Modeling human postural sway using an intermittent control and hemodynamic perturbations

Ground reaction force during human quiet stance is modulated synchronously with the cardiac cycle through hemodynamics [1]. This almost periodic hemodynamic force induces a small disturbance torque to the ankle joint, which is considered as a source of endogenous perturbation that induces postural sway. Here we consider postural sway dynamics of an inverted pendulum model with an intermittent control strategy, in comparison with the traditional continuous-time feedback controller. We examine whether each control model can exhibit human-like postural sway, characterized by its power law behavior at the low frequency band 0.1–0.7 Hz, when it is weakly perturbed by periodic and/or random forcing mimicking the hemodynamic perturbation. We show that the continuous control model with typical feedback gain parameters hardly exhibits the human-like sway pattern, in contrast with the intermittent control model. Further analyses suggest that deterministic, including chaotic, slow oscillations that characterize the intermittent control strategy, together with the small hemodynamic perturbation, could be a possible mechanism for generating the postural sway.     

Relating reflex gain modulation in posture control to underlying neural network properties using a neuromusculoskeletal model

During posture control, reflexive feedback allows humans to efficiently compensate for unpredictable mechanical disturbances. Although reflexes are involuntary, humans can adapt their reflexive settings to the characteristics of the disturbances. Reflex modulation is commonly studied by determining reflex gains: a set of parameters that quantify the contributions of Ia, Ib and II afferents to mechanical joint behavior. Many mechanisms, like presynaptic inhibition and fusimotor drive, can account for reflex gain modulations. The goal of this study was to investigate the effects of underlying neural and sensory mechanisms on mechanical joint behavior. A neuromusculoskeletal model was built, in which a pair of muscles actuated a limb, while being controlled by a model of 2,298 spiking neurons in six pairs of spinal populations. Identical to experiments, the endpoint of the limb was disturbed with force perturbations. System identification was used to quantify the control behavior with reflex gains. A sensitivity analysis was then performed on the neuromusculoskeletal model, determining the influence of the neural, sensory and synaptic parameters on the joint dynamics. The results showed that the lumped reflex gains positively correlate to their most direct neural substrates: the velocity gain with Ia afferent velocity feedback, the positional gain with muscle stretch over II afferents and the force feedback gain with Ib afferent feedback. However, position feedback and force feedback gains show strong interactions with other neural and sensory properties. These results give important insights in the effects of neural properties on joint dynamics and in the identifiability of reflex gains in experiments.     

Multi-stimulus multi-response posturography

In this study a method for the analysis of simultaneous multiple measurements of kinematics and stabilizing forces related to human postural dynamics is proposed. Each subject in a group of normal subjects (n=10) was tested with eyes-open and eyes-closed with simultaneous but uncorrelated vestibular and proprioceptive stimuli in order to investigate the contributions of individual sensory feedback loops. Statistical analysis was made by means of multi-input multi-output identification of a transfer function from stimuli to stabilizing forces of the feet and the resulting body position, the transfer function being compatible with a biomechanical model formulated as a stabilized segmented inverted pendulum subject to feedback of body sway and position. Each individual model estimated is effective in predicting a subject's response to new stimuli and in describing the interacting effects of stimuli on body kinetics. The proposed methodology responds to the current needs of data analysis of multi-stimulus multi-response experiments.     

Predicting dynamic postural instability using center of mass time-to-contact information

