A model of cerebellum stabilized and scheduled hybrid long-loop control of upright balance

Cerebellar transcranial magnetic stimulation for improving balance capacity and activity of daily living in stroke patients: a systematic review and meta-analysis

BACKGROUND

The application of cerebellar transcranial magnetic stimulation (TMS) in stroke patients has received increasing attention due to its neuromodulation mechanisms. However, studies on the effect and safety of cerebellar TMS to improve balance capacity and activity of daily living (ADL) for stroke patients are limited. This systematic review and meta-analysis aimed to investigate the effect and safety of cerebellar TMS on balance capacity and ADL in stroke patients.

METHOD

A systematic search of seven electronic databases (PubMed, Embase, Web of Science, Cochrane Central Register of Controlled Trials, China National Knowledge Infrastructure, Wanfang and Chinese Scientific Journal) were conducted from their inception to October 20, 2023. The randomized controlled trials (RCTs) of cerebellar TMS on balance capacity and/or ADL in stroke patients were enrolled. The quality of included studies were assessed by Physiotherapy Evidence Database (PEDro) scale.

RESULTS

A total of 13 studies involving 542 participants were eligible. The pooled results from 8 studies with 357 participants showed that cerebellar TMS could significantly improve the post-intervention Berg balance scale (BBS) score (MD = 4.24, 95%CI = 2.19 to 6.29, P < 0.00001; heterogeneity, I2 = 74%, P = 0.0003). The pooled results from 4 studies with 173 participants showed that cerebellar TMS could significantly improve the post-intervention Time Up and Go (TUG) (MD=-1.51, 95%CI=-2.8 to -0.22, P = 0.02; heterogeneity, I2 = 0%, P = 0.41). The pooled results from 6 studies with 280 participants showed that cerebellar TMS could significantly improve the post-intervention ADL (MD = 7.75, 95%CI = 4.33 to 11.17, P < 0.00001; heterogeneity, I2 = 56%, P = 0.04). The subgroup analysis showed that cerebellar TMS could improve BBS post-intervention and ADL post-intervention for both subacute and chronic stage stroke patients. Cerebellar high frequency TMS could improve BBS post-intervention and ADL post-intervention. Cerebellar TMS could still improve BBS post-intervention and ADL post-intervention despite of different cerebellar TMS sessions (less and more than 10 TMS sessions), different total cerebellar TMS pulse per week (less and more than 4500 pulse/week), and different cerebellar TMS modes (repetitive TMS and Theta Burst Stimulation). None of the studies reported severe adverse events except mild side effects in three studies.

CONCLUSIONS

Cerebellar TMS is an effective and safe technique for improving balance capacity and ADL in stroke patients. Further larger-sample, higher-quality, and longer follow-up RCTs are needed to explore the more reliable evidence of cerebellar TMS in the balance capacity and ADL, and clarify potential mechanisms.

Methods for integrating postural control into biomechanical human simulations: a systematic review

Understanding of the human body's internal processes to maintain balance is fundamental to simulate postural control behaviour. The body uses multiple sensory systems' information to obtain a reliable estimate about the current body state. This information is used to control the reactive behaviour to maintain balance. To predict a certain motion behaviour with knowledge of the muscle forces, forward dynamic simulations of biomechanical human models can be utilized. We aim to use predictive postural control simulations to give therapy recommendations to patients suffering from postural disorders in the future. It is important to know which types of modelling approaches already exist to apply such predictive forward dynamic simulations. Current literature provides different models that aim to simulate human postural control. We conducted a systematic literature research to identify the different approaches of postural control models. The different approaches are discussed regarding their applied biomechanical models, sensory representation, sensory integration, and control methods in standing and gait simulations. We searched on Scopus, Web of Science and PubMed using a search string, scanned 1253 records, and found 102 studies to be eligible for inclusion. The included studies use different ways for sensory representation and integration, although underlying neural processes still remain unclear. We found that for postural control optimal control methods like linear quadratic regulators and model predictive control methods are used less, when models' level of details is increasing, and nonlinearities become more important. Considering musculoskeletal models, reflex-based and PD controllers are mainly applied and show promising results, as they aim to create human-like motion behaviour considering physiological processes.

