Variability of the twitch parameters of the rat medial gastrocnemius motor units—experimental and modeling study

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.

Microendoscopy detects altered muscular contractile dynamics in a mouse model of amyotrophic lateral sclerosis

Amyotrophic lateral sclerosis (ALS) is a fatal disease involving motor neuron degeneration. Effective diagnosis of ALS and quantitative monitoring of its progression are crucial to the success of clinical trials. Second harmonic generation (SHG) microendoscopy is an emerging technology for imaging single motor unit contractions. To assess the potential value of microendoscopy for diagnosing and tracking ALS, we monitored motor unit dynamics in a B6.SOD1G93A mouse model of ALS for several weeks. Prior to overt symptoms, muscle twitch rise and relaxation time constants both increased, consistent with a loss of fast-fatigable motor units. These effects became more pronounced with disease progression, consistent with the death of fast fatigue-resistant motor units and superior survival of slow motor units. From these measurements we constructed a physiological metric that reflects the changing distributions of measured motor unit time constants and effectively diagnoses mice before symptomatic onset and tracks disease state. These results indicate that SHG microendoscopy provides a means for developing a quantitative, physiologic characterization of ALS progression.

A Comprehensive Mathematical Model of Motor Unit Pool Organization, Surface Electromyography, and Force Generation

Neuromuscular physiology is a vibrant research field that has recently seen exciting advances. Previous publications have focused on thorough analyses of particular aspects of neuromuscular physiology, yet an integration of the various novel findings into a single, comprehensive model is missing. In this article, we provide a unified description of a comprehensive mathematical model of surface electromyographic (EMG) measurements and the corresponding force signal in skeletal muscles, both consolidating and extending the results of previous studies regarding various components of the neuromuscular system. The model comprises motor unit (MU) pool organization, recruitment and rate coding, intracellular action potential generation and the resulting EMG measurements, as well as the generated muscular force during voluntary isometric contractions. Mathematically, it consists of a large number of linear PDEs, ODEs, and various stochastic nonlinear relationships, some of which are solved analytically, others numerically. A parameterization of the electrical and mechanical components of the model is proposed that ensures a physiologically meaningful EMG-force relation in the simulated signals, in particular taking the continuous, size-dependent distribution of MU parameters into account. Moreover, a novel nonlinear transformation of the common drive model input is proposed, which ensures that the model force output equals the desired target force. On a physiological level, this corresponds to adjusting the rate coding model to the force generating capabilities of the simulated muscle, while from a control theoretic point of view, this step is equivalent to an exact linearizing transformation of the controlled neuromuscular system. Finally, an alternative analytical formulation of the EMG model is proposed, which renders the physiological meaning of the model more clear and facilitates a mathematical proof that muscle fibers in this model at no point in time represent a net current source or sink. A consistent description of a complete physiological model as presented here, including thorough justification of model component choices, will facilitate the use of these advanced models in future research. Results of a numerical simulation highlight the model's capability to reproduce many physiological effects observed in experimental measurements, and to produce realistic synthetic data that are useful for the validation of signal processing algorithms.

Functional Diversity of Neurotrophin Actions on the Oculomotor System

Neurotrophins play a principal role in neuronal survival and differentiation during development, but also in the maintenance of appropriate adult neuronal circuits and phenotypes. In the oculomotor system, we have demonstrated that neurotrophins are key regulators of developing and adult neuronal properties, but with peculiarities depending on each neurotrophin. For instance, the administration of NGF (nerve growth factor), BDNF (brain-derived neurotrophic factor) or NT-3 (neurotrophin-3) protects neonatal extraocular motoneurons from cell death after axotomy, but only NGF and BDNF prevent the downregulation in ChAT (choline acetyltransferase). In the adult, in vivo recordings of axotomized extraocular motoneurons have demonstrated that the delivery of NGF, BDNF or NT-3 recovers different components of the firing discharge activity of these cells, with some particularities in the case of NGF. All neurotrophins have also synaptotrophic activity, although to different degrees. Accordingly, neurotrophins can restore the axotomy-induced alterations acting selectively on different properties of the motoneuron. In this review, we summarize these evidences and discuss them in the context of other motor systems.