Our purpose was to determine whether spatiotemporal measures of center of mass motion relative to the base of support boundary could predict stepping strategies after upper-body postural perturbations in humans. We expected that inclusion of center of mass acceleration in such time-to-contact (TtC) calculations would give better predictions and more advanced warning of perturbation severity. TtC measures were compared with traditional postural variables, which do not consider support boundaries, and with an inverted pendulum model of dynamic stability developed by Hof et al. [2005. The condition for dynamic stability. Journal of Biomechanics 38, 1-8]. A pendulum was used to deliver sequentially increasing perturbations to 10 young adults, who were strapped to a wooden backboard that constrained motion to sagittal-plane rotation about the ankle joint. Subjects were instructed to resist the perturbations, stepping only if necessary to prevent a fall. Peak center of mass and center of pressure velocity and acceleration demonstrated linear increases with postural challenge. In contrast, boundary-relevant minimum TtC values decreased nonlinearly with postural challenge, enabling prediction of stepping responses using quadratic equations. When TtC calculations incorporated center of mass acceleration, the quadratic fits were better and gave more accurate predictions of the TtC values that would trigger stepping responses. In addition, TtC minima occurred earlier with acceleration inclusion, giving more advanced warning of perturbation severity. Our results were in agreement with TtC predictions based on Hof's model, and suggest that TtC may function as a control parameter, influencing the postural control system's decision to transition from a stationary base of support to a stepping strategy.     

Swinging into art with pendulum paintings

Children are captivated with how things work and they like to build things and in many ways, engineering comes naturally for them. Progress does not come from technology alone but from the melding of technology and creative thinking through art and design. There has been a push for STEAM-based curricula to be included in science classrooms and the Next Generation Science Standards (NGSS) provides the framework for integrating engineering design into the structure of science education. The push for the STEAM platform is derived from the lack of creativity and innovation in recent college graduates in the United States. This STEAM-based unit meshes engineering design, representing and interpreting data, visual arts, and motion/stability. As students investigated and analyzed pendulum motion, they also created unique pendulum paintings. Throughout this unit our students applied their content knowledge across several disciplines and in turn allowed them to gain a better understanding and retention of these concepts. Through creating their own pendulum paintings, the students learned about pendulums and how they work, designed and constructed their own pendulums, and applied prior knowledge of forces and motion in a controlled experiment.     

Stepping threshold with platform-translation and shoulder-pull postural perturbation methods

The type of balance recovery, feet-in-place or stepping, is predicated on the perturbation intensity, often defined by the combination of applied force and displacement. Few studies examined the relationship between characteristics required to produce a stepping response with one of the postural perturbation methods. The purpose of this study was to investigate the relationship between perturbation characteristics (applied force and displacement) required to elicit a forward stepping response with platform-translation and shoulder-pull methods, and to establish whether a common set of perturbation characteristics existed across both perturbation methods. Fourteen young healthy males participated. Temporally unexpected platform translations and shoulder pulls were induced by release of free weights, which fell a controlled height exerting a pull on the platform or on the participant via a shoulder harness. Participants responded with either feet-in-place or stepping responses. The force and displacement were varied to investigate the range of force-displacement combinations required to elicit stepping responses. Force-displacement combinations that elicited stepping responses were recorded and normalized to the participant’s body weight (BW) and the base of support (BOS; participant’s foot length). The lowest force and associated displacement that elicited stepping responses showed an inverse linear relationship during both platform-translation and shoulder-pull trials. The lowest force-displacement combination common to both perturbation methods was found to be 8.75%BW and 105%BOS, which, in the future work, could enable a direct comparison of the neuromuscular and biomechanical responses to different perturbation methods in a manner that attempts to equilibrate the perturbation stimulus across the methods.     

Postural dynamics in maximal isometric ramp efforts

 A global biomechanical model of transient push efforts is proposed where transient efforts are taken into consideration, with the aim to examine in greater depth the postural adjustments associated with voluntary efforts. In this context, the push effort is considered as a perturbation of balance, and the other reaction forces as a counter-perturbation which is necessary for the task to be performed efficiently. The subjects were asked to exert maximal horizontal two-handed isometric pushes on a dynamometric bar, as rapidly as possible. They were seated on a custom-designed device which measured global and partitive dynamic quantities. The results showed that the horizontal reaction forces and the horizontal displacement of the centre of pressure increased quasi-proportionally with the perturbation. In addition, it was established that vertical reaction forces increased at seat level whereas they decreased at foot level, resulting in minor vertical acceleration and displacement of the centre of gravity. On the contrary, the anteroposterior reaction forces increased both at foot and at seat levels. Based on a detailed examination of the various terms of the model, it is concluded that transient muscular effort induces dynamics of the postural chain. These observations support the view that there is a postural counter-perturbation which is associated with motor activity. More generally, the model helped to specify the effect of postural dynamic phenomena. It makes it possible to stress the importance of adherence at the contact level between the subject and the seat in the course of transient efforts. Received: 1 February 2001 / Accepted in revised form: 20 February 2002     

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.     