Is essential tremor a disorder of primary GABA dysfunction? Yes

Dysfunction in gamma-aminobutyric acid (GABA) neurotransmission has emerged as a prime suspect for the underlying neurochemical dysfunction in essential tremor (ET). This dysfunction has been termed the GABA hypothesis. We review findings to date supporting the 4 steps in this hypothesis in studies of cerebrospinal fluid, pathology, genetics, animal models, imaging, computational models, and human drugs, while not overlooking the evidence of negative studies and controversies. It remains to be elucidated whether reduced GABAergic tone is a primary contributing factor to ET pathophysiology, a consequence of altered Purkinje cell function, or even a result of Purkinje cell death. More studies are clearly needed to confirm both the neurodegenerative nature of ET and the reduction in GABA activity in the cerebellum. Also necessary is to test further therapies to enhance GABA transmission specifically focused on the cerebellar area.

Performance Limitations in Sensorimotor Control: Trade-Offs Between Neural Computation and Accuracy in Tracking Fast Movements

The ability to move fast and accurately track moving objects is fundamentally constrained by the biophysics of neurons and dynamics of the muscles involved. Yet the corresponding trade-offs between these factors and tracking motor commands have not been rigorously quantified. We use feedback control principles to quantify performance limitations of the sensorimotor control system (SCS) to track fast periodic movements. We show that (1) linear models of the SCS fail to predict known undesirable phenomena, including skipped cycles, overshoot and undershoot, produced when tracking signals in the "fast regime," while nonlinear pulsatile control models can predict such undesirable phenomena, and (2) tools from nonlinear control theory allow us to characterize fundamental limitations in this fast regime. Using a validated and tractable nonlinear model of the SCS, we derive an analytical upper bound on frequencies that the SCS model can reliably track before producing such undesirable phenomena as a function of the neurons' biophysical constraints and muscle dynamics. The performance limitations derived here have important implications in sensorimotor control. For example, if the primary motor cortex is compromised due to disease or damage, the theory suggests ways to manipulate muscle dynamics by adding the necessary compensatory forces using an assistive neuroprosthetic device to restore motor performance and, more important, fast and agile movements. Just how one should compensate can be informed by our SCS model and the theory developed here.

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

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

Quantification of trunk segmental coordination and head stability in laterally unstable sitting identifies aging and cerebellar ataxia

BACKGROUND

We quantified trunk segmental coordination and head stability in unstable sitting and investigated whether it can discriminate postural control, age-related differences and presence of coordination disorder.

METHODS

Subjects were a healthy younger group (n = 7), a healthy elderly group (n = 7), and a cerebellar ataxia group (n = 8). The motion sensors and surface electrodes were located on the trunk and/or head segments to measure angle displacements, acceleration and electromyograms in unstable sitting during a lateral tilt task. Trunk lateral angle cross-correlation and electromyogram cross-correlation for the trunk segmental coordination, head root mean square (RMS) for the head stability, clinical performance scales, and gait parameters (velocity, coefficient of variation, and RMS ratio) were analyzed.

FINDINGS

Trunk lateral angle cross-correlation showed a significantly negative correlation in the healthy younger group compared with the two other groups (p < 0.01). Head RMS showed a significantly larger value in the cerebellar ataxia group compared with the two other groups (p < 0.01). Trunk lateral angle cross-correlation had moderate correlation with the clinical performance scale of ataxia and gait parameters; however, it was not correlated with head RMS. Classification using trunk lateral angle cross-correlation and head RMS was validated by discriminant analysis and hierarchical cluster analysis.

INTERPRETATION

We found that trunk lateral angle cross-correlation reflected age-related differences and head RMS characterized the pathology of cerebellar ataxia. Trunk segmental coordination and head stability, as two aspects of sitting postural control, can be used to discriminate the degree of aging and cerebellar ataxia.

