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.     

Estimation of the error between experimental tetanic force curves of MUs of rat medial gastrocnemius muscle and their models by summation of equal successive contractions

More accurate muscle models require appropriate modelling of individual twitches of motor units (MUs) and their unfused tetanic contractions. It was shown in our previous papers, using a few MUs, that modelling of unfused tetanic force curves by summation of equal twitches is not accurate, especially for slow MUs. The aim of this study was to evaluate this inaccuracy using a statistical number of MUs of the rat medial gastrocnemius muscle (15 of slow, 15 of fast resistant and 15 of fast fatigable type). Tetanic contractions were evoked by trains of 41 stimuli at random interpulse intervals and different mean frequencies, resembling discharge patterns observed during natural muscle activity. The tetanic curves were calculated by the summation of equal twitches according to the respective experimental patterns. The previously described 6-parameter analytical function for twitch modelling was used. Comparisons between the experimental and the modelled curves were made using two coefficients: the fit coefficient and the area coefficient. The errors between modelled and experimental tetanic forces were substantially different between the three MU types. The error was the most significant for slow MUs, which develop much higher forces in real contractions than could be predicted based on the summation of equal twitches, while the smallest error was observed for FF MUs – their recorded tetanic forces were similar to those predicted by modelling. The obtained results indicate the importance of the inclusion of the type-specific non-linearity in the summation of successive twitch-like contractions of MUs in order to increase the reliability of modelling skeletal muscle force.     

Summation of slow motor unit forces at constant and variable interpulse intervals in rat soleus muscle

Effects of the summation of forces generated by functionally isolated slow-twitch motor units (MU) of the rat soleus muscle were examined in this study. Initially, the twitch, fused tetanic and unfused tetanic contractions evoked by trains of stimuli at variable interpulse intervals were recorded for each MU. Then, two, three or four MUs were co-activated, and the recorded forces were compared to the algebraic sum of the forces of individual MUs. The mean cumulative force of twitches and the mean cumulative force of fused tetani were not statistically different from the respective algebraic sums of forces, which revealed a high degree of linearity in the summation. However, relaxation of the recorded tetanic contractions (either fused or unfused) was faster than that predicted by the linear summation of individual contractions. Moreover, for twitch and tetanic contractions, a tendency to shorten relaxation with an increasing number of co-active MUs was noted. The results indicate that forces of rat soleus slow MUs sum up more linearly than in the respective cat muscle as well as more linearly than for fast MUs in the medial gastrocnemius muscle.     

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.     

Time-related changes of motor unit properties in the rat medial gastrocnemius muscle after spinal cord injury. I. Effects of total spinal cord transection

The contractile properties of motor units (MUs) were electrophysiologically investigated in the medial gastrocnemius (MG) muscle in 17 Wistar three-month-old female rats: 14, 30, 90 and 180 days after the total transection of the thoracic spinal cord and compared to those in intact (control) rats. A sag phenomenon, regularly observed in unfused tetani of fast units in intact animals at 40 Hz stimulation, almost completely disappeared in spinal rats. Therefore, the MUs of intact and spinal rats were classified as fast or slow types basing on 20 Hz tetanus index, the value of which was lower or equal 2.0 for fast and higher than 2.0 for slow MUs. The MUs composition of MG muscle changed with time after the spinal cord transection: an increasing proportion of fast fatigable (FF) units starting one month after injury and a disappearance of slow (S) units within the three months were observed. In all MUs investigated the twitch contraction and half-relaxation time were significantly prolonged after injury (p < 0.01, Mann–Whitney U-test). Moreover, a decrease of the fatigue index for fast resistant (FR) and slow MUs was observed in subsequent groups of spinal rats. No significant changes were found between twitch forces in all MU types of spinal animals (p > 0.05). However, due to a decrease of the maximal tetanic force, a significant rise of the twitch-to-tetanus ratio of all MUs in spinal rats was detected (p < 0.01). The considerable reduction of ability to potentiate the force was noticed for fast, especially FF type MUs. In conclusion, the spinal cord transection leads to changes in the proportion of the three MU types in rat MG muscle. The majority of changes in MUs’ contractile properties were developed progressively with time after the spinal cord injury. However, the most intensive alterations of twitch-time parameters were observed in rats one month after the transection.     