Are age-related impairments in change-in-support balance reactions dependent on the method of balance perturbation?

Rapid “change-in-support” (stepping or grasping) balance-recovery reactions play a critical role in preventing falls. Studies investigating age-related impairments in these reactions using differing perturbation methods have shown contradictory results. The discrepancies could be due to the different mechanical and sensory stimuli provided by the different perturbation methods, but could also be due to other confounding factors (e.g. differences in perturbation predictability). This study compared two commonly used perturbation methods: weight-drop cable-pulls (CPs) and motor-driven surface-translations (STs). For each perturbation method, effects of aging on the change-in-support reactions were established by comparing 10 young (22–28 years) and 30 older (64–79 years) adults, using large unpredictable multi-directional perturbations similar to those used in previous studies showing age-related differences. Age-related differences in the pattern and spatio-temporal features of the limb movements were examined for stepping and grasping reactions evoked by antero-posterior perturbation of stance, as well as stepping reactions evoked by lateral perturbations delivered while subjects walked “in-place”. Although age-group effects were almost always more pronounced for ST perturbations, the direction of the effect was always the same for both perturbation methods; hence, the perturbation-dependent differences in mechanical and sensory stimuli did not seem to be a critical factor. Perturbation waveform appeared to be a more important factor. For the perturbation methods used here, the ST perturbations were more destabilising than the CP perturbations (leading to a more rapid rise in perturbatory ankle-torque and greater centre-of-mass motion prior to the onset of the postural reaction), and were consequently more effective in revealing age-related deficiencies.     

Musculature and biomechanics of the trunk in the maintenance of upright posture

Surface perturbation has been used for decades to study balance and postural control; however the behavior of the trunk in these postural responses has been largely overlooked. Thirteen healthy males (18–23 yrs) were exposed to horizontal support surface translations delivered randomly in one of eight different horizontal directions in both sitting and standing. A 4-segment model of the trunk was used to estimate the kinematics and kinetics associated with the postural response, while surface EMG was acquired, bilaterally, from seven trunk muscles and one hip muscle. Multi-segmental movement was observed in the trunk in both test postures. Both the biomechanical and neuromuscular aspects of the trunk response were significantly affected by translation direction and test posture, with an interaction effect between these variables. The response in sitting was closely tied to the movement of the support surface, while the response in standing occurred in two phases: the first related to the dynamic response in the lower limbs, and the second tied to the movement of the support surface. As such, the observed postural responses could be largely explained by the biomechanical constraints of the system, such that the neural control of trunk equilibrium is simplified.     

Effects of lateral perturbations and changing stance conditions on anticipatory postural adjustment

The study investigates the role of lateral muscles and changing stance conditions in anticipatory postural adjustments (APAs). Subjects stood laterally to an aluminum pendulum released by an experimenter and were required to stop it with their right or left hand. Stance conditions were manipulated by having the subjects stand in the following positions: on a single limb (SS), with feet together (narrow base of support, NB), and with feet shoulder width apart (regular base of support, RB). Bilateral EMG activity of dorsal, ventral, and lateral trunk and leg muscles and ground reaction forces were recorded and quantified within the time intervals typical of APAs. Anticipatory postural adjustments were seen in all experimental conditions, and their magnitudes depended on the stance and the side of perturbation. Accordingly, APAs in lateral muscles increased on the side of perturbation in SS condition, while simultaneous activation of dorsal muscles occurred on the contralateral side. Smaller APAs were seen in lateral muscles in conditions with a wider base of support (NB, RB) and APAs in dorsal muscles were smaller in NB – in comparison to RB – stance. The results of the present study provide new data on the role of lateral, ventral, and dorsal muscles in anticipatory postural control when dealing with lateral perturbations in conditions of postural instability.     

