Influences of premotoneuronal command statistics on the scaling of motor output variability during isometric plantar flexion

NeuroMechanics: Electrophysiological and computational methods to accurately estimate the neural drive to muscles in humans in vivo

The ultimate neural signal for muscle control is the neural drive sent from the spinal cord to muscles. This neural signal comprises the ensemble of action potentials discharged by the active spinal motoneurons, which is transmitted to the innervated muscle fibres to generate forces. Accurately estimating the neural drive to muscles in humans in vivo is challenging since it requires the identification of the activity of a sample of motor units (MUs) that is representative of the active MU population. Current electrophysiological recordings usually fail in this task by identifying small MU samples with over-representation of higher-threshold with respect to lower-threshold MUs. Here, we describe recent advances in electrophysiological methods that allow the identification of more representative samples of greater numbers of MUs than previously possible. This is obtained with large and very dense arrays of electromyographic electrodes. Moreover, recently developed computational methods of data augmentation further extend experimental MU samples to infer the activity of the full MU pool. In conclusion, the combination of new electrode technologies and computational modelling allows for an accurate estimate of the neural drive to muscles and opens new perspectives in the study of the neural control of movement and in neural interfacing.

Model-based closed-loop control of thalamic deep brain stimulation

Introduction: Closed-loop control of deep brain stimulation (DBS) is beneficial for effective and automatic treatment of various neurological disorders like Parkinson's disease (PD) and essential tremor (ET). Manual (open-loop) DBS programming solely based on clinical observations relies on neurologists' expertise and patients' experience. Continuous stimulation in open-loop DBS may decrease battery life and cause side effects. On the contrary, a closed-loop DBS system uses a feedback biomarker/signal to track worsening (or improving) of patients' symptoms and offers several advantages compared to the open-loop DBS system. Existing closed-loop DBS control systems do not incorporate physiological mechanisms underlying DBS or symptoms, e.g., how DBS modulates dynamics of synaptic plasticity. Methods: In this work, we propose a computational framework for development of a model-based DBS controller where a neural model can describe the relationship between DBS and neural activity and a polynomial-based approximation can estimate the relationship between neural and behavioral activities. A controller is used in our model in a quasi-real-time manner to find DBS patterns that significantly reduce the worsening of symptoms. By using the proposed computational framework, these DBS patterns can be tested clinically by predicting the effect of DBS before delivering it to the patient. We applied this framework to the problem of finding optimal DBS frequencies for essential tremor given electromyography (EMG) recordings solely. Building on our recent network model of ventral intermediate nuclei (Vim), the main surgical target of the tremor, in response to DBS, we developed neural model simulation in which physiological mechanisms underlying Vim-DBS are linked to symptomatic changes in EMG signals. By using a proportional-integral-derivative (PID) controller, we showed that a closed-loop system can track EMG signals and adjust the stimulation frequency of Vim-DBS so that the power of EMG reaches a desired control target. Results and discussion: We demonstrated that the model-based DBS frequency aligns well with that used in clinical studies. Our model-based closed-loop system is adaptable to different control targets and can potentially be used for different diseases and personalized systems.

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.

Effects of voluntary contraction on the soleus H-reflex of different amplitudes in healthy young adults and in the elderly

A number of H-reflex studies used a moderate steady voluntary contraction in an attempt to keep the motoneuron pool excitability relatively constant. However, it is not clear whether the voluntary muscle activation itself represents a confounding factor for the elderly, as a few ongoing mechanisms of reflex modulation might be compromised. Further, it is well-known that the amount of either inhibition or facilitation from a given conditioning depends on the size of the test H-reflex. The present study aimed at evaluating the effects of voluntary contraction over a wide range of reflex amplitudes. A significant reflex facilitation during an isometric voluntary contraction of the soleus muscle (15% of the maximal voluntary isometric contraction-MVC) was found for both young adults and the elderly (p < 0.05), regardless of their test reflex amplitudes (considering the ascending limb of the H-reflex recruitment curve-RC). No significant difference was detected in the level of reflex facilitation between groups for all the amplitude parameters extracted from the RC. Simulations with a computational model of the motoneuron pool driven by stationary descending commands yielded qualitatively similar amount of reflex facilitation, as compared to human experiments. Both the experimental and modeling results suggest that possible age-related differences in spinal cord mechanisms do not significantly influence the reflex modulation during a moderate voluntary muscle activation. Therefore, a background voluntary contraction of the ankle extensors (e.g., similar to the one necessary to maintain upright stance) can be used in experiments designed to compare the RCs of both populations. Finally, in an attempt to elucidate the controversy around changes in the direct motor response (M-wave) during contraction, the maximum M-wave (Mmax) was compared between groups and conditions. It was found that the Mmax significantly increases (p < 0.05) during contraction and decreases (p < 0.05) with age arguably due to muscle fiber shortening and motoneuron loss, respectively.