Changes in the properties of mechanomyographic signals and in the tension during the fatigue test of rat medial gastrocnemius muscle motor units

The influence of activity-related changes in tension on properties of the mechanomyogram (MMG) was investigated in fast fatigable, fast resistant and slow motor units (MUs). A standard fatigue test was used in which rhythmically repeated unfused tetani were evoked. The amplitudes of the rise in tension of the first and the last contraction within the unfused tetanus and the amplitudes of accompanying signals in MMG were calculated. For fast fatigable MUs a parallel decrease in the amplitudes of both analysed contractions and in the amplitudes of accompanying MMG signals during the fatigue test was observed. For majority of fast resistant MUs at the beginning of the fatigue test a potentiation occurred and this phenomenon increased the tension of the first contraction and of the peak tetanic tension. However, the potentiation coincided also with a decrease of the amplitude of the last contraction in the tension recording of an unfused tetanus. The MMG reflected both, the increase of amplitude of the first contraction and the decrease of the amplitude of the further contractions within the tetanus. The single twitch contraction evoked immediately before and after the fatigue test was additionally recorded. A decrease (fatigue) or an increase (potentiation) of the twitch tension after the fatigue test was reflected by a decrease or an increase in the amplitude of MMG, respectively. However, the fatigue failed to change significantly the time parameters of MMG. To conclude, fatigue and potentiation can occur during activity of fast MUs and both these phenomena involve changes in the amplitude of oscillations in tension of unfused tetani which are reflected in MMG.     

Summation of motor unit forces in rat medial gastrocnemius muscle

The summation of contractile forces of motor units (MUs) was analyzed by comparing the recorded force during parallel stimulation of two and four individual MUs or four groups of MUs to the algebraic sum of their individual forces. Contractions of functionally-isolated single MUs of the medial gastrocnemius muscle were evoked by electrical stimulation of thin filaments of the split L5 or L4 ventral roots of spinal nerves. Additionally, contractions of large groups of MUs were evoked by stimuli delivered to four parts of the divided L5 ventral root. Single twitches, 40 Hz unfused tetani, and 150 Hz fused maximum tetani were recorded. In these experimental situations the summation was more effective for unfused tetani than for twitches or maximum tetani. The results obtained for pairs of MUs were highly variable (more- or less-than-linear summation), but coactivation of more units led to progressively weaker effects of summation, which were usually less-than-linear in comparison to the algebraic sums of the individual forces. The variability of the results highlights the importance of the structure of the muscle and the architecture of its MUs. Moreover, the simultaneous activity of fast and slow MUs was considerably more effective than that of two fast units.     

A New Method for Nonlinear Dynamic Analysis of the Multi-kinetics Neural Mass Model

ObjectiveThe aim was to use a new method to analyze the nonlinear dynamic characteristics of the multi-kinetics neural mass model. We hope that this new method can be as an auxiliary judgment tool for the diagnosis of brain diseases and the identification of brain activity states.MethodsWe apply the Lorenz plot to analyze the nonlinear dynamic characteristics of electroencephalogram (EEG) signals from the multi-kinetics neural mass models. The standard deviations in two orthogonal directions of the Lorenz plot are further used to quantify the nonlinear dynamic characteristics of EEG signals.ResultsThe results show that the normalized signal frequency power spectrum may not be able to distinguish normal EEG signals and epileptiform spikes, but the Lorenz plot can distinguish the normal EEG signals and epileptiform spikes effectively. For EEG signals with multi-rhythms, the Lorenz plot of all the simulated signals are oval, but the value of SD1/SD2 increases monotonically when the multi-rhythm EEG signals change from low frequency to high frequency.ConclusionThe Lorenz plot of EEG signals with different rhythms presents different distribution. It is an effective nonlinear analysis method for EEG signals.     

Simulation analysis of interference EMG during fatiguing voluntary contractions. Part I: What do the intramuscular spike amplitude–frequency histograms reflect?