The age related slow and fast contributions to the overall changes in tibialis anterior contractile features disclosed by maximal single twitch scan

This work aimed to verify if maximal electrically evoked single twitch (STmax) scan discloses the relative functional weight of fast and slow small bundles of fibres (SBF) in determining the contractile features of tibialis anterior (TA) with ageing. SBFs were recruited by TA main motor point stimulation through 60 increasing levels of stimulation (LS): 20 stimuli at 2Hz for each LS. The lowest and highest LS provided the least ST and STmax, respectively. The scanned STmax was decomposed into individual SBF STs. They were identified when twitches from adjacent LS were significantly different and then subtracted from each other. Nine young (Y) and eleven old (O) subjects were investigated. Contraction time (CT) and STarea/STpeak (A/PT) were calculated per each SBF ST. 143 and 155 SBF STs were obtained in Y and O, respectively. Y: CT and A/PT range: 45-105ms and 67-183mNs/mN, respectively. Literature data set TA fast fibres at 34% so, from the arrays of CT and A/PT, 65ms and 100mNs/mN were identified as the upper limit for SBF fast ST classification. O: no SBF ST could be classified as fast.

CONCLUSIONS

STmax scan reveals age-related changes in the relative contribution of fast and slow SBFs to the overall muscle mechanics.

On Using Model Populations to Determine Mechanical Properties of Skeletal Muscle. Application to Concentric Contraction Simulation

In the field of computational biomechanics, the experimental evaluation of the material properties is crucial for the development of computational models that closely reproduce real organ systems. When simulations of muscle tissue are concerned, stress/strain relations for both passive and active behavior are required. These experimental relations usually exhibit certain variability. In this study, a set of material parameters involved in a 3D skeletal muscle model are determined by using a system biology approach in which the parameters are randomly varied leading to a population of models. Using a set of experimental results from an animal model, a subset of the entire population of models was selected. This reduced population predicted the mechanical response within the window of experimental observations. Hence, a range of model parameters, instead of a single set of them, was determined. Rat Tibialis Anterior muscle was selected for this study. Muscles ([Formula: see text]) were activated through the sciatic nerve and during contraction the tissue pulled a weight fixed to the distal tendon (concentric contraction). Three different weights 1, 2 and 3 N were used and the time course of muscle stretch was analyzed obtaining values of (mean [Formula: see text] standard deviation): [Formula: see text], [Formula: see text] and [Formula: see text] respectively. A paired two-sided sign rank test showed significant differences between the muscle response for the three weights ([Formula: see text]). This study shows that the Monte Carlo method could be used for determine muscle characteristic parameters considering the variability of the experimental population.

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.

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.

Sensorimotor responsiveness and resolution in the giraffe

The ability of an animal to detect and respond to changes in the environment is crucial to its survival. However, two elements of sensorimotor control - the time required to respond to a stimulus (responsiveness) and the precision of stimulus detection and response production (resolution) - are inherently limited by a competition for space in peripheral nerves and muscles. These limitations only become more acute as animal size increases. In this paper, we investigated whether the physiology of giraffes has found unique solutions for maintaining sensorimotor performance in order to compensate for their extreme size. To examine responsiveness, we quantified three major sources of delay: nerve conduction delay, muscle electromechanical delay and force generation delay. To examine resolution, we quantified the number and size distribution of nerve fibers in the sciatic nerve. Rather than possessing a particularly unique sensorimotor system, we found that our measurements in giraffes were broadly comparable to size-dependent trends seen across other terrestrial mammals. Consequently, both giraffes and other large animals must contend with greater sensorimotor delays and lower innervation density in comparison to smaller animals. Because of their unconventional leg length, giraffes may experience even longer delays compared with other animals of the same mass when sensing distal stimuli. While there are certainly advantages to being tall, there appear to be challenges as well - our results suggest that giraffes are less able to precisely and accurately sense and respond to stimuli using feedback alone, particularly when moving quickly.

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.