Modeling of summation of individual twitches into unfused tetanus for various types of rat motor units

Characterization of Motor Unit Firing and Twitch Properties for Decoding Musculoskeletal Force in the Human Ankle Joint In Vivo

Understanding how motor units (MUs) contribute to skeletal mechanical force is crucial for unraveling the underlying mechanism of human movement. Alterations in MU firing, contractile and force-generating properties emerge in response to physical training, aging or injury. However, how changes in MU firing and twitch properties dictate skeletal muscle force generation in healthy and impaired individuals remains an open question. In this work, we present a MU-specific approach to identify firing and twitch properties of MU samples and employ them to decode musculoskeletal function in vivo. First, MU firing events were decomposed offline from high-density electromyography (HD-EMG) of six lower leg muscles involved in ankle plantar-dorsi flexion. We characterized their twitch responses based on the statistical distributions of their firing properties and employed them to compute MU-specific activation dynamics. Subsequently, we decoded ankle joint moments by linking our framework to a subject-specific musculoskeletal model. We validated our approach at different ankle positions and levels of activation and compared it with traditional EMG-driven models. Our proposed MU-specific formulation achieves higher generalization across conditions than the EMG-driven models, with significantly lower coefficients of variation in torque predictions. Furthermore, our approach shows distinct neural strategies across a large repertoire of contractile conditions in different muscles. Our proposed approach may open new avenues for characterizing the relationship between MU firing and twitch properties and their influence on force capacity. This can facilitate the development of targeted rehabilitation strategies tailored to individuals with specific neuromuscular conditions.

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.

Estimating the neural spike train from an unfused tetanic signal of low-threshold motor units using convolutive blind source separation

BACKGROUND

Individual motor units have been imaged using ultrafast ultrasound based on separating ultrasound images into motor unit twitches (unfused tetanus) evoked by the motoneuronal spike train. Currently, the spike train is estimated from the unfused tetanic signal using a Haar wavelet method (HWM). Although this ultrasound technique has great potential to provide comprehensive access to the neural drive to muscles for a large population of motor units simultaneously, the method has a limited identification rate of the active motor units. The estimation of spikes partly explains the limitation. Since the HWM may be sensitive to noise and unfused tetanic signals often are noisy, we must consider alternative methods with at least similar performance and robust against noise, among other factors.

RESULTS

This study aimed to estimate spike trains from simulated and experimental unfused tetani using a convolutive blind source separation (CBSS) algorithm and compare it against HWM. We evaluated the parameters of CBSS using simulations and compared the performance of CBSS against the HWM using simulated and experimental unfused tetanic signals from voluntary contractions of humans and evoked contraction of rats. We found that CBSS had a higher performance than HWM with respect to the simulated firings than HWM (97.5 ± 2.7 vs 96.9 ± 3.3, p < 0.001). In addition, we found that the estimated spike trains from CBSS and HWM highly agreed with the experimental spike trains (98.0% and 96.4%).

CONCLUSIONS

This result implies that CBSS can be used to estimate the spike train of an unfused tetanic signal and can be used directly within the current ultrasound-based motor unit identification pipeline. Extending this approach to decomposing ultrasound images into spike trains directly is promising. However, it remains to be investigated in future studies where spatial information is inevitable as a discriminating factor.

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.

Optimization and comparison of two methods for spike train estimation in an unfused tetanic contraction of low threshold motor units

BACKGROUND

Recent findings have shown that imaging voluntarily activated motor units (MUs) by decomposing ultrasound-based displacement images provides estimates of unfused tetanic signals evoked by spinal motoneurons' neural discharges (spikes). Two methods have been suggested to estimate its spike trains: band-pass filter (BPM) and Haar wavelet transform (HWM). However, the methods' optimal parameters and which method performs the best are unknown. This study will answer these questions.

METHOD

HWM and BPM were optimized using simulations. Their performance was evaluated based on simulations and 21 experimental datasets, considering their rate of agreement, spike offset, and spike offset variability to the simulated or experimental spikes.

RESULTS

A range of parameter sets that resulted in the highest possible agreement with simulated spikes was provided. Both methods highly agreed with simulated and experimental spikes, but HWM was a better spike estimation method than BPM because it had a higher agreement, less bias, and less variation (p < 0.001).

CONCLUSIONS

The optimized HWM will be an important contributor to further developing the identification and analysis of MUs using imaging, providing indirect access to the neural drive of the spinal cord to the muscle by the unfused tetanic signals.