Walking with perturbations: a guide for biped humans and robots

This paper provides an update on the neural control of bipedal walking in relation to bioinspired models and robots. It is argued that most current models or robots are based on the construct of a symmetrical central pattern generator (CPG). However, new evidence suggests that CPG functioning is basically asymmetrical with its flexor half linked more tightly to the rhythm generator. The stability of bipedal gait, which is an important problem for robots and biological systems, is also addressed. While it is not possible to determine how biological biped systems guarantee stability, robot solutions can be useful to propose new hypotheses for biology. In the second part of this review, the focus is on gait perturbations, which is an important topic in robotics in view of the frequent falls of robots when faced with perturbations. From the human physiology it is known that the initial reaction often consists of a brief interruption followed by an adequate response. For instance, the successful recovery from a trip is achieved using some basic reactions (termed elevating and lowering strategies), that depend on the phase of the step cycle of the trip occurrence. Reactions to stepping unexpectedly in a hole depend on comparing expected and real feedback. Implementation of these ideas in models and robotics starts to emerge, with the most advanced robots being able to learn how to fall safely and how to deal with complicated disturbances such as provided by walking on a split-belt.

Muscle coactivation: definitions, mechanisms, and functions

The phenomenon of agonist-antagonist muscle coactivation is discussed with respect to its consequences for movement mechanics (such as increasing joint apparent stiffness, facilitating faster movements, and effects on action stability), implication for movement optimization, and involvement of different neurophysiological structures. Effects of coactivation on movement stability are ambiguous and depend on the effector representing a kinematic chain with a fixed origin or free origin. Furthermore, coactivation is discussed within the framework of the equilibrium-point hypothesis and the idea of hierarchical control with spatial referent coordinates. Relations of muscle coactivation to changes in one of the basic commands, the c-command, are discussed and illustrated. A hypothesis is suggested that agonist-antagonist coactivation reflects a deliberate neural control strategy to preserve effector-level control and avoid making it degenerate and facing the necessity to control at the level of signals to individual muscles. This strategy, in particular, allows stabilizing motor actions by covaried adjustments in spaces of control variables. This hypothesis is able to account for higher levels of coactivation in young healthy persons performing challenging tasks and across various populations with movement impairments.

Role of heel lifting in standing balance recovery: A simulation study

Although lifting the heels has frequently been observed during balance recovery, the function of this movement has generally been overlooked. The present study aimed to investigate the functional role of heel lifting during regaining balance from a perturbed state. Computer simulation was employed to objectively examine the effect of allowing/constraining heel lifting on balance performance. The human model consisted of 3 rigid body segments connected by frictionless joints. Movements were driven by joint torques depending on current joint angle, angular velocity, and activation level. Starting from forward-inclined and static straight-body postures, the optimization goal was to recover balance effectively (so that ground projection of the mass center returned to the inside of the base of support) and efficiently by adjusting ankle and hip joint activation levels. Allowing/constraining heel lifting resulted in virtually identical movements when balance was mildly perturbed at the smallest lean angle (8°). At larger lean angles (8.5° and 9°), heel lifting assisted balance recovery more evidently with larger joint movements. Partial and altered timings of ankle/hip torque activation due to constraining heel lifting reduced linear and angular momentum generation for avoiding forward falling, and resulted in hindered balancing performance.

Control of force during rapid visuomotor force-matching tasks can be described by discrete time PID control algorithms

Force trajectories during isometric force-matching tasks involving isometric contractions vary substantially across individuals. In this study, we investigated if this variability can be explained by discrete time proportional, integral, derivative (PID) control algorithms with varying model parameters. To this end, we analyzed the pinch force trajectories of 24 subjects performing two rapid force-matching tasks with visual feedback. Both tasks involved isometric contractions to a target force of 10% maximal voluntary contraction. One task involved a single action (pinch) and the other required a double action (concurrent pinch and wrist extension). 50,000 force trajectories were simulated with a computational neuromuscular model whose input was determined by a PID controller with different PID gains and frequencies at which the controller adjusted muscle commands. The goal was to find the best match between each experimental force trajectory and all simulated trajectories. It was possible to identify one realization of the PID controller that matched the experimental force produced during each task for most subjects (average index of similarity: 0.87 ± 0.12; 1 = perfect similarity). The similarities for both tasks were significantly greater than that would be expected by chance (single action: p = 0.01; double action: p = 0.04). Furthermore, the identified control frequencies in the simulated PID controller with the greatest similarities decreased as task difficulty increased (single action: 4.0 ± 1.8 Hz; double action: 3.1 ± 1.3 Hz). Overall, the results indicate that discrete time PID controllers are realistic models for the neural control of force in rapid force-matching tasks involving isometric contractions.

