A structurally optimal control model for predicting and analyzing human postural coordination

This paper proposes a closed-loop optimal control model predicting changes between in-phase and anti-phase postural coordination during standing and related supra-postural activities. The model allows the evaluation of the influence of body dynamics and balance constraints onto the adoption of postural coordination. This model minimizes the instantaneous norm of the joint torques with a controller in the head space, in contrast with classical linear optimal models used in the postural literature and defined in joint space. The balance constraint is addressed with an adaptive ankle torque saturation. Numerical simulations showed that the model was able to predict changes between in-phase and anti-phase postural coordination modes and other non-linear transient dynamics phenomena.     

Ankle intrinsic stiffness changes with postural sway

In standing, the human body is inherently unstable and its stabilization requires constant regulation of ankle torque, generated by a combination of ankle intrinsic properties, peripheral reflexes, and central contributions. Ankle intrinsic stiffness, which quantifies the joint intrinsic properties, has been usually assumed constant in standing; however, there is strong evidence that it is highly dependent on the joint torque, which changes significantly with sway in stance. In this study, we examined how ankle intrinsic stiffness changes with postural sway during standing. Ten subjects stood on a standing apparatus, while subjected to pulse perturbations of ankle position. The mean torque of a short period before the start of each pulse was used as a measure of background torque. Responses with similar background torques were grouped together and used to estimate the parameters of an intrinsic stiffness model. Stiffness estimates were normalized to the critical stiffness and the background torque was transformed to the center of pressure location. We found that in most subjects, the normalized stiffness increased linearly with the movement of center of pressure towards the toes, with an average slope of 2.11 ± 0.80 1/m·rad. This modulation of ankle intrinsic stiffness seems functionally appropriate, since the intrinsic stiffness increases quickly, as the center of pressure moves toward the toes and the limits of stability. These large changes of ankle intrinsic stiffness with postural sway must be incorporated in any model of stance control.     

Postural dynamics of walking in humans

The dynamics of postural control in human biped locomotion were studied using(1) a model, and(2) experimentally applied impulsive force disturbances. The model was planar, and contained five rigid segments, articulating at frictionless pin joints. The model was used to identify joint torque combinations which would successfully correct for an impulsive force disturbance applied at different points in the walking cycle. The simulation results suggested that(1) early responses (within 80ms) can be effective in compensating for impulsive disturbances,(2) the same strategies which successfully counteract similar disturbances during quiet standing are also effective in certain phases of the walking cycle,(3) modifications in the response strategies are needed to accomodate differences in the dynamics over the stride cycle, and(4) the swing leg is ineffective in compensating for disturbances in the short term. These model predictions were tested experimentally. Subject responses to an impulsive force disturbance applied during walking were studied. The electromyographic results generally support the model predictions.     

Optimal combination of minimum degrees of freedom to be actuated in the lower limbs to facilitate arm-free paraplegic standing

Arm-free paraplegic standing via functional electrical stimulation (FES) has drawn much attention in the biomechanical field as it might allow a paraplegic to stand and simultaneously use both arms to perform daily activities. However, current FES systems for standing require that the individual actively regulates balance using one or both arms, thus limiting the practical use of these systems. The purpose of the present study was to show that actuating only six out of 12 degrees of freedom (12-DOFs) in the lower limbs to allow paraplegics to stand freely is theoretically feasible with respect to multibody stability and physiological torque limitations of the lower limb DOF. Specifically, the goal was to determine the optimal combination of the minimum DOF that can be realistically actuated using FES while ensuring stability and able-bodied kinematics during perturbed arm-free standing. The human body was represented by a three-dimensional dynamics model with 12-DOFs in the lower limbs. Nakamura's method (Nakamura, Y., and Ghodoussi, U., 1989, "Dynamics Computation of Closed-Link Robot Mechanisms With Nonredundant and Redundant Actuators," IEEE Trans. Rob. Autom., 5(3), pp. 294-302) was applied to estimate the joint torques of the system using experimental motion data from four healthy subjects. The torques were estimated by applying our previous finding that only 6 (6-DOFs) out of 12-DOFs in the lower limbs need to be actuated to facilitate stable standing. Furthermore, it was shown that six cases of 6-DOFs exist, which facilitate stable standing. In order to characterize each of these cases in terms of the torque generation patterns and to identify a potential optimal 6-DOF combination, the joint torques during perturbations in eight different directions were estimated for all six cases of 6-DOFs. The results suggest that the actuation of both ankle flexionextension, both knee flexionextension, one hip flexionextension, and one hip abductionadduction DOF will result in the minimum torque requirements to regulate balance during perturbed standing. To facilitate unsupported FES-assisted standing, it is sufficient to actuate only 6-DOFs. An optimal combination of 6-DOFs exists, for which this system can generate able-bodied kinematics while requiring lower limb joint torques that are producible using contemporary FES technology. These findings suggest that FES-assisted arm-free standing of paraplegics is theoretically feasible, even when limited by the fact that muscles actuating specific DOFs are often denervated or difficult to access.     

