Computationally efficient models of neuromuscular recruitment and mechanics

A hybrid sensory feedback system for thermal nociceptive warning and protection in prosthetic hand

Background

Advanced prosthetic hands may embed nanosensors and microelectronics in their cosmetic skin. Heat influx may cause damage to these delicate structures. Protecting the integrity of the prosthetic hand becomes critical and necessary to ensure sustainable function. This study aims to mimic the sensorimotor control strategy of the human hand in perceiving nociceptive stimuli and triggering self-protective mechanisms and to investigate how similar neuromorphic mechanisms implemented in prosthetic hand can allow amputees to both volitionally release a hot object upon a nociceptive warning and achieve reinforced release via a bionic withdrawal reflex.

Methods

A steady-state temperature prediction algorithm was proposed to shorten the long response time of a thermosensitive temperature sensor. A hybrid sensory strategy for transmitting force and a nociceptive temperature warning using transcutaneous electrical nerve stimulation based on evoked tactile sensations was designed to reconstruct the nociceptive sensory loop for amputees. A bionic withdrawal reflex using neuromorphic muscle control technology was used so that the prosthetic hand reflexively opened when a harmful temperature was detected. Four able-bodied subjects and two forearm amputees randomly grasped a tube at the different temperatures based on these strategies.

Results

The average prediction error of temperature prediction algorithm was 8.30 ± 6.00%. The average success rate of six subjects in perceiving force and nociceptive temperature warnings was 86.90 and 94.30%, respectively. Under the reinforcement control mode in Test 2, the median reaction time of all subjects was 1.39 s, which was significantly faster than the median reaction time of 1.93 s in Test 1, in which two able-bodied subjects and two amputees participated. Results demonstrated the effectiveness of the integration of nociceptive sensory strategy and withdrawal reflex control strategy in a closed loop and also showed that amputees restored the warning of nociceptive sensation while also being able to withdraw from thermal danger through both voluntary and reflexive protection.

Conclusion

This study demonstrated that it is feasible to restore the sensorimotor ability of amputees to warn and react against thermal nociceptive stimuli. Results further showed that the voluntary release and withdrawal reflex can work together to reinforce heat protection. Nevertheless, fusing voluntary and reflex functions for prosthetic performance in activities of daily living awaits a more cogent strategy in sensorimotor control.

Motoneuron-driven computational muscle modelling with motor unit resolution and subject-specific musculoskeletal anatomy

The computational simulation of human voluntary muscle contraction is possible with EMG-driven Hill-type models of whole muscles. Despite impactful applications in numerous fields, the neuromechanical information and the physiological accuracy such models provide remain limited because of multiscale simplifications that limit comprehensive description of muscle internal dynamics during contraction. We addressed this limitation by developing a novel motoneuron-driven neuromuscular model, that describes the force-generating dynamics of a population of individual motor units, each of which was described with a Hill-type actuator and controlled by a dedicated experimentally derived motoneuronal control. In forward simulation of human voluntary muscle contraction, the model transforms a vector of motoneuron spike trains decoded from high-density EMG signals into a vector of motor unit forces that sum into the predicted whole muscle force. The motoneuronal control provides comprehensive and separate descriptions of the dynamics of motor unit recruitment and discharge and decodes the subject's intention. The neuromuscular model is subject-specific, muscle-specific, includes an advanced and physiological description of motor unit activation dynamics, and is validated against an experimental muscle force. Accurate force predictions were obtained when the vector of experimental neural controls was representative of the discharge activity of the complete motor unit pool. This was achieved with large and dense grids of EMG electrodes during medium-force contractions or with computational methods that physiologically estimate the discharge activity of the motor units that were not identified experimentally. This neuromuscular model advances the state-of-the-art of neuromuscular modelling, bringing together the fields of motor control and musculoskeletal modelling, and finding applications in neuromuscular control and human-machine interfacing research.

Muscle redundancy is greatly reduced by the spatiotemporal nature of neuromuscular control

Animals must control numerous muscles to produce forces and movements with their limbs. Current theories of motor optimization and synergistic control are predicated on the assumption that there are multiple highly diverse feasible activations for any motor task ("muscle redundancy"). Here, we demonstrate that the dimensionality of the neuromuscular control problem is greatly reduced when adding the temporal constraints inherent to any sequence of motor commands: the physiological time constants for muscle activation-contraction dynamics. We used a seven-muscle model of a human finger to fully characterize the seven-dimensional polytope of all possible motor commands that can produce fingertip force vector in any direction in 3D, in alignment with the core models of Feasibility Theory. For a given sequence of seven force vectors lasting 300 ms, a novel single-step extended linear program finds the 49-dimensional polytope of all possible motor commands that can produce the sequence of forces. We find that muscle redundancy is severely reduced when the temporal limits on muscle activation-contraction dynamics are added. For example, allowing a generous ± 12% change in muscle activation within 50 ms allows visiting only ∼ 7% of the feasible activation space in the next time step. By considering that every motor command conditions future commands, we find that the motor-control landscape is much more highly structured and spatially constrained than previously recognized. We discuss how this challenges traditional computational and conceptual theories of motor control and neurorehabilitation for which muscle redundancy is a foundational assumption.

