Simulation system of spinal cord motor nuclei and associated nerves and muscles, in a Web-based architecture

Neural Filtering of Physiological Tremor Oscillations to Spinal Motor Neurons Mediates Short-Term Acquisition of a Skill Learning Task

The acquisition of a motor skill involves adaptations of spinal and supraspinal pathways to alpha motoneurons. In this study, we estimated the shared synaptic contributions of these pathways to understand the neural mechanisms underlying the short-term acquisition of a new force-matching task. High-density surface electromyography (HDsEMG) was acquired from the first dorsal interosseous (FDI; 7 males and 6 females) and tibialis anterior (TA; 7 males and 4 females) during 15 trials of an isometric force-matching task. For two selected trials (pre- and post-skill acquisition), we decomposed the HDsEMG into motor unit spike trains, tracked motor units between trials, and calculated the mean discharge rate and the coefficient of variation of interspike interval (COVISI). We also quantified the post/pre ratio of motor units' coherence within delta, alpha, and beta bands. Force-matching improvements were accompanied by increased mean discharge rate and decreased COVISI for both muscles. Moreover, the area under the curve within alpha band decreased by ∼22% (TA) and ∼13% (FDI), with no delta or beta bands changes. These reductions correlated significantly with increased coupling between force/neural drive and target oscillations. These results suggest that short-term force-matching skill acquisition is mediated by attenuation of physiological tremor oscillations in the shared synaptic inputs. Supported by simulations, a plausible mechanism for alpha band reductions may involve spinal interneuron phase-cancelling descending oscillations. Therefore, during skill learning, the central nervous system acts as a matched filter, adjusting synaptic weights of shared inputs to suppress neural components unrelated to the specific task.

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.

Spectral characterization of human leg EMG signals from an open access dataset for the development of computational models

Large-scale neuromusculoskeletal models have been used for predicting mechanisms underlying neuromuscular functions in humans. Simulations of such models provide several types of signals of practical interest, such as surface electromyographic signals (EMG), which are compared with experimental data for interpretations of neurophysiological phenomena under study. Specifically, realistic characterization of spectral properties of simulated EMG signals is important for achieving powerful inferences, whereas considerations should be taken for myoelectric signals of different muscles. In this study, we characterized spectral properties of surface interference pattern EMG signals and motor unit action potentials (MUAP) acquired from three plantar flexor muscles: Soleus (SO), Medial Gastrocnemius (MG), and Lateral Gastrocnemius (LG); and one dorsiflexor muscle: Tibialis Anterior (TA). Surface EMG signals were acquired from 20 participants using the same convention for electrode placement. Specifically, interference pattern EMG signals were obtained during isometric constant force contractions at 5%, 10% and 20% of maximum voluntary contraction (MVC), whereas surface MUAPs were decomposed from surface EMG signals obtained at low contraction forces. We compared the spectrum median frequency (MDF) estimated from interference pattern EMG signals across muscles and contraction intensities. Additionally, we compared MDF and durations of MUAPs between muscles. Our results showed that MDF of interference pattern EMG signals acquired from TA were higher compared to SO, MG, and LG for all contraction intensities i.e., 5%, 10%, and 20% MVC. Consistently, MUAPs acquired from TA also had higher MDF values and shorter durations compared to the other leg muscles. We provide herein a dataset with the surface MUAPs waveforms and interference pattern EMG signals obtained for this study, which should be useful for implementing and validating the simulation of myoelectrical signals of leg muscles. Importantly, these results indicate that spectral properties of myoelectrical signals should be considered for improving EMG modeling in large-scale neuromusculoskeletal models.

Postinhibitory excitation in motoneurons can be facilitated by hyperpolarization-activated inward currents: A simulation study

Postinhibitory excitation is a transient overshoot of a neuron's baseline firing rate following an inhibitory stimulus and can be observed in vivo in human motoneurons. However, the biophysical origin of this phenomenon is still unknown and both reflex pathways and intrinsic motoneuron properties have been proposed. We hypothesized that postinhibitory excitation in motoneurons can be facilitated by hyperpolarization-activated inward currents (h-currents). Using an electrical circuit model, we investigated how h-currents can modulate the postinhibitory response of motoneurons. Further, we analyzed the spike trains of human motor units from the tibialis anterior muscle during reciprocal inhibition. The simulations revealed that the activation of h-currents by an inhibitory postsynaptic potential can cause a short-term increase in a motoneuron's firing probability. This result suggests that the neuron can be excited by an inhibitory stimulus. In detail, the modulation of the firing probability depends on the time delay between the inhibitory stimulus and the previous action potential. Further, the postinhibitory excitation's strength correlates with the inhibitory stimulus's amplitude and is negatively correlated with the baseline firing rate as well as the level of input noise. Hallmarks of h-current activity, as identified from the modeling study, were found in 50% of the human motor units that showed postinhibitory excitation. This study suggests that h-currents can facilitate postinhibitory excitation and act as a modulatory system to increase motoneuron excitability after a strong inhibition.

