A kinematic method for computing the motion of the body centre-of-mass (CoM) during walking: a Bayesian approach

The gait pattern of a particular patient can be altered in a large set of pathologies. Tracking the body centre-of-mass (CoM) during the gait allows a quantitative evaluation of these diseases at comparing the gait with normal patterns. A correct estimation of this variable is still an open question because of its non-linearity and inaccurate location. This paper presents a novel strategy for tracking the CoM, using a biomechanical gait model whose parameters are determined by a Bayesian strategy. A particle filter is herein implemented for predicting the model parameters from a set of markers located at the sacral zone. The present approach is compared with other conventional tracking methods and decreases the calculated root mean squared error in about a 56% in the x-axis and 59% in the y-axis.     

A bipedal compliant walking model generates periodic gait cycles with realistic swing dynamics

A simple spring mechanics model can capture the dynamics of the center of mass (CoM) during human walking, which is coordinated by multiple joints. This simple spring model, however, only describes the CoM during the stance phase, and the mechanics involved in the bipedality of the human gait are limited. In this study, a bipedal spring walking model was proposed to demonstrate the dynamics of bipedal walking, including swing dynamics followed by the step-to-step transition. The model consists of two springs with different stiffnesses and rest lengths representing the stance leg and swing leg. One end of each spring has a foot mass, and the other end is attached to the body mass. To induce a forward swing that matches the gait phase, a torsional hip joint spring was introduced at each leg. To reflect the active knee flexion for foot clearance, the rest length of the swing leg was set shorter than that of the stance leg, generating a discrete elastic restoring force. The number of model parameters was reduced by introducing dependencies among stiffness parameters. The proposed model generates periodic gaits with dynamics-driven step-to-step transitions and realistic swing dynamics. While preserving the mimicry of the CoM and ground reaction force (GRF) data at various gait speeds, the proposed model emulated the kinematics of the swing leg. This result implies that the dynamics of human walking generated by the actuations of multiple body segments is describable by a simple spring mechanics.     

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.     

Center of mass mechanics of chimpanzee bipedal walking

Center of mass (CoM) oscillations were documented for 81 bipedal walking strides of three chimpanzees. Full‐stride ground reaction forces were recorded as well as kinematic data to synchronize force to gait events and to determine speed. Despite being a bent‐hip, bent‐knee (BHBK) gait, chimpanzee walking uses pendulum‐like motion with vertical oscillations of the CoM that are similar in pattern and relative magnitude to those of humans. Maximum height is achieved during single support and minimum height during double support. The mediolateral oscillations of the CoM are more pronounced relative to stature than in human walking when compared at the same Froude speed. Despite the pendular nature of chimpanzee bipedalism, energy recoveries from exchanges of kinetic and potential energies are low on average and highly variable. This variability is probably related to the poor phasic coordination of energy fluctuations in these facultatively bipedal animals. The work on the CoM per unit mass and distance (mechanical cost of transport) is higher than that in humans, but lower than that in bipedally walking monkeys and gibbons. The pronounced side sway is not passive, but constitutes 10% of the total work of lifting and accelerating the CoM. CoM oscillations of bipedally walking chimpanzees are distinctly different from those of BHBK gait of humans with a flat trajectory, but this is often described as “chimpanzee‐like” walking. Human BHBK gait is a poor model for chimpanzee bipedal walking and offers limited insights for reconstructing early hominin gait evolution. Am J Phys Anthropol 156:422–433, 2015. © 2014 Wiley Periodicals, Inc.     

Resonance-based oscillations could describe human gait mechanics under various loading conditions

The oscillatory behavior of the center of mass (CoM) and the corresponding ground reaction force (GRF) of human gait for various gait speeds can be accurately described in terms of resonance using a spring–mass bipedal model. Resonance is a mechanical phenomenon that reflects the maximum responsiveness and energetic efficiency of a system. To use resonance to describe human gait, we need to investigate whether resonant mechanics is a common property under multiple walking conditions. Body mass and leg stiffness are determinants of resonance; thus, in this study, we investigated the following questions: (1) whether the estimated leg stiffness increased with inertia, (2) whether a resonance-based CoM oscillation could be sustained during a change in the stiffness, and (3) whether these relationships were consistently observed for different walking speeds. Seven healthy young subjects participated in over-ground walking trials at three different gait speeds with and without a 25-kg backpack. We measured the GRFs and the joint kinematics using three force platforms and a motion capture system. The leg stiffness was incorporated using a stiffness parameter in a compliant bipedal model that best fitted the empirical GRF data. The results showed that the leg stiffness increased with the load such that the resonance-based oscillatory behavior of the CoM was maintained for a given gait speed. The results imply that the resonance-based oscillation of the CoM is a consistent gait property and that resonant mechanics may be useful for modeling human gait.     