Decline in amplitude of EMG signals and in the rate of counts of intramuscularly recorded spikes during fatigue is often attributed to a progressive reduction of the neural drive only. As a rule, alterations in intracellular action potential (IAP) are not taken into account. To test correctness of the hypothesis, the effect of various discharge frequency patterns as well as changes in IAP shape and muscle fibre propagation velocity (MFPV) on the spike amplitude-frequency histogram of intramuscular interference EMG signals were simulated and analyzed. It was assumed that muscle was composed of four types of motor units (MUs): slow-twitch fatigue resistant, fast-twitch fatigue resistant, fast intermediate, and fast fatigable. MFPV and IAP duration at initial stage before fatigue as well as their changes differed for individual MU types. Fatigability of individual MU types in normal conditions as well as in the case of ischaemic or low oxygen conditions due to restricted blood flow was also taken into account. It was found that spike amplitude-frequency histogram is poorly sensitive to MU firing frequency, while it is highly sensitive to IAP profile lengthening. It is concluded that spike amplitude-frequency analysis can hardly provide a correct measure of MU rate-coding pattern during fatigue.     

Glutamate Regulates the Frequency of Spontaneous Synchronized Ca<Superscript>2+</Superscript> Spikes Through Group II Metabotropic Glutamate Receptor in Cultured Mouse Cortical Networks

1. Synchronized spontaneous intracellular Ca²⁺ spikes in networked neurons are believed to play a major role in the development and plasticity of neural circuits. Glutamate-induced signals through the ionotropic glutamate receptors (iGluRs) are profoundly involved in the generation of synchronized Ca²⁺ spikes.1 2. In this study, we examined the involvement of metabotropic glutamate receptors (mGluRs) in cultured mouse cortical neurons. We pharmacologically revealed that glutamate-induced signals through inclusive mGluRs decreased the frequency of Ca²⁺ spikes. Further experiments indicated that this suppressive effect on the spike frequency was mainly due to the signal through group II mGluR, inactivation of adenylate cyclase-cAMP-PKA signaling pathway. Group I mGluR had little involvement in the spike frequency.3. Taken together, glutamate generates the synchronized Ca²⁺ spikes through iGluRs and modulates simultaneously their frequency through group II mGluR–adenylate cyclase–cAMP–PKA signaling pathway in the present in vitro neural network. These results provide the evidence of the profound role of group II mGluR in the spontaneous and synchronous neural activities.     

The refractory periods and threshold potentials of sequential spikes measured by whole-cell recording

Neurons in the central nervous system are thought to program neural language via firing sequential spikes for guiding animal behaviors. The quantitative profiles of spike intrinsic properties are critically important to understand spike programming. We developed approaches with whole-cell recordings to measure the threshold potentials and refractory periods (RPs) of sequential spikes, and to analyze the relationships of these factors with spike timing precision and capacity at the regular-spiking and fast-spiking neurons in cortical slice. The RPs and threshold potentials of sequential spikes at these two groups of neurons are different and are linearly correlated with spike timing precision and capacity. These data suggest that RPs and threshold potentials essentially navigate the spike programming for the precise and loyal encoding of meaningful neural signals. Our study provides the avenues for decoding the spectrum of the neural signals quantitatively.     

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

Repeated stimulation of motor units (MUs) causes an increase of the force output that cannot be explained by linear summation of equal twitches evoked by the same stimulation pattern. To explain this phenomenon, an algorithm for reconstructing the individual twitches, that summate into an unfused tetanus is described in the paper. The algorithm is based on an analytical function for the twitch course modeling. The input parameters of this twitch model are lead time, contraction and half-relaxation times and maximal force. The measured individual twitches and unfused tetani at 10, 20, 30 and 40 Hz stimulation frequency of three rat motor units (slow, fast resistant to fatigue and fast fatigable) are processed. It is concluded that: (1) the analytical function describes precisely the course of individual twitches; (2) the summation of equal twitches does not follow the results from the experimentally measured unfused tetani, the differences depend on the type of the MU and are bigger for higher values of stimulation frequency and fusion index; (3) the reconstruction of individual twitches from experimental tetanic records can be successful if the tetanus is feebly fused (fusion index up to 0.7); (4) both the maximal forces and time parameters of individual twitches subtracted from unfused tetani change and influence the course of each tetanus. A discrepancy with respect to the relaxation phase was observed between experimental results and model prediction for tetani with fusion index exceeding 0.7. This phase was predicted longer than the experimental one for better fused tetani. Therefore, a separate series of physiological experiments and then, more complex model are necessary for explanation of this distinction.     

