Experimentally verified mathematical approach for the prediction of force developed by motor units at variable frequency stimulation patterns

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.

Muscle fibers and their synapses differentially adapt to aging and endurance training

BACKGROUND

This project aimed to determine the adaptability of the neuromuscular system to the stimuli of exercise training, and aging.

METHODS

Young adult, and aged male rats were randomly assigned to either exercise training, or sedentary control groups. Exercise training featured an 8 week program of treadmill running. At the end of the intervention period, neuromuscular function was quantified with ex vivo stimulation procedures on isolated soleus muscles. Morphological adaptations were determined by quantifying myofiber profiles (fiber size and type) of soleus muscles.

RESULTS

Ex vivo procedures confirmed that rested (fresh) young muscles were significantly (P < 0.05) stronger than aged ones. By the end of the 5 min stimulation protocol, however, young and aged muscles displayed similar levels of strength. Neuromuscular transmission efficacy as assessed by comparing force produced during indirect (neural) and direct (muscle) stimulation was unaffected by aging, or training, but under both conditions significantly declined over the stimulation protocol mimicking declines in strength. Myofiber size was unaffected by age, but training caused reductions in young, but not aged myofibers. Aged solei displayed a higher percentage of Type I fibers, along with a lower percentage of Type II fibers than young muscles.

CONCLUSIONS

The greater strength of young muscles has a neural, rather than a muscular focal point. The loss of strength discerned over the 5 min stimulation protocol was linked to similar fatigue-related impairments in neuromuscular transmission. The two components of the neuromuscular system, i.e. nerves and muscles, do not respond in concert to the stimulus of either aging, or exercise training.

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.

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

Unfused tetanic contractions evoked by trains of stimuli at variable interpulse intervals (IPIs) were recorded for 10 fast fatigable (FF), 10 fast resistant (FR), and 10 slow (S) motor units (MUs) and subsequently decomposed with a mathematical algorithm into trains of twitch-shape responses to successive stimuli. The mean stimulation frequencies were matched for each MU to evoke tetani of similar fusion degrees, whereas the variability range of IPIs was in each case 50-150% of the mean IPI. Force and time parameters of decomposed twitches were analyzed and related to the first response. Considerable variability of the analyzed twitch parameters was observed in each MU, although the largest range of variability occurred in slow MUs. In general, the decomposed twitch responses had longer duration and higher force than single-twitch contractions, although for nine FF and six FR MUs some of the decomposed responses were slightly weaker (but not faster) than the first twitches of these MUs. Comparison of the strongest decomposed twitch to the first decomposed twitch revealed ratios of forces up to 2.35, 3.33, and 6.89 for FF, FR, and S MUs and ratios of force-time areas up to 3.54, 4.67, and 14.26 for FF, FR, and S MUs, whereas for the contraction times the ratios of the longest decomposed twitch to the first twitch amounted to 2.46, 2.07, and 3.52 for FF, FR, and S MUs, respectively. The results indicate that contractile responses to successive action potentials are considerably variable, especially for slow MUs.

Limitations of the spike-triggered averaging for estimating motor unit twitch force: a theoretical analysis

Contractile properties of human motor units provide information on the force capacity and fatigability of muscles. The spike-triggered averaging technique (STA) is a conventional method used to estimate the twitch waveform of single motor units in vivo by averaging the joint force signal. Several limitations of this technique have been previously discussed in an empirical way, using simulated and experimental data. In this study, we provide a theoretical analysis of this technique in the frequency domain and describe its intrinsic limitations. By analyzing the analytical expression of STA, first we show that a certain degree of correlation between the motor unit activities prevents an accurate estimation of the twitch force, even from relatively long recordings. Second, we show that the quality of the twitch estimates by STA is highly related to the relative variability of the inter-spike intervals of motor unit action potentials. Interestingly, if this variability is extremely high, correct estimates could be obtained even for high discharge rates. However, for physiological inter-spike interval variability and discharge rate, the technique performs with relatively low estimation accuracy and high estimation variance. Finally, we show that the selection of the triggers that are most distant from the previous and next, which is often suggested, is not an effective way for improving STA estimates and in some cases can even be detrimental. These results show the intrinsic limitations of the STA technique and provide a theoretical framework for the design of new methods for the measurement of motor unit force twitch.

