Balancing on a narrow ridge: biomechanics and control.

The balance of standing humans is usually explained by the inverted pendulum model. The subject invokes a horizontal ground-reaction force in this model and controls it by changing the location of the centre of pressure under the foot or feet. In experiments I showed that humans are able to stand on a ridge of only a few millimetres wide on one foot for a few minutes. In the present paper I investigate whether the inverted pendulum model is able to explain this achievement. I found that the centre of mass of the subjects sways beyond the surface of support, rendering the inverted pendulum model inadequate. Using inverse simulations of the dynamics of the human body, I found that hip-joint moments of the stance leg are used to vary the horizontal component of the ground-reaction force. This force brings the centre of mass back over the surface of support. The subjects generate moments of force at the hip-joint of the swing leg, at the shoulder-joints and at the neck. These moments work in conjunction with a hip strategy of the stance leg to limit the angular acceleration of the head-arms-trunk complex. The synchrony of the variation in moments suggests that subjects use a motor programme rather than long latency reflexes.     

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.     

Oscillations of upper and lower body segments in the sagittal plane during standing: Spatiotemporal relationships

The balance control in the sagittal plane during standing without visual feedback has been studied in the context of the notion that a human body can be presented as a two-segment inverted pendulum. The oscillations of the center of pressure and of the upper and lower segments were recorded for 2 min (ten records for each of seven volunteers). It is shown that the correlation coefficients and dynamic similarity between the oscillation of the upper segment and the center of pressure are significantly higher than between the lower segment and the center of pressure. The dynamic similarity between the oscillations of the upper segment in different records are higher than between the oscillations of the lower one, which is supposedly connected with the necessity of stabilizing the head in space during standing. The oscillations of the lower segment occurred with a mean delay of 16.2 ± 9.0 ms relative to those of the upper segment. At the same time, the distribution of the delays has a peak at zero, indicating that two strategies of balance control are used during quiet standing, which are described in the one-segment and the two-segment inverted pendulum models.     

Spinal Mechanisms May Provide a Combination of Intermittent and Continuous Control of Human Posture: Predictions from a Biologically Based Neuromusculoskeletal Model

Several models have been employed to study human postural control during upright quiet stance. Most have adopted an inverted pendulum approximation to the standing human and theoretical models to account for the neural feedback necessary to keep balance. The present study adds to the previous efforts in focusing more closely on modelling the physiological mechanisms of important elements associated with the control of human posture. This paper studies neuromuscular mechanisms behind upright stance control by means of a biologically based large-scale neuromusculoskeletal (NMS) model. It encompasses: i) conductance-based spinal neuron models (motor neurons and interneurons); ii) muscle proprioceptor models (spindle and Golgi tendon organ) providing sensory afferent feedback; iii) Hill-type muscle models of the leg plantar and dorsiflexors; and iv) an inverted pendulum model for the body biomechanics during upright stance. The motor neuron pools are driven by stochastic spike trains. Simulation results showed that the neuromechanical outputs generated by the NMS model resemble experimental data from subjects standing on a stable surface. Interesting findings were that: i) an intermittent pattern of muscle activation emerged from this posture control model for two of the leg muscles (Medial and Lateral Gastrocnemius); and ii) the Soleus muscle was mostly activated in a continuous manner. These results suggest that the spinal cord anatomy and neurophysiology (e.g., motor unit types, synaptic connectivities, ordered recruitment), along with the modulation of afferent activity, may account for the mixture of intermittent and continuous control that has been a subject of debate in recent studies on postural control. Another finding was the occurrence of the so-called “paradoxical” behaviour of muscle fibre lengths as a function of postural sway. The simulations confirmed previous conjectures that reciprocal inhibition is possibly contributing to this effect, but on the other hand showed that this effect may arise without any anticipatory neural control mechanism.     