Investigating the roles of reflexes and central pattern generators in the control and modulation of human locomotion using a physiologically plausible neuromechanical model

Objective.Studying the neural components regulating movement in human locomotion is obstructed by the inability to perform invasive experimental recording in the human neural circuits. Neuromechanical simulations can provide insights by modeling the locomotor circuits. Past neuromechanical models proposed control of locomotion either driven by central pattern generators (CPGs) with simple sensory commands or by a purely reflex-based network regulated by state-machine mechanisms, which activate and deactivate reflexes depending on the detected gait cycle phases. However, the physiological interpretation of these state machines remains unclear. Here, we present a physiologically plausible model to investigate spinal control and modulation of human locomotion.Approach.We propose a bio-inspired controller composed of two coupled CPGs that produce the rhythm and pattern, and a reflex-based network simulating low-level reflex pathways and Renshaw cells. This reflex network is based on leaky-integration neurons, and the whole system does not rely on changing reflex gains according to the gait cycle state. The musculoskeletal model is composed of a skeletal structure and nine muscles per leg generating movement in sagittal plane.Main results.Optimizing the open parameters for effort minimization and stability, human kinematics and muscle activation naturally emerged. Furthermore, when CPGs were not activated, periodic motion could not be achieved through optimization, suggesting the necessity of this component to generate rhythmic behavior without a state machine mechanism regulating reflex activation. The controller could reproduce ranges of speeds from 0.3 to 1.9 m s-1. The results showed that the net influence of feedback on motoneurons (MNs) during perturbed locomotion is predominantly inhibitory and that the CPGs provide the timing of MNs' activation by exciting or inhibiting muscles in specific gait phases.Significance.The proposed bio-inspired controller could contribute to our understanding of locomotor circuits of the intact spinal cord and could be used to study neuromotor disorders.

Neural-driven activation of 3D muscle within a finite element framework: exploring applications in healthy and neurodegenerative simulations

This paper presents a novel computational framework for neural-driven finite element muscle models, with an application to amyotrophic lateral sclerosis (ALS). The multiscale neuromusculoskeletal (NMS) model incorporates physiologically accurate motor neurons, 3D muscle geometry, and muscle fiber recruitment. It successfully predicts healthy muscle force and tendon elongation and demonstrates a progressive decline in muscle force due to ALS, dropping from 203 N (healthy) to 155 N (120 days after ALS onset). This approach represents a preliminary step towards developing integrated neural and musculoskeletal simulations to enhance our understanding of neurodegenerative and neurodevelopmental conditions through predictive NMS models.

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.

Two motor neuron synergies, invariant across ankle joint angles, activate the triceps surae during plantarflexion

Recent studies have suggested that the nervous system generates movements by controlling groups of motor neurons (synergies) that do not always align with muscle anatomy. In this study, we determined whether these synergies are robust across tasks with different mechanical constraints. We identified motor neuron synergies using principal component analysis (PCA) and cross-correlations between smoothed discharge rates of motor neurons. In part 1, we used simulations to validate these methods. The results suggested that PCA can accurately identify the number of common inputs and their distribution across active motor neurons. Moreover, the results confirmed that cross-correlation can separate pairs of motor neurons that receive common inputs from those that do not receive common inputs. In part 2, 16 individuals performed plantarflexion at three ankle angles while we recorded EMG signals from the gastrocnemius lateralis (GL) and medialis (GM) and the soleus (SOL) with grids of surface electrodes. The PCA revealed two motor neuron synergies. These motor neuron synergies were relatively stable, with no significant differences in the distribution of motor neuron weights across ankle angles (P = 0.62). When the cross-correlation was calculated for pairs of motor units tracked across ankle angles, we observed that only 13.0% of pairs of motor units from GL and GM exhibited significant correlations of their smoothed discharge rates across angles, confirming the low level of common inputs between these muscles. Overall, these results highlight the modularity of movement control at the motor neuron level, suggesting a sensible reduction of computational resources for movement control. KEY POINTS: The CNS might generate movements by activating groups of motor neurons (synergies) with common inputs. We show here that two main sources of common inputs drive the motor neurons innervating the triceps surae muscles during isometric ankle plantarflexions. We report that the distribution of these common inputs is globally invariant despite changing the mechanical constraints of the tasks, i.e. the ankle angle. These results suggest the functional relevance of the modular organization of the CNS to control movements.

Linking cortex and contraction-Integrating models along the corticomuscular pathway

Computational models of the neuromusculoskeletal system provide a deterministic approach to investigate input-output relationships in the human motor system. Neuromusculoskeletal models are typically used to estimate muscle activations and forces that are consistent with observed motion under healthy and pathological conditions. However, many movement pathologies originate in the brain, including stroke, cerebral palsy, and Parkinson's disease, while most neuromusculoskeletal models deal exclusively with the peripheral nervous system and do not incorporate models of the motor cortex, cerebellum, or spinal cord. An integrated understanding of motor control is necessary to reveal underlying neural-input and motor-output relationships. To facilitate the development of integrated corticomuscular motor pathway models, we provide an overview of the neuromusculoskeletal modelling landscape with a focus on integrating computational models of the motor cortex, spinal cord circuitry, α-motoneurons  and skeletal muscle in regard to their role in generating voluntary muscle contraction. Further, we highlight the challenges and opportunities associated with an integrated corticomuscular pathway model, such as challenges in defining neuron connectivities, modelling standardisation, and opportunities in applying models to study emergent behaviour. Integrated corticomuscular pathway models have applications in brain-machine-interaction, education, and our understanding of neurological disease.

