Neural computations underlying the exertion of force: a model

We have developed a model that simulates possible mechanisms by which supraspinal neuronal signals coding forces could converge in the spinal cord and provide an ongoing integrated signal to the motoneuronal pools whose activation results in the exertion of force. The model consists of a three-layered neural network connected to a two-joint-six-muscle model of the arm. The network layers represent supraspinal populations, spinal cord interneurons, and motoneuronal pools. We propose an approach to train the network so that, after the synaptic connections between the layers are adjusted, the performance of the model is consistent with experimental data obtained on different organisms using different experimental paradigms: the stiffness characteristics of human arm; the structure of force fields generated by the stimulation of the frog's spinal cord; and a correlation between motor cortical activity and force exerted by monkey against an immovable object. The model predicts a specific pattern of connections between supraspinal populations coding forces and spinal cord interneurons: the weight of connection should be correlated with directional preference of interconnected units. Finally, our simulations demonstrate that the force generated by the sum of neural signals can be nearly equal to the vector sum of forces generated by each signal independently, in spite of the complex nonlinearities intervening between supraspinal commands and forces exerted by the arm in response to these commands.     

等长伸膝动作的运动单元放电特征分析

本研究基于表面肌电分解技术,分析伸膝动作中不同发力状态下大腿肌肉运动单元的解码准确性,并对比神经特征和肌电特征在肌肉激活程度估计中的效果. 12名大学生分别以2种发力速度和4种发力等级完成伸膝动作的等长收缩.实验同步采集受试者股内侧肌和股外侧肌处的高密度表面肌电信号和伸膝动作收缩力.基于卷积核补偿算法解码肌电信号得到运动单元动作电位,提取神经特征用于收缩力的互相关分析.结果发现,对于股内侧肌,2种任务及4种收缩力等级下平均解码得到(7±4)个运动单元,股外侧肌平均解码得到(9±5)个运动单元.它们的平均脉冲信噪比(pulse-to-noise ratio,PNR)为30.1 d B,对应解码准确率大于90%.股内侧肌的两种神经特征与力之间的平均相关性分别为(0.79±0.08)和(0.80±0.08),股外侧肌的两种神经特征与力之间的平均相关性分别为(0.85±0.05)和(0.85±0.06).综上可见,基于肌电分解技术可以准确识别不同发力状态下大腿肌肉的运动单元放电活动,并且运动单元放电频率与伸膝动作力高度相关,研究结果可用于运动康复、运动训练及人机接口等领域.     

Early neural responses to strength training

The neural adaptations that accompany strength training have yet to be fully determined. Here we sought to address this topic by testing the idea that strength training might share similar mechanisms with some forms of motor learning. Since ballistic motor learning is accompanied by a shift in muscle twitches induced by transcranial magnetic stimulation (TMS) toward the training direction, we sought to investigate if these changes also occur after single isometric strength training sessions with various contraction duration and rate of force development characteristics (i.e., brief or sustained ballistic contractions or slow, sustained contractions). Twitch force resultant vectors and motor-evoked potentials (MEPs) induced by TMS were measured before and after single sessions of strength training involving the forearm muscles. Participants (n = 12) each performed three training protocols (each consisting of 4 sets of 10 repetitions) and served as their own control in a counterbalanced order. All three training protocols caused a significant (P < 0.05) shift in TMS-induced twitch force resultant vectors toward the training direction, followed by a gradual shift back toward the pretraining direction. The strongest effect was found when training involved both ballistic and sustained force components. There were no large or consistent changes in the direction of twitches evoked by motor nerve stimulation for any of the three training protocols. We suggest that these early neural responses to strength training, which share similar corticospinal changes to motor learning, might reflect an important process that precedes more long-term neural adaptation that ultimately enhance strength.     