Linking Essential Tremor to the Cerebellum: Neurochemical Evidence

The pathophysiology and the exact anatomy of essential tremor (ET) is not well known. One of the pillars that support the cerebellum as the main anatomical locus in ET is neurochemistry. This review examines the link between neurochemical abnormalities found in ET and cerebellum. The review is based on published data about neurochemical abnormalities described in ET both in human and in animal studies. We try to link those findings with cerebellum. γ-aminobutyric acid (GABA) is the main neurotransmitter involved in the pathophysiology of ET. There are several studies about GABA that clearly points to a main role of the cerebellum. There are few data about other neurochemical abnormalities in ET. These include studies with noradrenaline, glutamate, adenosine, proteins, and T-type calcium channels. One single study reveals high levels of noradrenaline in the cerebellar cortex. Another study about serotonin neurotransmitter results negative for cerebellum involvement. Finally, studies on T-type calcium channels yield positive results linking the rhythmicity of ET and cerebellum. Neurochemistry supports the cerebellum as the main anatomical locus in ET. The main neurotransmitter involved is GABA, and the GABA hypothesis remains the most robust pathophysiological theory of ET to date. However, this hypothesis does not rule out other mechanisms and may be seen as the main scaffold to support findings in other systems. We clearly need to perform more studies about neurochemistry in ET to better understand the relations among the diverse systems implied in ET. This is mandatory to develop more effective pharmacological therapies.

Generation of the Human Biped Stance by a Neural Controller Able to Compensate Neurological Time Delay

The development of a physiologically plausible computational model of a neural controller that can realize a human-like biped stance is important for a large number of potential applications, such as assisting device development and designing robotic control systems. In this paper, we develop a computational model of a neural controller that can maintain a musculoskeletal model in a standing position, while incorporating a 120-ms neurological time delay. Unlike previous studies that have used an inverted pendulum model, a musculoskeletal model with seven joints and 70 muscular-tendon actuators is adopted to represent the human anatomy. Our proposed neural controller is composed of both feed-forward and feedback controls. The feed-forward control corresponds to the constant activation input necessary for the musculoskeletal model to maintain a standing posture. This compensates for gravity and regulates stiffness. The developed neural controller model can replicate two salient features of the human biped stance: (1) physiologically plausible muscle activations for quiet standing; and (2) selection of a low active stiffness for low energy consumption.

Current concepts of essential tremor

Essential tremor is clinically defined but there is increasing evidence that it is not a unique entity. Its pathophysiology has been studied with many methods but may also vary between subtypes. Neurophysiologically, there is strong evidence that a specific cerebello-thalamo-cortical loop is abnormally oscillating. The cause of its uncontrolled oscillation is not yet understood. The clear proof of a degenerative cause is still lacking and abnormal receptors or other causes of altered non-progressive functional disturbance cannot be excluded. Strong evidence supports the major involvement of the cerebellum and there is ample evidence that GABA is the main neurotransmitter involved in the pathophysiology in ET. Genetics have provided so far only a few rare subtypes which are due to specific mutations but there is no doubt that it is mostly a hereditary condition. There is evidence that the large subgroup of late onset tremor is a separate condition and this tremor is an independent risk factor for earlier mortality and comes with signs of premature aging (aging-related tremor). It will be important to improve phenotyping of patients in more detail possibly to include not only features of the tremor itself but also other clinical assessments like force measurements or cognitive testing. Based on these variables, we may be able to better understand the presumably different mechanisms underlying different variants of the disease.