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.

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.

Our experimental understanding of the firing behaviour of motoneuron (MN) pools during human voluntary muscle contractions is currently limited to the observation of small samples of active MNs obtained from EMG decomposition. EMG decomposition therefore provides an important but incomplete description of the role of individual MNs in the firing activity of the complete MN pool, which limits our understanding of the neural strategies of the whole MN pool and of how the firing activity of each MN contributes to the neural drive to muscle. Here, we combine decomposed high-density EMG (HDEMG) data and a physiologically realistic model of MN population to predict the unknown recruitment and firing activity of the remaining unidentified MNs in the complete MN pool. In brief, an experimental estimation of the synaptic current is input to a cohort of MN models, which are calibrated using the available decomposed HDEMG data, and predict the MN spike trains fired by the entire MN population. This novel approach is experimentally validated and applied to muscle force prediction from neuromuscular modelling.

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.

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.

In-silico neuro musculoskeletal model reproduces the movement types obtained by spinal micro stimulation

BACKGROUND AND OBJECTIVES

Virtual patients and physiologies allow experimentation, design, and early-stage clinical trials in-silico. Virtual patient technology for human movement systems that encompasses musculoskeleton and its neural control are few and far in between. Our major goal is to create a neuro- musculoskeletal upper limb in-silico model, which is modular in architecture and generates movement as an emergent phenomenon out of a multiscale co-simulation of spinal cord neural control and musculoskeletal dynamics.

METHODS

The model is developed on the NEUROiD movement simulation platform that enables a co-simulation of popular neural simulator NEURON and the musculoskeletal simulator OpenSim. We further characterized and demonstrated the use of this model in generating a range of commonly observed upper limb movements by means of a spatio-temporal stimulation pattern delivered to the cervical spinal cord.

RESULTS

We were able to characterize the model based on proprioception (Ia, Ib and II fibers), afferent conduction delay and inital postures of the musculoskeletal system. A smooth movement was achieved in all the considered experiments. The generated movements in all degrees of freedom were reproduced in accordance with the previous experimental studies.

CONCLUSION

In this work, design and development of the upper limb model was described in a modular fashion, while reusing existing models and modules. We believe this work enables a first and small step towards an in-silico paradigms for understanding upper limb movement, disease pathology, medication, and rehabilitation.

Integration of neural architecture within a finite element framework for improved neuromusculoskeletal modeling

Neuromusculoskeletal (NMS) models can aid in studying the impacts of the nervous and musculoskeletal systems on one another. These computational models facilitate studies investigating mechanisms and treatment of musculoskeletal and neurodegenerative conditions. In this study, we present a predictive NMS model that uses an embedded neural architecture within a finite element (FE) framework to simulate muscle activation. A previously developed neuromuscular model of a motor neuron was embedded into a simple FE musculoskeletal model. Input stimulation profiles from literature were simulated in the FE NMS model to verify effective integration of the software platforms. Motor unit recruitment and rate coding capabilities of the model were evaluated. The integrated model reproduced previously published output muscle forces with an average error of 0.0435 N. The integrated model effectively demonstrated motor unit recruitment and rate coding in the physiological range based upon motor unit discharge rates and muscle force output. The combined capability of a predictive NMS model within a FE framework can aid in improving our understanding of how the nervous and musculoskeletal systems work together. While this study focused on a simple FE application, the framework presented here easily accommodates increased complexity in the neuromuscular model, the FE simulation, or both.

Identification of Motor Unit Twitch Properties in the Intact Human In Vivo

Restoring natural motor function in neurologically injured individuals is challenging, largely due to the lack of personalization in current neurorehabilitation technologies. Signal-driven neuro-musculoskeletal models may offer a novel paradigm for devising novel closed-loop rehabilitation strategies according to an individual's physiology. However, current modelling techniques are constrained to bipolar electromyography (EMG), thereby lacking the resolution necessary to extract the activity of individual motor units (MUs) in vivo. In this work, we decoded MU spike trains from high-density (HD)-EMG to obtain relevant neural properties across multiple isometric plantar-dorsiflexion tasks. Then, we sampled MU statistical distributions and used them to reproduce MU specific activation profiles. Results showed bimodal distributions which may correspond to slow and fast MU populations. The estimated activation profiles showed a high degree of similarity to the reference torque (R²>0.8) across the recorded muscles. This suggests that the estimation of MU twitch properties is a crucial step for the translation of neural information into muscle force.Clinical Relevance- This work has multiple implications for understanding the underlying mechanism of motor impairment and for developing closed-loop strategies for modulating alpha motor circuitries in neurologically injured individuals.

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.