Time-related changes of motor unit properties in the rat medial gastrocnemius muscle after the spinal cord injury. II. Effects of a spinal cord hemisection

The contractile properties of motor units (MUs) were investigated in the medial gastrocnemius (MG) muscle in rats after the spinal cord hemisection at a low thoracic level. Hemisected animals were divided into 4 groups: 14, 30, 90 and 180 days after injury. Intact rats formed a control group. The mass of the MG muscle did not change significantly after spinal cord hemisection, hind limb locomotor pattern was almost unchanged starting from two weeks after injury, but contractile properties of MUs were however altered. Contraction time (CT) and half-relaxation time (HRT) of MUs were prolonged in all investigated groups of hemisected rats. The twitch-to-tetanus ratio (Tw/Tet) of fast MUs after the spinal cord hemisection increased. For slow MUs Tw/Tet values did not change in the early stage after the injury, but significantly decreased in rats 90 and 180 days after hemisection. As a result of hemisection the fatigue resistance especially of slow and fast resistant MU types was reduced, as well as fatigue index (Fat I) calculated for the whole examined population of MUs decreased progressively with the time. After spinal cord hemisection a reduced number of fast MUs presented the sag at frequencies 30 and 40 Hz, however more of them revealed sag in 20 Hz tetanus in comparison to control group. Due to considerable changes in twitch contraction time and disappearance of sag effect in unfused tetani of some MUs in hemisected animals, the classification of MUs in all groups of rats was based on the 20 Hz tetanus index (20 Hz Tet I) but not on the standard criteria usually applied for MUs classification. MU type differentiations demonstrated some clear changes in MG muscle composition in hemisected animals consisting of an increase in the proportion of slow MUs (likely due to an increased participation of the studied muscle in tonic antigravity activity) together with an increase in the percentage of fast fatigable MUs.     

Role of A-type K+ channels in spike broadening observed in soma and axon of Hermissenda type-B photoreceptors: A simulation study

In Hermissenda type-B photoreceptors, the spike is generated in the axon and back-propagated to the soma, resulting in smaller somatic spikes. Experimentally, blocking the A-type K⁺ current (I_K,A) results in broadening of somatic spikes. Similarly, in a compartmental model of the photoreceptor, reducing the maximum A-type K⁺ conductance (g_K,Amax) results in broadening of somatic spikes. However, simulations predict that little or no broadening of axonal spikes occurs when g_K,Amax is reduced. The results can be explained by the voltage-dependent properties of I_K,A and the different potential ranges that the somatic and axonal spike traverse. Because of the steeper I-V curve and faster activation of the K⁺ channels at higher potentials, the recruitment of additional K⁺ channels in the axon is able to compensate for the decrease in K⁺ conductance, yielding less spike broadening. These results also support the idea that spike duration in the axon may not be reliably inferred based upon recordings collected from the soma. Action Editor: Jonathan D. Victor     

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.     

An information-geometric framework for statistical inferences in the neural spike train space

Statistical inferences are essentially important in analyzing neural spike trains in computational neuroscience. Current approaches have followed a general inference paradigm where a parametric probability model is often used to characterize the temporal evolution of the underlying stochastic processes. To directly capture the overall variability and distribution in the space of the spike trains, we focus on a data-driven approach where statistics are defined and computed in the function space in which spike trains are viewed as individual points. To this end, we at first develop a parametrized family of metrics that takes into account different warpings in the time domain and generalizes several currently used spike train distances. These new metrics are essentially penalized L ^p norms, involving appropriate functions of spike trains, with penalties associated with time-warping. The notions of means and variances of spike trains are then defined based on the new metrics when p = 2 (corresponding to the “Euclidean distance”). Using some restrictive conditions, we present an efficient recursive algorithm, termed Matching-Minimization algorithm, to compute the sample mean of a set of spike trains with arbitrary numbers of spikes. The proposed metrics as well as the mean spike trains are demonstrated using simulations as well as an experimental recording from the motor cortex. It is found that all these methods achieve desirable performance and the results support the success of this novel framework.     