Kinematics of lower limbs during walking are emulated by springy walking model with a compliantly connected,off-centered curvy foot

The dynamics of the center of mass (CoM) during walking and running at various gait conditions are well described by the mechanics of a simple passive spring loaded inverted pendulum (SLIP). Due to its simplicity, however, the current form of the SLIP model is limited at providing any further information about multi-segmental lower limbs that generate oscillatory CoM behaviors and their corresponding ground reaction forces. Considering that the dynamics of the CoM are simply achieved by mass-spring mechanics, we wondered whether any of the multi-joint motions could be demonstrated by simple mechanics. In this study, we expand a SLIP model of human locomotion with an off-centered curvy foot connected to the leg by a springy segment that emulates the asymmetric kinematics and kinetics of the ankle joint. The passive dynamics of the proposed expansion of the SLIP model demonstrated the empirical data of ground reaction forces, center of mass trajectories, ankle joint kinematics and corresponding ankle joint torque at various gait speeds. From the mechanically simulated trajectories of the ankle joint and CoM, the motion of lower-limb segments, such as thigh and shank angles, could be estimated from inverse kinematics. The estimation of lower limb kinematics showed a qualitative match with empirical data of walking at various speeds. The representability of passive compliant mechanics for the kinetics of the CoM and ankle joint and lower limb joint kinematics implies that the coordination of multi-joint lower limbs during gait can be understood with a mechanical framework.     

Compliant bipedal model with the center of pressure excursion associated with oscillatory behavior of the center of mass reproduces the human gait dynamics

Although the compliant bipedal model could reproduce qualitative ground reaction force (GRF) of human walking, the model with a fixed pivot showed overestimations in stance leg rotation and the ratio of horizontal to vertical GRF. The human walking data showed a continuous forward progression of the center of pressure (CoP) during the stance phase and the suspension of the CoP near the forefoot before the onset of step transition. To better describe human gait dynamics with a minimal expense of model complexity, we proposed a compliant bipedal model with the accelerated pivot which associated the CoP excursion with the oscillatory behavior of the center of mass (CoM) with the existing simulation parameter and leg stiffness. Owing to the pivot acceleration defined to emulate human CoP profile, the arrival of the CoP at the limit of the stance foot over the single stance duration initiated the step-to-step transition. The proposed model showed an improved match of walking data. As the forward motion of CoM during single stance was partly accounted by forward pivot translation, the previously overestimated rotation of the stance leg was reduced and the corresponding horizontal GRF became closer to human data. The walking solutions of the model ranged over higher speed ranges (~1.7 m/s) than those of the fixed pivoted compliant bipedal model (~1.5 m/s) and exhibited other gait parameters, such as touchdown angle, step length and step frequency, comparable to the experimental observations. The good matches between the model and experimental GRF data imply that the continuous pivot acceleration associated with CoM oscillatory behavior could serve as a useful framework of bipedal model.     

Estimation of unmeasured ground reaction force data based on the oscillatory characteristics of the center of mass during human walking

To enhance the wearability of portable motion-monitoring devices, the size and number of sensors are minimized, but at the expense of quality and quantity of data collected. For example, owing to the size and weight of low-frequency force transducers, most currently available wearable gait measurement systems provide only limited, if any, elements of ground reaction force (GRF) data. To obtain the most GRF information possible with a minimal use of sensors, we propose a GRF estimation method based on biomechanical knowledge of human walking. This includes the dynamics of the center of mass (CoM) during steady human gait resembling the oscillatory behaviors of a mass-spring system. Available measurement data were incorporated into a spring-loaded inverted pendulum with translating pivot. The spring stiffness and simulation parameters were tuned to match, as accurately as possible, the available data and oscillatory characteristics of walking. Our results showed that the model simulation estimated reasonably well the unmeasured GRF. Using the vertical GRF and CoP profile for gait speeds ranging from 0.93 to 1.89 m/s, the anterior-posterior (A-P) GRF was estimated and resulted in an average correlation coefficient of R = 0.982 ± 0.009. Even when the ground contact timing and gait speed information were alone available, our method estimated GRFs resulting in R = 0.969 ± 0.022 for the A-P and R = 0.891 ± 0.101 for the vertical GRFs. This research demonstrates that the biomechanical knowledge of human walking, such as inherited oscillatory characteristics of the CoM, can be used to gain unmeasured information regarding human gait dynamics.     