Feedforward modulation of gamma motor neuron activity can improve motor command accuracy

Objective. Coactivation of gamma and alpha motor neuron activity ensures that muscle spindle responsiveness is maintained during muscle contractions. However, some evidence suggests that the activity of gamma motor neurons is phase-advanced with respect to that of alpha motor neurons during manual control tasks. We hypothesized that this might be a deliberate control strategy to maximize movement accuracy.Approach. Using a computational model of the neural activation of a muscle and its type Ia sensory feedback to the motor neurons, we systematically investigated the impact of the phase difference between oscillatory descending input to alpha and dynamic gamma motor neurons. Specifically, the amplification of the alpha motor neuron drive to the muscle was investigated as a function of the frequency of the synaptic input (1-9 Hz individually or superimposed) and the alpha-gamma phase difference (0-2π).Main results. Simulation results showed that when the phase advance of the dynamic gamma drive resulted in delays between muscle velocity and type Ia afferent feedback similar to those previously observed experimentally, low-frequency components (1 and 2 Hz) of the motor neuron synaptic input were amplified (gain up to 1.7). On the other hand, synaptic input at higher frequencies was unaffected.Significance. This finding suggests that by imposing a phase advance of the input to dynamic gamma motor neurons, components of the neural drive usually associated with voluntary control are amplified. In this way, our study suggests that this neural strategy increases the control-to-neural-noise ratio of the motor output during movement.

Experimental and Computational Study on Motor Control and Recovery After Stroke: Toward a Constructive Loop Between Experimental and Virtual Embodied Neuroscience

Being able to replicate real experiments with computational simulations is a unique opportunity to refine and validate models with experimental data and redesign the experiments based on simulations. However, since it is technically demanding to model all components of an experiment, traditional approaches to modeling reduce the experimental setups as much as possible. In this study, our goal is to replicate all the relevant features of an experiment on motor control and motor rehabilitation after stroke. To this aim, we propose an approach that allows continuous integration of new experimental data into a computational modeling framework. First, results show that we could reproduce experimental object displacement with high accuracy via the simulated embodiment in the virtual world by feeding a spinal cord model with experimental registration of the cortical activity. Second, by using computational models of multiple granularities, our preliminary results show the possibility of simulating several features of the brain after stroke, from the local alteration in neuronal activity to long-range connectivity remodeling. Finally, strategies are proposed to merge the two pipelines. We further suggest that additional models could be integrated into the framework thanks to the versatility of the proposed approach, thus allowing many researchers to achieve continuously improved experimental design.

Rate of Information Flow Across Layered Neuro-Spike Network in the Spinal Cord

Spinal Cord Injury (SCI) is a severe condition that can result in loss of motor and sensory functions by disrupting communication among neurons, i.e., neuro-spike communication. Future information and communication technology (ICT) based treatment techniques for SCI are expected to rely on nano networks, deployed inside the body. In this respect, modeling neuro-spike communication channels in the spinal cord and revealing the relationship between channel metrics and SCI are required to realize these treatment techniques and diagnosis tools such as replacement neural implants, high-performance diagnosis tools, which are based on ICT metrics instead of large medical data. Therefore, in this study, we focus on a spinal cord network, namely the descending spinal cord pathway, which is responsible for the transmission of brain motor signals to the spinal cord. We aim to analyze the rate of motor information flow to the corresponding muscle. To this end, we model the spinal cord motor network as a layered network consisting of a cascade of two independent neuro-spike channels, which are brain-spinal cord network and spinal cord interneuron-spinal cord motoneuron network. We derive upper and lower bounds for the total rate across the brain-spinal cord network and interneuron-spinal cord network. Our evaluations demonstrate that the total rate in the case of upper motor neuron syndrome (UMNS), which manifests itself with muscle weakness, approaches zero, where the brain-spinal cord network becomes a bottleneck. In lower motor neuron syndrome (LMNS), which results in muscle atrophy, the total rate again approaches zero with the loss of spinal cord motoneurons (MN).

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 Tool to Select FES Parameters for chronic SCI

Functional electrical stimulation has been used in rehabilitation programs for patients with chronic spinal cord injury. When used correctly it is able to improve the well-being of patients. However, when the stimulus is not adequate it can accelerate the process of fatigue, reducing the time available for training the programmed motor activity. To optimize the configuration of the stimulatory parameters, we developed a tool capable of simulating the muscle strength performance in response to different stimulatory profiles. The tool was able to reproduce the behavior of motoneurons in chronic spinal cord injury and to estimate the muscular strength resulting from the application of different stimuli. We consider that this FES Simulator is a promising tool to design and simulate different profiles of electrical stimulation, optimizing the decision process of the stimulation parameters.

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.

Cross-Frequency Coupling in Descending Motor Pathways: Theory and Simulation

Coupling of neural oscillations is essential for the transmission of cortical motor commands to motoneuron pools through direct and indirect descending motor pathways. Most studies focus on iso-frequency coupling between brain and muscle activities, i.e., cortico-muscular coherence, which is thought to reflect motor command transmission in the mono-synaptic corticospinal pathway. Compared to this direct pathway, indirect corticobulbospinal motor pathways involve multiple intermediate synaptic connections via spinal interneurons. Neuronal processing of synaptic inputs can lead to modulation of inter-spike intervals which produces cross-frequency coupling. This theoretical study aims to evaluate the effect of the number of synaptic layers in descending pathways on the expression of cross-frequency coupling between supraspinal input and the cumulative output of the motoneuron pool using a computer simulation. We simulated descending pathways as various layers of interneurons with a terminal motoneuron pool using Hogdkin–Huxley styled neuron models. Both cross- and iso-frequency coupling between the supraspinal input and the motorneuron pool output were computed using a novel generalized coherence measure, i.e., n:m coherence. We found that the iso-frequency coupling is only dominant in the mono-synaptic corticospinal tract, while the cross-frequency coupling is dominant in multi-synaptic indirect motor pathways. Furthermore, simulations incorporating both mono-synaptic direct and multi-synaptic indirect descending pathways showed that increased reliance on a multi-synaptic indirect pathway over a mono-synaptic direct pathway enhances the dominance of cross-frequency coupling between the supraspinal input and the motorneuron pool output. These results provide the theoretical basis for future human subject study quantitatively assessing motor command transmission in indirect vs. direct pathways and its changes after neurological disorders such as unilateral brain injury.

