The equations of motion for a standing human reveal three mechanisms for balance

The equations of motion for a standing multi-segment human model are derived. Output quantity of these equations is the horizontal acceleration of the whole-body centre of mass (CoM). There are three input terms and they can be identified as the three mechanisms by which balance can be maintained: (1) by moving the centre of pressure with respect to the vertical projection of the CoM, (2) by counter-rotating segments around the CoM, and (3) by applying an external force, other than the ground reaction force. For the first two mechanisms the respective contributions to CoM acceleration can be obtained from force plate recordings. This is illustrated by some example data from experiments, which show that the contribution from mechanism 2 can be considerable, e.g. in one-legged standing.     

Modelling the dynamic margins of stability for use in evaluations of balance following a support-surface perturbation

The dynamic margin of stability provides a method that captures the center of mass (CoM) state (position-velocity) in relation to the base of support (BoS). However, the model upon which this concept was derived does not consider how the inertial characteristics of forced support-surface perturbations would influence balance control. Within the current article, the inverted pendulum model was restructured to account for fixed, piecewise accelerations of the BoS. From this logic, two variations of the adjusted margin of stability, each maintaining a similar definition of extrapolated CoM, are proposed; one ignoring horizontal ground contact and inertial forces applied to the BoS, the other incorporating these forces. Unique within the proposed models is the time-variant BoS boundaries that depend on the perturbation applied. Verification of the solution for each model is provided, along with a comparison of obtained values to previous methods of defining CoM position-velocity stability metrics using a computational model and optimal control. For the simpler model variation (ignoring forces), we also assessed how CoM position and perturbation parameter selection over/underestimate the predicted maximal permissible velocity. The results of these analyses suggest that factors which increase the acceleration impulse decrease the difference between the two models; the opposite was observed for factors increasing displacements between the CoM and BoS boundary. Lastly, use of the proposed adjusted margin of stability within an experimental data set highlights the ability of our model to predict instability (stepping strategies; negative margin of stability) relative to the use of the extrapolated CoM alone.     

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.     

An Artificial Neural Network Estimation of Gait Balance Control in the Elderly Using Clinical Evaluations

The use of motion analysis to assess balance is essential for determining the underlying mechanisms of falls during dynamic activities. Clinicians evaluate patients using clinical examinations of static balance control, gait performance, cognition, and neuromuscular ability. Mapping these data to measures of dynamic balance control, and the subsequent categorization and identification of community dwelling elderly fallers at risk of falls in a quick and inexpensive manner is needed. The purpose of this study was to demonstrate that given clinical measures, an artificial neural network (ANN) could determine dynamic balance control, as defined by the interaction of the center of mass (CoM) with the base of support (BoS), during gait. Fifty-six elderly adults were included in this study. Using a feed-forward neural network with back propagation, combinations of five functional domains, the number of hidden layers and error goals were evaluated to determine the best parameters to assess dynamic balance control. Functional domain input parameters included subject characteristics, clinical examinations, cognitive performance, muscle strength, and clinical balance performance. The use of these functional domains demonstrated the ability to quickly converge to a solution, with the network learning the mapping within 5 epochs, when using up to 30 hidden nodes and an error goal of 0.001. The ability to correctly identify the interaction of the CoM with BoS demonstrated correlation values up to 0.89 (P<.001). On average, using all clinical measures, the ANN was able to estimate the dynamic CoM to BoS distance to within 1 cm and BoS area to within 75 cm². Our results demonstrated that an ANN could be trained to map clinical variables to biomechanical measures of gait balance control. A neural network could provide physicians and patients with a cost effective means to identify dynamic balance issues and possible risk of falls from routinely collected clinical examinations.     