A Biorealistic Computational Model Unfolds Human-Like Compliant Properties for Control of Hand Prosthesis

Objective: Human neuromuscular reflex control provides a biological model for a compliant hand prosthesis. Here we present a computational approach to understanding the emerging human-like compliance, force and position control, and stiffness adaptation in a prosthetic hand with a replica of human neuromuscular reflex. Methods: A virtual twin of prosthetic hand was constructed in the MuJoCo environment with a tendon-driven anthropomorphic hand structure. Biorealistic mathematic models of muscle, spindle, spiking-neurons and monosynaptic reflex were implemented in neuromorphic chips to drive the virtual hand for real-time control. Results: Simulation showed that the virtual hand acquired human-like ability to control fingertip position, force and stiffness for grasp, as well as the capacity to interact with soft objects by adaptively adjusting hand stiffness. Conclusion: The biorealistic neuromorphic reflex model restores human-like neuromuscular properties for hand prosthesis to interact with soft objects.

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.

Force variability is mostly not motor noise: Theoretical implications for motor control

Variability in muscle force is a hallmark of healthy and pathological human behavior. Predominant theories of sensorimotor control assume 'motor noise' leads to force variability and its 'signal dependence' (variability in muscle force whose amplitude increases with intensity of neural drive). Here, we demonstrate that the two proposed mechanisms for motor noise (i.e. the stochastic nature of motor unit discharge and unfused tetanic contraction) cannot account for the majority of force variability nor for its signal dependence. We do so by considering three previously underappreciated but physiologically important features of a population of motor units: 1) fusion of motor unit twitches, 2) coupling among motoneuron discharge rate, cross-bridge dynamics, and muscle mechanics, and 3) a series-elastic element to account for the aponeurosis and tendon. These results argue strongly against the idea that force variability and the resulting kinematic variability are generated primarily by 'motor noise.' Rather, they underscore the importance of variability arising from properties of control strategies embodied through distributed sensorimotor systems. As such, our study provides a critical path toward developing theories and models of sensorimotor control that provide a physiologically valid and clinically useful understanding of healthy and pathologic force variability.

Bayesian State Estimation in Sensorimotor Systems With Particle Filtering

In sensorimotor control, sensory feedback integrates with forward models to alleviate the impacts of sensory noise and delay on state estimation. The sensorimotor integration is subject to Bayesian inference and has been formulated by the Kalman filter in computational neuroscience. However, the Kalman filter, as an artificial optimal estimator to address the abstract characteristics of spatial perception, is inadequate to present the neural computation in the cerebellum. Besides, the nonlinear neuromuscular dynamics with tightly coupled state variables also substantially impedes the implementation of Kalman filter in realistic sensorimotor systems. Here we address the sensorimotor state estimate by using the particle filter, a nonlinear Bayesian estimator that can be implemented in arbitrary dynamic systems with the neurocomputational compatibility. Particle filtering is explicitly implemented in a biophysically realistic sensorimotor model of an upper limb integrating Hill-type muscles, tendons, skeleton, and primary afferents. By involving the command noises, the constructed neuromusculoskeletal model qualitatively represents the experimental variability in center-out reaching movements. Despite the initial estimation uncertainty and sensorimotor noises, the particle filter is able to approximate the actual states in forward-reaching movements. Furthermore, the simulated hand-position estimate is consistent with the experimental results, in the presence of forward model errors, neural noises, and sensory delays. The particle filter is demonstrated to effectively implement the Bayesian state estimation in biophysically realistic sensorimotor systems and provide better compatibility with neuronal computation than the Kalman filter.

Proprioceptive Recognition with Artificial Neural Networks Based on Organizations of Spinocerebellar Tract and Cerebellum

Muscle kinematics and kinetics are nonlinearly encoded by proprioceptors, and the changes in muscle length and velocity are integrated into Ia afferent. Besides, proprioceptive signals from multiple muscles are probably mixed in afferent pathways, which all lead to difficulties in proprioceptive recognition for the cerebellum. In this study, the artificial neural networks, whose organizations are biologically based on the spinocerebellar tract and cerebellum, are utilized to decode the proprioceptive signals. Consistent with the controversy of the proprioceptive division in the dorsal spinocerebellar tract, the spinocerebellar tract networks incorporated two distinct inferences, (1) the centralized networks, which mixed Ia, II, and Ib and processed them together; (2) the decentralized networks, which processed Ia, II, and Ib afferents separately. The cerebellar networks were based on the Marr-Albus model to recognize the kinematic states. The networks were trained by a specific movement, and the trained networks were subsequently required to predict kinematic states of six movements. The results demonstrated that the centralized networks, which were more consistent with the physiological findings in recent years, had better recognition accuracy than the decentralized networks, and the networks were still effective even when proprioceptive afferents from multiple muscles were integrated.