THE COEVOLUTION OF HUMAN HANDS AND FEET

Human hands and feet have longer, more robust first digits, and shorter lateral digits compared to African apes. These similarities are often assumed to be independently evolved adaptations for manipulative activities and bipedalism, respectively. However, hands and feet are serially homologous structures that share virtually identical developmental blueprints, raising the possibility that digital proportions coevolved in human hands and feet because of underlying developmental linkages that increase phenotypic covariation between them. Here we show that phenotypic covariation between serially homologous fingers and toes in Homo and Pan is not only higher than expected, it also causes these digits to evolve along highly parallel trajectories under episodes of simulated directional selection, even when selection pressures push their means in divergent directions. Further, our estimates of the selection pressures required to produce human‐like fingers and toes from an African ape‐like ancestor indicate that selection on the toes was substantially stronger, and likely led to parallel phenotypic changes in the hands. Our data support the hypothesis that human hands and feet coevolved, and suggest that the evolution of long robust big toes and short lateral toes for bipedalism led to changes in hominin fingers that may have facilitated the emergence of stone tool technology.     

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.     

An automated method to morph finite element whole-body human models with a wide range of stature and body shape for both men and women

Field data analyses have shown that small female, obese, and/or older occupants are at increased risks of death and serious injury in motor-vehicle crashes compared with mid-size young men. The current adult finite element (FE) human models represent occupants in the same three body sizes (large male, mid-size male, and small female) as those for the contemporary adult crash dummies. Further, the time needed to develop an FE human model using the traditional method is measured in months or even years. In the current study, an improved regional mesh morphing method based on landmark-based radial basis function (RBF) interpolation was developed to rapidly morph a mid-size male FE human model into different geometry targets. A total of 100 human models with a wide range of human attributes were generated. A pendulum chest impact condition was applied to each model as an initial assessment of the resulting variability in response. The morphed models demonstrated mesh quality similar to the baseline model. The peak impact forces and chest deflections in the chest pendulum impacts varied substantially with different models, supportive of consideration of population variation in evaluating the occupant injury risks. The method developed in this study will enable future safety design optimizations targeting at various vulnerable populations that cannot be considered with the current models.     

Predictive feedback in human simulated pendulum balancing

In studies of human balance, it is common to fit stimulus-response data by tuning the time-delay and gain parameters of a simple delayed feedback model. Many interpret this fitted model, a simple delayed feedback model, as evidence that predictive processes are not required to explain existing data on standing balance. However, two questions lead us to doubt this approach. First, does fitting a delayed feedback model lead to reliable estimates of the time-delay? Second, can a non-predictive controller provide an explanation compatible with the independently estimated time delay? For methodological and experimental clarity, we study human balancing of a simulated inverted pendulum via joystick and screen. A two-step approach to data analysis is used: firstly a non-parametric model—the closed-loop impulse response—is estimated from the experimental data; second, a parametric model is fitted to the non-parametric impulse-response by adjusting time-delay and controller parameters. To support the second step, a new explicit formula relating controller parameters to closed-loop impulse response is derived. Two classes of controller are investigated within a common state-space context: non-predictive and predictive. It is found that the time-delay estimate arising from the second step is strongly dependent on which controller class is assumed; in particular, the non-predictive control assumption leads to time-delay estimates that are smaller than those arising from the predictive assumption. Moreover, the time-delays estimated using the non-predictive control assumption are not consistent with a lower-bound on the time-delay of the non-parametric model whereas the corresponding predictive result is consistent. Thus while the goodness of fit only marginally favoured predictive over non-predictive control, if we add the additional constraint that the model must reproduce the non-parametric time delay, then the non-predictive control model fails. We conclude (1) the time-delay should be estimated independently of fitting a low order parametric model, (2) that balance of the simulated inverted pendulum could not be explained by the non-predictive control model and (3) that predictive control provided a better explanation than non-predictive control.     

A multisensory integration model of human stance control

A model is presented to study and quantify the contribution of all available sensory information to human standing based on optimal estimation theory. In the model, delayed sensory information is integrated in such a way that a best estimate of body orientation is obtained. The model approach agrees with the present theory of the goal of human balance control. The model is not based on purely inverted pendulum body dynamics, but rather on a three-link segment model of a standing human on a movable support base. In addition, the model is non-linear and explicitly addresses the problem of multisensory integration and neural time delays. A predictive element is included in the controller to compensate for time delays, necessary to maintain erect body orientation. Model results of sensory perturbations on total body sway closely resemble experimental results. Despite internal and external perturbations, the controller is able to stabilise the model of an inherently unstable standing human with neural time delays of 100 ms. It is concluded, that the model is capable of studying and quantifying multisensory integration in human stance control. We aim to apply the model in (1) the design and development of prostheses and orthoses and (2) the diagnosis of neurological balance disorders. Received: 25 August 1997 / Accepted in revised form: 8 December 1998     

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.     