Monte Carlo simulation using PRIMO code as a tool for checking the credibility of commissioning and quality assurance of 6 MV TrueBeam STx varian LINAC

AimTo validate and implement Monte Carlo simulation using PRIMO code as a tool for checking the credibility of measurements in LINAC initial commissioning and routine Quality Assurance (QA). Relative and absolute doses of 6 MV photon beam from TrueBeam STx Varian Linear Accelerator (LINAC) were simulated and validated with experimental measurement, Analytical Anisotropic Algorithm (AAA) calculation, and golden beam.Methods and MaterialsVarian phase-space files were imported to the PRIMO code and four blocks of jaws were simulated to determine the field size of the photon beam. Water phantom was modeled in the PRIMO code with water equivalent density. Golden beam data, experimental measurement, and AAA calculation results were imported to PRIMO code for gamma comparison.ResultsPRIMO simulations of Percentage Depth Dose (PDD) and in-plane beam profiles had good agreement with experimental measurements, AAA calculations and golden beam. However, PRIMO simulations of cross-plane beam profiles have a better agreement with AAA calculation and golden beam than the experimental measurement. Furthermore, PRIMO simulations of absolute dose agreed well with experimental results with ±0.8% uncertainty.ConclusionThe PRIMO code has good accuracy and is appropriate for use as a tool to check the credibility of beam scanning and output measurement in initial commissioning and routine QA.     

Spike-sorting analysis of neural electrical signals evoked by acupuncture based on model

Acupuncturing the Zusanli (ST 36) point with different types of manual acupuncture manipulations (MAs) and different frequencies can evoke a lot of neural response activities in spinal dorsal root neurons. The action potential is the basic unit of communication in the neural response process. With the rapid development of the electrode acquisition technology, we can simultaneously obtain neural electrical signals of multiple neurons in the target area. So it is crucial to extract spike trains of each neuron from raw recorded data. To solve the problem of variability of the spike waveform, this paper adopts a optimization algorithm based on model to improve the wave-cluster algorithm, which can provide higher accuracy and reliability. Further, through this optimization algorithm, we make a statistical analysis on spike events evoked by different MAs. Results suggest that numbers of response spikes under reinforcing manipulations are far more than reducing manipulations, which mainly embody in synchronous spike activities.     

多通道神经元锋电位检测和分类的新方法

大脑神经元胞外单细胞动作电位(即锋电位)的检测和分类是提取神经元脉冲序列、研究神经系统信息处理机制的关键．为了提高锋电位的检出率和分类的正确性,设计了一种处理多通道锋电位记录信号的算法,用于分析微电极阵列记录的大鼠海马神经元锋电位信号,电极阵列上的测量点排列紧密,4个通道可以同时记录到来自相同神经元的信号．该算法首先利用一种多通道阈值检测法检出四通道记录信号中的锋电位,然后利用一种基于复合锋电位的主成分特征参数分类法将锋电位分类．仿真数据和实验记录信号的检验结果表明：与相应的单通道算法相比,该算法的锋电位检出率和分类的正确性显著提高,并且可以增加单次实验测得的神经元数目．因此,该算法为实现神经元锋电位的自动检测提供了一种简单有效的新 方法．     

VolPy: Automated and scalable analysis pipelines for voltage imaging datasets

Voltage imaging enables monitoring neural activity at sub-millisecond and sub-cellular scale, unlocking the study of subthreshold activity, synchrony, and network dynamics with unprecedented spatio-temporal resolution. However, high data rates (>800MB/s) and low signal-to-noise ratios create bottlenecks for analyzing such datasets. Here we present VolPy, an automated and scalable pipeline to pre-process voltage imaging datasets. VolPy features motion correction, memory mapping, automated segmentation, denoising and spike extraction, all built on a highly parallelizable, modular, and extensible framework optimized for memory and speed. To aid automated segmentation, we introduce a corpus of 24 manually annotated datasets from different preparations, brain areas and voltage indicators. We benchmark VolPy against ground truth segmentation, simulations and electrophysiology recordings, and we compare its performance with existing algorithms in detecting spikes. Our results indicate that VolPy’s performance in spike extraction and scalability are state-of-the-art.