Dynamic changes of twitchlike responses to successive stimuli studied by decomposition of motor unit tetanic contractions in rat medial gastrocnemius

Skeletal muscle models composed of motor units: A review

The mathematical muscle models should include several aspects of muscle structure and physiology. First, muscle force is the sum of forces of multiple motor units (MUs), which have different contractile properties and play different roles in generating muscle force. Second, whole muscle activity is an effect of net excitatory inputs to a pool of motoneurons innervating the muscle, which have different excitability, influencing MU recruitment. In this review, we compare various methods for modeling MU twitch and tetanic forces and then discuss muscle models composed of different MU types and number. We first present four different analytical functions used for twitch modeling and show limitations related to the number of twitch describing parameters. We also show that a nonlinear summation of twitches should be considered in modeling tetanic contractions. We then compare different muscle models, most of which are variations of Fuglevand's model, adopting a common drive hypothesis and the size principle. We pay attention to integrating previously developed models into a consensus model based on physiological data from in vivo experiments on the rat medial gastrocnemius muscle and its respective motoneurons. Finally, we discuss the shortcomings of existing models and potential applications for studying MU synchronization, potentiation, and fatigue.

Measuring and modeling the effects of vagus nerve stimulation on heart rate and laryngeal muscles

BACKGROUND

Reduced heart rate (HR) during vagus nerve stimulation (VNS) is associated with therapy for heart failure, but stimulation frequency and amplitude are limited by patient tolerance. An understanding of physiological responses to parameter adjustments would allow differential control of therapeutic and side effects. To investigate selective modulation of the physiological responses to VNS, we quantified the effects and interactions of parameter selection on two physiological outcomes: one related to therapy (reduced HR) and one related to side effects (laryngeal muscle EMG).

METHODS

We applied a broad range of stimulation parameters (mean pulse rates (MPR), intra-burst frequencies, and amplitudes) to the vagus nerve of anesthetized mice. We leveraged the in vivo recordings to parameterize and validate computational models of HR and laryngeal muscle activity across amplitudes and temporal patterns of VNS. We constructed a finite element model of excitation of fibers within the mouse cervical vagus nerve.

RESULTS

HR decreased with increased amplitude, increased MPR, and decreased intra-burst frequency. EMG increased with increased MPR. Preferential HR effects over laryngeal EMG effects required combined adjustments of amplitude and MPR. The model of HR responses highlighted contributions of ganglionic filtering to VNS-evoked changes in HR at high stimulation frequencies. Overlap in activation thresholds between small and large modeled fibers was consistent with the overlap in dynamic ranges of related physiological measures (HR and EMG).

CONCLUSION

The present study provides insights into physiological responses to VNS required for informed parameter adjustment to modulate selectively therapeutic effects and side effects.

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.

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

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

The synchronization of firings of motor units (MUs), the smallest functional elements of skeletal muscle increases fluctuations in muscle force, known as physiological tremor, which can disturb high-precision movements. In this study, we adopted a recently proposed muscle model consisting of MUs of three different types (fast fatigable, fast resistant to fatigue, and slow) to study four different scenarios of MU synchronization during a steady level of excitatory input to motoneurons. The discharge patterns were synchronized between pairs of MUs by shifting in time individual pulses, which occurred within a short time interval, and a degree of synchronization was then estimated. The increased synchronization index resulted in increased force variability for all MU types as well as for the whole muscle output; however, the mean force levels remained nearly unchanged, whereas the frequencies of the force oscillations were decreased. The absolute range of force variability was higher for fast than for slow MUs, indicating their dominant influence on muscle tremor at strong contractions, but the highest relative increase in force variability was observed for synchronized slow MUs, indicating their significant contribution to tremor during weak contractions, in which only slow MUs are active.

Contractile history affects sag and boost properties of unfused tetanic contractions in human quadriceps muscles

PURPOSE

A period of extra-efficient force production ("boost") followed by a decline in force ("sag") is often observed at the onset of unfused tetanic contractions. We tested the hypothesis that in human muscle boost and sag are diminished in repeated contractions separated by short rest periods and are re-established or enhanced following long rest periods.

METHODS

Two sets of 3 unfused tetanic contractions were evoked in the right quadriceps muscle group of 29 participants via percutaneous stimulation of the femoral nerve. Contractions consisted of 20 pulses evoked at inter-pulse intervals of 1.25 × twitch time to peak torque. Contractions were evoked 5 s apart and sets were evoked 5 min apart.