Dynamic stability of a human standing on a balance board

The neuromuscular system used to stabilize upright posture in humans is a nonlinear dynamical system with time delays. The analysis of this system is important for improving balance and for early diagnosis of neuromuscular disease. In this work, we study the dynamic coupling between the neuromuscular system and a balance board—an unstable platform often used to improve balance in young athletes, and older or neurologically impaired patients. Using a simple inverted pendulum model of human posture on a balance board, we describe a surprisingly broad range of divergent and oscillatory CoP/CoM responses associated with instabilities of the upright equilibrium. The analysis predicts that a variety of sudden changes in the stability of upright postural equilibrium occurs with slow continuous deterioration in balance board stiffness, neuromuscular gain, and time delay associated with the changes in proprioceptive/vestibular/visual-neuromuscular feedback. The analysis also provides deeper insight into changes in the control of posture that enable stable upright posture on otherwise unstable platforms.     

Stability and Control of Human Trunk Movement During Walking

A mathematical model has been developed to study the control mechanisms of human trunk movement during walking. The trunk is modeled as a base-excited inverted pendulum with two-degrees of rotational freedom. The base point, corresponding to the bony landmark of the sacrum, can move in three-dimensional space in a general way. Since the stability of upright posture is essential for human walking, a controller has been designed such that the stability of the pendulum about the upright position is guaranteed. The control laws are developed based on Lyapunov' stability theory and include feedforward and linear feedback components. It is found that the feedforward component plays a critical role in keeping postural stability, and the linear feedback component, (resulting from viscoelastic function of the musculoskeletal system) can effectively duplicate the pattern of trunk movement. The mathematical model is validated by comparing the simulation results with those based on gait measurements performed in the Biomechanics Laboratory at the University of Manitoba.     

Stability and Control of Human Trunk Movement During Walking

A mathematical model has been developed to study the control mechanisms of human trunk movement during walking. The trunk is modeled as a base-excited inverted pendulum with two-degrees of rotational freedom. The base point, corresponding to the bony landmark of the sacrum, can move in three-dimensional space in a general way. Since the stability of upright posture is essential for human walking, a controller has been designed such that the stability of the pendulum about the upright position is guaranteed. The control laws are developed based on Lyapunov's stability theory and include feedforward and linear feedback components. It is found that the feedforward component plays a critical role in keeping postural stability, and the linear feedback component, (resulting from viscoelastic function of the musculoskeletal system) can effectively duplicate the pattern of trunk movement. The mathematical model is validated by comparing the simulation results with those based on gait measurements performed in the Biomechanics Laboratory at the University of Manitoba.     

All leg joints contribute to quiet human stance: A mechanical analysis

According to the state of the art model (single inverted pendulum) the regulation of quiet human stance seems to be dominated by ankle joint actions. Recent findings substantiated both in-phase and anti-phase fluctuations of ankle and hip joint kinematics can be identified in quiet human stance. Thus, we explored in an experimental study to what extent all three leg joints actually contribute to the balancing problem of quiet human stance. We also aimed at distinguishing kinematic from torque contributions. Thereto, we directly measured ankle, knee, and hip joint kinematics with high spatial resolution and ground reaction forces. Then, we calculated the six respective joint torques and, additionally, the centre of mass kinematics. We searched for high cross-correlations between all these mechanical variables. Beyond confirming correlated anti-phase kinematics of ankle and hip, the main results are: (i) ankle and knee joint fluctuate tightly (torque) coupled and (ii) the bi-articular muscles of the leg are well suited to fulfil the requirements of fluctuations around static equilibrium. Additionally, we (iii) identified high-frequency oscillations of the shank between about 4 and 8 Hz and (iv) discriminated potentially passive and active joint torque contributions. These results demonstrate that all leg joints contribute actively and concertedly to quiet human stance, even in the undisturbed case. Moreover, they substantiate the single inverted pendulum paradigm to be an invalid model for quiet human stance.     