Cardinal features of involuntary force variability can arise from the closed-loop control of viscoelastic afferented muscles

Involuntary force variability below 15 Hz arises from, and is influenced by, many factors including descending neural drive, proprioceptive feedback, and mechanical properties of muscles and tendons. However, their potential interactions that give rise to the well-structured spectrum of involuntary force variability are not well understood due to a lack of experimental techniques. Here, we investigated the generation, modulation, and interactions among different sources of force variability using a physiologically-grounded closed-loop simulation of an afferented muscle model. The closed-loop simulation included a musculotendon model, muscle spindle, Golgi tendon organ (GTO), and a tracking controller which enabled target-guided force tracking. We demonstrate that closed-loop control of an afferented musculotendon suffices to replicate and explain surprisingly many cardinal features of involuntary force variability. Specifically, we present 1) a potential origin of low-frequency force variability associated with co-modulation of motor unit firing rates (i.e.,'common drive'), 2) an in-depth characterization of how proprioceptive feedback pathways suffice to generate 5-12 Hz physiological tremor, and 3) evidence that modulation of those feedback pathways (i.e., presynaptic inhibition of Ia and Ib afferents, and spindle sensitivity via fusimotor drive) influence the full spectrum of force variability. These results highlight the previously underestimated importance of closed-loop neuromechanical interactions in explaining involuntary force variability during voluntary 'isometric' force control. Furthermore, these results provide the basis for a unifying theory that relates spinal circuitry to various manifestations of altered involuntary force variability in fatigue, aging and neurological disease.

Static Characteristics of a New Three-Dimensional Linear Homeomorphic Saccade Model

A linear homeomorphic saccade model that produces 3D saccadic eye movements consistent with physiological and anatomical evidence is introduced. Central to the model is the implementation of a time-optimal controller with six linear muscles and pulleys that represent the saccade oculomotor plant. Each muscle is modeled as a parallel combination of viscosity [Formula: see text] and series elasticity [Formula: see text] connected to the parallel combination of active-state tension generator [Formula: see text], viscosity element [Formula: see text], and length tension elastic element [Formula: see text]. Additionally, passive tissues involving the eyeball include a viscosity element [Formula: see text], elastic element [Formula: see text], and moment of inertia [Formula: see text]. The neural input for each muscle is separately maintained, whereas the effective pulling direction is modulated by its respective mid-orbital constraint from the pulleys. Initial parameter values for the oculomotor plant are based on anatomical and physiological evidence. The oculomotor plant uses a time-optimal, 2D commutative neural controller, together with the pulley system that actively functions to implement Listing's law during both static and dynamic conditions. In a companion paper, the dynamic characteristics of the saccade model is analyzed using a time domain system identification technique to estimate the final parameter values and neural inputs from saccade data. An excellent match between the model estimates and the data is observed, whereby a total of 20 horizontal, 5 vertical, and 64 oblique saccades are analyzed.

Physiological tremor increases when skeletal muscle is shortened: implications for fusimotor control

KEY POINTS

In tonic, isometric, plantarflexion contractions, physiological tremor increases as the ankle joint becomes plantarflexed. Modulation of physiological tremor as a function of muscle stretch differs from that of the stretch reflex amplitude. Amplitude of physiological tremor may be altered as a function of reflex pathway gains. Healthy humans likely increase their γ-static fusimotor drive when muscles shorten. Quantification of physiological tremor by manipulation of joint angle may be a useful experimental probe of afferent gains and/or the integrity of automatic fusimotor control.

ABSTRACT

The involuntary force fluctuations associated with physiological (as distinct from pathological) tremor are an unavoidable component of human motor control. While the origins of physiological tremor are known to depend on muscle afferentation, it is possible that the mechanical properties of muscle-tendon systems also affect its generation, amplification and maintenance. In this paper, we investigated the dependence of physiological tremor on muscle length in healthy individuals. We measured physiological tremor during tonic, isometric plantarflexion torque at 30% of maximum at three ankle angles. The amplitude of physiological tremor increased as calf muscles shortened in contrast to the stretch reflex whose amplitude decreases as muscle shortens. We used a published closed-loop simulation model of afferented muscle to explore the mechanisms responsible for this behaviour. We demonstrate that changing muscle lengths does not suffice to explain our experimental findings. Rather, the model consistently required the modulation of  γ-static fusimotor drive to produce increases in physiological tremor with muscle shortening - while successfully replicating the concomitant reduction in stretch reflex amplitude. This need to control γ-static fusimotor drive explicitly as a function of muscle length has important implications. First, it permits the amplitudes of physiological tremor and stretch reflex to be decoupled. Second, it postulates neuromechanical interactions that require length-dependent γ drive modulation to be independent from α drive to the parent muscle. Lastly, it suggests that physiological tremor can be used as a simple, non-invasive measure of the afferent mechanisms underlying healthy motor function, and their disruption in neurological conditions.