Curated Model Development Using NEUROiD: A Web-Based NEUROmotor Integration and Design Platform

Decades of research on neuromotor circuits and systems has provided valuable information on neuronal control of movement. Computational models of several elements of the neuromotor system have been developed at various scales, from sub-cellular to system. While several small models abound, their structured integration is the key to building larger and more biologically realistic models which can predict the behavior of the system in different scenarios. This effort calls for integration of elements across neuroscience and musculoskeletal biomechanics. There is also a need for development of methods and tools for structured integration that yield larger in silico models demonstrating a set of desired system responses. We take a small step in this direction with the NEUROmotor integration and Design (NEUROiD) platform. NEUROiD helps integrate results from motor systems anatomy, physiology, and biomechanics into an integrated neuromotor system model. Simulation and visualization of the model across multiple scales is supported. Standard electrophysiological operations such as slicing, current injection, recording of membrane potential, and local field potential are part of NEUROiD. The platform allows traceability of model parameters to primary literature. We illustrate the power and utility of NEUROiD by building a simple ankle model and its controlling neural circuitry by curating a set of published components. NEUROiD allows researchers to utilize remote high-performance computers for simulation, while controlling the model using a web browser.

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.

Amplitude cancellation influences the association between frequency components in the neural drive to muscle and the rectified EMG signal

The rectified surface EMG signal is commonly used as an estimator of the neural drive to muscles and therefore to infer sources of synaptic input to motor neurons. Loss of EMG amplitude due to the overlap of motor unit action potentials (amplitude cancellation), however, may distort the spectrum of the rectified EMG and thereby its correlation with the neural drive. In this study, we investigated the impact of amplitude cancelation on this correlation using analytical derivations and a computational model of motor neuron activity, force, and the EMG signal. First, we demonstrated analytically that an ideal rectified EMG signal without amplitude cancellation (EMG_nc) is superior to the actual rectified EMG signal as estimator of the neural drive to muscle. This observation was confirmed by the simulations, as the average coefficient of determination (r²) between the neural drive in the 1–30 Hz band and EMG_nc (0.59±0.08) was matched by the correlation between the rectified EMG and the neural drive only when the level of amplitude cancellation was low (<40%) at low contraction levels (<5% of maximum voluntary contraction force; MVC). This correlation, however, decreased linearly with amplitude cancellation (r = -0.83) to values of r² <0.2 at amplitude cancellation levels >60% (contraction levels >15% MVC). Moreover, the simulations showed that a stronger (i.e. more variable) neural drive implied a stronger correlation between the rectified EMG and the neural drive and that amplitude cancellation distorted this correlation mainly for low-frequency components (<5 Hz) of the neural drive. In conclusion, the results indicate that amplitude cancellation distorts the spectrum of the rectified EMG signal. This implies that valid use of the rectified EMG as an estimator of the neural drive requires low contraction levels and/or strong common synaptic input to the motor neurons.

The rectified surface EMG signal is commonly used to analyze the neural activation of muscles. However, since this signal is most often exposed to so-called amplitude cancellation (loss of EMG amplitude due to overlap of positive and negative phases of different motor unit action potentials), the frequency content of the rectified EMG may not fully reflect that of the neural drive to the muscle. In this study we prove this notion analytically and demonstrate, using simulations, that the rectified EMG signal accurately reflects the neural drive to the muscle only in a limited set of conditions. Specifically, these conditions include low contraction levels and/or high variability of the neural drive. In other conditions, the rectified EMG signal from a muscle is a poor predictor of its neural input. This finding has potentially large implications for the way neural drive to muscles and neural connectivity (e.g. across muscles or between the brain and a muscle) should be analyzed.

Corticomotoneuronal Model for Intraoperative Neurophysiological Monitoring During Direct Brain Stimulation

Intraoperative neurophysiological monitoring during brain surgery uses direct cortical stimulation to map the motor cortex by recording muscle activity induced by the excitation of alpha motor neurons (MNs). Computational models have been used to understand local brain stimulation. However, a computational model revealing the stimulation process from the cortex to MNs has not yet been proposed. Thus, the aim of the current study was to develop a corticomotoneuronal (CMN) model to investigate intraoperative stimulation during surgery. The CMN combined the following three processes into one system for the first time: (1) induction of an electric field in the brain based on a volume conductor model; (2) activation of pyramidal neuron (PNs) with a compartment model; and (3) formation of presynaptic connections of the PNs to MNs using a conductance-based synaptic model coupled with a spiking model. The implemented volume conductor model coupled with the axon model agreed with experimental strength-duration curves. Additionally, temporal/spatial and facilitation effects of CMN synapses were implemented and verified. Finally, the integrated CMN model was verified with experimental data. The results demonstrated that our model was necessary to describe the interaction between frequency and pulses to assess the difference between low-frequency and multi-pulse high-frequency stimulation in cortical stimulation. The proposed model can be used to investigate the effect of stimulation parameters on the cortex to optimize intraoperative monitoring.