Mechanisms of adaptation from a multiple to a single step recovery strategy following repeated exposure to forward loss of balance in older adults

When released from an initial, static, forward lean angle and instructed to recover with a single step, some older adults are able to meet the task requirements, whereas others either stumble or fall. The purpose of the present study was to use the concept of margin of stability (MoS) to investigate balance recovery responses in the anterior-posterior direction exhibited by older single steppers, multiple steppers and those that are able to adapt from multiple to single steps following exposure to repeated forward loss of balance. One hundred and fifty-one healthy, community dwelling, older adults, aged 65-80 years, participated in the study. Participants performed four trials of the balance recovery task from each of three initial lean angles. Balance recovery responses in the anterior-posterior direction were quantified at three events; cable release (CR), toe-off (TO) and foot contact (FC), for trials performed at the intermediate lean angle. MoS was computed as the anterior-posterior distance between the forward boundary of the Base of Support (BoS) and the vertical projection of the velocity adjusted centre of mass position (XCoM). Approximately one-third of participants adapted from a multiple to a single step recovery strategy following repeated exposure to the task. MoS at FC for the single and multiple step trials in the adaptation group were intermediate between the exclusively single step group and the exclusively multiple step group, with the single step trials having a significant, 3.7 times higher MoS at FC than the multiple step trials. Consistent with differences between single and multiple steppers, adaptation from multiple to single steps was attributed to an increased BoS at FC, a reduced XCoM at FC and an increased rate of BoS displacement from TO to FC. Adaptations occurred within a single test session and suggest older adults that are close to the threshold of successful recovery can rapidly improve dynamic stability following repeated exposure to a forward loss of balance.     

Origins of Balance Disorders during a Daily Living Movement in Obese: Can Biomechanical Factors Explain Everything?

Obese people suffer from postural deficits and are more subject to falls than their lean counterpart. To improve prevention and post-fall rehabilitation programs, it seems important to better understand the posturo-kinetic disorders in daily life situations by determining the contribution of some key factors, mainly morphological characteristics and physical activity level, in the apparition of these disorders.Twelve severe android obese and eight healthy non obese adults performed a reaching task mobilizing the whole body. To further determine the origin of the postural and motor behavior differences, non obese individuals also performed an experimental session with additional constraints which simulated some of the obese morphological characteristics. Impact of the sedentary lifestyle was also studied by dissociation of the obese in two subgroups: physically « active » and physically « inactive ». Movement kinetics and kinematics were characterized with an optoelectronic system synchronized to a force platform. The mechanical equilibrium pattern was evaluated through the displacements of the Centre of Mass (CoM) and the centre of foot pressure within the Base of Support (BoS).Results showed that obesity decreased movement speed (≈−23%, p<0.01), strongly increased CoM displacement (≈+30%, p<0.05) and induced an important spatio-temporal desynchronization (≈+40%, p<0.05) of the focal and postural components of the movement during the transition between the descending and ascending movements.The role of some morphological characteristics and of physical activity on obese patients'' postural control disorder is discussed and set back in the more general context of overall factors contributing to postural deficits with obesity.     

IMU: Inertial sensing of vertical CoM movement

The purpose of this study was to use a quaternion rotation matrix in combination with an integration approach to transform translatory accelerations of the centre of mass (CoM) from an inertial measurement unit (IMU) during walking, from the object system onto the global frame. Second, this paper utilises double integration to determine the relative change in position of the CoM from the vertical acceleration data. Five participants were tested in which an IMU, consisting of accelerometers, gyroscopes and magnetometers was attached on the lower spine estimated centre of mass. Participants were asked to walk three times through a calibrated volume at their self-selected walking speed. Synchronized data were collected by an IMU and an optical motion capture system (OMCS); both measured at 100 Hz. Accelerations of the IMU were transposed onto the global frame using a quaternion rotation matrix. Translatory acceleration, speed and relative change in position from the IMU were compared with the derived data from the OMCS. Peak acceleration in vertical axis showed no significant difference (p?0.05). Difference between peak and trough speed showed significant difference (p<0.05) but relative peak-trough position between the IMU and OMCS did not show any significant difference (p?0.05). These results indicate that quaternions, in combination with Simpsons rule integration, can be used in transforming translatory acceleration from the object frame to the global frame and therefore obtain relative change in position, thus offering a solution for using accelerometers in accurate global frame kinematic gait analyses.     