Long-latency reflexes account for limb biomechanics through several supraspinal pathways

Accurate control of body posture is enforced by a multitude of corrective actions operating over a range of time scales. The earliest correction is the short-latency reflex (SLR) which occurs between 20–45 ms following a sudden displacement of the limb and is generated entirely by spinal circuits. In contrast, voluntary reactions are generated by a highly distributed network but at a significantly longer delay after stimulus onset (greater than 100 ms). Between these two epochs is the long-latency reflex (LLR) (around 50–100 ms) which acts more rapidly than voluntary reactions but shares some supraspinal pathways and functional capabilities. In particular, the LLR accounts for the arm’s biomechanical properties rather than only responding to local muscle stretch like the SLR. This paper will review how the LLR accounts for the arm’s biomechanical properties and the supraspinal pathways supporting this ability. Relevant experimental paradigms include clinical studies, non-invasive brain stimulation, neural recordings in monkeys, and human behavioral studies. The sum of this effort indicates that primary motor cortex and reticular formation (RF) contribute to the LLR either by generating or scaling its structured response appropriate for the arm’s biomechanics whereas the cerebellum scales the magnitude of the feedback response. Additional putative pathways are discussed as well as potential research lines.

Cerebellar damage diminishes long-latency responses to multijoint perturbations

Damage to the cerebellum can cause significant problems in the coordination of voluntary arm movements. One prominent idea is that incoordination stems from an inability to predictively account for the complex mechanical interactions between the arm's several joints. Motivated by growing evidence that corrective feedback control shares important capabilities and neural substrates with feedforward control, we asked whether cerebellar damage impacts feedback stabilization of the multijoint arm appropriate for the arm's intersegmental dynamics. Specifically, we tested whether cerebellar dysfunction impacts the ability of posterior deltoid to incorporate elbow motion in its long-latency response (R2 = 45-75 ms and R3 = 75-100 ms after perturbation) to an unexpected torque perturbation. Healthy and cerebellar-damaged subjects were exposed to a selected pattern of shoulder-elbow displacements to probe the response pattern from this shoulder extensor muscle. The healthy elderly subjects expressed a long-latency response linked to both shoulder and elbow motion, including an increase/decrease in shoulder extensor activity with elbow flexion/extension. Critically, cerebellar-damaged subjects displayed the normal pattern of activity in the R3 period indicating an intact ability to rapidly integrate multijoint motion appropriate to the arm's intersegmental dynamics. However, cerebellar-damaged subjects had a lower magnitude of activity that was specific to the long-latency period (both R2 and R3) and a slightly delayed onset of multijoint sensitivity. Taken together, our results suggest that the basic motor pattern of the long-latency response is housed outside the cerebellum and is scaled by processes within the cerebellum.

Analysis of the Body Control System Related to Mental Workload

In this paper, we present a model-based analysis of the standing posture control mechanism with consideration to mental workload and the physiological features of sensory feedback. It has been known that standing posture control is not performed autonomously or unconsciously but is affected by “working memory” [ 1 ]. In order to investigate how mental workload in working memory influences standing posture control, we consider the feedback groups in the standing posture control mechanism which include the viscoelastic characteristics of the musculoskeletal system and sensory feedback. We use a centre of pressure (COP)-based tracking task to investigate the influence of mental workload on voluntary (tracking) movement. Maurer-Peterka's model is applied to analyse the standing posture control mechanism, with respect to a change in the internal processes. The simulation results show the relationship of the feedback gain and its delay from the central nervous system with the standing posture control performance. The proposed model-based scheme provides a comprehensive view for physiological data analysis of human body movement in relation to mental workload.

Postural compensation for unilateral vestibular loss

Postural control of upright stance was investigated in well-compensated, unilateral vestibular loss (UVL) subjects compared to age-matched control subjects. The goal was to determine how sensory weighting for postural control in UVL subjects differed from control subjects, and how sensory weighting related to UVL subjects' functional compensation, as assessed by standardized balance and dizziness questionnaires. Postural control mechanisms were identified using a model-based interpretation of medial-lateral center-of-mass body-sway evoked by support-surface rotational stimuli during eyes-closed stance. The surface-tilt stimuli consisted of continuous pseudorandom rotations presented at four different amplitudes. Parameters of a feedback control model were obtained that accounted for each subject's sway response to the surface-tilt stimuli. Sensory weighting factors quantified the relative contributions to stance control of vestibular sensory information, signaling body-sway relative to earth-vertical, and proprioceptive information, signaling body-sway relative to the surface. Results showed that UVL subjects made significantly greater use of proprioceptive, and therefore less use of vestibular, orientation information on all tests. There was relatively little overlap in the distributions of sensory weights measured in UVL and control subjects, although UVL subjects varied widely in the amount they could use their remaining vestibular function. Increased reliance on proprioceptive information by UVL subjects was associated with their balance being more disturbed by the surface-tilt perturbations than control subjects, thus indicating a deficiency of balance control even in well-compensated UVL subjects. Furthermore, there was some tendency for UVL subjects who were less able to utilize remaining vestibular information to also indicate worse functional compensation on questionnaires.