Enabling Detailed, Biophysics-Based Skeletal Muscle Models on HPC Systems

Realistic simulations of detailed, biophysics-based, multi-scale models often require very high resolution and, thus, large-scale compute facilities. Existing simulation environments, especially for biomedical applications, are typically designed to allow for high flexibility and generality in model development. Flexibility and model development, however, are often a limiting factor for large-scale simulations. Therefore, new models are typically tested and run on small-scale compute facilities. By using a detailed biophysics-based, chemo-electromechanical skeletal muscle model and the international open-source software library OpenCMISS as an example, we present an approach to upgrade an existing muscle simulation framework from a moderately parallel version toward a massively parallel one that scales both in terms of problem size and in terms of the number of parallel processes. For this purpose, we investigate different modeling, algorithmic and implementational aspects. We present improvements addressing both numerical and parallel scalability. In addition, our approach includes a novel visualization environment which is based on the MegaMol framework and is capable of handling large amounts of simulated data. We present the results of a number of scaling studies at the Tier-1 supercomputer HazelHen at the High Performance Computing Center Stuttgart (HLRS). We improve the overall runtime by a factor of up to 2.6 and achieve good scalability on up to 768 cores.

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.

Modeling trans-spinal direct current stimulation for the modulation of the lumbar spinal motor pathways

OBJECTIVE

Trans-spinal direct current stimulation (tsDCS) is a potential new technique for the treatment of spinal cord injury (SCI). TsDCS aims to facilitate plastic changes in the neural pathways of the spinal cord with a positive effect on SCI recovery. To establish tsDCS as a possible treatment option for SCI, it is essential to gain a better understanding of its cause and effects. We seek to understand the acute effect of tsDCS, including the generated electric field (EF) and its polarization effect on the spinal circuits, to determine a cellular target. We further ask how these findings can be interpreted to explain published experimental results.

APPROACH

We use a realistic full body finite element volume conductor model to calculate the EF of a 2.5 mA direct current for three different electrode configurations. We apply the calculated electric field to realistic motoneuron models to investigate static changes in membrane resting potential. The results are combined with existing knowledge about the theoretical effect on a neuronal level and implemented into an existing lumbar spinal network model to simulate the resulting changes on a network level.

MAIN RESULTS

Across electrode configurations, the maximum EF inside the spinal cord ranged from 0.47 V m^-1 to 0.82 V m^-1. Axon terminal polarization was identified to be the dominant cellular target. Also, differences in electrode placement have a large influence on axon terminal polarization. Comparison between the simulated acute effects and the electrophysiological long-term changes observed in human tsDCS studies suggest an inverse relationship between the two.

SIGNIFICANCE

We provide methods and knowledge for better understanding the effects of tsDCS and serve as a basis for a more targeted and optimized application of tsDCS.

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.

The human motor neuron pools receive a dominant slow-varying common synaptic input

KEY POINTS

Motor neurons in a pool receive both common and independent synaptic inputs, although the proportion and role of their common synaptic input is debated. Classic correlation techniques between motor unit spike trains do not measure the absolute proportion of common input and have limitations as a result of the non-linearity of motor neurons. We propose a method that for the first time allows an accurate quantification of the absolute proportion of low frequency common synaptic input (<5 Hz) to motor neurons in humans. We applied the proposed method to three human muscles and determined experimentally that they receive a similar large amount (>60%) of common input, irrespective of their different functional and control properties. These results increase our knowledge about the role of common and independent input to motor neurons in force control.

ABSTRACT

Motor neurons receive both common and independent synaptic inputs. This observation is classically based on the presence of a significant correlation between pairs of motor unit spike trains. The functional significance of different relative proportions of common input across muscles, individuals and conditions is still debated. One of the limitations in our understanding of correlated input to motor neurons is that it has not been possible so far to quantify the absolute proportion of common input with respect to the total synaptic input received by the motor neurons. Indeed, correlation measures of pairs of output spike trains only allow for relative comparisons. In the present study, we report for the first time an approach for measuring the proportion of common input in the low frequency bandwidth (<5 Hz) to a motor neuron pool in humans. This estimate is based on a phenomenological model and the theoretical fitting of the experimental values of coherence between the permutations of groups of motor unit spike trains. We demonstrate the validity of this theoretical estimate with several simulations. Moreover, we applied this method to three human muscles: the abductor digiti minimi, tibialis anterior and vastus medialis. Despite these muscles having different functional roles and control properties, as confirmed by the results of the present study, we estimate that their motor pools receive a similar and large (>60%) proportion of common low frequency oscillations with respect to their total synaptic input. These results suggest that the central nervous system provides a large amount of common input to motor neuron pools, in a similar way to that for muscles with different functional and control properties.

Principles of Motor Unit Physiology Evolve With Advances in Technology

Movements are generated by the coordinated activation of motor units. Recent technological advances have made it possible to identify the concurrent activity of several tens of motor units, in contrast with much smaller samples available in classic studies. We discuss how these advances in technology have enabled the development of a population perspective of how the central nervous system controls motor unit activity and thereby the forces exerted by muscles.

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.