The influence of the way the muscle force is modeled on the predicted results obtained by solving indeterminate problems for a fast elbow flexion

A critical point in models of the human limbs when the aim is to investigate the motor control is the muscle model. More often the mechanical output of a muscle is considered as one musculotendon force that is a design variable in optimization tasks solved predominantly by static optimization. For dynamic conditions, the relationship between the developed force, the length and the contraction velocity of a muscle becomes important and rheological muscle models can be incorporated in the optimization tasks. Here the muscle activation can be a design variable as well. Recently a new muscle model was proposed. A muscle is considered as a mixture of motor units (MUs) with different peculiarities and the muscle force is calculated as a sum of the MUs twitches. The aim of the paper is to compare these three ways for presenting the muscle force. Fast elbow flexion is investigated using a planar model with five muscles. It is concluded that the rheological models are suitable for calculation of the current maximal muscle forces that can be used as weight factors in the objective functions. The model based on MUs has many advantages for precise investigations of motor control. Such muscle presentation can explain the muscle co-contraction and the role of the fast and the slow MUs. The relationship between the MUs activation and the mechanical output is more clear and closer to the reality.     

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.     

Deficient Grip Force Control in Schizophrenia: Behavioral and Modeling Evidence for Altered Motor Inhibition and Motor Noise

Whether upper limb sensorimotor control is affected in schizophrenia and how underlying pathological mechanisms may potentially intervene in these deficits is still being debated. We tested voluntary force control in schizophrenia patients and used a computational model in order to elucidate potential cerebral mechanisms underlying sensorimotor deficits in schizophrenia. A visuomotor grip force-tracking task was performed by 17 medicated and 6 non-medicated patients with schizophrenia (DSM-IV) and by 15 healthy controls. Target forces in the ramp-hold-and-release paradigm were set to 5N and to 10% maximal voluntary grip force. Force trajectory was analyzed by performance measures and Principal Component Analysis (PCA). A computational model incorporating neural control signals was used to replicate the empirically observed motor behavior and to explore underlying neural mechanisms. Grip task performance was significantly lower in medicated and non-medicated schizophrenia patients compared to controls. Three behavioral variables were significantly higher in both patient groups: tracking error (by 50%), coefficient of variation of force (by 57%) and duration of force release (up by 37%). Behavioral performance did not differ between patient groups. Computational simulation successfully replicated these findings and predicted that decreased motor inhibition, together with an increased signal-dependent motor noise, are sufficient to explain the observed motor deficits in patients. PCA also suggested altered motor inhibition as a key factor differentiating patients from control subjects: the principal component representing inhibition correlated with clinical severity. These findings show that schizophrenia affects voluntary sensorimotor control of the hand independent of medication, and suggest that reduced motor inhibition and increased signal-dependent motor noise likely reflect key pathological mechanisms of the sensorimotor deficit.     

Modular neuromuscular control of human locomotion by central pattern generator

The central pattern generators (CPG) in the spinal cord are thought to be responsible for producing the rhythmic motor patterns during rhythmic activities. For locomotor tasks, this involves much complexity, due to a redundant system of muscle actuators with a large number of highly nonlinear muscles. This study proposes a reduced neural control strategy for the CPG, based on modular organization of the co-active muscles, i.e., muscle synergies. Four synergies were extracted from the EMG data of the major leg muscles of two subjects, during two gait trials each, using non-negative matrix factorization algorithm. A Matsuoka׳s four-neuron CPG model with mutual inhibition, was utilized to generate the rhythmic activation patterns of the muscle synergies, using the hip flexion angle and foot contact force information from the sensory afferents as inputs. The model parameters were tuned using the experimental data of one gait trial, which resulted in a good fitting accuracy (RMSEs between 0.0491 and 0.1399) between the simulation and experimental synergy activations. The model׳s performance was then assessed by comparing its predictions for the activation patterns of the individual leg muscles during locomotion with the relevant EMG data. Results indicated that the characteristic features of the complex activation patterns of the muscles were well reproduced by the model for different gait trials and subjects. In general, the CPG- and muscle synergy-based model was promising in view of its simple architecture, yet extensive potentials for neuromuscular control, e.g., resolving redundancies, distributed and fast control, and modulation of locomotion by simple control signals.     