Analysis of reflex modulation with a biologically realistic neural network

In this study, a neuromusculoskeletal model was built to give insight into the mechanisms behind the modulation of reflexive feedback strength as experimentally identified in the human shoulder joint. The model is an integration of a biologically realistic neural network consisting of motoneurons and interneurons, modeling 12 populations of spinal neurons, and a one degree-of-freedom musculoskeletal model, including proprioceptors. The model could mimic the findings of human postural experiments, using presynaptic inhibition of the Ia afferents to modulate the feedback gains. In a pathological case, disabling one specific neural connection between the inhibitory interneurons and the motoneurons could mimic the experimental findings in complex regional pain syndrome patients. It is concluded that the model is a valuable tool to gain insight into the spinal contributions to human motor control. Applications lay in the fields of human motor control and neurological disorders, where hypotheses on motor dysfunction can be tested, like spasticity, clonus, and tremor. Action Editor: Karen Sigvardt     

Adaptation of reflexive feedback during arm posture to different environments

 In this study we have examined the ability of the central nervous system (CNS) to use spinal reflexes to minimize displacements during postural control while continuous force perturbations were applied at the hand. The subjects were instructed to minimize the displacements of the hand from a reference position that resulted from the force perturbations. The perturbations were imposed in one direction by means of a hydraulic manipulator of which the virtual mass and damping were varied. Resistance to the perturbations came from intrinsic and reflexive stiffness, and from the virtual environment. It is hypothesized that reflexive feedback during posture maintenance is optimally adjusted such that position deviations are minimal for a given virtual environment. Frequency response functions were estimated, capturing all mechanical properties of the arm at the end point (hand) level. Intrinsic and reflexive parameters were quantified by fitting a linear neuromuscular model to the frequency responses. The reflexive length feedback gain increased strongly with damping and little with the eigenfrequency of the total combined system (i.e. arm plus environment). The reflexive velocity feedback gain decreased slightly with relative damping at the largest eigenfrequency and more markedly at smaller eigenfrequencies. In the case of highest reflex gains, the total system remained stable and sufficiently damped while the responses of only the arm were severely underdamped and sometimes even unstable. To further analyse these results, a model optimization was performed. Intrinsic and reflexive parameters were optimized such that two criterion functions were minimized. The first concerns performance and penalized hand displacements from a reference point. The second one weights afferent control effort to avoid inefficient feedback. The simulations showed good similarities with the estimated values. Length feedback was adequately predicted by the model for all conditions. The predicted velocity feedback gains were larger in all cases, probably indicating a mutual gain limiting relation between length and velocity afferent signals. The results suggest that both reflex gains seem to be adjusted by the CNS, where in particular the length feedback gain was optimal so as to maximize performance at minimum control effort. Received: 23 July 2001 / Accepted in revised form: 15 January 2002     

Models of Postural Control: Shared Variance in Joint and COM Motions

This paper investigated the organization of the postural control system in human upright stance. To this aim the shared variance between joint and 3D total body center of mass (COM) motions was analyzed using multivariate canonical correlation analysis (CCA). The CCA was performed as a function of established models of postural control that varied in their joint degrees of freedom (DOF), namely, an inverted pendulum ankle model (2DOF), ankle-hip model (4DOF), ankle-knee-hip model (5DOF), and ankle-knee-hip-neck model (7DOF). Healthy young adults performed various postural tasks (two-leg and one-leg quiet stances, voluntary AP and ML sway) on a foam and rigid surface of support. Based on CCA model selection procedures, the amount of shared variance between joint and 3D COM motions and the cross-loading patterns we provide direct evidence of the contribution of multi-DOF postural control mechanisms to human balance. The direct model fitting of CCA showed that incrementing the DOFs in the model through to 7DOF was associated with progressively enhanced shared variance with COM motion. In the 7DOF model, the first canonical function revealed more active involvement of all joints during more challenging one leg stances and dynamic posture tasks. Furthermore, the shared variance was enhanced during the dynamic posture conditions, consistent with a reduction of dimension. This set of outcomes shows directly the degeneracy of multivariate joint regulation in postural control that is influenced by stance and surface of support conditions.     