Evaluation of time-to-contact measures for assessing postural stability

Postural stability has traditionally been examined through spatial measures of the center of mass (CoM) or center of pressure (CoP), where larger amounts of CoM or CoP movements are considered signs of postural instability. However, for stabilization, the postural control system may utilize additional information about the CoM or CoP such as velocity, acceleration, and the temporal margin to a stability boundary. Postural time-to-contact (TtC) is a variable that can take into account this additional information about the CoM or CoP. Postural TtC is the time it would take the CoM or CoP, given its instantaneous trajectory, to contact a stability boundary. This is essentially the time the system has to reverse any perturbation before stance is threatened. Although this measure shows promise in assessing postural stability, the TtC values derived between studies are highly ambiguous due to major differences in how they are calculated. In this study, various methodologies used to assess postural TtC were compared during quiet stance and induced-sway conditions. The effects of the different methodologies on TtC values will be assessed, and issues regarding the interpretation of TtC data will also be discussed.     

Countermovement strategy changes with vertical jump height to accommodate feasible force constraints

In this study, we developed a curve-fit model of countermovement dynamics and examined whether the characteristics of a countermovement jump can be quantified using the model parameter and its scaling; we expected that the model-based analysis would facilitate an understanding of the basic mechanisms of force reduction and propulsion with a simplified framework of the center of mass (CoM) mechanics. Ten healthy young subjects jumped straight up to five different levels ranging from approximately 10% to 35% of their body heights. The kinematic and kinetic data on the CoM were measured using a force plate system synchronized with motion capture cameras. All subjects generated larger vertical forces compared with their body weights from the countermovement and sufficiently lowered their CoM position to support the work performed by push-off as the vertical elevations became more challenging. The model simulation reasonably reproduced the trajectories of vertical force during the countermovement, and the model parameters were replaced by linear and polynomial regression functions in terms of the vertical jump height. Gradual scaling trends of the individual model parameters were observed as a function of the vertical jump height with different degrees of scaling, depending on the subject. The results imply that the subjects may be aware of the jumping dynamics when subjected to various vertical jump heights and may select their countermovement strategies to effectively accommodate biomechanical constraints, i.e., limited force generation for the standing vertical jump.     

Persistence of Motor-Equivalent Postural Fluctuations during Bipedal Quiet Standing

Theoretical and empirical work indicates that the central nervous system is able to stabilize motor performance by selectively suppressing task-relevant variability (TRV), while allowing task-equivalent variability (TEV) to occur. During unperturbed bipedal standing, it has previously been observed that, for task variables such as the whole-body center of mass (CoM), TEV exceeds TRV in amplitude. However, selective control (and correction) of TRV should also lead to different temporal characteristics, with TEV exhibiting higher temporal persistence compared to TRV. The present study was specifically designed to test this prediction. Kinematics of prolonged quiet standing (5 minutes) was measured in fourteen healthy young participants, with eyes closed. Using the uncontrolled manifold analysis, postural variability in six sagittal joint angles was decomposed into TEV and TRV with respect to four task variables: (1) center of mass (CoM) position, (2) head position, (3) trunk orientation and (4) head orientation. Persistence of fluctuations within the two variability components was quantified by the time-lagged auto-correlation, with eight time lags between 1 and 128 seconds. The pattern of results differed between task variables. For three of the four task variables (CoM position, head position, trunk orientation), TEV significantly exceeded TRV over the entire 300 s-period.The autocorrelation analysis confirmed our main hypothesis for CoM position and head position: at intermediate and longer time delays, TEV exhibited higher persistence than TRV. Trunk orientation showed a similar trend, while head orientation did not show a systematic difference between TEV and TRV persistence. The combination of temporal and task-equivalent analyses in the present study allow a refined characterization of the dynamic control processes underlying the stabilization of upright standing. The results confirm the prediction, derived from computational motor control, that task-equivalent fluctuations for specific task variables show higher temporal persistence compared to task-relevant fluctuations.     