Electrophysiological and functional signs of Guillain-Barré syndrome predicted by a multiscale neuromuscular computational model

Objective. The diagnosis of nerve disorders in humans has relied heavily on the measurement of electrical signals from nerves or muscles in response to electrical stimuli applied at appropriate locations on the body surface. The present study investigated the demyelinating subtype of Guillain-Barré syndrome using multiscale computational model simulations to verify how demyelination of peripheral axons may affect plantar flexion torque as well as the ongoing electromyogram (EMG) during voluntary isometric or isotonic contractions. Approach. Changes in axonal conduction velocities, mimicking those found in patients with the disease at different stages, were imposed on a multiscale computational neuromusculoskeletal model to simulate subjects performing unipodal plantar flexion force and position tasks. Main results. The simulated results indicated changes in the torque signal during the early phase of the disease while performing isotonic tasks, as well as in torque variability after partial conduction block while performing both isometric and isotonic tasks. Our results also indicated changes in the root mean square values and in the power spectrum of the soleus EMG signal as well as changes in the synchronisation index computed from the firing times of the active motor units. All these quantitative changes in functional indicators suggest that the adoption of such additional measurements, such as torques and ongoing EMG, could be used with advantage in the diagnosis and be relevant in providing extra information for the neurologist about the level of the disease. Significance. Our findings enrich the knowledge of the possible ways demyelination affects force generation and position control during plantarflexion. Moreover, this work extends computational neuroscience to computational neurology and shows the potential of biologically compatible neuromuscular computational models in providing relevant quantitative signs that may be useful for diagnosis in the clinic, complementing the tools traditionally used in neurological electrodiagnosis.

Estimation of the firing behaviour of a complete motoneuron pool by combining electromyography signal decomposition and realistic motoneuron modelling

Our understanding of the firing behaviour of motoneuron (MN) pools during human voluntary muscle contractions is currently limited to electrophysiological findings from animal experiments extrapolated to humans, mathematical models of MN pools not validated for human data, and experimental results obtained from decomposition of electromyographical (EMG) signals. These approaches are limited in accuracy or provide information on only small partitions of the MN population. Here, we propose a method based on the combination of high-density EMG (HDEMG) data and realistic modelling for predicting the behaviour of entire pools of motoneurons in humans. The method builds on a physiologically realistic model of a MN pool which predicts, from the experimental spike trains of a smaller number of individual MNs identified from decomposed HDEMG signals, the unknown recruitment and firing activity of the remaining unidentified MNs in the complete MN pool. The MN pool model is described as a cohort of single-compartment leaky fire-and-integrate (LIF) models of MNs scaled by a physiologically realistic distribution of MN electrophysiological properties and driven by a spinal synaptic input, both derived from decomposed HDEMG data. The MN spike trains and effective neural drive to muscle, predicted with this method, have been successfully validated experimentally. A representative application of the method in MN-driven neuromuscular modelling is also presented. The proposed approach provides a validated tool for neuroscientists, experimentalists, and modelers to infer the firing activity of MNs that cannot be observed experimentally, investigate the neuromechanics of human MN pools, support future experimental investigations, and advance neuromuscular modelling for investigating the neural strategies controlling human voluntary contractions.

Neural data-driven model of spinal excitability changes induced by transcutaneous electrical stimulation in spinal cord injury subjects

The efficacy of trans-spinal direct current stimulation (tsDCS) as neurorehabilitation technology remains sub-optimal, partly due to the variability introduced by subject-specific neurophysiological features and stimulation conditions (e.g. electrode placement, stimulating amplitude, polarity, etc.) Hence, current therapies apply tsDCS in an open-loop fashion, resulting in a lack of standardized protocols for controlling elicited neuronal adaptations in closed-loop. Through the combination of high-density electromyogram (HD-EMG) decomposition, biophysical neuronal modelling and metaheuristic optimization, this work presents a novel neural data-driven framework for estimating subject-specific features and quantifying acute neuronal adaptations elicited by tsDCS on incomplete spinal cord injury subjects. This approach consists of calibrating the anatomical parameters (e.g. soma diameter) of in silico $\alpha-$motoneuron (MN) models for firing similarly to in vivo MNs decoded from HD-EMG. Assuming that cathodal-tsDCS elicits excitability changes in the MN pool, while preserving their anatomical parameters, optimization of an excitability gain common to the entire pool was performed to minimize discrepancies in firing rate and recruitment time between in vivo and in silico MNs after cathodal-tsDCS. This quantification of excitability changes on MN models calibrated in a person specific way enables closing the loop with neuro-modulation devices to tailor neurorehabilitation therapies. Clinical Relevance - This framework addresses a key limitation in non-invasive neuro-modulative technologies via a novel model-assisted framework that enables quantifying acute excitability changes induced on a person-specific in silico MN pool calibrated using in vivo neural data. This will enable the development of advanced controllers for modulating targeted neuronal adaptations in closed-loop.