Postural feedback scaling deficits in Parkinson's disease

Many differences in postural responses have been associated with age and Parkinson's disease (PD), but until now there has been no quantitative model to explain these differences. We developed a feedback control model of body dynamics that could reproduce the postural responses of young subjects, elderly subjects, and subjects with PD, and we investigated whether the postural impairments of subjects with PD can be described as an abnormal scaling of postural feedback gain. Feedback gains quantify how the nervous system generates compensatory joint torques based on kinematic responses. Seven subjects in each group experienced forward postural perturbations to seven different backward support surface translations ranging from 3- to 15-cm amplitudes and with a constant duration of 275 ms. Ground reaction forces and joint kinematics were measured to obtain joint torques from inverse dynamics. A full-state feedback controller with a two-segment body dynamic model was used to simulate joint kinematics and kinetics in response to perturbations. Results showed that all three subject groups gradually scaled postural feedback gains as a function of perturbation amplitudes, and the scaling started even before the maximum allowable ankle torque was reached. This result implies that the nervous system takes body dynamics into account and adjusts postural feedback gains to accommodate biomechanical constraints. PD subjects showed significantly smaller than normal ankle feedback gain with low scaling and larger hip feedback gain, which led to an early violation of the flat-foot constraint and unusually small (bradykinetic) postural responses. Our postural feedback control model quantitatively described the postural abnormality of the patients with PD as abnormal feedback gains and reduced ability to modify postural feedback gain with changes in postural challenge.

Neuromusculoskeletal Torque-Generation Process Has a Large Destabilizing Effect on the Control Mechanism of Quiet Standing

The delay of the sensory-motor feedback loop is a destabilizing factor within the neural control mechanism of quiet standing. The purposes of this study were 1) to experimentally identify the neuromusculoskeletal torque-generation process during standing posture and 2) to investigate the effect of the delay induced by this system on the control mechanism of balance during quiet standing. Ten healthy adults participated in this study. The ankle torque, ankle angle, and electromyograms from the right lower leg muscles were measured. A ground-fixed support device was used to support the subject at his/her knees, without changing the natural ankle angle during quiet standing. Each subject was asked to mimic the ankle torque fluctuation by exerting voluntary ankle extension while keeping the supported standing posture. Using the rectified soleus electromyogram as the input and the ankle torque as the output, a critically damped, second-order system (twitch contraction time of 0.152 ± 0.027 s) successfully described the dynamics of the torque-generation process. According to the performed Bode analysis, the phase delay induced by this torque-generation process in the frequency region of spontaneous body sway during quiet standing was considerably large, corresponding to an effective time delay of about 200 to 380 ms. We compared the stability of the balance control system with and without the torque-generation process and demonstrated that a much smaller number of gain combinations can stabilize the model with the torque-generation process than without it. We concluded that the phase delay induced by the torque-generation process is a more destabilizing factor in the control mechanism of quiet standing than previously assumed, which restricts the control strategies that can stabilize the entire system.

A robotic device for understanding neuromechanical interactions during standing balance control

Postural stability in standing balance results from the mechanics of body dynamics as well as active neural feedback control processes. Even when an animal or human has multiple legs on the ground, active neural regulation of balance is required. When the postural configuration, or stance, changes, such as when the feet are placed further apart, the mechanical stability of the organism changes, but the degree to which this alters the demands on neural feedback control for postural stability is unknown. We developed a robotic system that mimics the neuromechanical postural control system of a cat in response to lateral perturbations. This simple robotic system allows us to study the interactions between various parameters that contribute to postural stability and cannot be independently varied in biological systems. The robot is a 'planar', two-legged device that maintains compliant balance control in a variety of stance widths when subject to perturbations of the support surface, and in this sense reveals principles of lateral balance control that are also applicable to bipeds. Here we demonstrate that independent variations in either stance width or delayed neural feedback gains can have profound and often surprisingly detrimental effects on the postural stability of the system. Moreover, we show through experimentation and analysis that changing stance width alters fundamental mechanical relationships important in standing balance control and requires a coordinated adjustment of delayed feedback control to maintain postural stability.