Leg stiffness increases with speed to modulate gait frequency and propulsion energy

Bipedal walking models with compliant legs have been employed to represent the ground reaction forces (GRFs) observed in human subjects. Quantification of the leg stiffness at varying gait speeds, therefore, would improve our understanding of the contributions of spring-like leg behavior to gait dynamics. In this study, we tuned a model of bipedal walking with damped compliant legs to match human GRFs at different gait speeds. Eight subjects walked at four different gait speeds, ranging from their self-selected speed to their maximum speed, in a random order. To examine the correlation between leg stiffness and the oscillatory behavior of the center of mass (CoM) during the single support phase, the damped natural frequency of the single compliant leg was compared with the duration of the single support phase. We observed that leg stiffness increased with speed and that the damping ratio was low and increased slightly with speed. The duration of the single support phase correlated well with the oscillation period of the damped complaint walking model, suggesting that CoM oscillations during single support may take advantage of resonance characteristics of the spring-like leg. The theoretical leg stiffness that maximizes the elastic energy stored in the compliant leg at the end of the single support phase is approximated by the empirical leg stiffness used to match model GRFs to human GRFs. This result implies that the CoM momentum change during the double support phase requires maximum forward propulsion and that an increase in leg stiffness with speed would beneficially increase the propulsion energy. Our results suggest that humans emulate, and may benefit from, spring-like leg mechanics.     

The oscillatory behavior of the CoM facilitates mechanical energy balance between push-off and heel strike

Humans use equal push-off and heel strike work during the double support phase to minimize the mechanical work done on the center of mass (CoM) during the gait. Recently, a step-to-step transition was reported to occur over a period of time greater than that of the double support phase, which brings into question whether the energetic optimality is sensitive to the definition of the step-to-step transition. To answer this question, the ground reaction forces (GRFs) of seven normal human subjects walking at four different speeds (1.1-2.4 m/s) were measured, and the push-off and heel strike work for three differently defined step-to-step transitions were computed based on the force, work, and velocity. To examine the optimality of the work and the impulse data, a hybrid theoretical-empirical analysis is presented using a dynamic walking model that allows finite time for step-to-step transitions and incorporates the effects of gravity within this period. The changes in the work and impulse were examined parametrically across a range of speeds. The results showed that the push-off work on the CoM was well balanced by the heel strike work for all three definitions of the step-to-step transition. The impulse data were well matched by the optimal impulse predictions (R(2)>0.7) that minimized the mechanical work done on the CoM during the gait. The results suggest that the balance of push-off and heel strike energy is a consistent property arising from the overall gait dynamics, which implies an inherited oscillatory behavior of the CoM, possibly by spring-like leg mechanics.     

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.     

Patterns of mechanical energy change in tetrapod gait: pendula, springs and work

Kinematic and center of mass (CoM) mechanical variables used to define terrestrial gaits are compared for various tetrapod species. Kinematic variables (limb phase, duty factor) provide important timing information regarding the neural control and limb coordination of various gaits. Whereas, mechanical variables (potential and kinetic energy relative phase, %Recovery, %Congruity) provide insight into the underlying mechanisms that minimize muscle work and the metabolic cost of locomotion, and also influence neural control strategies. Two basic mechanisms identified by Cavagna et al. (1977. Am J Physiol 233:R243-R261) are used broadly by various bipedal and quadrupedal species. During walking, animals exchange CoM potential energy (PE) with kinetic energy (KE) via an inverted pendulum mechanism to reduce muscle work. During the stance period of running (including trotting, hopping and galloping) gaits, animals convert PE and KE into elastic strain energy in spring elements of the limbs and trunk and regain this energy later during limb support. The bouncing motion of the body on the support limb(s) is well represented by a simple mass-spring system. Limb spring compliance allows the storage and return of elastic energy to reduce muscle work. These two distinct patterns of CoM mechanical energy exchange are fairly well correlated with kinematic distinctions of limb movement patterns associated with gait change. However, in some cases such correlations can be misleading. When running (or trotting) at low speeds many animals lack an aerial period and have limb duty factors that exceed 0.5. Rather than interpreting this as a change of gait, the underlying mechanics of the body's CoM motion indicate no fundamental change in limb movement pattern or CoM dynamics has occurred. Nevertheless, the idealized, distinctive patterns of CoM energy fluctuation predicted by an inverted pendulum for walking and a bouncing mass spring for running are often not clear cut, especially for less cursorial species. When the kinematic and mechanical patterns of a broader diversity of quadrupeds and bipeds are compared, more complex patterns emerge, indicating that some animals may combine walking and running mechanics at intermediate speeds or at very large size. These models also ignore energy costs that are likely associated with the opposing action of limbs that have overlapping support times during walking. A recent model of terrestrial gait (Ruina et al., 2005. J Theor Biol, in press) that treats limb contact with the ground in terms of collisional energy loss indicates that considerable CoM energy can be conserved simply by matching the path of CoM motion perpendicular to limb ground force. This model, coupled with the earlier ones of pendular exchange during walking and mass-spring elastic energy savings during running, provides compelling argument for the view that the legged locomotion of quadrupeds and other terrestrial animals has generally evolved to minimize muscle work during steady level movement.     