Relationship between vastus medialis Hoffmann reflex excitability and knee extension biomechanics during different tasks in women with patellofemoral pain

BACKGROUND

Impaired knee extension biomechanics and spinal excitability have been reported in women with patellofemoral pain, but their relationship has not been explored. A significant relationship between them could indicate the need for investigating the potential benefits of disinhibitory interventions for women with patellofemoral pain. Thus, this study aimed to investigate the relationship between vastus medialis Hoffmann reflex and (1) maximal isometric, concentric and eccentric knee extensor strength and rate of torque development; (2) knee extensor torque steadiness; and (3) knee extensor moment during functional tasks; in women with patellofemoral pain.

METHODS

Spinal excitability of twenty-four participants was assessed by the amplitude of maximal vastus medialis Hoffmann reflex. Knee extensor strength, rate of torque development and torque steadiness were assessed using an isokinetic dynamometer. Knee extensor moment during step-down and stair descent tasks were obtained using a three-dimensional motion analysis system.

FINDINGS

A moderate negative relationship was found between vastus medialis Hoffmann reflex and knee extensor torque steadiness (r = -0.35; p = 0.05); whereas a moderate positive relationship was found with maximal isometric knee extensor strength (r = 0.37; p = 0.044). No significant relationships were found between vastus medialis Hoffmann reflex and the other variables.

INTERPRETATION

Our findings provide insight on the relationship between spinal excitability and neuromuscular control of maximal and submaximal isometric torque production in women with patellofemoral pain. Conversely, spinal excitability does not seem to be related with dynamic torques and moments of the knee extensors in women with patellofemoral pain.

Optimization framework for the model-based estimation of in vivo α-motoneuron properties in the intact human

The in vivo estimation of α-motoneuron (MN) properties in humans is crucial to characterize the effect that neurorehabilitation technologies may elicit over the composite neuro-musculoskeletal system. Here, we combine biophysical neuronal modelling, high-density electromyography and convolutive blind-source separation along with numerical optimization to estimate geometrical and electrophysiological properties of in vivo decoded human MNs. The proposed methodology implements multi-objective optimization to automatically tune ionic channels conductance and soma size of MN models for minimizing the error between several features of simulated and in vivo decoded MN spike trains. This approach will open new avenues for the closed-loop control of motor restorative technologies such as wearable robots and neuromodulation devices.Clinical Relevance- This work proposes a non-invasive framework for the in vivo estimation of person-specific α-motoneuron properties. This will enable predicting neuronal adaptations in response to neurorehabilitation therapies in the intact human.

Force Steadiness: From Motor Units to Voluntary Actions

Voluntary actions are controlled by the synaptic inputs that are shared by pools of spinal motor neurons. The slow common oscillations in the discharge times of motor units due to these synaptic inputs are strongly correlated with the fluctuations in force during submaximal isometric contractions (force steadiness) and moderately associated with performance scores on some tests of motor function. However, there are key gaps in knowledge that limit the interpretation of differences in force steadiness.

Reliable measurement of incisal bite force for understanding the control of masticatory muscles

OBJECTIVE

In the present study, we aimed at evaluating the steadiness of incisal bite force during isometric contractions of masticatory muscles.

DESIGN

Two separate experiments were carried out in 11 healthy young women. A first experiment was performed to test the reliability of our protocol for measurement of incisal bite force steadiness. The second experiment aimed to evaluate the steadiness of incisal bite force at four submaximal (i.e., percentage of maximum voluntary contraction, MVC) levels (5 %MVC, 10 %MVC, 15 %MVC, and 20 %MVC), along with the bilateral myoelectric activity of two masticatory muscles (temporalis and masseter).