Vertical displacement of the centre of mass during walking in people with diabetes and diabetic neuropathy does not explain their higher metabolic cost of walking

People with diabetes display biomechanical gait alterations compared to controls and have a higher metabolic cost of walking (CoW), but it remains unknown whether differences in the vertical displacement of the body centre of mass (CoM) may play a role in this higher CoW. The aim of this study was to investigate vertical CoM displacement (and step length as a potential underpinning factor) as an explanatory factor in the previously observed increased CoW with diabetes. Thirty-one non-diabetic controls (Ctrl); 22 diabetic patients without peripheral neuropathy (DM) and 14 patients with moderate/severe Diabetic Peripheral Neuropathy (DPN), underwent gait analysis using a motion analysis system and force plates while walking at a range of matched speeds between 0.6 and 1.6 m/s. Vertical displacement of the CoM was measured over the gait cycle, and was not different in either diabetes patients with or without diabetic peripheral neuropathy compared to controls across the range of matched walking speeds examined (at 1 m/s: Ctrl: 5.59 (SD: 1.6), DM: 5.41 (1.63), DPN: 4.91 (1.66) cm; p > 0.05). The DPN group displayed significantly shorter steps (at 1 m/s: Ctrl: 69, DM: 67, DPN: 64 cm; p > 0.05) and higher cadence (at 1 m/s: Ctrl: 117 (SD1.12), DM: 119 (1.08), DPN: 122 (1.25) steps per minute; p > 0.05) across all walking speeds compared to controls. The vertical CoM displacement is therefore unlikely to be a factor in itself that contributes towards the higher CoW observed recently in people with diabetic neuropathy. The higher CoW in patients with diabetes may not be explained by the CoM displacement, but rather may be more related to shorter step lengths, increased cadence and the associated increased internal work and higher muscle forces developed by walking with more flexed joints.     

Investigating centre of mass stabilisation as the goal of posture and movement coordination during human whole body reaching

In the light of experimental results showing significant forward centre of mass (CoM) displacements within the base of support, this study investigated if whole body reaching movements can be executed whilst keeping the CoM fixed in the horizontal axis. Using kinematic simulation techniques, angular configurations were recreated from experimental data imposing two constraints: a constant horizontal position of the CoM and an identical trajectory of the hand to grasp an object. The comparison between recorded and simulated trials showed that stabilisation of the CoM was associated with greater backward hip displacements, which became more marked with increasing object distance. This was in contrast to recorded trials showing reductions in backward hip displacements with increasing distance. Results also showed that modifications to angular displacements were necessary only at the shoulder and hip joints, but that these modifications were within the limits of joint mobility. The analysis of individual joint torques revealed that the pattern and timing of simulated trials were similar to those recorded experimentally. Peak joint torque values showed particularly that keeping the CoM at a constant horizontal position resulted in significantly smaller ankle peak flexor and extensor torques. It may be concluded from this study that `stabilising' the CoM during human whole body reaching represents a feasible strategy, but not the one chosen by subjects under experimental conditions. Our results also do not support the idea of the CoM as the stabilised reference value for the coordination between posture and goal-directed movements. Received: 22 September 1998 / Accepted in revised form: 2 June 1999     

Humans adjust the height of their center of mass within one step when running across camouflaged changes in ground level