Comparison of decomposition algorithms for identification of single motor units in ultrafast ultrasound image sequences of low force voluntary skeletal muscle contractions

OBJECTIVE

In this study, the aim was to compare the performance of four spatiotemporal decomposition algorithms (stICA, stJADE, stSOBI, and sPCA) and parameters for identifying single motor units in human skeletal muscle under voluntary isometric contractions in ultrafast ultrasound image sequences as an extension of a previous study. The performance was quantified using two measures: (1) the similarity of components' temporal characteristics against gold standard needle electromyography recordings and (2) the agreement of detected sets of components between the different algorithms.

RESULTS

We found that out of these four algorithms, no algorithm significantly improved the motor unit identification success compared to stICA using spatial information, which was the best together with stSOBI using either spatial or temporal information. Moreover, there was a strong agreement of detected sets of components between the different algorithms. However, stJADE (using temporal information) provided with complementary successful detections. These results suggest that the choice of decomposition algorithm is not critical, but there may be a methodological improvement potential to detect more motor units.

Basic characteristics between mechanomyogram and muscle force during twitch and tetanic contractions in rat skeletal muscles

The mechanomyogram (MMG) is a signal measured by various vibration sensors for slight vibrations induced by muscle contraction, and it reflects the muscle force during electrically induced-contraction or until 60%-70% maximum voluntary contraction, so the MMG is considered an alternative and novel measurement tool for muscle strength. We simultaneously measured the MMG and muscle force in the gastrocnemius (GC), vastus intermedius (VI), and soleus (SOL) muscles of rats. The muscle force was measured by attaching a hook to the tendon using a load cell, and the MMG was measured using a charged-coupled device-type displacement sensor at the middle of the target muscle. The MMG-twitch waveform was very similar to that of the muscle force; however, the half relaxation time and relaxation time (10%), which are relaxation parameters, were prolonged compared to those of the muscle force. The MMG amplitude correlated with the muscle force. Since stimulation frequencies that are necessary to evoke tetanic progression have a significant correlation with the twitch parameter, there is a close relationship between twitch and tetanus in the MMG signal. Therefore, we suggest that the MMG, which is electrically induced and detected by a laser displacement sensor, may be an alternative tool for measuring muscle strength.

The force-generation capacity of the tibialis anterior muscle at different muscle-tendon lengths depends on its motor unit contractile properties

Purpose

Muscle–tendon length can influence central and peripheral motor unit (MU) characteristics, but their interplay is unknown. This study aims to explain the effect of muscle length on MU firing and contractile properties by applying deconvolution of high-density surface EMG (HDEMG), and torque signals on the same MUs followed at different lengths during voluntary contractions.

Methods

Fourteen participants performed isometric ankle dorsiflexion at 10% and 20% of the maximal voluntary torque (MVC) at short, optimal, and long muscle lengths (90°, 110°, and 130° ankle angles, respectively). HDEMG signals were recorded from the tibialis anterior, and MUs were tracked by cross-correlation of MU action potentials across ankle angles and torques. Torque twitch profiles were estimated using model-based deconvolution of the torque signal based on composite MU spike trains.

Results

Mean discharge rate of matched motor units was similar across all muscle lengths (P = 0.975). Interestingly, the increase in mean discharge rate of MUs matched from 10 to 20% MVC force levels at the same ankle angle was smaller at 110° compared with the other two ankle positions (P = 0.003), and the phenomenon was explained by a greater increase in twitch torque at 110° compared to the shortened and lengthened positions (P = 0.002). This result was confirmed by the deconvolution of electrically evoked contractions at different stimulation frequencies and muscle–tendon lengths.

Conclusion

Higher variations in MU twitch torque at optimal muscle lengths likely explain the greater force-generation capacity of muscles in this position.

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.