RESULTS

The results from the first experiment showed that our protocol is substantially reliable (intraclass correlation coefficient, ICC > 0.80) for estimating force variability and moderate reliable (0.60 < ICC < 0.80) for estimating spectral properties of force signals. In the second experiment, we found that force standard deviation (SD) increased proportionally to the power of mean force, and coefficient of variation (CoV) was higher at low-intensity contractions and maintained at an approximately constant level for high-intensity contractions. The force-EMG relationships were linear for both muscles at the contraction intensities evaluated in the study (5 %MVC to 20 %MVC), and the median frequency did not change with contraction intensity.

CONCLUSION

Therefore, we presented a reliable method to estimate the incisal bite force, along with additional data on force control and myoelectric activity of jaw elevator muscles during isometric steady contractions.

Neurophysiological correlates of force control improvement induced by sinusoidal vibrotactile stimulation

OBJECTIVE

An optimal level of vibrotactile stimulation has been shown to improve sensorimotor control in healthy and diseased individuals. However, the underlying neurophysiological mechanisms behind the enhanced motor performance caused by vibrotactile stimulation are yet to be fully understood. Therefore, here we aim to evaluate the effect of a cutaneous vibration on the firing behavior of motor units in a condition of improved force steadiness.

APPROACH

Participants performed a visuomotor task, which consisted of low-intensity isometric contractions of the first dorsal interosseous (FDI) muscle, while sinusoidal (175 Hz) vibrotactile stimuli with different intensities were applied to the index finger. High-density surface electromyogram was recorded from the FDI muscle, and a decomposition algorithm was used to extract the motor unit spike trains. Additionally, computer simulations were performed using a multiscale neuromuscular model to provide a potential explanation for the experimental findings.

MAIN RESULTS

Experimental outcomes showed that an optimal level of vibration significantly improved force steadiness (estimated as the coefficient of variation of force). The decreased force variability was accompanied by a reduction in the variability of the smoothed cumulative spike train (as an estimation of the neural drive to the muscle), and the proportion of common inputs to the FDI motor nucleus. However, the interspike interval variability did not change significantly with the vibration. A mathematical approach, together with computer simulation results suggested that vibrotactile stimulation would reduce the variance of the common synaptic input to the motor neuron pool, thereby decreasing the low frequency fluctuations of the neural drive to the muscle and force steadiness.

SIGNIFICANCE

Our results demonstrate that the decreased variability in common input accounts for the enhancement in force control induced by vibrotactile stimulation.

A computer simulation study on the influences of loss and damage of primary muscle spindle afferents on soleus muscle stretch reflex

Sensory loss is detrimental to sensorimotor control. Several studies have reported that loss and/or damage of primary (Ia) muscle spindle afferents significantly influence the stretch reflex responses of leg and foot muscles. However, a systematic experimental evaluation on how the impairment of Ia muscle spindle afferents affects the stretch reflex is difficult due to technical and ethical issues. In the present study, the aim was to use computer simulations of a multiscale neuromusculoskeletal model to investigate how changes in: i) the number of Ia afferents, ii) the synaptic conductance between Ia sensory fibers and spinal motor neurons (MNs), and iii) the conduction velocities (CVs) of Ia afferents, would influence the stretch reflex of a leg muscle (soleus). Simulation results showed that both anatomical and functional loss of Ia afferents exerted an influence on the amplitude of short-latency stretch reflex response (M1) and the late phase of medium-latency response (M2). Additionally, changes in CVs of Ia afferents mainly influenced the latency of M1 and the amplitude of M2. Our findings provide conceptual evidence that a combination of anatomical and functional loss, as well as changes in CVs of Ia afferents due to demyelination, can explain the stretch reflex responses observed in peripheral neuropathies.

Association Between Plantarflexion Torque Variability In Quiet Stance And During Force And Position Tasks

