Individual and collective properties of computationally efficient motoneuron models of types S and F with active dendrites

Personalized Alpha-Motoneuron Pool Models Driven by Neural Data Encode the Mechanisms Controlling Rate of Force Development

The central nervous system employs distinct motor control strategies depending on task demands. Accordingly, the activity of alpha-motoneuron (MN) pools innervating skeletal muscle fibers is modulated based on muscle force and rate of force development (RFD). In human subjects, biophysical MN models enable inferring in vivo the neural processes (e.g., synaptic input, activity of the entire MN pool, etc.) underlying this modulation, which are otherwise challenging to measure experimentally. Due to unique neurophysiological characteristics of individuals, personalizing these models is essential to study motor control in humans. Therefore, this work studied the mechanisms involved in the modulation of RFD using person-specific MN pool models driven by in vivo common synaptic input estimates (i.e., derived from surface high-density electromyography). Specifically, we assessed how in vivo MN activity changed across RFD and muscle force. This included modulation of recruitment and rate coding in the complete MN pool, as well as model-based estimates of excitatory synaptic gains ( ∆ IF). We found RFD-specific changes in MN activity associated to changes in ∆ IF. Moreover, we showed that MN pool models driven by RFD-specific ∆ IFs reproduced in vivo MN firing features and associated force profiles at different RFDs. Altogether, this work represents a step towards modelling the mechanisms of force generation in humans and creating person-specific models of the spinal circuitry. This will open a window for studying in vivo human neuromechanics and motor restoring interventions.

Onion skin is not a universal firing pattern for spinal motoneurons: simulation study

Muscle force is modulated by sequential recruitment and firing rates of motor units (MUs). However, discrepancies exist in the literature regarding the relationship between MU firing rates and their recruitment, presenting two contrasting firing-recruitment schemes. The first firing scheme, known as "onion skin," exhibits low-threshold MUs firing faster than high-threshold MUs, forming separate layers akin to an onion. This contradicts the other firing scheme, known as "reverse onion skin" or "afterhyperpolarization (AHP)," with low-threshold MUs firing slower than high-threshold MUs. To study this apparent dichotomy, we used a high-fidelity computational model that prioritizes physiological fidelity and heterogeneity, allowing versatility in the recruitment of different motoneuron types. Our simulations indicate that these two schemes are not mutually exclusive but rather coexist. The likelihood of observing each scheme depends on factors such as the motoneuron pool activation level, synaptic input activation rates, and MU type. The onion skin scheme does not universally govern the encoding rates of MUs but tends to emerge in unsaturated motoneurons (cells firing < their fusion frequency that generates peak force), whereas the AHP scheme prevails in saturated MUs (cells firing at their fusion frequency), which is highly probable for slow (S)-type MUs. When unsaturated, fast fatigable (FF)-type MUs always show the onion skin scheme, whereas S-type MUs do not show either one. Fast fatigue-resistant (FR)-type MUs are generally similar but show weaker onion skin behaviors than FF-type MUs. Our results offer an explanation for the longstanding dichotomy regarding MU firing patterns, shedding light on the factors influencing the firing-recruitment schemes.NEW & NOTEWORTHY The literature reports two contrasting schemes, namely the onion skin and the afterhyperpolarization (AHP) regarding the relationship between motor units (MUs) firing rates and recruitment order. Previous studies have examined these schemes phenomenologically, imposing one scheme on the firing-recruitment relationship. Here, we used a high-fidelity computational model that prioritizes biological fidelity and heterogeneity to investigate motoneuron firing schemes without bias toward either scheme. Our objective findings offer an explanation for the longstanding dichotomy on MU firing patterns.

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.

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.

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.

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.

The effects of model composition design choices on high-fidelity simulations of motoneuron recruitment and firing behaviors

OBJECTIVE

Computational models often require tradeoffs, such as balancing detail with efficiency; yet optimal balance should incorporate sound design features that do not bias the results of the specific scientific question under investigation. The present study examines how model design choices impact simulation results.