Modeling and Identification of a Realistic Spiking Neural Network and Musculoskeletal Model of the Human Arm, and an Application to the Stretch Reflex

This study develops a multi-level neuromuscular model consisting of topological pools of spiking motor, sensory and interneurons controlling a bi-muscular model of the human arm. The spiking output of motor neuron pools were used to drive muscle actions and skeletal movement via neuromuscular junctions. Feedback information from muscle spindles were relayed via monosynaptic excitatory and disynaptic inhibitory connections, to simulate spinal afferent pathways. Subject-specific model parameters were identified from human experiments by using inverse dynamics computations and optimization methods. The identified neuromuscular model was used to simulate the biceps stretch reflex and the results were compared to an independent dataset. The proposed model was able to track the recorded data and produce dynamically consistent neural spiking patterns, muscle forces and movement kinematics under varying conditions of external forces and co-contraction levels. This additional layer of detail in neuromuscular models has important relevance to the research communities of rehabilitation and clinical movement analysis by providing a mathematical approach to studying neuromuscular pathology.

The phase difference between neural drives to antagonist muscles in essential tremor is associated with the relative strength of supraspinal and afferent input

The pathophysiology of essential tremor (ET), the most common movement disorder, is not fully understood. We investigated which factors determine the variability in the phase difference between neural drives to antagonist muscles, a long-standing observation yet unexplained. We used a computational model to simulate the effects of different levels of voluntary and tremulous synaptic input to antagonistic motoneuron pools on the tremor. We compared these simulations to data from 11 human ET patients. In both analyses, the neural drive to muscle was represented as the pooled spike trains of several motor units, which provides an accurate representation of the common synaptic input to motoneurons. The simulations showed that, for each voluntary input level, the phase difference between neural drives to antagonist muscles is determined by the relative strength of the supraspinal tremor input to the motoneuron pools. In addition, when the supraspinal tremor input to one muscle was weak or absent, Ia afferents provided significant common tremor input due to passive stretch. The simulations predicted that without a voluntary drive (rest tremor) the neural drives would be more likely in phase, while a concurrent voluntary input (postural tremor) would lead more frequently to an out-of-phase pattern. The experimental results matched these predictions, showing a significant change in phase difference between postural and rest tremor. They also indicated that the common tremor input is always shared by the antagonistic motoneuron pools, in agreement with the simulations. Our results highlight that the interplay between supraspinal input and spinal afferents is relevant for tremor generation.

The optimal neural strategy for a stable motor task requires a compromise between level of muscle cocontraction and synaptic gain of afferent feedback

Increasing joint stiffness by cocontraction of antagonist muscles and compensatory reflexes are neural strategies to minimize the impact of unexpected perturbations on movement. Combining these strategies, however, may compromise steadiness, as elements of the afferent input to motor pools innervating antagonist muscles are inherently negatively correlated. Consequently, a high afferent gain and active contractions of both muscles may imply negatively correlated neural drives to the muscles and thus an unstable limb position. This hypothesis was systematically explored with a novel computational model of the peripheral nervous system and the mechanics of one limb. Two populations of motor neurons received synaptic input from descending drive, spinal interneurons, and afferent feedback. Muscle force, simulated based on motor unit activity, determined limb movement that gave rise to afferent feedback from muscle spindles and Golgi tendon organs. The results indicated that optimal steadiness was achieved with low synaptic gain of the afferent feedback. High afferent gains during cocontraction implied increased levels of common drive in the motor neuron outputs, which were negatively correlated across the two populations, constraining instability of the limb. Increasing the force acting on the joint and the afferent gain both effectively minimized the impact of an external perturbation, and suboptimal adjustment of the afferent gain could be compensated by muscle cocontraction. These observations show that selection of the strategy for a given contraction implies a compromise between steadiness and effectiveness of compensations to perturbations. This indicates that a task-dependent selection of neural strategy for steadiness is necessary when acting in different environments.

Common synaptic input to motor neurons, motor unit synchronization, and force control

In considering the role of common synaptic input to motor neurons in force control, we hypothesize that the effective neural drive to muscle replicates the common input and is, thus, the main determinant of force production. Such a perspective argues against a significant role for motor unit synchronization in force control.

Power spectrum of the rectified EMG: when and why is rectification beneficial for identifying neural connectivity?

OBJECTIVE

The identification of common oscillatory inputs to motor neurons in the electromyographic (EMG) signal power spectrum is often preceded by EMG rectification for enhancing the low-frequency oscillatory components. However, rectification is a nonlinear operator and its influence on the EMG signal spectrum is not fully understood. In this study, we aim at determining when EMG rectification is beneficial in the study of oscillatory inputs to motor neurons.

APPROACH

We provide a full mathematical description of the power spectrum of the rectified EMG signal and the influence of the average shape of the motor unit action potentials on it. We also provide a validation of these theoretical results with both simulated and experimental EMG signals.

MAIN RESULTS

Simulations using an advanced computational model and experimental results demonstrated the accuracy of the theoretical derivations on the effect of rectification on the EMG spectrum. These derivations proved that rectification is beneficial when assessing the strength of low-frequency (delta and alpha bands) common synaptic inputs to the motor neurons, when the duration of the action potentials is short, and when the level of cancellation is relatively low. On the other hand, rectification may distort the estimation of common synaptic inputs when studying higher frequencies (beta and gamma), in a way dependent on the duration of the action potentials, and may introduce peaks in the coherence function that do not correspond to physiological shared inputs.