This study examined the association between plantarflexion torque variability during quiet bipedal standing (QS) and during plantarflexion force- and position-matching tasks (FT and PT, respectively). In QS, participants stood still over a force plate, and the mean plantarflexion torque level exerted by each subject in QS (divided by 2 to give the torque due to a single leg) served as the target torque level for right leg FT and PT (performed with the participants seated with their right knee fully extended). During FT participants controlled the force level exerted by the foot against a rigid restraint, while during PT they controlled the angular position of the ankle when sustaining equivalent inertial loads. Standard deviation (SD) of plantarflexion torque was computed from torque signals acquired during periods with and without visual feedback. Significant correlations were found between plantarflexion torque variability in QS and FT (r = 0.8615, p < 0.0001 and r = 0.8838, p = 0.0003 for visual and no visual conditions, respectively) as well as between QS and PT (r = 0.8046, p = 0.003 and r = 0.7332, p = 0.0103 for visual and no visual conditions, respectively), regardless of vision availability. No significant differences were found between the correlations for Qs vs FT and QS vs PT (t(8) = 0.4778, p = 0.6455 and t(8) = 1.6819, p = 0.1310 for visual and no visual conditions, respectively), as assessed by "Hotelling-Williams" tests for equality among dependent correlations. The results indicate that simple measurements of plantarflexion torque fluctuations during FT and PT may be used to estimate balance ability. From a practical standpoint, it is suggested that rehabilitation protocols designed to regain/improve balance function may be based on the performance of FTs or PTs executed in a seated position.

Multiscale modeling of the neuromuscular system: Coupling neurophysiology and skeletal muscle mechanics

Mathematical models and computer simulations have the great potential to substantially increase our understanding of the biophysical behavior of the neuromuscular system. This, however, requires detailed multiscale, and multiphysics models. Once validated, such models allow systematic in silico investigations that are not necessarily feasible within experiments and, therefore, have the ability to provide valuable insights into the complex interrelations within the healthy system and for pathological conditions. Most of the existing models focus on individual parts of the neuromuscular system and do not consider the neuromuscular system as an integrated physiological system. Hence, the aim of this advanced review is to facilitate the prospective development of detailed biophysical models of the entire neuromuscular system. For this purpose, this review is subdivided into three parts. The first part introduces the key anatomical and physiological aspects of the healthy neuromuscular system necessary for modeling the neuromuscular system. The second part provides an overview on state-of-the-art modeling approaches representing all major components of the neuromuscular system on different time and length scales. Within the last part, a specific multiscale neuromuscular system model is introduced. The integrated system model combines existing models of the motor neuron pool, of the sensory system and of a multiscale model describing the mechanical behavior of skeletal muscles. Since many sub-models are based on strictly biophysical modeling approaches, it closely represents the underlying physiological system and thus could be employed as starting point for further improvements and future developments. This article is categorized under: Physiology > Mammalian Physiology in Health and Disease Analytical and Computational Methods > Computational Methods Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models.

Oscillations in neural drive and age-related reductions in force steadiness with a cognitive challenge

A cognitive challenge when imposed during a low-force isometric contraction will exacerbate sex- and age-related decreases in force steadiness, but the mechanism is not known. We determined the role of oscillations in the common synaptic input to motor units on force steadiness during a muscle contraction with a concurrent cognitive challenge. Forty-nine young adults (19-30 yr; 25 women, 24 men) and 36 old adults (60-85 yr; 19 women, 17 men) performed a cognitive challenge (counting backward by 13) during an isometric elbow flexion task at 5% of maximal voluntary contraction. Single-motor units were decomposed from high-density surface EMG recordings. For a subgroup of participants, motor units were matched during control and cognitive challenge trials, so the same motor unit was analyzed across conditions. Reduced force steadiness was associated with greater oscillations in the synaptic input to motor units during both control and cognitive challenge trials ( r = 0.45-0.47, P < 0.01). Old adults and young women showed greater oscillations in the common synaptic input to motor units and decreased force steadiness when the cognitive challenge was imposed, but young men showed no change across conditions (session × age × sex, P < 0.05). Oscillations in the common synaptic input to motor units is a potential mechanism for altered force steadiness when a cognitive challenge is imposed during low-force contractions in young women and old adults. NEW & NOTEWORTHY We found that oscillations in the common synaptic input to motor units were associated with a reduction in force steadiness when a cognitive challenge was imposed during low-force contractions of the elbow flexor muscles in young women and old men and women but not young men. Age- and sex-related muscle weakness was associated with these changes.

Simulation of electromyographic recordings following transcranial magnetic stimulation