Neural computational modeling reveals a major role of corticospinal gating of central oscillations in the generation of essential tremor

Essential tremor, also referred to as familial tremor, is an autosomal dominant genetic disease and the most common movement disorder. It typically involves a postural and motor tremor of the hands, head or other part of the body. Essential tremor is driven by a central oscillation signal in the brain. However, the corticospinal mechanisms involved in the generation of essential tremor are unclear. Therefore, in this study, we used a neural computational model that includes both monosynaptic and multisynaptic corticospinal pathways interacting with a propriospinal neuronal network. A virtual arm model is driven by the central oscillation signal to simulate tremor activity behavior. Cortical descending commands are classified as alpha or gamma through monosynaptic or multisynaptic corticospinal pathways, which converge respectively on alpha or gamma motoneurons in the spinal cord. Several scenarios are evaluated based on the central oscillation signal passing down to the spinal motoneurons via each descending pathway. The simulated behaviors are compared with clinical essential tremor characteristics to identify the corticospinal pathways responsible for transmitting the central oscillation signal. A propriospinal neuron with strong cortical inhibition performs a gating function in the generation of essential tremor. Our results indicate that the propriospinal neuronal network is essential for relaying the central oscillation signal and the production of essential tremor.

The Dynamics of Voluntary Force Production in Afferented Muscle Influence Involuntary Tremor

Voluntary control of force is always marked by some degree of error and unsteadiness. Both neural and mechanical factors contribute to these fluctuations, but how they interact to produce them is poorly understood. In this study, we identify and characterize a previously undescribed neuromechanical interaction where the dynamics of voluntary force production suffice to generate involuntary tremor. Specifically, participants were asked to produce isometric force with the index finger and use visual feedback to track a sinusoidal target spanning 5-9% of each individual's maximal voluntary force level. Force fluctuations and EMG activity over the flexor digitorum superficialis (FDS) muscle were recorded and their frequency content was analyzed as a function of target phase. Force variability in either the 1-5 or 6-15 Hz frequency ranges tended to be largest at the peaks and valleys of the target sinusoid. In those same periods, FDS EMG activity was synchronized with force fluctuations. We then constructed a physiologically-realistic computer simulation in which a muscle-tendon complex was set inside of a feedback-driven control loop. Surprisingly, the model sufficed to produce phase-dependent modulation of tremor similar to that observed in humans. Further, the gain of afferent feedback from muscle spindles was critical for appropriately amplifying and shaping this tremor. We suggest that the experimentally-induced tremor may represent the response of a viscoelastic muscle-tendon system to dynamic drive, and therefore does not fall into known categories of tremor generation, such as tremorogenic descending drive, stretch-reflex loop oscillations, motor unit behavior, or mechanical resonance. Our findings motivate future efforts to understand tremor from a perspective that considers neuromechanical coupling within the context of closed-loop control. The strategy of combining experimental recordings with physiologically-sound simulations will enable thorough exploration of neural and mechanical contributions to force control in health and disease.

Bio-Inspired Controller on an FPGA Applied to Closed-Loop Diaphragmatic Stimulation

Cervical spinal cord injury can disrupt connections between the brain respiratory network and the respiratory muscles which can lead to partial or complete loss of ventilatory control and require ventilatory assistance. Unlike current open-loop technology, a closed-loop diaphragmatic pacing system could overcome the drawbacks of manual titration as well as respond to changing ventilation requirements. We present an original bio-inspired assistive technology for real-time ventilation assistance, implemented in a digital configurable Field Programmable Gate Array (FPGA). The bio-inspired controller, which is a spiking neural network (SNN) inspired by the medullary respiratory network, is as robust as a classic controller while having a flexible, low-power and low-cost hardware design. The system was simulated in MATLAB with FPGA-specific constraints and tested with a computational model of rat breathing; the model reproduced experimentally collected respiratory data in eupneic animals. The open-loop version of the bio-inspired controller was implemented on the FPGA. Electrical test bench characterizations confirmed the system functionality. Open and closed-loop paradigm simulations were simulated to test the FPGA system real-time behavior using the rat computational model. The closed-loop system monitors breathing and changes in respiratory demands to drive diaphragmatic stimulation. The simulated results inform future acute animal experiments and constitute the first step toward the development of a neuromorphic, adaptive, compact, low-power, implantable device. The bio-inspired hardware design optimizes the FPGA resource and time costs while harnessing the computational power of spike-based neuromorphic hardware. Its real-time feature makes it suitable for in vivo applications.