LaDIVA: A neurocomputational model providing laryngeal motor control for speech acquisition and production

Many voice disorders are the result of intricate neural and/or biomechanical impairments that are poorly understood. The limited knowledge of their etiological and pathophysiological mechanisms hampers effective clinical management. Behavioral studies have been used concurrently with computational models to better understand typical and pathological laryngeal motor control. Thus far, however, a unified computational framework that quantitatively integrates physiologically relevant models of phonation with the neural control of speech has not been developed. Here, we introduce LaDIVA, a novel neurocomputational model with physiologically based laryngeal motor control. We combined the DIVA model (an established neural network model of speech motor control) with the extended body-cover model (a physics-based vocal fold model). The resulting integrated model, LaDIVA, was validated by comparing its model simulations with behavioral responses to perturbations of auditory vocal fundamental frequency (f_o) feedback in adults with typical speech. LaDIVA demonstrated capability to simulate different modes of laryngeal motor control, ranging from short-term (i.e., reflexive) and long-term (i.e., adaptive) auditory feedback paradigms, to generating prosodic contours in speech. Simulations showed that LaDIVA’s laryngeal motor control displays properties of motor equivalence, i.e., LaDIVA could robustly generate compensatory responses to reflexive vocal f_o perturbations with varying initial laryngeal muscle activation levels leading to the same output. The model can also generate prosodic contours for studying laryngeal motor control in running speech. LaDIVA can expand the understanding of the physiology of human phonation to enable, for the first time, the investigation of causal effects of neural motor control in the fine structure of the vocal signal.     

An oscillator theory of motor unit recruitment

The phenomenon of systematic recruitment of motor units with increasing demand load is usually explained by the size principle. Though this principle successfully explains the gain-related aspects of muscle force generation, it does not address the need for desynchronization of motor unit activities in order to produce a smooth tension profile at the level of whole muscle, while individual muscle fibers are "twitching." We propose an oscillator model of motor neurons in which a pool of motor neurons fires a bundle of muscle fibers. Although individual muscle fibers have a complicated tension profile, the tension produced by the entire bundle is regulated and follows a command signal accurately. This is shown to be possible because of uncorrelated activity produced by local inhibitory connections among motor neurons. Connections that produce synchronized oscillations result in uncontrolled contractions of the muscle. These results seem to suggest that while synchronized activity indicates pathology and disease, desynchronized activity is the precondition for normal muscle function. Physiological evidence for the proposed theory of motor unit synchronization is presented.     

Control of rabbit nictitating membrane movements

Our objective in this study is to synthesize existing experimental data by constructing a realistic neuromechanical control model of rabbit nictitating membrane (NM) movements. We model the retractor bulbi muscle at the motor unit level because this is the level of nervous system control and also facilitates comparison with experimental data. Our motor unit model is derived from an earlier model of muscle activation based on calcium kinetics and includes a post-activation potentiation mechanism. Motor units are combined into a model of whole muscle that includes length-tension and force-velocity effects. Finally, we incorporate the muscle model into a biomechanical model in which the globe and NM are represented as a system of inertial, viscous, and elastic elements. The model takes patterns of neural signals (in the form of impulses) as input and produces movement of the NM as output. Our muscle model quantitatively accounts for data on isometric force development and decay for twitch, double shock, and tetanic stimulation. The complete model may be used for analysis of the relationship of motoneuron activity to behavior or as a realistic response generator in models of NM conditioning. This study also highlights gaps in the experimental data on the rabbit NM effector system.     