Transcranial magnetic stimulation (TMS) is a technique that enables noninvasive manipulation of neural activity and holds promise in both clinical and basic research settings. The effect of TMS on the motor cortex is often measured by electromyography (EMG) recordings from a small hand muscle. However, the details of how TMS generates responses measured with EMG are not completely understood. We aim to develop a biophysically detailed computational model to study the potential mechanisms underlying the generation of EMG signals following TMS. Our model comprises a feed-forward network of cortical layer 2/3 cells, which drive morphologically detailed layer 5 corticomotoneuronal cells, which in turn project to a pool of motoneurons. EMG signals are modeled as the sum of motor unit action potentials. EMG recordings from the first dorsal interosseous muscle were performed in four subjects and compared with simulated EMG signals. Our model successfully reproduces several characteristics of the experimental data. The simulated EMG signals match experimental EMG recordings in shape and size, and change with stimulus intensity and contraction level as in experimental recordings. They exhibit cortical silent periods that are close to the biological values and reveal an interesting dependence on inhibitory synaptic transmission properties. Our model predicts several characteristics of the firing patterns of neurons along the entire pathway from cortical layer 2/3 cells down to spinal motoneurons and should be considered as a viable tool for explaining and analyzing EMG signals following TMS. NEW & NOTEWORTHY A biophysically detailed model of EMG signal generation following transcranial magnetic stimulation (TMS) is proposed. Simulated EMG signals match experimental EMG recordings in shape and amplitude. Motor-evoked potential and cortical silent period properties match experimental data. The model is a viable tool to analyze, explain, and predict EMG signals following TMS.

A latent low-dimensional common input drives a pool of motor neurons: a probabilistic latent state-space model

Motor neurons appear to be activated with a common input signal that modulates the discharge activity of all neurons in the motor nucleus. It has proven difficult for neurophysiologists to quantify the variability in a common input signal, but characterization of such a signal may improve our understanding of how the activation signal varies across motor tasks. Contemporary methods of quantifying the common input to motor neurons rely on compiling discrete action potentials into continuous time series, assuming the motor pool acts as a linear filter, and requiring signals to be of sufficient duration for frequency analysis. We introduce a space-state model in which the discharge activity of motor neurons is modeled as inhomogeneous Poisson processes and propose a method to quantify an abstract latent trajectory that represents the common input received by motor neurons. The approach also approximates the variation in synaptic noise in the common input signal. The model is validated with four data sets: a simulation of 120 motor units, a pair of integrate-and-fire neurons with a Renshaw cell providing inhibitory feedback, the discharge activity of 10 integrate-and-fire neurons, and the discharge times of concurrently active motor units during an isometric voluntary contraction. The simulations revealed that a latent state-space model is able to quantify the trajectory and variability of the common input signal across all four conditions. When compared with the cumulative spike train method of characterizing common input, the state-space approach was more sensitive to the details of the common input current and was less influenced by the duration of the signal. The state-space approach appears to be capable of detecting rather modest changes in common input signals across conditions.NEW & NOTEWORTHY We propose a state-space model that explicitly delineates a common input signal sent to motor neurons and the physiological noise inherent in synaptic signal transmission. This is the first application of a deterministic state-space model to represent the discharge characteristics of motor units during voluntary contractions.

Nonlinear Frequency-Domain Analysis of the Transformation of Cortical Inputs by a Motoneuron Pool-Muscle Complex

Corticomotor coherence in the beta and/or gamma bands has been described in different motor tasks, but the role of descending brain oscillations on force control has been elusive. Large-scale computational models of a motoneuron pool and the muscle it innervates have been used as tools to advance the knowledge of how neural elements may influence force control. Here, we present a frequency domain analysis of a NARX model fitted to a large-scale neuromuscular model by the means of generalized frequency response functions (GFRF). The results of such procedures indicated that the computational neuromuscular model was capable of transforming an oscillatory synaptic input (e.g., at 20 Hz) into a constant mean muscle force output. The nonlinearity uncovered by the GFRFs of the NARX model was responsible for the demodulation of an oscillatory input (e.g., a beta band oscillation coming from the brain and forming the input to the motoneuron pool). This suggests a manner by which brain rhythms descending as command signals to the spinal cord and acting on a motoneuron pool can regulate a maintained muscle force. In addition to the scientific aspects of these results, they provide new interpretations that may further neural engineering applications associated with quantitative neurological diagnoses and robotic systems for artificial limbs.

Reassessment of Non-Monosynaptic Excitation from the Motor Cortex to Motoneurons in Single Motor Units of the Human Biceps Brachii