Coordinated alpha and gamma control of muscles and spindles in movement and posture

Mounting evidence suggests that both α and γ motoneurons are active during movement and posture, but how does the central motor system coordinate the α-γ controls in these tasks remains sketchy due to lack of in vivo data. Here a computational model of α-γ control of muscles and spindles was used to investigate α-γ integration and coordination for movement and posture. The model comprised physiologically realistic spinal circuitry, muscles, proprioceptors, and skeletal biomechanics. In the model, we divided the cortical descending commands into static and dynamic sets, where static commands (α_s and γ_s) were for posture maintenance and dynamic commands (α_d and γ_d) were responsible for movement. We matched our model to human reaching movement data by straightforward adjustments of descending commands derived from either minimal-jerk trajectories or human EMGs. The matched movement showed smooth reach-to-hold trajectories qualitatively close to human behaviors, and the reproduced EMGs showed the classic tri-phasic patterns. In particular, the function of γ_d was to gate the α_d command at the propriospinal neurons (PN) such that antagonistic muscles can accelerate or decelerate the limb with proper timing. Independent control of joint position and stiffness could be achieved by adjusting static commands. Deefferentation in the model indicated that accurate static commands of α_s and γ_s are essential to achieve stable terminal posture precisely, and that the γ_d command is as important as the α_d command in controlling antagonistic muscles for desired movements. Deafferentation in the model showed that losing proprioceptive afferents mainly affected the terminal position of movement, similar to the abnormal behaviors observed in human and animals. Our results illustrated that tuning the simple forms of α-γ commands can reproduce a range of human reach-to-hold movements, and it is necessary to coordinate the set of α-γ descending commands for accurate and stable control of movement and posture.

Conduction block in myelinated axons induced by high-frequency (kHz) non-symmetric biphasic stimulation

This study used the Frankenhaeuser-Huxley axonal model to analyze the effects of non-symmetric waveforms on conduction block of myelinated axons induced by high-frequency (10-300 kHz) biphasic electrical stimulation. The results predict a monotonic relationship between block threshold and stimulation frequency for symmetric waveform and a non-monotonic relationship for non-symmetric waveforms. The symmetric waveform causes conduction block by constantly activating both sodium and potassium channels at frequencies of 20-300 kHz, while the non-symmetric waveforms share the same blocking mechanism from 20 kHz up to the peak threshold frequency. At the frequencies above the peak threshold frequency the non-symmetric waveforms block axonal conduction by either hyperpolarizing the membrane (if the positive pulse is longer) or depolarizing the membrane (if the negative pulse is longer). This simulation study further increases our understanding of conduction block in myelinated axons induced by high-frequency biphasic electrical stimulation, and can guide future animal experiments as well as optimize stimulation parameters that might be used for electrically induced nerve block in clinical applications.

ADVANCES REGARDING POWERED PROSTHESIS FOR TRANSTIBIAL AMPUTATION

The necessity for developing advanced prostheses are apparent in light of projections that the forecast for the number of people enduring amputation will double by the year 2050. The transtibial powered prosthesis that enables positive mechanical work about the ankle during the powered plantar flexion aspect of stance phase constitutes a paradigm shift in available transtibial prostheses. The objective of the review is to advocate the state of the art regarding the transtibial powered prosthesis. The historic origins of the prosthesis and motivations for amputation are clarified. The phases of gait and the compensatory mechanisms and asymmetries inherent with passive transtibial prostheses are described. The three general classes of transtibial prosthesis (passive, energy storage and return and powered prostheses) are defined. Subsystems that are integral to the powered prosthesis are explained, such as the series elastic actuator and control architecture. Gait analysis systems and their role for the test and evaluation of energy storage and return and powered prostheses are demonstrated. Future advanced concepts; such as the integration of titin into novel muscle models that account for force enhancement and force depression including their implications for cutting edge bio-inspired actuators are elucidated. The review accounts for the evolution of the prosthetic device with regards to the scope of transtibial amputation and assesses the current state-of-the-art.