Neuromuscular dysfunction with the experimental arm acting as its own reference following eccentric and isometric exercise

Eccentric exercise has been extensively used as a model to study muscle damage-induced neuromuscular impairment, adopting mainly a bilateral matching task between the reference (unexercised) arm and the indicator (exercised) arm. However, little attention has been given to the muscle proprioceptive function when the exercised arm acts as its own reference. This study investigated muscle proprioception and motor control, with the arm acting both as reference and indicator, following eccentric exercise and compared them with those observed after isometric exercise. Fourteen young male volunteers were equally divided into two groups and performed an eccentric or isometric exercise protocol with the elbow flexors of the non-dominant arm on an isokinetic dynamometer. Both exercise protocols induced significant changes in indicators of muscle damage, that is, muscle soreness, range of motion and maximal isometric force post-exercise (p < 0.05–0.001), and neuromuscular function was similarly affected following both protocols. Perception of force was impaired over the 4-day post-exercise period (p < 0.001), with the applied force being systematically overestimated. Perception of joint position was significantly disturbed (i.e., target angle was underestimated) only at one elbow angle on day 4 post-exercise (p < 0.05). The misjudgements and disturbed motor output observed when the exercised arm acted as its own reference concur with the view that they could be a result of a mismatch between the central motor command and an impaired motor control after muscle damage.     

Neurobiology of muscle fatigue.

Muscle fatigue encompasses a class of acute effects that impair motor performance. The mechanisms that can produce fatigue involve all elements of the motor system, from a failure of the formulation of the descending drive provided by suprasegmental centers to a reduction in the activity of the contractile proteins. We propose four themes that provide a basis for the systematic evaluation of the neural and neuromuscular fatigue mechanisms: 1) task dependency to identify the conditions that activate the various mechanisms; 2) force-fatigability relationship to explore the interaction between the mechanisms that results in a hyperbolic relationship between force and endurance time; 3) muscle wisdom to examine the association among a concurrent decline in force, relaxation rate, and motor neuron discharge that results in an optimization of force; and 4) sense of effort to determine the role of effort in the impairment of performance. On the basis of this perspective with an emphasis on neural mechanisms, we suggest a number of experiments to advance our understanding of the neurobiology of muscle fatigue.     

Mathematical and philosophical reflections on motor control systems

In line with the tradition of the Dutch school of functional morphology, an attempt is made to integrate numerical models of sarcomeres, muscle fibres, muscles, bone-connective-tissue systems, joints, muscle spindles and neural networks into one model simulating motor control. There are two purposes for this attempt. Firstly, to indicate whether numerical properties of the organs forming a system of motor control can be explained in terms of its motor functions. Secondly, to indicate properties that emerge from the integration of the organs into a system of motor control: how much more is an integrated motor system than the sum of its functional components. The motor control system of chewing has been taken as an example, particularly that in rats.     

Analysis of an optimal control model of multi-joint arm movements

 In this paper, we propose a model of biological motor control for generation of goal-directed multi-joint arm movements, and study the formation of muscle control inputs and invariant kinematic features of movements. The model has a hierarchical structure that can determine the control inputs for a set of redundant muscles without any inverse computation. Calculation of motor commands is divided into two stages, each of which performs a transformation of motor commands from one coordinate system to another. At the first level, a central controller in the brain accepts instructions from higher centers, which represent the motor goal in the Cartesian space. The controller computes joint equilibrium trajectories and excitation signals according to a minimum effort criterion. At the second level, a neural network in the spinal cord translates the excitation signals and equilibrium trajectories into control commands to three pairs of antagonist muscles which are redundant for a two-joint arm. No inverse computation is required in the determination of individual muscle commands. The minimum effort controller can produce arm movements whose dynamic and kinematic features are similar to those of voluntary arm movements. For fast movements, the hand approaches a target position along a near-straight path with a smooth bell-shaped velocity. The equilibrium trajectories in X and Y show an ‘N’ shape, but the end-point equilibrium path zigzags around the hand path. Joint movements are not always smooth. Joint reversal is found in movements in some directions. The excitation signals have a triphasic (or biphasic) pulse pattern, which leads to stereotyped triphasic (or biphasic) bursts in muscle control inputs, and a dynamically modulated joint stiffness. There is a fixed sequence of muscle activation from proximal muscles to distal muscles. The order is preserved in all movements. For slow movements, it is shown that a constant joint stiffness is necessary to produce a smooth movement with a bell-shaped velocity. Scaled movements can be reproduced by varying the constraints on the maximal level of excitation signals according to the speed of movement. When the inertial parameters of the arm are altered, movement trajectories can be kept invariant by adjusting the pulse height values, showing the ability to adapt to load changes. These results agree with a wide range of experimental observations on human voluntary movements. Received: 4 December 1995 / Accepted in revised form: 17 September 1996     