An approach for simulation of the muscle force modeling it by summation of motor unit contraction forces

Muscle force is due to the cumulative effect of repetitively contracting motor units (MUs). To simulate the contribution of each MU to whole muscle force, an approach implemented in a novel computer program is proposed. The individual contraction of an MU (the twitch) is modeled by a 6-parameter analytical function previously proposed; the force of one MU is a sum of its contractions due to an applied stimulation pattern, and the muscle force is the sum of the active MUs. The number of MUs, the number of slow, fast-fatigue-resistant, and fast-fatigable MUs, and their six parameters as well as a file with stimulation patterns for each MU are inputs for the developed software. Different muscles and different firing patterns can be simulated changing the input data. The functionality of the program is illustrated with a model consisting of 30 MUs of rat medial gastrocnemius muscle. The twitches of these MUs were experimentally measured and modeled. The forces of the MUs and of the whole muscle were simulated using different stimulation patterns that included different regular, irregular, synchronous, and asynchronous firing patterns of MUs. The size principle of MUs for recruitment and derecruitment was also demonstrated using different stimulation paradigms.

Extraocular muscle motor units characterized by spike-triggered averaging in alert monkey

Single-unit recording in macaque monkeys has been widely used to study extraocular motoneuron behavior during eye movements. However, primate extraocular motor units have only been studied using electrical stimulation in anesthetized animals. To study motor units in alert, behaving macaques, we combined chronic muscle force transducer (MFT) and single-unit extracellular motoneuron recordings. During steady fixation with low motoneuron firing rates, we used motoneuron spike-triggered averaging of MFT signals (STA-MFT) to extract individual motor unit twitches, thereby characterizing each motor unit in terms of twitch force and dynamics. It is then possible, as in conventional studies, to determine motoneuron activity during eye movements, but now with knowledge of underlying motor unit characteristics. We demonstrate the STA-MFT technique for medial rectus motor units. Recordings from 33 medial rectus motoneurons in three animals identified 20 motor units, which had peak twitch tensions of 0.5-5.25mg, initial twitch delays averaging 2.4 ms, and time to peak contraction averaging 9.3 ms. These twitch tensions are consistent with those reported in unanesthetized rabbits, and with estimates of the total number of medial rectus motoneurons and twitch tension generated by whole-nerve stimulation in monkey, but are substantially lower than those reported for lateral rectus motor units in anesthetized squirrel monkey. Motor units were recruited in order of twitch tension magnitude with stronger motor units reaching threshold further in the muscle's ON-direction, showing that, as in other skeletal muscles, medial rectus motor units are recruited according to the "size principle".

The tetanic depression in fast motor units of mammalian skeletal muscle can be evoked by lengthening of one initial interpulse interval

A lower than expected tetanic force (the tetanic depression) is regularly observed in fast motor units (MUs) when a higher stimulation frequency immediately follows a lower one. The aim of the present study was to determine whether prolongation of only the first interpulse interval (IPI) resulted in tetanic depression. The experiments were carried out on fast MUs of the medial gastrocnemius muscle in cats and rats. The tetanic depression was measured in each case as the force decrease of a tetanus with one IPI prolonged in relation to the tetanic force at the respective constant stimulation frequency. Force depression was observed in all cases studied and was considerably greater in cats. For cats, the mean values of force depression amounted to 28.64% for FR and 10.86% for FF MUs whereas for rats 9.30 and 7.21% for FR and FF motor units, respectively. Since the phenomenon of tetanic depression in mammalian muscle is commonly observed even after a change in only the initial interpulse interval within a stimulation pattern, it can effectively influence processes of force regulation during voluntary activity of a muscle, when motoneurones progressively increase the firing rate.