Effects of spinal cord injury-induced changes in muscle activation on foot drag in a computational rat ankle model

Spinal cord injury (SCI) can lead to changes in muscle activation patterns and atrophy of affected muscles. Moderate levels of SCI are typically associated with foot drag during the swing phase of locomotion. Foot drag is often used to assess locomotor recovery, but the causes remain unclear. We hypothesized that foot drag results from inappropriate muscle coordination preventing flexion at the stance-to-swing transition. To test this hypothesis and to assess the relative contributions of neural and muscular changes on foot drag, we developed a two-dimensional, one degree of freedom ankle musculoskeletal model with gastrocnemius and tibialis anterior muscles. Anatomical data collected from sham-injured and incomplete SCI (iSCI) female Long-Evans rats as well as physiological data from the literature were used to implement an open-loop muscle dynamics model. Muscle insertion point motion was calculated with imposed ankle trajectories from kinematic analysis of treadmill walking in sham-injured and iSCI animals. Relative gastrocnemius deactivation and tibialis anterior activation onset times were varied within physiologically relevant ranges based on simplified locomotor electromyogram profiles. No-atrophy and moderate muscle atrophy as well as normal and injured muscle activation profiles were also simulated. Positive moments coinciding with the transition from stance to swing phase were defined as foot swing and negative moments as foot drag. Whereas decreases in activation delay caused by delayed gastrocnemius deactivation promote foot drag, all other changes associated with iSCI facilitate foot swing. Our results suggest that even small changes in the ability to precisely deactivate the gastrocnemius could result in foot drag after iSCI.

Modular control of movement and posture by the corticospinal alpha-gamma motor systems

It is widely assumed that neural control of movement is carried out by the a motor system sufficiently. The role of the γ motor system in movement and posture has not been adequately addressed in motor control studies. Here, we propose a modular control model for movement and posture based on propriospinal neuronal (PN) network and spinal α-γ motor system. In the modular control model, the a and γ motor commands are divided into static and dynamic functions. The static commands are specified by the higher center of brain for posture control, and the dynamic commands for movement generation, respectively. Centrally planned kinematics based on the minimal jerk criterion is conveyed to the periphery via the γ motor system, while centrally programmed bi-phasic burst pattern of muscle activation is relayed to a pair of antagonistic muscles through the a motor system via the PN. Results of simulation showed that elbow kinematics and biceps and triceps activations displayed the similar kinematic and EMG features of fast reaching movement in human. This suggests a hypothesis that the α-γ motor systems can achieve modular control of movement and posture in parallel.

Simulation of a computational winding filament model with an exponential spring to represent titin

The goal of developing high fidelity simulation of muscle force is of considerable interest for the biomedical community. Traditionally Hill models have been incorporated. However, feasible scope of the Hill model is inherently limited, especially in light of the growing relevance of muscle history dependence. History dependence is considered to be significant for motor control and stability. Attempts have been made to augment the Hill model to emulate history dependence. The titin winding filament model best elucidates history dependence of muscle force including force enhancement. The recent version of the titin winding filament model accounts for the functionality of titin through a pulley linked with the contractile element and a linear spring to represent the elastic properties of titin. A new and more realistic amendment to the winding filament model is incorporation of an exponential spring to characterize the elastic properties of titin. A sensitivity study as a function of the titin exponential spring constant is presented. Overall the amalgamation of the titin exponential spring to the winding filament model improves the respective force enhancement characteristics with a relatively more optimal exponential spring constant that provides a maximal averaged coefficient of determination.

Effect of non-symmetric waveform on conduction block induced by high-frequency (kHz) biphasic stimulation in unmyelinated axon

The effect of a non-symmetric waveform on nerve conduction block induced by high-frequency biphasic stimulation is investigated using a lumped circuit model of the unmyelinated axon based on Hodgkin-Huxley equations. The simulation results reveal that the block threshold monotonically increases with the stimulation frequency for the symmetric stimulation waveform. However, a non-monotonic relationship between block threshold and stimulation frequency is observed when the stimulation waveform is non-symmetric. Constant activation of potassium channels by the high-frequency stimulation results in the increase of block threshold with increasing frequency. The non-symmetric waveform with a positive pulse 0.4-0.8 μs longer than the negative pulse blocks axonal conduction by hyperpolarizing the membrane and causes a decrease in block threshold as the frequency increases above 12-16 kHz. On the other hand, the non-symmetric waveform with a negative pulse 0.4-0.8 μs longer than the positive pulse blocks axonal conduction by depolarizing the membrane and causes a decrease in block threshold as the frequency increases above 40-53 kHz. This simulation study is important for understanding the potential mechanisms underlying the nerve block observed in animal studies, and may also help to design new animal experiments to further improve the nerve block method for clinical applications.