Model study of time‐dependent muscle response to pulsed electrical stimulation

A systems‐level model analysis of neuromuscular response to external electrical stimulation is presented. Action potential (AP) generation, dynamics of voltage‐based calcium release at the motor endplates controlled by the arrival of APs, and muscle force production are all comprehensively included. Numerical predictions exhibit trends that are qualitatively similar to measurements of muscle response in rats from a burst of cortical stimulation and a nanosecond impulse. Modulation of neural membrane conductances (including possible electroporation) that alters the neural impulse generation frequency is hypothesized as a possible mechanism leading to observed changes in muscle force production. Other possibilities such as calcium release at nerve end endings also exist. It is also proposed that multipulsing strategies and changing the electric field direction by using multielectrode systems would be useful. Bioelectromagnetics 31:361–370, 2010. © 2010 Wiley‐Liss, Inc.     

Hierarchical genetic algorithm versus static optimization-investigation of elbow flexion and extension movements

The applicability of static optimization (and, respectively, frequently used objective functions) for prediction of individual muscle forces for dynamic conditions has often been discussed. Some of the problems are whether time-independent objective functions are suitable, and how to incorporate muscle physiology in models. The present paper deals with a twofold task: (1) implementation of hierarchical genetic algorithm (HGA) based on the properties of the motor units (MUs) twitches, and using multi-objective, time-dependent optimization functions; and (2) comparison of the results of the HGA application with those obtained through static optimization with a criterion "minimum of a weighted sum of the muscle forces raised to the power of n". HGA and its software implementation are presented. The moments of neural stimulation of all MUs are design variables coding the problem in the terms of HGA. The main idea is in using genetic operations to find these moments, so that the sum of MUs twitches satisfies the imposed goals (required joint moments, minimal sum of muscle forces, etc.). Elbow flexion and extension movements with different velocities are considered as proper illustration. It is supposed that they are performed by two extensor muscles and three flexor muscles. The results show that HGA is a suitable means for precise investigation of motor control. Many experimentally observed phenomena (such as antagonistic co-contraction, three-phasic behavior of the muscles during fast movements) can find their explanation by the properties of the MUs twitches. Static optimization is also able to predict three-phasic behavior and could be used as practicable and computationally inexpensive method for total estimation of the muscle forces.     

Schema-based learning of adaptable and flexible prey-catching in anurans I. The basic architecture

A motor action often involves the coordination of several motor synergies and requires flexible adjustment of the ongoing execution based on feedback signals. To elucidate the neural mechanisms underlying the construction and selection of motor synergies, we study prey-capture in anurans. Experimental data demonstrate the intricate interaction between different motor synergies, including the interplay of their afferent feedback signals (Weerasuriya 1991; Anderson and Nishikawa 1996). Such data provide insights for the general issues concerning two-way information flow between sensory centers, motor circuits and periphery in motor coordination. We show how different afferent feedback signals about the status of the different components of the motor apparatus play a critical role in motor control as well as in learning. This paper, along with its companion paper, extend the model by Liaw et al. (1994) by integrating a number of different motor pattern generators, different types of afferent feedback, as well as the corresponding control structure within an adaptive framework we call Schema-Based Learning. We develop a model of the different MPGs involved in prey-catching as a vehicle to investigate the following questions: What are the characteristic features of the activity of a single muscle? How can these features be controlled by the premotor circuit? What are the strategies employed to generate and synchronize motor synergies? What is the role of afferent feedback in shaping the activity of a MPG? How can several MPGs share the same underlying circuitry and yet give rise to different motor patterns under different input conditions? In the companion paper we also extend the model by incorporating learning components that give rise to more flexible, adaptable and robust behaviors. To show these aspects we incorporate studies on experiments on lesions and the learning processes that allow the animal to recover its proper functioning     

Neural control of muscle blood flow during exercise.