Normalized maximal rate of torque development during voluntary and stimulated static contraction in human tibialis anterior: Influence of age

The risk of falling in older adults has been related, among other factors, to the reduction of the rate of torque development (RTD) with age. It is well known that both structural/peripheral and neural factors can influence the RTD. The purpose of this study was to compare the normalized RTD in young and older participants obtained during a) rapid voluntary tension production and b) neuromuscular electrical stimulation. The tibialis anterior of 19 young subjects (10 males and 9 females; age 21-33 years old) and 19 older participants (10 males and 9 females; age 65-80 years old) was studied. The subjects performed a series of maximal isometric explosive dorsiflexions and underwent trains of supra-maximal electrical stimulations (35 Hz) on the tibialis anterior motor point. Muscle shortening was indirectly measured using a laser (surface mechanomyogram, MMG). Both torque and MMG were normalized to their maximum value. Using a 20 ms sliding window on the normalized torque signal, the normalized maximum RTD was calculated for both voluntary and stimulated contractions. Active stiffness of the muscle- tendon unit was calculated as the area of the normalized torque with respect to the normalized MMG. Normalized maximum RTD was found significantly lower in older adults during voluntary activity (young: 751.9 ± 216.3%/s and old: 513.9 ± 173.9%/s; P < .001), and higher during stimulated contractions (young: 753.1 ± 225.9%/s and old: 890.1 ± 221.3%/s; P = .009). Interestingly, active stiffness was also higher in older adults (young: 3524.6 ± 984.6‰ and old 4144.6 ± 816.6‰; P = .041) and significantly correlated to the normalized maximum RTD during stimulated contractions. This dichotomy suggests that modifications in the structural/peripheral muscle properties are not sufficient to counteract the age-related decrease in neural drive to the muscle during voluntary isometric contractions in aged participants.

A brief contraction has complex effects on summation of twitch pairs in human adductor pollicis

NEW FINDINGS

What is the central question of this study? How do contraction-induced reductions in twitch duration, without changes in twitch force, affect summation of twitch pairs into higher force contractions in skeletal muscle? What is the main finding and its importance? Abbreviating twitch duration with a brief contraction resulted in enhanced summation of fully fused twitch pairs, but impaired summation in partially fused twitch pairs even after accounting for the differences in relaxation of the first twitch. An inherent mechanism which enhances relaxation without sacrificing force generation in forceful contractions would benefit cyclic muscle activities, such as locomotion.

ABSTRACT

During electrically evoked contractions of skeletal muscle, the interplay between twitch duration and the time between electrical stimuli (inter-pulse interval, IPI) determines how effectively twitch forces summate into high force contractions. A brief muscle contraction can impair summation by abbreviating twitch duration, though it is not clear if these impairments occur at all physiologically relevant IPI. This study was designed to test how a brief contraction affects summation of nominally isometric twitch pairs with IPIs lasting 10-5000 ms. Left adductor pollicis muscles of human participants (n = 9) were electrically activated using stimulus pairs applied both before (Pre) and after (Post) a 10 Hz, 1.0 s contraction. Force-time records were mathematically separated into Pulse 1 (single twitch) and Pulse 2 (summated twitch) components. The ratio of Pulse 2 peak force to Pulse 1 peak force was used as our measure of summation effectiveness. Consistent with the observed decline of Pulse 1 duration at Post relative to Pre (4.7 ± 0.6%; P < 0.001; duration was defined as the time from stimulation to the time required for active force to decline by 50%), summation effectiveness was higher at Pre than at Post at IPIs of 100-333 ms. Summation effectiveness was not different between Pre and Post at IPIs of 50-83 ms or 500-5000 ms. Intriguingly, summation effectiveness was higher at Post than at Pre at IPIs of 10-25 ms. In summary, a brief contraction has complex effects on the relationship between inter-pulse interval and summation effectiveness. Future experiments are needed to reveal the mechanisms behind this novel observation.

Multiscale Hill-type modeling of the mechanical muscle behavior driven by the neural drive in isometric conditions

In this study, we present a new model describing the mechanical behavior of the skeletal muscle during isometric contraction. This model is based on a former Hill-inspired model detailing the electromechanical behavior of the muscle based on the Huxley formulation. However, in this new multiscale model the muscle is represented at the Motor Unit (MU) scale. The proposed model is driven by a physiological input describing the firing moments of the activated MUs. Definition of both voluntary and evoked MU recruitment schemes are described, enabling the study of both contractions in isometric conditions. During this type of contraction, there is no movement of the joints and the tendon-muscle complex remains at the same length. Moreover, some well-established macroscopic relationships such as force-length or force-velocity properties are considered. A comparison with a twitch model using the same input definition is provided with both recruitment schemes exhibiting limitations of twitch type models. Finally, the proposed model is validated with a comparison between simulated and recorded force profiles following eight electrical stimulations pulses in isometric conditions. The simulated muscle force was generated to mimic the one recorded from the quadriceps of a patient implanted with a functional electrical stimulation neuroprosthesis. This validation demonstrates the ability of the proposed model to reproduce realistically the skeletal muscle contractions and to take into account subject-specific parameters.