A feedback model reproduces muscle activity during human postural responses to support-surface translations

Although feedback models have been used to simulate body motions in human postural control, it is not known whether muscle activation patterns generated by the nervous system during postural responses can also be explained by a feedback control process. We investigated whether a simple feedback law could explain temporal patterns of muscle activation in response to support-surface translations in human subjects. Previously, we used a single-link inverted-pendulum model with a delayed feedback controller to reproduce temporal patterns of muscle activity during postural responses in cats. We scaled this model to human dimensions and determined whether it could reproduce human muscle activity during forward and backward support-surface perturbations. Through optimization, we found three feedback gains (on pendulum acceleration, velocity, and displacement) and a common time delay that allowed the model to best match measured electromyographic (EMG) signals. For each muscle and each subject, the entire time courses of EMG signals during postural responses were well reconstructed in muscles throughout the lower body and resembled the solution derived from an optimal control model. In ankle muscles, >75% of the EMG variability was accounted for by model reconstructions. Surprisingly, >67% of the EMG variability was also accounted for in knee, hip, and pelvis muscles, even though motion at these joints was minimal. Although not explicitly required by our optimization, pendulum kinematics were well matched to subject center-of-mass (CoM) kinematics. Together, these results suggest that a common set of feedback signals related to task-level control of CoM motion is used in the temporal formation of muscle activity during postural control.

Optimal sensorimotor transformations for balance

Here we have identified a sensorimotor transformation that is used by a mammalian nervous system to produce a multijoint motor behavior. Using a simple biomechanical model, a delayed-feedback rule based on an optimal tradeoff between postural error and neural effort explained patterns of muscle activation in response to a sudden loss of balance in cats. Following the loss of large sensory afferents, changes in these muscle-activation patterns reflected an optimal reweighting of sensory feedback gains to minimize postural instability. Specifically, a loss of center-of-mass-acceleration information, which allowed for a rapid initial rise in the muscle activity in intact animals, was absent after large-fiber sensory neuropathy. Our results demonstrate that a simple and flexible neural feedback control strategy coordinates multiple muscles over time via a small set of extrinsic, task-level variables during complex multijoint natural movements.

A balance control model of quiet upright stance based on an optimal control strategy

Models of balance control can aid in understanding the mechanisms by which humans maintain balance. A balance control model of quiet upright stance based on an optimal control strategy is presented here. In this model, the human body was represented by a simple single-segment inverted pendulum during upright stance, and the neural controller was assumed to be an optimal controller that generates ankle control torques according to a certain performance criterion. This performance criterion was defined by several physical quantities relevant to sway. In order to accurately simulate existing experimental data, an optimization procedure was used to specify the set of model parameters to minimize the scalar error between experimental and simulated sway measures. Thirty-two independent simulations were performed for both younger and older adults. The model's capabilities, in terms of reflecting sway behaviors and identifying aging effects, were then analyzed based on the simulation results. The model was able to accurately predict center-of-pressure-based sway measures, and identify potential changes in balance control mechanisms caused by aging. Correlations between sway measures and model parameters are also discussed.

A neurobiological model of the recovery strategies from perturbed walking

This paper proposes a human mimetic neuro-musculo-skeletal model to simulate the recovery reactions from perturbations during walking. The computational model incorporates nonlinear viscoelastic muscular mechanics, supraspinal control of the center-of-mass, spinal pattern generator including muscle synergy network, spinal reflexes, and long-loop reflexes. Especially the long-loop reflexes specify recovery strategies based on the experimental observations [Schillings, A.M., van Wezel, B.M.H., Mulder, T.H., Duysen, J., 2000. Muscular responses and movement strategies during stumbling over obstacles. J. Neurophysiol. 83, 2093-2102; Eng, J.J., Winter, D.A., Patla, A.E., 1994. Strategies for recovery from a trip in early and late swing during human walking. Exp. Brain Res. 102, 339-349]. The model demonstrates two typical recovery strategies, i.e., elevating and lowering strategies against pulling over a swing leg. Sensed perturbation triggers a simple tonic pulse from the cortex. Depending on the swing phase, the tonic pulse activates a different compound of muscles over lower limbs. The compound induces corresponding recovery strategies. The reproduction of principal recovery behaviors may support the model's proposed functional and/or anatomical correspondence.