Perturbation velocity affects linearly estimated neuromechanical wrist joint properties

The dynamic behavior of the wrist joint is governed by nonlinear properties, yet applied mathematical models, used to describe the measured input-output (perturbation-response) relationship, are commonly linear. Consequently, the linearly estimated model parameters will depend on properties of the applied perturbation properties (such perturbation amplitude and velocity). We aimed to systematically address the effects of perturbation velocity on linearly estimated neuromechanical parameters.Using a single axis manipulator ramp and hold perturbations were applied to the wrist joint. Effects of perturbation velocity (0.5, 1 and 3 rad/s) were investigated at multiple background torque levels (0, 0.5 and 1 N·m). With increasing perturbation velocity, estimated joint stiffness remained constant, while damping and reflex gain decreased. This variation in model parameters is dependent on background torque levels, i.e. muscle contraction.These observations support the future development of nonlinear models that are capable of describing wrist joint behavior over a larger range of loading conditions, exceeding the restricted range of operation that is required for linearization.     

Optimization and evaluation of a proportional derivative controller for planar arm movement

In most clinical applications of functional electrical stimulation (FES), the timing and amplitude of electrical stimuli have been controlled by open-loop pattern generators. The control of upper extremity reaching movements, however, will require feedback control to achieve the required precision. Here we present three controllers using proportional derivative (PD) feedback to stimulate six arm muscles, using two joint angle sensors. Controllers were first optimized and then evaluated on a computational arm model that includes musculoskeletal dynamics. Feedback gains were optimized by minimizing a weighted sum of position errors and muscle forces. Generalizability of the controllers was evaluated by performing movements for which the controller was not optimized, and robustness was tested via model simulations with randomly weakened muscles. Robustness was further evaluated by adding joint friction and doubling the arm mass. After optimization with a properly weighted cost function, all PD controllers performed fast, accurate, and robust reaching movements in simulation. Oscillatory behavior was seen after improper tuning. Performance improved slightly as the complexity of the feedback gain matrix increased.     

Effects of tibialis anterior vibration on postural control when exposed to support surface translations

The sensory re-weighting theory suggests unreliable inputs may be down-weighted to favor more reliable sensory information and thus maintain proper postural control. This study investigated the effects of tibialis anterior (TA) vibration on center of pressure (COP) motion in healthy individuals exposed to support surface translations to further explore the concept of sensory re-weighting. Twenty healthy young adults stood with eyes closed and arms across their chest while exposed to randomized blocks of five trials. Each trial lasted 8?s, with TA vibration either on or off. After 2?s, a sudden backward or forward translation occurred. Anterior–posterior (A/P) COP data were evaluated during the preparatory (first 2?s), perturbation (next 3?s), and recovery (last 3?s) phases to assess the effect of vibration on perturbation response features. The knowledge of an impending perturbation resulted in reduced anterior COP motion with TA vibration in the preparatory phase relative to the magnitude of anterior motion typically observed during TA vibration. During the perturbation phase, vibration did not influence COP motion. However, during the recovery phase vibration induced greater anterior COP motion than during trials without vibration. The fact that TA vibration produced differing effects on COP motion depending upon the phase of the perturbation response may suggest that the immediate context during which postural control is being regulated affects A/P COP responses to TA vibration. This indicates that proprioceptive information is likely continuously re-weighted according to the context in order to maintain effective postural control.     

NACOB presentation CSB New Investigator Award. Balance recovery from medio-lateral perturbations of the upper body during standing. North American Congress on Biomechanics.