Perturbation-dependent selection of postural feedback gain and its scaling

In this study we examined whether the selection of postural feedback gain and its scaling is dependent on perturbation type. We compare forward pushes applied to the back of a standing subject to previous work on responses to support translation. As was done in the previous work, we quantified the subject's response in terms of perturbation-dependent feedback gains. Seven healthy young subjects (25±3 yr) experienced five different magnitudes of forward push applied by a 1.25 m-long pendulum falling from the height of 1.4m toward the center of mass of the subject's torso. The loads on the pendulum ranged from 2 to 10 kg. Impulsive force, ground reaction forces and joint kinematics were measured, and joint torques were calculated from inverse dynamics. A full-state feedback control model was used to quantify the empirical data, and the feedback gains that minimized the fitting error between the data and model simulation were identified. As in previously published feedback gains for support translation trials, gradual gain scaling with push perturbation magnitude was consistently observed, but a different feedback gain set was obtained. The results imply that the nervous system may be aware of body dynamics being subjected to various perturbation types and may select perturbation-dependent postural feedback gains that satisfy postural stability and feasible joint torque constraints.     

Relative Roles of the Ankle and Hip Muscles in Human Postural Control in the Frontal Plane during Standing

The main goal was to evaluate the relative roles of the ankle and hip muscles in human postural control in the frontal plane during normal upright standing. Experiments were designed to compare upright standing with and without the involvement of the ankle joint. The results demonstrated that standing balance in the frontal plane depended largely on the hip muscles and just slightly on the ankle muscles, which performed only small adjusting movements in the frontal plane. During quiet standing, the human body swayed in the frontal plane as a two-component inverted pendulum or, when no ankle joint torque was permitted, as an inverted pendulum consisting of only one component.     

Uncertainty of knee joint muscle activity during knee joint torque exertion: the significance of controlling adjacent joint torque.

In the single-joint torque exertion task, which has been widely used to control muscle activity, only the relevant joint torque is specified. However, the neglect of the neighboring joint could make the procedure unreliable, considering our previous result that even monoarticular muscle activity level is indefinite without specifying the adjacent joint torque. Here we examined the amount of hip joint torque generated with knee joint torque and its influence on the activity of the knee joint muscles. Twelve healthy subjects were requested to exert various levels of isometric knee joint torque. The knee and hip joint torques were obtained by using a custom-made device. Because no information about hip joint torque was provided to the subjects, the hip joint torque measured here was a secondary one associated with the task. The amount of hip joint torque varied among subjects, indicating that they adopted various strategies to achieve the task. In some subjects, there was a considerable internal variability in the hip joint torque. Such variability was not negligible, because the knee joint muscle activity level with respect to the knee joint torque, as quantified by surface electromyography (EMG), changed significantly when the subjects were requested to change the strategy. This change occurred in a very systematic manner: in the case of the knee extension, as the hip flexion torque was larger, the activity of mono- and biarticular knee extensors decreased and increased, respectively. These results indicate that the conventional single knee joint torque exertion has the drawback that the intersubject and/or intertrial variability is inevitable in the relative contribution among mono- and biarticular muscles because of the uncertainty of the hip joint torque. We discuss that the viewpoint that both joint torques need to be considered will bring insights into various controversial problems such as the shape of the EMG-force relationship, neural factors that help determine the effect of muscle strength training, and so on.     