A model of cerebrocerebello-spinomuscular interaction in the sagittal control of human walking

A computationally developed model of human upright balance control (Jo and Massaquoi on Biol cybern 91:188-202, 2004) has been enhanced to describe biped walking in the sagittal plane. The model incorporates (a) non-linear muscle mechanics having activation level -dependent impedance, (b) scheduled cerebrocerebellar interaction for control of center of mass position and trunk pitch angle, (c) rectangular pulse-like feedforward commands from a brainstem/ spinal pattern generator, and (d) segmental reflex modulation of muscular synergies to refine inter-joint coordination. The model can stand when muscles around the ankle are coactivated. When trigger signals activate, the model transitions from standing still to walking at 1.5 m/s. Simulated natural walking displays none of seven pathological gait features. The model can simulate different walking speeds by tuning the amplitude and frequency in spinal pattern generator. The walking is stable against forward and backward pushes of up to 70 and 75 N, respectively, and with sudden changes in trunk mass of up to 18%. The sensitivity of the model to changes in neural parameters and the predicted behavioral results of simulated neural system lesions are examined. The deficit gait simulations may be useful to support the functional and anatomical correspondences of the model. The model demonstrates that basic human-like walking can be achieved by a hierarchical structure of stabilized-long loop feedback and synergy-mediated feedforward controls. In particular, internal models of body dynamics are not required.

A model of nonlinear motor cortical integration and its relation to movement speed profile control

It is recognized that natural point-to-point movements are characterized by bell-shaped speed profiles. However, the neural basis of this smooth, substantially symmetric time course is unknown. Here it is demonstrated via a simplified compartmental model of tufted layer V (TL5) pyramidal neurons, the principal output units of the motor cortex, that nonlinear integration may underlie the bell-shaped profile. Specifically, it is shown that TL5 neuronal output depends upon an approximately multiplicative relationship between inputs to its apical or basal regions (zones A and B, respectively) and those to its central zone (C). This is because the latter facilitate Ca²⁺dependent bursting that enhances responsiveness to other inputs. As a result, when part of TL5 output returns to zones A and C via thalamocortical and cerebrocerebellar feedback, TL5 neuronal firing rate initially increases before decreasing, rather than progressively decrease as would the output of a linear integrator. This yields a sigmoidal position vs. time response in the musculoskeletal plant and therefore a bell-shaped speed curve. Because of this mechanism, smooth movements may be triggered and modulated by step-like and tonic inputs to zone C as might be received from SMA or basal ganglia. The model thus gives possible insight into the basis of certain features of motor dysfunction in Parkinson's and cerebellar disease.

Stability analysis of paraplegic standing while wearing an orthosis

Paraplegics can maintain a standing posture, called the "C-posture", while wearing an orthosis. The significant feature of the C-posture is that the body's center of mass is located behind the hip joint. In this study, we investigate the C-posture mechanism and assess the relationship between posture and stability, the aim being to restore standing function. We first measured the standing postures of paraplegic subjects wearing an orthosis. The subjects maintained the standing posture for 30 s. Next, assuming the C-posture to be an equilibrium attractor in the musculoskeletal system, we used a dynamic model of the musculoskeletal system to analyze the relationship between posture and stability, and also to assess the influence of ankle stiffness. We calculated the standing posture on the basis of a return map. The calculated standing postures show some features of the C-posture. The stability analysis revealed that, despite a limitation in the range of stable postures, the C-posture is more stable than the postures of normal people. The results suggest that although the C-posture is an appropriate posture for paraplegic standing, sufficient ankle stiffness and an appropriate alignment of ankle angle are necessary and preventing hip flexion movements is desirable.