Factors contributing to sag in unfused tetanic contractions of fast motor units in rat medial gastrocnemius

The sag phenomenon can be observed in fast motor units (MUs) as a transitional decline in force during unfused tetanic contractions; however, its mechanisms are poorly understood. The study aimed to identify in the rat muscle factors that contribute to sag in two types of fast MUs: fast fatigable (FF) and fast resistant to fatigue (FR). First, we performed mathematical decomposition of sagging tetanic contractions of FF and FR MUs into twitch-like responses to consecutive stimuli. This process indicated an increase in the amplitudes of a few initial responses (up to the 2nd-3rd for FF and up to the 2nd-7th for FR MUs), followed by a decrease in the amplitudes of later responses. In comparison to the first twitch, the relative increase in force amplitudes of the several subsequent decomposed responses was smaller, and their contraction and relaxation times were shorter for FF than for FR units, which corresponded to observed differences in their sag profiles. Additionally, after occlusion of the blood circulation, sag disappeared, but it reappeared after restoration of the blood supply. This indicates that the presence of sag depends on the proper circulation in the muscle.

The sag response in human muscle contraction

PURPOSE

We examined how muscle length and time between stimuli (inter-pulse interval, IPI) influence declines in force (sag) seen during unfused tetani in the human adductor pollicis muscle.

METHODS

A series of 16-pulse contractions were evoked with IPIs between 1 × and 5 × the twitch time to peak tension (TPT) at large (long muscle length) and small (short muscle length) thumb adduction angles. Unfused tetani were mathematically deconstructed into a series of overlapping twitch contractions to examine why sag exhibits length- and IPI-dependencies.

RESULTS

Across all IPIs tested, sag was 62% greater at short than long muscle length, and sag increased as IPI was increased at both muscle lengths. Force attributable to the second stimulus increased as IPI was decreased. Twitch force declined from maximal values across all IPI tested, with the greatest reductions seen at short muscle length and long IPI. At IPI below 2 × TPT, the twitch with highest force occurred earlier than the peak force of the corresponding unfused tetani. Contraction-induced declines in twitch duration (TPT + half relaxation time) were only observed at IPI longer than 1.75 × TPT, and were unaffected by muscle length.

CONCLUSIONS

Sag is an intrinsic feature of healthy human adductor pollicis muscle. The length-dependence of sag is related to greater diminution of twitch force at short relative to long muscle length. The dependence of sag on IPI is related to IPI-dependent changes in twitch duration and twitch force, and the timing of peak twitch force relative to the peak force of the associated unfused tetanus.

Analysis of the sEMG/force relationship using HD-sEMG technique and data fusion: A simulation study

The relationship between the surface Electromyogram (sEMG) signal and the force of an individual muscle is still ambiguous due to the complexity of experimental evaluation. However, understanding this relationship should be useful for the assessment of neuromuscular system in healthy and pathological contexts. In this study, we present a global investigation of the factors governing the shape of this relationship. Accordingly, we conducted a focused sensitivity analysis of the sEMG/force relationship form with respect to neural, functional and physiological parameters variation. For this purpose, we used a fast generation cylindrical model for the simulation of an 8×8 High Density-sEMG (HD-sEMG) grid and a twitch based force model for the muscle force generation. The HD-sEMG signals as well as the corresponding force signals were simulated in isometric non-fatiguing conditions and were based on the Biceps Brachii (BB) muscle properties. A total of 10 isometric constant contractions of 5s were simulated for each configuration of parameters. The Root Mean Squared (RMS) value was computed in order to quantify the sEMG amplitude. Then, an image segmentation method was used for data fusion of the 8×8 RMS maps. In addition, a comparative study between recent modeling propositions and the model proposed in this study is presented. The evaluation was made by computing the Normalized Root Mean Squared Error (NRMSE) of their fitting to the simulated relationship functions. Our results indicated that the relationship between the RMS (mV) and muscle force (N) can be modeled using a 3rd degree polynomial equation. Moreover, it appears that the obtained coefficients are patient-specific and dependent on physiological, anatomical and neural parameters.

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.