APPROACH

We developed a rigorously-validated high-fidelity computational model of the spinal motoneuron pool to study three long-standing model design practices which have yet to be examined for their impact on motoneuron recruitment, firing rate, and force simulations. The practices examined were the use of: (1) generic cell models to simulate different motoneuron types, (2) discrete property ranges for different motoneuron types, and (3) biological homogeneity of cell properties within motoneuron types.

MAIN RESULTS

Our results show that each of these practices accentuates conditions of motoneuron recruitment based on the size principle, and minimizes conditions of mixed and reversed recruitment orders, which have been observed in animal and human recordings. Specifically, strict motoneuron orderly size recruitment occurs, but in a compressed range, after which mixed and reverse motoneuron recruitment occurs due to the overlap in electrical properties of different motoneuron types. Additionally, these practices underestimate the motoneuron firing rates and force data simulated by existing models.

SIGNIFICANCE

Our results indicate that current modeling practices increase conditions of motoneuron recruitment based on the size principle, and decrease conditions of mixed and reversed recruitment order, which, in turn, impacts the predictions made by existing models on motoneuron recruitment, firing rate, and force. Additionally, mixed and reverse motoneuron recruitment generated higher muscle force than orderly size motoneuron recruitment in these simulations and represents one potential scheme to increase muscle efficiency. The examined model design practices, as well as the present results, are applicable to neuronal modeling throughout the nervous system.

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.

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.

Development of modified cable models to simulate accurate neuronal active behaviors

In large network and single three-dimensional (3-D) neuron simulations, high computing speed dictates using reduced cable models to simulate neuronal firing behaviors. However, these models are unwarranted under active conditions and lack accurate representation of dendritic active conductances that greatly shape neuronal firing. Here, realistic 3-D (R3D) models (which contain full anatomical details of dendrites) of spinal motoneurons were systematically compared with their reduced single unbranched cable (SUC, which reduces the dendrites to a single electrically equivalent cable) counterpart under passive and active conditions. The SUC models matched the R3D model's passive properties but failed to match key active properties, especially active behaviors originating from dendrites. For instance, persistent inward currents (PIC) hysteresis, frequency-current (FI) relationship secondary range slope, firing hysteresis, plateau potential partial deactivation, staircase currents, synaptic current transfer ratio, and regional FI relationships were not accurately reproduced by the SUC models. The dendritic morphology oversimplification and lack of dendritic active conductances spatial segregation in the SUC models caused significant underestimation of those behaviors. Next, SUC models were modified by adding key branching features in an attempt to restore their active behaviors. The addition of primary dendritic branching only partially restored some active behaviors, whereas the addition of secondary dendritic branching restored most behaviors. Importantly, the proposed modified models successfully replicated the active properties without sacrificing model simplicity, making them attractive candidates for running R3D single neuron and network simulations with accurate firing behaviors. The present results indicate that using reduced models to examine PIC behaviors in spinal motoneurons is unwarranted.

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

This study focuses on neuromuscular mechanisms behind ankle torque and EMG variability during a maintained isometric plantar flexion contraction. Experimentally obtained torque standard deviation (SD) and soleus, medial gastrocnemius, and lateral gastrocnemius EMG envelope mean and SD increased with mean torque for a wide range of torque levels. Computer simulations were performed on a biophysically-based neuromuscular model of the triceps surae consisting of premotoneuronal spike trains (the global input, GI) driving the motoneuron pools of the soleus, medial gastrocnemius, and lateral gastrocnemius muscles, which activate their respective muscle units. Two types of point processes were adopted to represent the statistics of the GI: Poisson and Gamma. Simulations showed a better agreement with experimental results when the GI was modeled by Gamma point processes having lower orders (higher variability) for higher target torques. At the same time, the simulations reproduced well the experimental data of EMG envelope mean and SD as a function of mean plantar flexion torque, for the three muscles. These results suggest that the experimentally found relations between torque-EMG variability as a function of mean plantar flexion torque level depend not only on the intrinsic properties of the motoneuron pools and the muscle units innervated, but also on the increasing variability of the premotoneuronal GI spike trains when their mean rates increase to command a higher plantar flexion torque level. The simulations also provided information on spike train statistics of several hundred motoneurons that compose the triceps surae, providing a wide picture of the associated mechanisms behind torque and EMG variability.