The Sense of Effort and two Models of Single-Joint Motor Control

Two sets of experiments were carried out. In the first set, human subjects were asked to make the same effort with the elbow flexors at different joint angles under isometric conditions. In some experiments, the subjects were standing with the arm in a vertical (parasagittal) plane; in others, they were seated with the arm in a horizontal (transverse) plane. When muscular torque at a given effort level (ordinate) was plotted as a function of elbow joint angle (abscissa), the resulting isoeffort torque-angle profiles tended to be flat or negatively sloping over a range from 45° to 135°, and they were often nonmonotonic. Increases in effort up to near-maximal levels caused the isoeffort torque-angle profiles to shift upward with little alteration in shape. In the second set of experiments, seated subjects with the arm horizontal resisted baseline torques produced by a motor that acted to extend the elbow joint. Unexpected increases and decreases in torque were superimposed on the baseline torque. The subjects either were instructed to intervene and return the elbow to the initial (90°) position, or were told, “Do not intervene voluntarily; let the motor move your arm.” Effort was reported both under baseline conditions and after the changes in torque. It was found that changes in effort were a function of the changes in torque opposed by the elbow flexors, and were similar whether the subject had repositioned the arm or allowed it to be moved by the motor. In the latter case, the arm came to rest after displacements that were a function of the size and direction of the torque change. For individual subjects, the largest angular displacements ranged from ° 10° to °20° for changes in torque of ° 10 N.m. There was no evidence for any angular dependence of the effort judgments at a given torque over this angular range. Depending on whether effort is primarily an efferent perception proportional to voluntary motor activity or also has a significant afferent (involuntary) component, different models of motor control are supported by these data.     

Biomechanical analyses of rising from a chair

Quantification of the biomechanical factors that underlie the inability to rise from a chair can help explain why this disability occurs and can aid in the design of chairs and of therapeutic intervention programs. Experimental data collected earlier from 17 young adult and two groups of elderly subjects, 23 healthy and 11 impaired, rising from a standard chair under controlled conditions were analyzed using a planar biomechanical model. The joint torque strength requirements and the location of the floor reaction force at liftoff from the seat in the different groups and under several conditions were calculated. Analyses were also made of how body configurations and the use of hand force affect these joint torques and reaction locations.

In all three groups, the required torques at liftoff were modest compared to literature data on voluntary strengths. Among the three groups rising with the use of hands, at the time of liftoff from the seat, the impaired old subjects, on an average, placed the reaction force the most anterior, the healthy old subjects placed it intermediately and the young subjects placed it the least anterior, within the foot support area. Moreover, the results suggest that, at liftoff, all subjects placed more importance on locating the floor reaction force to achieve acceptable postural stability than on diminishing the magnitudes of the needed joint muscle strengths.     

Evaluation of the roles of passive and active control of balance using a balance control model

At present there is a lack of consensus regarding the relative roles of passive and active control of quiet upright stance. In the current work, this issue was investigated using two simulation models based on contemporary theories. Specifically, the two models, both of which assumed active control torques to be generated from an optimal neural controller, differed with respect to whether or not passive control torques (stiffness and damping) were included. Model parameters were specified using experimental center-of-pressure (COP) time series obtained during upright stance, and comparisons then made between simulated and actual COP-based measures. Including both active and passive joint torques in the control model did not appear to lead to any improvement in the ability to simulate COP compared with only including active joint torque. Further, simulated passive control torques were typically less than 10% of the active control torques, though some exceptions were found. These results, along with existing empirical evidence, suggest that active control torque is dominant in maintaining balance during upright stance.     

Postural reactions of humans in upright stance: Dependence on different visual conditions and the level of stiffness in the ankle joints

We checked on the supposition that the magnitude of postural reactions to an unexpected postural disturbance in upright stance in humans can be determined to a considerable extent by the level of background stiffness in the ankle joints. For this purpose, we estimated changes in the joint stiffness under different conditions of visual control; these values were estimated within the period of background body oscillations (i.e., before the beginning of a compensatory motor reaction) and compared with those in the course of postural reactions evoked by vibrational stimulation of the ankle (shin) muscles. Experiments were carried where the subjects stood with open and closed eyes (OE and CE, respectively) and while standing wearing spectacles with frosted glass passing only diffuse light (DL). In the course of the tests, the subjects stood in the usual comfortable vertical position (hereafter, standard stance) or in the same position but with the possibility to lightly touch an immobile object by a finger (stance with additional support). Such technique was used to weaken the effects of CE and DL on background sways of the body and to lead these sways close to the level typical of OE conditions. The joint stiffness was estimated using an approach based on frequency filtration of oscillations of the center of pressure of the feet (CPF) that allowed us to select signals proportional to displacements of the total center of gravity (CG) of the body and to calculate the difference between oscillations of the CPF and CG (a CPF-CG variable). The CPF-CG variable is proportional to the horizontal acceleration of the CG and, therefore, can be used for estimation of the changes in stiffness in the ankle joints. Under conditions of standard stance, the usual conditions rather similarly influenced both variables (CG and CPF-CG) in the course of both background body oscillations and a postural response. The examined variables were the greatest under CE conditions, decreased under conditions of perception of DL, and became smallest with OE. At standing with additional support, the dependence of the examined variables on visual conditions disappeared within the period of background body oscillations (before the beginning of postural reactions). In this case, the magnitude of oscillations of the CPF-CG variable under CE and DL conditions decreased to the level observed at standing under OE conditions. The magnitude of CG displacements induced by vibrational stimulations of the muscles remained, nevertheless, clearly dependent on visual conditions (the same regularities were observed as in the case of standing with no additional support). Thus, our findings demonstrate that the correlation between the characteristics of postural reactions in the upright stance and the level of ankle joint stiffness is not single-valued. Neirofiziologiya/Neurophysiology, Vol. 39, No. 2, pp. 146–153, March–April, 2007.     