Corticospinal excitation is mediated by polysynaptic pathways in several vertebrates, including dexterous monkeys. However, indirect non-monosynaptic excitation has not been clearly observed following transcranial electrical stimulation (TES) or cervicomedullary stimulation (CMS) in humans. The present study evaluated indirect motor pathways in normal human subjects by recording the activities of single motor units (MUs) in the biceps brachii (BB) muscle. The pyramidal tract was stimulated with weak TES, CMS, and transcranial magnetic stimulation (TMS) contralateral to the recording side. During tasks involving weak co-contraction of the BB and hand muscles, all stimulation methods activated MUs with short latencies. Peristimulus time histograms (PSTHs) showed that responses with similar durations were induced by TES (1.9 ± 1.4 ms) and CMS (2.0 ± 1.4 ms), and these responses often showed multiple peaks with the PSTH peak having a long duration (65.3% and 44.9%, respectively). Such long-duration excitatory responses with multiple peaks were rarely observed in the finger muscles following TES or in the BB following stimulation of the Ia fibers. The responses obtained with TES were compared in the same 14 BB MUs during the co-contraction and isolated BB contraction tasks. Eleven and three units, respectively, exhibited activation with multiple peaks during the two tasks. In order to determine the dispersion effects on the axon conduction velocities (CVs) and synaptic noise, a simulation study that was comparable to the TES experiments was performed with a biologically plausible neuromuscular model. When the model included the monosynaptic-pyramidal tract, multiple peaks were obtained in about 34.5% of the motoneurons (MNs). The experimental and simulation results indicated the existence of task-dependent disparate inputs from the pyramidal tract to the MNs of the upper limb. These results suggested that intercalated interneurons are present in the spinal cord and that these interneurons might be equivalent to those identified in animal experiments.

Fast Oscillatory Commands from the Motor Cortex Can Be Decoded by the Spinal Cord for Force Control

Oscillations in the beta and gamma bands (13-30 Hz; 35-70 Hz) have often been observed in motor cortical outputs that reach the spinal cord, acting on motoneurons and interneurons. However, the frequencies of these oscillations are above the muscle force frequency range. A current view is that the transformation of the motoneuron pool inputs into force is linear. For this reason possible roles for these oscillations are unclear, since if this transformation is linear, the high frequencies in the motoneuron inputs (e.g., 20 Hz from pyramidal tract neurons) would be filtered out by the muscle and have no effect on force control. A biologically inspired mathematical model of the neuromuscular system was used to investigate the impact of high-frequency cortical oscillatory activity on force control. The model simulation results evidenced that a typical motoneuron pool has a nonlinear behavior that enables the decoding of a high-frequency oscillatory input. An input at a single frequency (e.g., beta band) leads to an increase in the steady-state force generated by the muscle. When the input oscillation was amplitude modulated at a given low frequency, the force oscillated at this frequency. In both cases, the mechanism relies on the recruitment and derecruitment of motor units in response to the oscillatory descending drive. Therefore, the results from this study suggest a potential role in force control for cortical oscillations at frequencies at or above the beta band, despite the low-pass behavior of the muscles.

SIGNIFICANCE STATEMENT

The role of cortical oscillations in motor control has been a long-standing question, one view being that they are an epiphenomenon. Fast oscillations are known to reach the spinal cord, and hence they have been thought to affect muscle behavior. However, experimental limitations have hampered further advances to explain how they could influence muscle force. An approach for such a challenge was adopted in the present research: to study the problem through computer simulations of an advanced biologically compatible mathematical model. Using such a model, we found that the well-known mechanism of recruitment and derecruitment of the spinal cord motoneurons can allow the muscle to respond to cortical oscillations, suggesting that these oscillations are not epiphenomena in motor control.

D1 and D2 Inhibitions of the Soleus H-Reflex Are Differentially Modulated during Plantarflexion Force and Position Tasks

Presynaptic inhibition (PSI) has been shown to modulate several neuronal pathways of functional relevance by selectively gating the connections between sensory inputs and spinal motoneurons, thereby regulating the contribution of the stretch reflex circuitry to the ongoing motor activity. In this study, we investigated whether a differential regulation of Ia afferent inflow by PSI may be associated with the performance of two types of plantarflexion sensoriomotor tasks. The subjects (in a seated position) controlled either: 1) the force level exerted by the foot against a rigid restraint (force task, FT); or 2) the angular position of the ankle when sustaining inertial loads (position task, PT) that required the same level of muscle activation observed in FT. Subjects were instructed to maintain their force/position at target levels set at ~10% of maximum isometric voluntary contraction for FT and 90° for PT, while visual feedback of the corresponding force/position signals were provided. Unconditioned H-reflexes (i.e. control reflexes) and H-reflexes conditioned by electrical pulses applied to the common peroneal nerve with conditioning-to-test intervals of 21 ms and 100 ms (corresponding to D1 and D2 inhibitions, respectively) were evoked in a random fashion. A significant main effect for the type of the motor task (FT vs PT) (p = 0.005, η²_p = 0.603) indicated that PTs were undertaken with lower levels of Ia PSI converging onto the soleus motoneuron pool. Additionally, a significant interaction between the type of inhibition (D1 vs D2) and the type of motor task (FT vs PT) (p = 0.038, η²_p = 0.395) indicated that D1 inhibition was associated with a significant reduction in PSI levels from TF to TP (p = 0.001, η²_p = 0.731), whereas no significant difference between the tasks was observed for D2 inhibition (p = 0.078, η²_p = 0.305). These results suggest that D1 and D2 inhibitions of the soleus H-reflex are differentially modulated during the performance of plantarflexion FT and PT. The reduced level of ongoing PSI during PT suggests that, in comparison to FT, there is a larger reliance on inputs from muscle spindles primary afferents when the neuromuscular system is required to maintain position-controlled plantarflexion contractions.