Comparison of the Spasmolytic Effects of Jakyak-Gamcho Decoctions Derived via Different Extractants

Aim. To investigate whether differences in the amounts of effective index components in Jakyak-Gamcho decoctions derived via extraction with either water or ethanol were associated with differential spasmolytic effectiveness. Methods. The amounts of effective index components (paeoniflorin, benzoic acid, glycyrrhizin, and isoliquiritin) contained in water-extracted Jakyak-Gamcho decoction and 70% ethanol-extracted Jakyak-Gamcho decoction were compared by high-performance liquid chromatography. Muscle cramp reduction rates were compared between the two decoctions by comparing the degrees of muscle contraction, measured as the tension developed during electrical stimulation, before and 1 and 2 h after injection in rats. Results. The relative amounts of effective index components were, on average, about 43% higher in the 70% ethanol-extracted decoction than in the water-extracted decoction. Two hours after injection, 0.25 g/kg of 70% ethanol-extracted decoction produced a significantly greater spasmolytic effect than 0.25 g/kg of water-extracted Jakyak-Gamcho decoction or distilled water (both p < 0.05). Conclusion. Differences in the amounts of effective index components resulting from the use of different extractants were associated with differences in spasmolytic effectiveness. Hence, it may be worthwhile to investigate alternative extraction methods in terms of extraction efficiency and in vivo effectiveness for various herbal medicines in the future.

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.

Concomitant changes in afterhyperpolarization and twitch following repetitive stimulation of fast motoneurones and motor units

The study aimed at determining changes in a course of motoneuronal afterhyperpolarization (AHP) and in contractile twitches of motor units (MUs) during activity evoked by increasing number of stimuli (from 1 to 5), at short interspike intervals (5 ms). The stimulation was applied antidromically to spinal motoneurones or to isolated axons of MUs of the medial gastrocnemius muscle within two separate series of experiments on anesthetized rats. Alterations in the amplitude and time parameters of the AHP of successive spikes were compared to changes in force and time course of successive twitches obtained by mathematical subtraction of tetanic contractions evoked by one to five stimuli. The extent of changes of the studied parameters depended on a number of applied stimuli. The maximal modulation of the AHP and twitch parameters (a prolongation and an increase in the AHP and twitch amplitudes) was typically observed after the second pulse, while higher number of pulses at the same frequency did not induce so prominent changes. One may conclude that changes observed in parameters of action potentials of motoneurons are concomitant to changes in contractile properties of MU twitches. This suggests that both modulations of the AHP and twitch parameters reflect mechanisms leading to force development at the beginning of MU activity.

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".

Modelling the isometric force response to multiple pulse stimuli in locust skeletal muscle

An improved model of locust skeletal muscle will inform on the general behaviour of invertebrate and mammalian muscle with the eventual aim of improving biomedical models of human muscles, embracing prosthetic construction and muscle therapy. In this article, the isometric response of the locust hind leg extensor muscle to input pulse trains is investigated. Experimental data was collected by stimulating the muscle directly and measuring the force at the tibia. The responses to constant frequency stimulus trains of various frequencies and number of pulses were decomposed into the response to each individual stimulus. Each individual pulse response was then fitted to a model, it being assumed that the response to each pulse could be approximated as an impulse response and was linear, no assumption were made about the model order. When the interpulse frequency (IPF) was low and the number of pulses in the train small, a second-order model provided a good fit to each pulse. For moderate IPF or for long pulse trains a linear third-order model provided a better fit to the response to each pulse. The fit using a second-order model deteriorated with increasing IPF. When the input comprised higher IPFs with a large number of pulses the assumptions that the response was linear could not be confirmed. A generalised model is also presented. This model is second-order, and contains two nonlinear terms. The model is able to capture the force response to a range of inputs. This includes cases where the input comprised of higher frequency pulse trains and the assumption of quasi-linear behaviour could not be confirmed.

Isometric force generated by locust skeletal muscle: responses to single stimuli

A mathematical model of the locust hind leg extensor muscle is described. The model accounts for the force response of the muscle to well-separated input stimuli under isometric conditions. Experimental data was collected by stimulating the extensor muscle and measuring the force generated at the tibia. In developing a model it was assumed that the response to a single isolated stimulus was linear. A linear model was found to fit well to the response to an isolated stimulus. No assumptions were made about the model order and models of various order were fitted to data in the frequency domain, using a least squares fit. The stimulus can be approximated as an impulse, with the response to each stimulus well described by a linear second-order system. Using a third-order model provided a better fit to data, but the improvement in fit was marginal and the model uses one extra parameter. A fourth-order model, which is often used to describe the behaviour of isometric muscle was found to overfit the data. Using a second-order model provides a simpler way of describing the behaviour of an isometric twitch.