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.     

A procedure to determine equilibrium postural configurations for arbitrary locations of the feet

This research was directed toward predicting postural equilibrium configurations in normal humans for asymmetric locations of the feet. The objective of the study was to identify trends in the variation of the location of ground center of pressure (COP) with increasing levels of asymmetry in the foot placement. The procedure developed here minimized the muscular effort (active torques) in the lower extremities while maximizing postural stability margins for given foot locations. Minimizing muscular effort led to fully extended knees, and maximal stability margin led to the COP moving toward the rear foot in asymmetric stance. A combined analytical-numerical optimization scheme was used to avoid singularities that can arise due to the fact that at equilibrium postural configurations, the torso lies at or near the workspace boundary of the lower extremities. Experiments were conducted and the results obtained were in keeping with the model predictions. This basic understanding of asymmetric stance is important for studying asymmetric postural mechanics in the presence of external disturbances, and for extending the results from normal subjects to humans at both ends of the life span.     

The interaction of muscle moment arm,knee laxity,and torque in a multi-scale musculoskeletal model of the lower limb

IntroductionMusculoskeletal modeling allows insight into the interaction of muscle force and knee joint kinematics that cannot be measured in the laboratory. However, musculoskeletal models of the lower extremity commonly use simplified representations of the knee that may limit analyses of the interaction between muscle forces and joint kinematics. The goal of this research was to demonstrate how muscle forces alter knee kinematics and consequently muscle moment arms and joint torque in a musculoskeletal model of the lower limb that includes a deformable representation of the knee.MethodsTwo musculoskeletal models of the lower limb including specimen-specific articular geometries and ligament deformability at the knee were built in a finite element framework and calibrated to match mean isometric torque data collected from 12 healthy subjects. Muscle moment arms were compared between simulations of passive knee flexion and maximum isometric knee extension and flexion. In addition, isometric torque results were compared with predictions using simplified knee models in which the deformability of the knee was removed and the kinematics at the joint were prescribed for all degrees of freedom.ResultsPeak isometric torque estimated with a deformable knee representation occurred between 45° and 60° in extension, and 45° in flexion. The maximum isometric flexion torques generated by the models with deformable ligaments were 14.6% and 17.9% larger than those generated by the models with prescribed kinematics; by contrast, the maximum isometric extension torques generated by the models were similar. The change in hamstrings moment arms during isometric flexion was greater than that of the quadriceps during isometric extension (a mean RMS difference of 9.8 mm compared to 2.9 mm, respectively).DiscussionThe large changes in the moment arms of the hamstrings, when activated in a model with deformable ligaments, resulted in changes to flexion torque. When simulating human motion, the inclusion of a deformable joint in a multi-scale musculoskeletal finite element model of the lower limb may preserve the realistic interaction of muscle force with knee kinematics and torque.     

Age and gender differences in peak lower extremity joint torques and ranges of motion used during single-step balance recovery from a forward fall.

Previous studies have found substantial age and gender group differences in the ability of healthy adults to regain balance with a single step after a forward fall. It was hypothesized that differences in lower extremity joint strengths and ranges of motion (ROM) may have contributed to these observed differences. Kinematic and forceplate data were therefore used with a rigid-link biomechanical model simulating stepped leg dynamics to examine the joint torques and ROM used by subjects during successful single-step balance recoveries after release from a forward lean. The peak ROM and torques used by subjects in the study were compared to published estimates or measured values of the available maxima. No significant age or gender group differences were found in the mean ROM used by the subjects for any given initial lean angle. As initial lean angle increased, larger knee ROM and significantly larger hip ROM were used in the successful recoveries. There were substantial gender differences and some age group differences in peak lower extremity joint torques used in successful recoveries. Both young and older females often used nearly maximal joint torques to recover balance. Subjects' maximum joint strengths in plantarflexion and hip flexion were not good predictors of single-step balance recovery ability, particularly among the female subjects.     

