unfused tetanus of fast and slow motor units. J. Electromyogr. Kinesiol. 2008, 18, 741–751. 31. Tansey K.E., Botterman B.R.: Activation of type-identified motor units during centrally evoked contractions in the cat medial gastrocnemius muscle. II. Motoneuron firing-rate modulation. J. Neurophysiol. 1996, 75, 38–50. 32. Erim Z., De Luca C., Mineo K., Aoki T.: Rank-ordered regulation of motor units. Muscle Nerve 1996, 19, 563–573. 33. Tansey K.E., Yee A.K., Botterman B.R.: Activation of type-identified motor units during centrally evoked contractions in the cat medial gastrocnemius muscle. III. Muscle-unit force modulation. J. Neurophysiol. 1996, 75, 51–59. 34. Mrówczyński W., Celichowski J., Krutki P.: Interspecies differences in the force-frequency relationship of the medial gastrocnemius motor units. J. Physiol. Pharmacol. 2006, 57, 491–501. 35. Indurthy M., Griffin L.: Effect of random interpulse interval modulation on neuromuscular fatigue. Muscle Nerve 2007, 36, 807–815. 36. Kebaetse M.B., Lee S.C.K., Binder-Macleod S.A.: A novel stimulation pattern improves performance during repetitive dynamic contractions. Muscle Nerve 2001, 24, 744–752. 37. Laouris Y., Bevan L., Reinking R.M., Stuart D.G.: Associations between force and motor units of a cat hindlimb muscle. Canad. J. Physiol. Pharmacol. 2004, 82, 577–588. 38. Matsuoka A.J., Abbas P.J., Rubinstein J.T., Miller C.A.: The neuronal response to electrical constantamplitude pulse train stimulation: evoked compound action potential recordings. Hear. Res. 2000, 149, 115–128.

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P. Krutki, J. Celichowski, R. Raikova

39. van Lunteren E., Sankey C.B.: Catchlike property of rat diaphragm: subsequent train frequency effects in variable-train stimulation. J. Appl. Physiol. 2000, 88, 586–598. 40. Celichowski J., Grottel K., Bichler E.: The area under the record of contractile tension: estimation of work performed by contracting motor unit. Acta Neurobiol. Exp. 1998, 58, 165–168. 41. Celichowski J., Grottel K., Bichler E.: Relationship betwen the tension-time area and the frequency of stimulation in motor units of the rat medial gastrocnemius muscle. J. Physiol. Pharmacol. 2000, 51, 2: 291–302. 42. Enoka R.M.: Neuromechanics of human movement, Human Kinetics, USA, 2002. 43. Zajac F.E., Young J.L.: Discharge properties of hind-limb motoneurons in decerebrate cats during locomotion induced by mesencephalic stimulation. J. Neurophysiol. 1980, 43, 1221–1235. 44. MacIntosh B.R., Jones D., Devrome AN., Rassier D.E.: Prediction of summation in incompletely fused tetanic contractions of rat muscle. Journal of Biomechanics 2007, 40, 1066–1072. 45. Stein R.B., Parmiggiani F.: Optimal motor patterns for activating mammalian muscle. Brain Res. 1979, 175, 372–376. 46. Stein R.B., Parmiggiani F.: Nonlinear summation of contractions in cat muscles. I. Early depression. J. Gen. Physiol. 1981,78, 277–293. 47. Raikova R.T., Celichowski J., Pogrzebna M., Aladjov H., Krutki P.: Modeling of summation of individual twitches into unfused tetanus for various types of rat motor units. J. Electromyogr. Kinesiol. 2007, 17, 121–130. 48. Raikova R.T., Pogrzebna M., Drzymała H., Celichowski J., Aladjov H.: Variability of successive contractions subtracted from unfused tetanus of fast and slow motor units. J. Electromyogr. Kinesiol. 2008, 18, 741–751, 49. Beck T.W., Housh T.J., Johnson G.O., Cramer J.T., Weir J.P., Coburn J.W., Malek M.H.: Does the frequency content of the surface mechanomyographic signal reflect motor unit firing rates? A brief review. J. Electromyogr. Kinesiol. 2007, 17, 1–13. 50. Chou L-W., Binder-Macleod S.A.: The effects of stimulation frequency and fatigue on the forceintensity relationship for human skeletal muscle. Clin. Neurophysiol. 2007, 118, 1387–1396. 51. Giroux-Metges M.A., Pennec J.P., Petit J., Goanvec C., Dorange G., Gioux M.: Motor unit properties in the soleus muscle after its distal tendon transfer to the plantaris muscle tendon in the rat. Physiol. Soc. 2003, 553, 925–933. 52. Huijing P.A., Langenberg R.W., Meesters J.J., Baan G.C.: Extramuscular myofascial force transmission also occurs between synergistic muscles and antagonistic muscles. J. Electromyogr. Kinesiol. 2007, 17, 680–689. 53. Rijkelijkhuizen J.T., Meijer H.J.M., Baan G.C., Huijing P.A.: Myofascial force transmission also occurs between antagonistic muscle located within opposite compartments of the rat lower hind limb. J. Electromyogr. Kinesiol. 2007, 21, 690–697. 54. Vydevska-Chichova M., Mileva K., Radicheva N.: Differential changes in myoelectric characteristics of slow and fast fatigable frog muscle fibres during long-lasting activity. J. Electromyogr. Kinesiol. 2007, 17, 131–141. 55. Piotrkiewicz M., Celichowski J.: Tetanic potentiation in motor units of rat medial gastrocnemius. Acta Neurobiol. Exp. 2007, 67, 35–42 56. Wexler A.S., Ding J., Binder-Macleod S.A.: A mathematical model that predicts skeletal muscle force. Transact. Biomed.l Engin. 1997, 40, 337–348. 57. Lim K.Y., Thomas C.K., Rymer W.Z.: Computational methods for improving estimates of motor unit twitch contraction properties. Muscle Nerve 1995, 18, 165–174. 58. Fuglevand A.J., Winter D.A., Patla A.E.: Models of recruitment and rate coding organization in motor-unit pools. J. Neurophysiol. 1993, 70, 2470–2488.