In running, humans use different control strategies that are most likely influenced by environmental conditions. For example, when human runners face a change in ground level, they adapt the height of their center of mass (CoM) in preparation. In a situation in which a drop might occur but without visual cues regarding its actual height, such a preparation is not possible. We here used camouflaged drops (which occurred by chance) as mechanical disturbances and analyzed the adaptations in the vertical oscillation of the runners CoM. We found that humans lowered their CoM by about 25% of the possible drop height in preparation for the camouflaged contact, regardless of whether a drop occurred or not. In flight phase following the disturbance, the CoM was lowered by about 90% of the drop height in the case of the camouflaged drop and remained almost unaffected (+5%) in the case of level ground. Thus, runners resort to a CoM-control strategy with a fixed desired trajectory height in the flight phase following the camouflaged ground contact. In contrast to previously reported results which show that visible ground level changes were compensated within several steps, this strategy compensates ground level disturbances instantly within a single step.     

Maximum walking speed and lower limb length in hominids

In 1984, Helene (Am. J. Physics 52:656) and Alexander (Am. Scientist 72:348–354) presented equations which purported to explain how lower limb length limited maximum walking speed in humans. The equations were based on a simplified model of human walking in which the center of mass (CoM) “vaults” over the supporting leg. Increasing walking speed by increasing stride frequency or stride length would increase the upward acceleration of the CoM in the first half of stance phase, to the point that it would be greater than the downward pull of gravity, and the individual would become airborne. This constitutes running by most definitions. While these models ignored various mechanical factors, such as knee flexion during midstance, that reduce the vertical movement of the CoM, the general idea is plausible inasmuch as the CoM of the body does oscillate vertically with each step. One hypothesis tested here is whether it is indeed the interaction between the pull of gravity and the individual's own upward acceleration that determines at what speed (or cadence) he changes from walking to running. Another hypothesis considered is that increased lower limb length (L) was selected for in early hominids, because of the locomotor advantages of longer lower limbs. Results indicate, however, that while L was clearly related to maximum possible walking speed, it was not an important factor in determining maximum “comfortable” walking speed. These and other results from the recent literature suggest that increased lower limb length provided no selective advantage in locomotion, and other explanations should be sought. © 1996 Wiley-Liss, Inc.     

Regulation of angular impulse during two forward translating tasks

Angular impulse generation is dependent on the position of the total body center of mass (CoM) relative to the ground reaction force (GRF) vector during contact with the environment. The purpose of this study was to determine how backward angular impulse was regulated during two forward translating tasks. Control of the relative angle between the CoM and the GRF was hypothesized to be mediated by altering trunk-leg coordination. Eight highly skilled athletes performed a series of standing reverse somersaults and reverse timers. Sagittal plane kinematics, GRF, and electromyograms of lower extremity muscles were acquired during the take-off phase of both tasks. The magnitude of the backward angular impulse generated during the push interval of both tasks was mediated by redirecting the GRF relative to the CoM. During the reverse timer, backward angular impulse generated during the early part of the take-off phase was negated by limiting backward trunk rotation and redirecting the GRF during the push interval. Biarticular muscles crossing the knee and hip coordinated the control of GRF direction and CoM trajectory via modulation of trunk-leg coordination.     

Age-related changes in force and power associated with balance of women in quiet bilateral stance on a firm surface

Quantitative assessment of the fluctuations of the body centre of mass (CM) while in a stationary bilateral stance on a firm surface is an important criterion of the functional state of human motor-vestibular and sensory apparatus. From analysis of the literature we conclude that more objective characteristics of human balance in quiet standing may be the amount of energy used to maintain the CM in a constant position. Further analysis of the references showed that these characteristics have not been investigated in neurological practice.In this study, the displacement of CM in participants standing in a normal anatomical position was analysed. Forty-five healthy women in three age groups: 18–24, 45–55 and over 60 years participated in the experiments, which consisted of recording changes in partial body weight on the force platform (under one leg) in situations with opened and closed eyes. The specific power of oscillation of body sway and force of lateral swing of CM were calculated. Results indicated that the maximum specific power of oscillation and force of lateral swing were observed in the group of women older than 60 years, especially in the absence of vision. Minimum values occurred in the group of 18–24 years.We also found a considerable variability in all indices in all age groups. This indicates that the stability of the vertical posture in humans depends also on the individual biological characteristics of the central nervous and muscular systems.     