Divisive gain modulation of motoneurons by inhibition optimizes muscular control

When using muscles, the precision with which force is delivered is as important as the delivery of force itself. Force is regulated by both the number of recruited motoneurons and their spike frequency. While it is known that the recruitment is ordered to reduce variability in force, it remains unclear whether the motoneuron gain, i.e., the slope of the transformation between synaptic input and spiking output, is also modulated to reduce variability in force. To address this issue, we use turtle hindlimb scratching as a model for fine motor control, since this behavior involves precise limb movement to rub the location of somatic nuisance touch. We recorded intracellularly from motoneurons in a reduced preparation where the limbs were removed to increase mechanical stability and the motor nerve activity served as a surrogate for muscle force. We found that not only is the gain of motoneurons regulated on a subsecond timescale, it is also adjusted to minimize variability. The modulation is likely achieved via an expansive nonlinearity between spike rate and membrane potential with inhibition having a divisive influence. These findings reveal a versatile mechanism of modulating neuronal sensitivity and suggest that such modulation is fundamentally linked to optimization.

Spinal mechanisms may provide a combination of intermittent and continuous control of human posture: predictions from a biologically based neuromusculoskeletal model

Several models have been employed to study human postural control during upright quiet stance. Most have adopted an inverted pendulum approximation to the standing human and theoretical models to account for the neural feedback necessary to keep balance. The present study adds to the previous efforts in focusing more closely on modelling the physiological mechanisms of important elements associated with the control of human posture. This paper studies neuromuscular mechanisms behind upright stance control by means of a biologically based large-scale neuromusculoskeletal (NMS) model. It encompasses: i) conductance-based spinal neuron models (motor neurons and interneurons); ii) muscle proprioceptor models (spindle and Golgi tendon organ) providing sensory afferent feedback; iii) Hill-type muscle models of the leg plantar and dorsiflexors; and iv) an inverted pendulum model for the body biomechanics during upright stance. The motor neuron pools are driven by stochastic spike trains. Simulation results showed that the neuromechanical outputs generated by the NMS model resemble experimental data from subjects standing on a stable surface. Interesting findings were that: i) an intermittent pattern of muscle activation emerged from this posture control model for two of the leg muscles (Medial and Lateral Gastrocnemius); and ii) the Soleus muscle was mostly activated in a continuous manner. These results suggest that the spinal cord anatomy and neurophysiology (e.g., motor unit types, synaptic connectivities, ordered recruitment), along with the modulation of afferent activity, may account for the mixture of intermittent and continuous control that has been a subject of debate in recent studies on postural control. Another finding was the occurrence of the so-called “paradoxical” behaviour of muscle fibre lengths as a function of postural sway. The simulations confirmed previous conjectures that reciprocal inhibition is possibly contributing to this effect, but on the other hand showed that this effect may arise without any anticipatory neural control mechanism.

The control of upright stance is a challenging task since the objective is to maintain the equilibrium of an intrinsically unstable biomechanical system. Somatosensory information is used by the central nervous system to modulate muscle contraction, which prevents the body from falling. While the visual and vestibular systems also provide important additional sensory information, a human being with only somatosensory inputs is able to maintain an upright stance. In this study, we used a biologically-based large-scale neuromusculoskeletal model driven only by somatosensory feedback to investigate human postural control from a neurophysiological point of view. No neural structures above the spinal cord were included in the model. The results showed that the model based on a spinal control of posture can reproduce several neuromechanical outcomes previously reported in the literature, including an intermittent muscle activation. Since this intermittent muscular recruitment is an emergent property of this spinal-like controller, we argue that the so-called intermittent control of upright stance might be produced by an interplay between spinal cord properties and modulated sensory inflow.