Design and simulation of closed-loop electrical stimulation orthoses for restoration of quiet standing in paraplegia

Simulation models of quiet standing have been developed to study the potential use of closed-loop stimulation orthoses in mid-thoracic spinal cord injury. The first model (static) consists of a multi-link inverted pendulum. The second model (dynamic) consists of a single-link inverted pendulum, with electrically stimulated muscles providing balancing activation at the ankle joint and stabilization of the knee and hip joints. The initial simulations have shown that it may be possible to restore quiet standing in paraplegic individuals within certain limits subject to biomechanical constraints and to the available torque produced by the stimulated muscle.     

An active balance board system with real-time control of stiffness and time-delay to assess mechanisms of postural stability

Increased time-delay in the neuromuscular system caused by neurological disorders, concussions, or advancing age is an important factor contributing to balance loss (Chagdes et al., 2013, 2016a,b). We present the design and fabrication of an active balance board system that allows for a systematic study of stiffness and time-delay induced instabilities in standing posture. Although current commercial balance boards allow for variable stiffness, they do not allow for manipulation of time-delay. Having two controllable parameters can more accurately determine the cause of balance deficiencies, and allows us to induce instabilities even in healthy populations. An inverted pendulum model of human posture on such an active balance board predicts that reduced board rotational stiffness destabilizes upright posture through board tipping, and limit cycle oscillations about the upright position emerge as feedback time-delay is increased. We validate these two mechanisms of instability on the designed balance board, showing that rotational stiffness and board time-delay induced the predicted postural instabilities in healthy, young adults. Although current commercial balance boards utilize control of rotational stiffness, real-time control of both stiffness and time-delay on an active balance board is a novel and innovative manipulation to reveal balance deficiencies and potentially improve individualized balance training by targeting multiple dimensions contributing to standing balance.     

Differential activation of the plantar flexor muscles in balance control across different feet orientations on the ground

The ankle plantar flexor muscles act synergistically to control quiet and dynamic body balance. Previous research has shown that the medial (MG) and lateral (LG) gastrocnemii, and soleus (SOL) are differentially activated as a function of motor task requirements. In the present investigation, we evaluated modulation of the plantar flexors' activation from feet orientation on the ground in an upright stance and the ensuing reactive response to a perturbation. A single group of young participants (n = 24) was evaluated in a task requiring initial stabilization of body balance against a backward pulling load (5% or 10% of body weight) attached to their trunk, and then the balance was suddenly perturbed, releasing the load. Four feet orientations were compared: parallel (0°), outward orientation at 15° and 30°, and the preferred orientation (M = 10.5°). Results revealed a higher activation magnitude of SOL compared to MG-LG when sustaining quiet balance against the 10% load. In the generation of reactive responses, MG was characterized by earlier, steeper, and proportionally higher activation than LG-SOL. Feet orientation at 30° led to higher muscular activation than the other orientations, while the activation relationship across muscles was unaffected by feet orientation. Our results support the conclusion of task-specific differential modulation of the plantar flexor muscles for balance control.     

Muscle mechanical work requirements during normal walking: the energetic cost of raising the body's center-of-mass is significant

Inverted pendulum models of walking predict that little muscle work is required for the exchange of body potential and kinetic energy in single-limb support. External power during walking (product of the measured ground reaction force and body center-of-mass (COM) velocity) is often analyzed to deduce net work output or mechanical energetic cost by muscles. Based on external power analyses and inverted pendulum theory, it has been suggested that a primary mechanical energetic cost may be associated with the mechanical work required to redirect the COM motion at the step-to-step transition. However, these models do not capture the multi-muscle, multi-segmental properties of walking, co-excitation of muscles to coordinate segmental energetic flow, and simultaneous production of positive and negative muscle work. In this study, a muscle-actuated forward dynamic simulation of walking was used to assess whether: (1). potential and kinetic energy of the body are exchanged with little muscle work; (2). external mechanical power can estimate the mechanical energetic cost for muscles; and (3.) the net work output and the mechanical energetic cost for muscles occurs mostly in double support. We found that the net work output by muscles cannot be estimated from external power and was the highest when the COM moved upward in early single-limb support even though kinetic and potential energy were exchanged, and muscle mechanical (and most likely metabolic) energetic cost is dominated not only by the need to redirect the COM in double support but also by the need to raise the COM in single support.