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.

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

In the present study a previously proposed model of a twitch based on an analytical function with four-parameters (lead, contraction and half-relaxation times and maximum force of the twitch) was validated on 115 motor units (MUs), divided into slow (S), fast-fatigue resistant (FR) and fast fatigable (FF) types. The original records were collected from electrophysiological experiments performed on MUs from the medial gastrocnemius muscle of five rats. Besides the easy calculation of the twitch parameters and their variability, the usefulness of the model was confirmed by eliminating artifacts and noise in the original twitch records, as well as by calculations of the velocity of force increase and decrease, the area under force records, and by normalization of all twitches with respect to the maximal force and contraction time. It was concluded that: (1) the four-parameter twitch model describes precisely the individual contractions of various MUs; (2) all physiological twitch parameters are distributed continuously and located within overlapping intervals for different MU types; this distribution is not linear, but exponential; (3) S MUs can be distinguished from fast ones on the basis of some twitch parameters (contraction and half-relaxation times, velocity of contraction), but the same cannot be applied for FF and FR MUs; (4) the analysis of the normalized twitches reveals the differences in shapes for different types of MUs, which shows that twitches of different MUs cannot be obtained from one standard pattern scaled in time and force. These results may have functional implications for studying effectiveness of twitch summation during tetanic contractions and the work performed by various types of MUs.

Variability of successive contractions subtracted from unfused tetanus of fast and slow motor units

Stimulation of motor units (MUs) with repeated pulses evokes tetanic contractions, which consist of overlapping mechanical responses. The summation of these responses into tetanus is a nonlinear process due to the dynamic changes in the amplitudes and time parameters of the successive components. In order to study these changes, two MUs (one fast and one slow) of rat medial gastrocnemius muscle were stimulated with a progressively increasing number of pulses, from one (i=1) to sixteen (i=16) at a frequency of 15 Hz for the slow MU and 60 Hz for the fast MU. The individual responses were calculated by subtracting the (i)th from the (i+1)th tetanus recording. The contractions obtained following subtraction were modeled using a novel 6-parameter analytical function. The main conclusions of this study are (1) the newly presented analytical function is able to precisely describe the variable shape of all subtracted experimental contractions; (2) the shapes of successive contractions are variable and the subtracted contractions differ from the individual twitches; (3) as the pulse number increases, the parameters of the subtracted contractions change in a different manner for the slow and fast MUs: for the slow MU, the maximal forces and the time parameters increase considerably up to the 4th response, after which they remain nearly constant or show only a slight increase; for the fast MU, the maximal forces and durations also increase, whereas the remaining time parameters initially increase and then maintain a constant level or decrease, which explains the sag phenomenon visible in the unfused tetanus of fast MUs.

Prediction of summation in incompletely fused tetanic contractions of rat muscle

Summation is the accumulating contractile force resulting from sequential activations applied to a muscle without sufficient interval to permit complete relaxation. The purpose of this study was to evaluate summation in the rat medial gastrocnemius muscle, and to determine if the contractile responses during summation could be predicted from the relationship between force and activation pattern. In the first part of this study, the consistency of summation in the rat gastrocnemius muscle was assessed and prediction equations were derived. The second part compared predicted summation with actual contractions obtained in a new set experiments. Summation was assessed by calculation of the contractile response, per stimulation, for up to five stimulating pulses at these frequencies: 20, 40, 60 and 80Hz. This was done by subtraction of the force transient for j-1 pulses of stimulation (where j=1-5 pulses) from the force response with j pulses of stimulation. Each of these force differences was evaluated for peak rate of force development, contraction time and half-relaxation time. Contraction and half-relaxation times changed by only a small magnitude from values obtained for the twitch. Peak rate of force development was proportional to the active force for all force transients obtained by subtraction. The force per activation increased from the first to the fifth stimulus, and was dependent on interpulse delay. In the second series of experiments, the predicted force was related to the actual force for brief tetanic contractions at 40, 50 and 60Hz (r(2)=0.875). These experiments demonstrate that the force response to sequential activations is consistent and predictable. Summation can be predicted, knowing only the amplitude of the twitch contraction and the relationship between delay and force for each activating stimulus.