Evaluation of a generalized model of human postural dynamics and control in the sagittal plane

A two-step identification method is used to evaluate a generalized model of human postural control in the sagittal plane. Postural dynamics are represented as a planar open-chain linkage system supported by a triangular foot. The control mechanism is modeled as a state feedback element in which the torque acting at a given link is an arbitrary function of the state variables — angles and angular velocities. To validate the approach, six normal subjects underwent two series of experiments. The first series were used to determine an appropriate model of the system dynamics. The second series were used to estimate the parameters of the feedback model. A computer simulation of the complete system shows that the model predictions closely match the observed responses. These results suggest that the proposed model provides a useful framework for analysis of postural control mechanisms.This work was supported by the National Institutes of Health under Grant NS 21363     

Comparative analysis of methods for estimating arm segment parameters and joint torques from inverse dynamics

A common problem in the analyses of upper limb unfettered reaching movements is the estimation of joint torques using inverse dynamics. The inaccuracy in the estimation of joint torques can be caused by the inaccuracy in the acquisition of kinematic variables, body segment parameters (BSPs), and approximation in the biomechanical models. The effect of uncertainty in the estimation of body segment parameters can be especially important in the analysis of movements with high acceleration. A sensitivity analysis was performed to assess the relevance of different sources of inaccuracy in inverse dynamics analysis of a planar arm movement. Eight regression models and one water immersion method for the estimation of BSPs were used to quantify the influence of inertial models on the calculation of joint torques during numerical analysis of unfettered forward arm reaching movements. Thirteen subjects performed 72 forward planar reaches between two targets located on the horizontal plane and aligned with the median plane. Using a planar, double link model for the arm with a floating shoulder, we calculated the normalized joint torque peak and a normalized root mean square (rms) of torque at the shoulder and elbow joints. Statistical analyses quantified the influence of different BSP models on the kinetic variable variance for given uncertainty on the estimation of joint kinematics and biomechanical modeling errors. Our analysis revealed that the choice of BSP estimation method had a particular influence on the normalized rms of joint torques. Moreover, the normalization of kinetic variables to BSPs for a comparison among subjects showed that the interaction between the BSP estimation method and the subject specific somatotype and movement kinematics was a significant source of variance in the kinetic variables. The normalized joint torque peak and the normalized root mean square of joint torque represented valuable parameters to compare the effect of BSP estimation methods on the variance in the population of kinetic variables calculated across a group of subjects with different body types. We found that the variance of the arm segment parameter estimation had more influence on the calculated joint torques than the variance of the kinematics variables. This is due to the low moments of inertia of the upper limb, especially when compared with the leg. Therefore, the results of the inverse dynamics of arm movements are influenced by the choice of BSP estimation method to a greater extent than the results of gait analysis.     

Biomechanics of human quadriceps muscles during electrical stimulation

The quadriceps muscles of neurologically intact and spinal cord injured (SCI) human subjects were stimulated with constant current pulses. Up to three, separately adjustable stimulating electrodes over the motor points for vastus medialis (VM), vastus lateralis (VL) and rectus femoris (RF) muscles were used to maximize torque generation while minimizing discomfort. The torque generated by stimulation increased as the knee was slowly flexed to about 1 rad (50-60 degrees) and decreased beyond that point (a 'negative slope' on a torque-angle curve). Despite this region of negative slope the force generated by small oscillations remained positively correlated to the angle changes. When the knee was slowly extended again from a flexed position, the torque continued to decline and therefore showed a large degree of 'hysteresis'. Of the three heads studied, only stimulation of RF muscle generally produced this behavior. VL and VM had torques that increased monotonically with knee flexion over the range studied. The torques generated with electrical stimulation of normal subjects represented up to about 30% of maximum voluntary contraction. When subjects generated similar torques voluntarily, the negative slope region and substantial hysteresis were not observed. Thus, SCI subjects may be adversely affected by hysteresis during electrically-induced transitions from sitting to standing and vice versa, while normal subjects are not.     

Trunk acceleration for neuroprosthetic control of standing: a pilot study

This pilot study investigated the potential of using trunk acceleration feedback control of center of pressure (COP) against postural disturbances with a standing neuroprosthesis following paralysis. Artificial neural networks (ANNs) were trained to use three-dimensional trunk acceleration as input to predict changes in COP for able-bodied subjects undergoing perturbations during bipedal stance. Correlation coefficients between ANN predictions and actual COP ranged from 0.67 to 0.77. An ANN trained across all subject-normalized data was used to drive feedback control of ankle muscle excitation levels for a computer model representing a standing neuroprosthesis user. Feedback control reduced average upper-body loading during perturbation onset and recovery by 42% and peak loading by 29% compared with optimal, constant excitation.