SIGNIFICANCE

This study clarifies the conditions when rectifying the surface EMG is appropriate for studying neural connectivity.

Predicting electromyographic signals under realistic conditions using a multiscale chemo-electro-mechanical finite element model

This paper presents a novel multiscale finite element-based framework for modelling electromyographic (EMG) signals. The framework combines (i) a biophysical description of the excitation-contraction coupling at the half-sarcomere level, (ii) a model of the action potential (AP) propagation along muscle fibres, (iii) a continuum-mechanical formulation of force generation and deformation of the muscle, and (iv) a model for predicting the intramuscular and surface EMG. Owing to the biophysical description of the half-sarcomere, the model inherently accounts for physiological properties of skeletal muscle. To demonstrate this, the influence of membrane fatigue on the EMG signal during sustained contractions is investigated. During a stimulation period of 500 ms at 100 Hz, the predicted EMG amplitude decreases by 40% and the AP propagation velocity decreases by 15%. Further, the model can take into account contraction-induced deformations of the muscle. This is demonstrated by simulating fixed-length contractions of an idealized geometry and a model of the human tibialis anterior muscle (TA). The model of the TA furthermore demonstrates that the proposed finite element model is capable of simulating realistic geometries, complex fibre architectures, and can include different types of heterogeneities. In addition, the TA model accounts for a distributed innervation zone, different fibre types and appeals to motor unit discharge times that are based on a biophysical description of the α motor neurons.

Axon-somatic back-propagation in detailed models of spinal alpha motoneurons

Antidromic action potentials following distal stimulation of motor axons occasionally fail to invade the soma of alpha motoneurons in spinal cord, due to their passing through regions of high non-uniformity. Morphologically detailed conductance-based models of cat spinal alpha motoneurons have been developed, with the aim to reproduce and clarify some aspects of the electrophysiological behavior of the antidromic axon-somatic spike propagation. Fourteen 3D morphologically detailed somata and dendrites of cat spinal alpha motoneurons have been imported from an open-access web-based database of neuronal morphologies, NeuroMorpho.org, and instantiated in neurocomputational models. An axon hillock, an axonal initial segment and a myelinated axon are added to each model. By sweeping the diameter of the axonal initial segment (AIS) and the axon hillock, as well as the maximal conductances of sodium channels at the AIS and at the soma, the developed models are able to show the relationships between different geometric and electrophysiological configurations and the voltage attenuation of the antidromically traveling wave. In particular, a greater than usually admitted sodium conductance at AIS is necessary and sufficient to overcome the dramatic voltage attenuation occurring during antidromic spike propagation both at the myelinated axon-AIS and at the AIS-soma transitions.

Physiological recruitment of motor units by high-frequency electrical stimulation of afferent pathways

Neuromuscular electrical stimulation (NMES) is commonly used in rehabilitation, but electrically evoked muscle activation is in several ways different from voluntary muscle contractions. These differences lead to challenges in the use of NMES for restoring muscle function. We investigated the use of low-current, high-frequency nerve stimulation to activate the muscle via the spinal motoneuron (MN) pool to achieve more natural activation patterns. Using a novel stimulation protocol, the H-reflex responses to individual stimuli in a train of stimulation pulses at 100 Hz were reliably estimated with surface EMG during low-level contractions. Furthermore, single motor unit recruitment by afferent stimulation was analyzed with intramuscular EMG. The results showed that substantially elevated H-reflex responses were obtained during 100-Hz stimulation with respect to a lower stimulation frequency. Furthermore, motor unit recruitment using 100-Hz stimulation was not fully synchronized, as it occurs in classic NMES, and the discharge rates differed among motor units because each unit was activated only after a specific number of stimuli. The most likely mechanism behind these observations is the temporal summation of subthreshold excitatory postsynaptic potentials from Ia fibers to the MNs. These findings and their interpretation were also verified by a realistic simulation model of afferent stimulation of a MN population. These results suggest that the proposed stimulation strategy may allow generation of considerable levels of muscle activation by motor unit recruitment that resembles the physiological conditions.

A functional model and simulation of spinal motor pools and intrafascicular recordings of motoneuron activity in peripheral nerve

Decoding motor intent from recorded neural signals is essential for the development of effective neural-controlled prostheses. To facilitate the development of online decoding algorithms we have developed a software platform to simulate neural motor signals recorded with peripheral nerve electrodes, such as longitudinal intrafascicular electrodes (LIFEs). The simulator uses stored motor intent signals to drive a pool of simulated motoneurons with various spike shapes, recruitment characteristics, and firing frequencies. Each electrode records a weighted sum of a subset of simulated motoneuron activity patterns. As designed, the simulator facilitates development of a suite of test scenarios that would not be possible with actual data sets because, unlike with actual recordings, in the simulator the individual contributions to the simulated composite recordings are known and can be methodically varied across a set of simulation runs. In this manner, the simulation tool is suitable for iterative development of real-time decoding algorithms prior to definitive evaluation in amputee subjects with implanted electrodes. The simulation tool was used to produce data sets that demonstrate its ability to capture some features of neural recordings that pose challenges for decoding algorithms.

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.