Corticomuscular transmission of tremor signals by propriospinal neurons in Parkinson's disease

Cortical oscillatory signals of single and double tremor frequencies act together to cause tremor in the peripheral limbs of patients with Parkinson's disease (PD). But the corticospinal pathway that transmits the tremor signals has not been clarified, and how alternating bursts of antagonistic muscle activations are generated from the cortical oscillatory signals is not well understood. This paper investigates the plausible role of propriospinal neurons (PN) in C3–C4 in transmitting the cortical oscillatory signals to peripheral muscles. Kinematics data and surface electromyogram (EMG) of tremor in forearm were collected from PD patients. A PN network model was constructed based on known neurophysiological connections of PN. The cortical efferent signal of double tremor frequencies were integrated at the PN network, whose outputs drove the muscles of a virtual arm (VA) model to simulate tremor behaviors. The cortical efferent signal of single tremor frequency actuated muscle spindles. By comparing tremor data of PD patients and the results of model simulation, we examined two hypotheses regarding the corticospinal transmission of oscillatory signals in Parkinsonian tremor. Hypothesis I stated that the oscillatory cortical signals were transmitted via the mono-synaptic corticospinal pathways bypassing the PN network. The alternative hypothesis II stated that they were transmitted by way of PN multi-synaptic corticospinal pathway. Simulations indicated that without the PN network, the alternating burst patterns of antagonistic muscle EMGs could not be reliably generated, rejecting the first hypothesis. However, with the PN network, the alternating burst patterns of antagonist EMGs were naturally reproduced under all conditions of cortical oscillations. The results suggest that cortical commands of single and double tremor frequencies are further processed at PN to compute the alternating burst patterns in flexor and extensor muscles, and the neuromuscular dynamics demonstrated a frequency dependent damping on tremor, which may prevent tremor above 8 Hz to occur.

An approach for simulation of the muscle force modeling it by summation of motor unit contraction forces

Muscle force is due to the cumulative effect of repetitively contracting motor units (MUs). To simulate the contribution of each MU to whole muscle force, an approach implemented in a novel computer program is proposed. The individual contraction of an MU (the twitch) is modeled by a 6-parameter analytical function previously proposed; the force of one MU is a sum of its contractions due to an applied stimulation pattern, and the muscle force is the sum of the active MUs. The number of MUs, the number of slow, fast-fatigue-resistant, and fast-fatigable MUs, and their six parameters as well as a file with stimulation patterns for each MU are inputs for the developed software. Different muscles and different firing patterns can be simulated changing the input data. The functionality of the program is illustrated with a model consisting of 30 MUs of rat medial gastrocnemius muscle. The twitches of these MUs were experimentally measured and modeled. The forces of the MUs and of the whole muscle were simulated using different stimulation patterns that included different regular, irregular, synchronous, and asynchronous firing patterns of MUs. The size principle of MUs for recruitment and derecruitment was also demonstrated using different stimulation paradigms.

A Simplified Spinal-Like Controller Facilitates Muscle Synergies and Robust Reaching Motions

We develop an adaptive controller for multi-joint, multi-muscle arm movements based on simplified spinal-like circuits found in the periphery, muscle synergies, and interpretations of gain-field projections from reach related neurons in the Superior Colliculus. The resulting innovation provides a highly robust sensory based controller that can be adapted to systems which require multi-muscle co-ordination. It provides human-like responses during perturbations elicited either internally or by the environment and for simple point-to-point reaching. We simulate limb motion and EMGs in Simulink using Virtual Muscle models and a variety of paradigms, including motion with external perturbations, and varying levels of antagonist muscle co-contractions. The results show that the system can exhibit smooth coordinated motions, without explicit kinematic or dynamic planning even in the presence of perturbations. In addition, we show by varying the level of muscle co-contractions from 0% to 40%, that the effects of external perturbations on joint trajectories can be reduced by up to 42%. The improved controller design is novel providing robust behavior during dynamic events and an automatic adaptive response from sensory-integration.

Evaluation of feedforward and feedback contributions to hand stiffness and variability in multijoint arm control

The purpose of this study is to validate a neuromechanical model of the virtual arm (VA) by comparing emerging behaviors of the model to those of experimental observations. Hand stiffness of the VA model was obtained by either theoretical computation or simulated perturbations. Variability in hand position of the VA was generated by adding signal dependent noise (SDN) to the motoneuron pools of muscles. Reflex circuits of Ia, Ib and Renshaw cells were included to regulate the motoneuron pool outputs. Evaluation of hand stiffness and variability was conducted in simulations with and without afferent feedback under different patterns of muscle activations during postural maintenance. The simulated hand stiffness and variability ellipses captured the experimentally observed features in shape, magnitude and orientation. Steady state afferent feedback contributed significantly to the increase in hand stiffness by 35.75±16.99% in area, 18.37±7.80% and 16.15±7.15% in major and minor axes; and to the reduction of hand variability by 49.41±21.19% in area, 36.89±12.78% and 18.87±23.32% in major and minor axes. The VA model reproduced the neuromechanical behaviors that were consistent with experimental data, and it could be a useful tool for study of neural control of posture and movement, as well as for application to rehabilitation.