RESULTS

The ratio of the angular impulse of pulses 1-10 to the angular impulse of pulses 11-20 was used as the boost indicator. By this metric, boost was higher (P < 0.05) in the first relative to the second and third contractions within a set, but did not differ between sets (Set 1: 1.31 ± 0.15, 1.18 ± 0.12, 1.14 ± 0.12 vs Set 2: 1.34 ± 0.17, 1.17 ± 0.13, 1.14 ± 0.13). Sag (the percent decline in torque within each contraction) was also higher (P < 0.05) in the first relative to the second and third contractions within a set, but did not differ between sets (Set 1: 40.8 ± 7.5%, 35.4 ± 6.8%, 33.2 ± 7.8% vs Set 2: 42.1 ± 8.0%, 35.5 ± 6.8%, 33.9 ± 7.2%). Participants' sex and resistance training background did not influence boost or sag.

CONCLUSION

Boost and sag are sensitive to contractile history in whole human quadriceps. Optimizing boost may have application in strength and power sports.

Biomechanical conditioning of the motor unit transitory force decrease following a reduction in stimulation rate

BACKGROUND

The biomechanical background of the transitory force decrease following a sudden reduction in the stimulation frequency under selected experimental conditions was studied on fast resistant motor units (MUs) of rat medial gastrocnemius in order to better understand the mechanisms of changes in force transmission.

METHODS

Firstly, MUs were stimulated with three-phase trains of stimuli (low-high-low frequency pattern) to identify patterns when the strongest force decrease (3-36.5%) following the middle high frequency stimulation was observed. Then, in the second part of experiments, the MUs which presented the largest force decrease in the last low-frequency phase were alternatively tested under one of five conditions to analyse the influence of biomechanical factors of the force decrease: (1) determine the influence of muscle stretch on amplitude of the force decrease, (2) determine the numbers of interpulse intervals necessary to evoke the studied phenomenon, (3) study the influence of coactivation of other MUs on the studied force decrease, (4) test the presence of the transitory force decrease at progressive changes in stimulation frequency, (5) and perform mathematical analysis of changes in twitch-shape responses to individual stimuli within a tetanus phase with the studied force decrease.

RESULTS

Results indicated that (1) the force decrease was highest when the muscle passive stretch was optimal for the MU twitch (100 mN); (2) the middle high-frequency burst of stimuli composed of at least several pulses was able to evoke the force decrease; (3) the force decrease was eliminated by a coactivation of 10% or more MUs in the examined muscle; (4) the transitory force decrease occured also at the progressive decrease in stimulation frequency; and (5) a mathematical decomposition of contractions with the transitory force decrease into twitch-shape responses to individual stimuli revealed that the force decrease in question results from the decrease of twitch forces and a shortening in contraction time whereas further force restitution is related to the prolongation of relaxation.

CONCLUSIONS

High sensitivity to biomechanical conditioning indicates that the transitory force decrease is dependent on disturbances in the force transmission predominantly by collagen surrounding active muscle fibres.

A model of the rat medial gastrocnemius muscle based on inputs to motoneurons and on an algorithm for prediction of the motor unit force

The muscle force is the sum of forces of multiple motor units (MUs), which have different contractile properties. During movements, MUs develop unfused tetani, which result from summation of twitch-shape responses to individual stimuli, which are variable in amplitude and duration. The aim of the study was to develop a realistic muscle model that would integrate previously developed models of MU contractions and an algorithm for the prediction of tetanic forces. The proposed model of rat medial gastrocnemius muscle is based on physiological data: excitability and firing frequencies of motoneurons, contractile properties, and the number and proportion of MUs in the muscle. The MU twitches were modeled by a six-parameter analytical function. The excitability of motoneurons was modeled according to a distribution of their rheobase currents measured experimentally. Processes of muscle force regulation were modeled according to a common drive hypothesis. The excitation signal to motoneurons was modeled by two form types: triangular and trapezoid. The discharge frequencies of MUs, calculated individually for each MU, corresponded to those recorded for rhythmic firing of motoneurons. The force of the muscle was calculated as the sum of all recruited MUs. Participation of the three types of MUs in the developed muscle force was presented at different levels of the excitation signal to motoneurons. The model appears highly realistic and open for input data from various skeletal muscles with different compositions of MU types. The results were compared with three other models with different distribution of the input parameters. NEW & NOTEWORTHY The proposed mathematical model of rat medial gastrocnemius muscle is highly realistic because it is based strictly on experimentally determined motor unit contractile parameters and motoneuron properties. It contains the actual number and proportion of motor units and takes into consideration their different contributions to the whole muscle force, depending on the level of the excitation signal. The model is open for input data from other muscles, and additional physiological parameters can also be included.