Postural control strategies have in the past been predominantly characterized by kinematics, surface forces, and EMG responses (e.g. Horak and Nashner, 1986, Journal of Neurophysiology 55(6), 1369-1381). The goal of this study was to provide unique and novel insights into the underlying motor mechanisms used in postural control by determining the joint moments during balance recovery from medio-lateral (M/L) perturbations. Ten adult males received medio-lateral (M/L) pushes to the trunk or pelvis. The inverted pendulum model of balance control (Winter et al., 1998, Journal of Neurophysiology 80, 1211-1221) was validated even though the body did not behave as a single pendulum, indicating that the centre of pressure (COP) is the variable used to control the centre of mass (COM). The perturbation magnitude was random, and the central nervous system (CNS) responded with an estimate of the largest anticipated perturbation. The observed joint moments served to move the COP in the appropriate direction and to control the lateral collapse of the trunk. The individual joints involved in controlling the COP contributed differing amounts to the total recovery response: the hip and spinal moments provided the majority of the recovery (approximately 85%), while the ankles contributed a small, but significant amount (15%). The differing contributions are based on the anatomical constraints and the functional requirements of the balance task. The onset of the joint moment was synchronous with the joint angle change, and occurred too early (56-116 ms) to be result of active muscle contraction. Therefore, the first line of defense was provided by muscle stiffness, not reflex-activated muscle activity.     

Simulating mechanical consequences of voluntary movement upon whole-body equilibrium: the arm-raising paradigm revisited

Voluntary arm-raising movement performed during the upright human stance position imposes a perturbation to an already unstable bipedal posture characterised by a high body centre of mass (CoM). Inertial forces due to arm acceleration and displacement of the CoM of the arm which alters the CoM position of the whole body represent the two sources of disequilibrium. A current model of postural control explains equilibrium maintenance through the action of anticipatory postural adjustments (APAs) that would offset any destabilising effect of the voluntary movement. The purpose of this paper was to quantify, using computer simulation, the postural perturbation due to arm raising movement. The model incorporated four links, with shoulder, hip, knee and ankle joints constrained by linear viscoelastic elements. The input of the model was a torque applied at the shoulder joint. The simulation described mechanical consequences of the arm-raising movement for different initial conditions. The variables tested were arm inertia, the presence or not of gravity field, the initial standing position and arm movement direction. Simulations showed that the mechanical effect of arm-raising movement was mainly local, that is to say at the level of trunk and lower limbs and produced a slight forward displacement of the CoM (1.5 mm). Backward arm-raising movement had the same effect on the CoM displacement as the forward arm-raising movement. When the mass of the arm was increased, trunk rotation increased producing a CoM displacement in the opposite direction when compared to arm movement performed without load. Postural disturbance was minimised for an initial standing posture with the CoM vertical projection corresponding to the ankle joint axis of rotation. When the model was reduced to two degrees of freedom (ankle and shoulder joints only) the postural perturbation due to arm-raising movement increased compared to the four-joints model. On the basis of these results the classical assumption that APAs stabilise the CoM is challenged.     

Modelling 3D control of upright stance using an optimal control strategy

A 3D balance control model of quiet upright stance is presented, based on an optimal control strategy, and evaluated in terms of its ability to simulate postural sway in both the anterior-posterior and medial-lateral directions. The human body was represented as a two-segment inverted pendulum. Several assumptions were made to linearise body dynamics, for example, that there was no transverse rotation during upright stance. The neural controller was presumed to be an optimal controller that generates ankle control torque and hip control torque according to certain performance criteria. An optimisation procedure was used to determine the values of unspecified model parameters including random disturbance gains and sensory delay times. This model was used to simulate postural sway behaviours characterised by centre-of-pressure (COP)-based measures. Confidence intervals for all normalised COP-based measures contained unity, indicating no significant differences between any of the simulated COP-based measures and corresponding experimental references. In addition, mean normalised errors for the traditional measures were 相似文献