Fusimotor control of spindle sensitivity regulates central and peripheral coding of joint angles

Proprioceptive afferents from muscle spindles encode information about peripheral joint movements for the central nervous system (CNS). The sensitivity of muscle spindle is nonlinearly dependent on the activation of gamma (γ) motoneurons in the spinal cord that receives inputs from the motor cortex. How fusimotor control of spindle sensitivity affects proprioceptive coding of joint position is not clear. Furthermore, what information is carried in the fusimotor signal from the motor cortex to the muscle spindle is largely unknown. In this study, we addressed the issue of communication between the central and peripheral sensorimotor systems using a computational approach based on the virtual arm (VA) model. In simulation experiments within the operational range of joint movements, the gamma static commands (γ(s)) to the spindles of both mono-articular and bi-articular muscles were hypothesized (1) to remain constant, (2) to be modulated with joint angles linearly, and (3) to be modulated with joint angles nonlinearly. Simulation results revealed a nonlinear landscape of Ia afferent with respect to both γ(s) activation and joint angle. Among the three hypotheses, the constant and linear strategies did not yield Ia responses that matched the experimental data, and therefore, were rejected as plausible strategies of spindle sensitivity control. However, if γ(s) commands were quadratically modulated with joint angles, a robust linear relation between Ia afferents and joint angles could be obtained in both mono-articular and bi-articular muscles. With the quadratic strategy of spindle sensitivity control, γ(s) commands may serve as the CNS outputs that inform the periphery of central coding of joint angles. The results suggest that the information of joint angles may be communicated between the CNS and muscles via the descending γ(s) efferent and Ia afferent signals.

Mammalian muscle model for predicting force and energetics during physiological behaviors

Muscles convert metabolic energy into mechanical work. A computational model of muscle would ideally compute both effects efficiently for the entire range of muscle activation and kinematic conditions (force and length). We have extended the original Virtual Muscle algorithm (Cheng , 2000) to predict energy consumption for both slow- and fast-twitch muscle fiber types, partitioned according to the activation process (E(a)), cross-bridge cycling (E(xb)) and ATP/PCr recovery (E(recovery)). Because the terms of these functions correspond to identifiable physiological processes, their coefficients can be estimated directly from the types of experiments that are usually performed and extrapolated to dynamic conditions of natural motor behaviors. We also implemented a new approach to lumped modeling of the gradually recruited and frequency modulated motor units comprising each fiber type, which greatly reduced computational time. The emergent behavior of the model has significant implications for studies of optimal motor control and development of rehabilitation strategies because its trends were quite different from traditional estimates of energy (e.g., activation, force, stress, work, etc.). The model system was scaled to represent three different human experimental paradigms in which muscle heat was measured during voluntary exercise; predicted and observed energy rate agreed well both qualitatively and quantitatively.

Dynamic simulation of perturbation responses in a closed-loop virtual arm model

A closed-loop virtual arm (VA) model has been developed in SIMULINK environment by adding spinal reflex circuits and propriospinal neural networks to the open-loop VA model developed in early study [1]. An improved virtual muscle model (VM4.0) is used to speed up simulation and to generate more precise recruitment of muscle force at low levels of muscle activation. Time delays in the reflex loops are determined by their synaptic connections and afferent transmission back to the spinal cord. Reflex gains are properly selected so that closed-loop responses are stable. With the closed-loop VA model, we are developing an approach to evaluate system behaviors by dynamic simulation of perturbation responses. Joint stiffness is calculated based on simulated perturbation responses by a least-squares algorithm in MATLAB. This method of dynamic simulation will be essential for further evaluation of feedforward and reflex control of arm movement and position.

On the use of musculoskeletal models to interpret motor control strategies from performance data

The intrinsic viscoelastic properties of muscle are central to many theories of motor control. Much of the debate over these theories hinges on varying interpretations of these muscle properties. In the present study, we describe methods whereby a comprehensive musculoskeletal model can be used to make inferences about motor control strategies that would account for behavioral data. Muscle activity and kinematic data from a monkey were recorded while the animal performed a single degree-of-freedom pointing task in the presence of pseudo-random torque perturbations. The monkey's movements were simulated by a musculoskeletal model with accurate representations of musculotendon morphometry and contractile properties. The model was used to quantify the impedance of the limb while moving rapidly, the differential action of synergistic muscles, the relative contribution of reflexes to task performance and the completeness of recorded EMG signals. Current methods to address these issues in the absence of musculoskeletal models were compared with the methods used in the present study. We conclude that musculoskeletal models and kinetic analysis can improve the interpretation of kinematic and electrophysiological data, in some cases by illuminating shortcomings of the experimental methods or underlying assumptions that may otherwise escape notice.