How many nerve fibres can be separated as donor from an integral nerve trunk when reconstructing a peripheral nerve trauma with amplification method by artificial biochitin conduit?

Using portion of a nearby nerve trunk to reconstruct a severe nerve lesion by artificial biodegradable chitin conduit is the core practicable method based on peripheral nerve amplification regeneration. However, the quantitative influences on skeletal muscle function corresponding to the injury of the donated nerve fibres were not previously reported. Here, we aimed to explore the compensative capacity in tibialis anterior muscles of rats with the models of acute tibialis anterior nerve branch injuries. The tibialis anterior branch of deep peroneal nerve was transected in various levels each time. Both the decreased treads of maximal compound muscle action potential (CMAP) amplitude and complete tetanic tension of the tibialis anterior muscle in rats were similar with the increasing numbers of damaged nerve fibres, which showed two S-shaped curves. When the nerve injury level was less than approximately 10%, the skeletal muscle function remained normal through complete compensation of motor endplates. As the injury degree went from 10% to 85%, the muscle function was partially impaired due to the broken compensation of motor endplates. When the nerve injury level was over approximately 85%, the skeletal muscle function was totally lost. It suggests that within a certain level of nerve injury, the skeletal muscle function maintained basically unchanged via complete compensation of motor endplates. Such nerve fibres may be used as donor nerve to repair peripheral nerve injury.

Estimating the minimum stimulation frequency necessary to evoke tetanic progression based on muscle twitch parameters

The summation of the muscle force caused by an increase in the firing rate is named a tetanic contraction (tetanus), and the minimum stimulation frequency necessary to evoke an unfused/fused tetanus is related to the contraction time (CT) and relaxation time (RT) of the twitch. In particular, the fusion index (FI) is a very useful indicator, and it is used to evaluate the change in the muscle fiber component ratio. However, the measurement of the FI is invasive, because most patients experience pain during the electrical stimulation for tetanus. We expect that the twitch parameters CT and RT can substitute for the FI in the future. We found that the minimum stimulation frequency necessary to evoke the unfused/fused tetanus can be estimated from the twitch parameters as a first step. The results showed that (1) the minimum stimulation frequencies calculated from twitch parameters during unfused/fused tetanus were very similar to those calculated from FI parameters, and (2) they were also strongly correlated with FI parameters regardless of fiber components. The basic characteristics of tetanic progression in different fiber types could be estimated from twitch parameters.

A General Mathematical Algorithm for Predicting the Course of Unfused Tetanic Contractions of Motor Units in Rat Muscle

An unfused tetanus of a motor unit (MU) evoked by a train of pulses at variable interpulse intervals is the sum of non-equal twitch-like responses to these stimuli. A tool for a precise prediction of these successive contractions for MUs of different physiological types with different contractile properties is crucial for modeling the whole muscle behavior during various types of activity. The aim of this paper is to develop such a general mathematical algorithm for the MUs of the medial gastrocnemius muscle of rats. For this purpose, tetanic curves recorded for 30 MUs (10 slow, 10 fast fatigue-resistant and 10 fast fatigable) were mathematically decomposed into twitch-like contractions. Each contraction was modeled by the previously proposed 6-parameter analytical function, and the analysis of these six parameters allowed us to develop a prediction algorithm based on the following input data: parameters of the initial twitch, the maximum force of a MU and the series of pulses. Linear relationship was found between the normalized amplitudes of the successive contractions and the remainder between the actual force levels at which the contraction started and the maximum tetanic force. The normalization was made according to the amplitude of the first decomposed twitch. However, the respective approximation lines had different specific angles with respect to the ordinate. These angles had different and non-overlapping ranges for slow and fast MUs. A sensitivity analysis concerning this slope was performed and the dependence between the angles and the maximal fused tetanic force normalized to the amplitude of the first contraction was approximated by a power function. The normalized MU contraction and half-relaxation times were approximated by linear functions depending on the normalized actual force levels at which each contraction starts. The normalization was made according to the contraction time of the first contraction. The actual force levels were calculated initially from the recorded tetanic curves and subsequently from the modeled curves obtained from the summation of all models of the preceding contractions (the so called “full prediction”). The preciseness of the prediction was verified by two coefficients estimating the error between the modeled and the experimentally recorded curves. The proposed approach was tested for 30 MUs from the database and for three additional MUs, not included in the initial set. It was concluded that this general algorithm can be successfully used for modeling of a unfused tetanus course of a single MU of fast and slow type.