Ground reaction forces and center of mass mechanics of bipedal capuchin monkeys: Implications for the evolution of human bipedalism

Tufted capuchin monkeys are known to use both quadrupedalism and bipedalism in their natural environments. Although previous studies have investigated limb kinematics and metabolic costs, their ground reaction forces (GRFs) and center of mass (CoM) mechanics during two and four‐legged locomotion are unknown. Here, we determine the hind limb GRFs and CoM energy, work, and power during bipedalism and quadrupedalism over a range of speeds and gaits to investigate the effect of differential limb number on locomotor performance. Our results indicate that capuchin monkeys use a “grounded run” during bipedalism (0.83–1.43 ms^?1) and primarily ambling and galloping gaits during quadrupedalism (0.91–6.0 ms^?1). CoM energy recoveries are quite low during bipedalism (2–17%), and in general higher during quadrupedalism (4–72%). Consistent with this, hind limb vertical GRFs as well as CoM work, power, and collisional losses are higher in bipedalism than quadrupedalism. The positive CoM work is 2.04 ± 0.40 Jkg^?1 m^?1 (bipedalism) and 0.70 ± 0.29 Jkg^?1 m^?1 (quadrupedalism), which is within the range of published values for two and four‐legged terrestrial animals. The results of this study confirm that facultative bipedalism in capuchins and other nonhuman primates need not be restricted to a pendulum‐like walking gait, but rather can include running, albeit without an aerial phase. Based on these results and similar studies of other facultative bipeds, we suggest that important transitions in the evolution of hominin locomotor performance were the emergences of an obligate, pendulum‐like walking gait and a bouncy running gait that included a whole‐body aerial phase. Am J Phys Anthropol, 2013. © 2012 Wiley Periodicals, Inc.     

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.     

Upper body accelerations during planned gait termination in young and older women

Transitory tasks, such as gait termination, involve interactions between neural and biomechanical factors that challenge postural stability and head stabilization patterns in older adults. The aim of the study was to compare upper body patterns of acceleration during planned gait termination at different speeds between young and older women. Ten young and 10 older women were asked to carry out three gait termination trials at slow, comfortable and fast speed. A stereophotogrammetric system and a 15-body segments model were used to calculate antero-posterior whole-body Center of Mass (AP CoM) speed and to reconstruct the centroids of head, trunk and pelvis segments. RMS of three-dimensional linear accelerations were calculated for each segment and the transmission of acceleration between two segments was expressed as a percentage difference. Older women reported lower AP CoM speed and acceleration RMS of the three upper body segments than young women across the three speed conditions. A lower pelvis-to-trunk attenuation of accelerations in the transverse plane was observed in older compared to young women, and mainly in the medio-lateral direction. As possible explanations, older women may not need to reduce acceleration as young women because of their lower progression speed and the subsequent acceleration at upper body levels. On the other hand, older women may prioritize a decrease in the whole body progression speed at expense of the involvement of upper body segments. This limits the attenuation of the accelerations, particularly in the transverse plane, implying an increased dynamic unbalance in performing this transitory task.     

A method for determining minimal sets of markers for the estimation of center of mass,linear and angular momentum

A new method is proposed for finding small sets of points on the body giving sufficient information for estimating the whole body center of mass (CoM), as well as the linear momenta (LM) and angular momenta (AM). In the underlying model each point (whose trajectory is tracked by a marker) is a point mass: Hence the body is represented by a simple system of point masses. The first step is to determine the appropriate set of points and the mass of each point, which is assumed to be specific for the movement performed. The distribution of the mass to each marker is determined from training data for which the true (or reference) trajectories of the CoM, LM or AM are known. This leads to a quadratic optimization problem with inequality constraints. The use of the method is demonstrated on data from discus throw. Results indicate reasonably small errors, considering the magnitude of other error sources, in CoM position (average magnitude of estimation error 1–2 cm), and moderate errors in AM (13–20% of peak value).     

Comparison of hierarchical and six degrees-of-freedom marker sets in analyzing gait kinematics

The objective of this study was to determine how marker spacing, noise, and joint translations affect joint angle calculations using both a hierarchical and a six degrees-of-freedom (6DoF) marker set. A simple two-segment model demonstrates that a hierarchical marker set produces biased joint rotation estimates when sagittal joint translations occur whereas a 6DoF marker set mitigates these bias errors with precision improving with increased marker spacing. These effects were evident in gait simulations where the 6DoF marker set was shown to be more accurate at tracking axial rotation angles at the hip, knee, and ankle.     

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 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.