Subject-specific body segment parameters' estimation using biplanar X-rays: a feasibility study

In order to improve the reliability of children's models, the aim of this study was to determine the subject-specific masses and 3D locations of the centres of mass (CoM) of body segments using biplanar X-rays. Previous methods, validated on upper leg segments, were applied to the whole body. Six children and six adults were studied. The low-dose X-ray system EOS(?) was used to simultaneously get head-to-foot biplanar X-rays in the upright position. Specific methods were used to get 3D reconstructions of bones and body shape. The densities from the literature were used to define the masses. To assess the accuracy of the reconstructions, a force plate was used to compare the mass and the projection of the CoM. A mean distance of 4.5?mm between the measured and the calculated projections of the CoM was found. The mean error between the estimated and the actual body mass was 2.6%. Such a method will be useful in obtaining the body segment parameters in children, hard to obtain using direct measurement techniques.     

Controlling propulsive forces in gait initiation in transfemoral amputees

During prosthetic gait initiation, transfemoral (TF) amputees control the spatial and temporal parameters that modulate the propulsive forces, the positions of the center of pressure (CoP), and the center of mass (CoM). Whether their sound leg or the prosthetic leg is leading, the TF amputees reach the same end velocity. We wondered how the CoM velocity build up is influenced by the differences in propulsive components in the legs and how the trajectory of the CoP differs from the CoP trajectory in able bodied (AB) subjects. Seven TF subjects and eight AB subjects were tested on a force plate and on an 8 m long walkway. On the force plate, they initiated gait two times with their sound leg and two times with their prosthetic leg. Force measurement data were used to calculate the CoM velocity curves in horizontal and vertical directions. Gait initiated on the walkway was used to determine the leg preference. We hypothesized that because of the differences in propulsive components, the motions of the CoP and the CoM have to be different, as ankle muscles are used to help generate horizontal ground reaction force components. Also, due to the absence of an active ankle function in the prosthetic leg, the vertical CoM velocity during gait initiation may be different when leading with the prosthetic leg compared to when leading with the sound leg. The data showed that whether the TF subjects initiated a gait with their prosthetic leg or with their sound leg, their horizontal end velocity was equal. The subjects compensated the loss of propulsive force under the prosthesis with the sound leg, both when the prosthetic leg was leading and when the sound leg was leading. In the vertical CoM velocity, a tendency for differences between the two conditions was found. When initiating gait with the sound leg, the downward vertical CoM velocity at the end of the gait initiation was higher compared to when leading with the prosthetic leg. Our subjects used a gait initiation strategy that depended mainly on the active ankle function of the sound leg; therefore, they changed the relative durations of the gait initiation anticipatory postural adjustment phase and the step execution phase. Both legs were controlled in one single system of gait propulsion. The shape of the CoP trajectories, the applied forces, and the CoM velocity curves are described in this paper.     

Stability and manoeuvrability of terrestrial vertebrates

For a standing animal to be statically stable, a vertical linethrough its centre of mass must pass through the polygon ofsupport defined by its feet. Statically stable gaits are possiblefor quadrupeds but do not seem to be used. Physical and mathematicalmodels have shown that bipedal gaits can be dynamically stable.Accelerations and decelerations of animals may be limited bymuscle strength, by the coefficient of friction with the groundor by considerations of stability. Cornering ability similarlymay be limited by strength or by the coefficient of friction.It may be faster to use a longer route involving corners oflarger radius than a shorter one with sharper corners.     

A Comparative Analysis of Algorithms for Estimating the Movement of the Center of Mass According to Force Plate Data

Biophysics - The approaches to determining the horizontal coordinates of the center of mass (CoM) applicablefor force plate are compared. The force plate for which only vertical forces are the...