Activation of skeletal muscle fibers by somatic nerves results in vasodilation and functional hyperemia. Sympathetic nerve activity is integral to vasoconstriction and the maintenance of arterial blood pressure. Thus the interaction between somatic and sympathetic neuroeffector pathways underlies blood flow control to skeletal muscle during exercise. Muscle blood flow increases in proportion to the intensity of activity despite concomitant increases in sympathetic neural discharge to the active muscles, indicating a reduced responsiveness to sympathetic activation. However, increased sympathetic nerve activity can restrict blood flow to active muscles to maintain arterial blood pressure. In this brief review, we highlight recent advances in our understanding of the neural control of the circulation in exercising muscle by focusing on two main topics: 1) the role of motor unit recruitment and muscle fiber activation in generating vasodilator signals and 2) the nature of interaction between sympathetic vasoconstriction and functional vasodilation that occurs throughout the resistance network. Understanding how these control systems interact to govern muscle blood flow during exercise leads to a clear set of specific aims for future research.     

Dynamic responses of series force receptors innervating the opener muscle apodeme in the blue crab, Callinectes sapidus

Receptors monitoring muscle force innervate the opener muscle apodeme in the walking legs of the blue crab, Callinectes sapidus. Biocytin backfills reveal 9–15 bipolar neurons with somata as large as 60 μm positioned at the distal end of the apodeme. Sensory endings insert into the apodeme and are in series with the opener muscle. The axons of these neurons form the opener apodeme sensory nerve that merges with the most distal branch of the opener motor nerve. Recordings reveal that the receptors are not spontaneously active nor do they respond to passive muscle stretch. Isometric muscle contraction evoked by stimulating the opener excitor motor neuron is the adequate stimulus for receptor firing. Most significant is the finding that during contraction, over a wide range of forces, the firing rate of individual receptors closely parallels the rate of change of isometric force. The peak instantaneous frequency typically occurs at the force derivative maximum, but not at maximum force development. Thus, receptors of the opener apodeme sensory nerve more closely monitor changes in isometric force rather than the total force achieved. Accepted: 20 September 1996     

In vitro studies of skeletal muscle membranes

Summary Sarcolemmal membranes were prepared from slow-twitch (red) and fasttwitch (white) skeletal muscle of the rat. A sensitive adenylate cyclase assay was used and basal, fluoride- and catecholamine-stimulated activities measured. The greaterin vivo sensitivity of red muscle to the effects of catecholamines correlates, in the present study, with approximately a twofold stimulation of its sarcolemmal adenylate cyclase with isoproterenol (10 m). The white muscle enzyme, on the other hand, is only minimally stimulated (20%) at the same concentration of -adrenergic agonist. Fast-twitch muscle is known to be physiologically insensitive to catecholaminein vivo.A course of sciatic nerve denervation was followed to further distinguish these two metabolic types of skeletal muscle and their respective adenylate cyclases. The slow-twitch muscle enzyme activities were completely and permanently lost on denervation. The white muscle enzyme, however, recovered almost completely after an initial reduction in specific activity the first week. Interestingly, the NaF-stimulated activity lagged behind both the basal and hormone-stimulated activities of the white muscle enzyme, in returning to control levels. The activities of cyclic nucleotide phosphodiesterase were evaluated in homogenates of the two muscle types in innervated rats and following denervation, in order to further define the neural influence on skeletal muscle cyclic nucleotide metabolism.The results suggest that the motor nerve may regulate some of the metabolic properties of slow-twitch muscle (which may involve cyclic AMP) by controlling the responsiveness of its sarcolemmal-bound adenylate cyclase system.Presented in part at the 60th Annual Meeting, Federation of American Societies for Experimental Biology, April, 1976, Anaheim, California.