Analysis of two components of the human center of mass trajectory in quiet standing

The assumption that two subsystems control the balance during quiet standing in humans is considered. Their function is to control the slow movement of the reference point and rapid stabilization of the center of mass (COM) relative to this point. A method allowing the COM trajectory to be divided into the corresponding two components, which was developed earlier, has been used to analyze and compare the time patterns of these processes. The results of this analysis have shown that the movement of the reference point is dominant in terms of the oscillation amplitude. Therefore, the oscillations of the COM trajectory reflect the slow movement of the reference point and are practically unrelated to the stabilization of the COM relative to this point. The possibility of applying the decomposition of the COM trajectory into components to fundamental and clinical research is discussed.     

Increased musculoskeletal stiffness during load carriage at increasing walking speeds maintains constant vertical excursion of the body center of mass

The primary objective of this research was to determine changes in body and joint stiffness parameters and kinematics of the knee and body center of mass (COM), that result from wearing a backpack (BP) with a 40% body weight load at increasing speeds of walking. It was hypothesized that there would be speed and load-related increases in stiffness that would prevent significant deviations in the COM trajectory and in lower-extremity joint angles. Three independent biomechanical models employing kinematic data were used to estimate global lower-extremity stiffness, vertical stiffness and knee joint rotational stiffness in the sagittal plane during walking on a treadmill at speeds of 0.6-1.6 ms(-1) in 0.2 ms(-1) increments in BP and no backpack conditions. Kinematic data were collected using an Optotrak, three-dimensional motion analysis system. Knee angles and vertical excursion of the COM during the compression (loading phase) increased as a function of speed but not load. All three estimates of stiffness showed significant increases as a function of both speed and load. Significant interaction effects indicated a convergence of load-related stiffness values at lower speeds. Results suggested that increases in muscle-mediated stiffness are used to maintain a constant vertical excursion of the COM under load across the speeds tested, and thereby limit increases in metabolic cost that would occur if the COM would travel through greater vertical range of motion.     

American Society of Biomechanics Journal of Biomechanics Award 2018: Adaptive motor planning of center-of-mass trajectory during goal-directed walking in novel environments

To aid in the successful execution of goal-directed walking (discrete movement from a start location to an end target) the central nervous system forms a predictive motor plan. For the motor plan to be effective, it must be adapted in response to environmental changes. Despite motor planning being inherent to goal-directed walking, it is not understood how the nervous system adapts these plans to interact with changing environments. Our objective was to understand how people adapt motor plans of center of mass (COM) trajectory during goal-directed walking in response to a consistent change in environmental dynamics. Participants preformed a series of goal-directed walking trials in a novel environment created by a cable robot that applied a lateral force field to their COM. We hypothesized that participants would adapt to the environment by forming an internal model of their COM trajectory within the force field. Our findings support this hypothesis. Initially, we found COM trajectory significantly deviated in the same direction as the applied field, relative to baseline (no field) (p = 0.002). However, with practice in the field, COM trajectory adapted back to the baseline (p = 0.6). When we unexpectedly removed the field, participants demonstrated after-effects, COM trajectory deviated in the direction opposite of the field relative to baseline (p < 0.001). Our findings suggest that when performing a goal-directed walking task, people adapt a motor plan that predicts the COM trajectory that will emerge from the interaction between a specific set of motor commands and the external environment.     

Influence of body segment parameters and modeling assumptions on the estimate of center of mass trajectory

This study sought to determine the effect of inaccuracies in body segment parameters and modeling assumptions on the estimate of antero-posterior center of mass (COM) trajectory. Four different methods, one based on segmental kinematics, and three methods based on kinetic recordings were compared via simulation. Kinematic patterns (quiet stance, ankle-related sway, hip-ankle-related sway, sit-up and sit-up-sit-down) were tested with a 2D four-link model of the body and the ground reaction force vector was obtained by inverse dynamics. Errors in the estimation of body segment parameters were simulated by applying a +/-10% variation to one or more parameters at a time. These errors propagated differently to the COM estimated location between methods, between parameters within the same method, and between tasks. The kinematics-based method was the most sensitive to body segment parameters, with special regards to segment lengths and head-arms-trunk parameters. Root mean square error between estimated and simulated COM location reached 19mm in balance-related tasks and 38.3mm in sit-up-sit-down. The kinetics-based methods were largely less sensitive to inaccuracies in body segment parameters. In particular, the technique proposed by Zatsiorsky and King (J. Biomech. 31 (1998) 161), was completely insensitive to segment parameters. On the other hand the kinetics-based methods showed an intrinsic estimation error, due to the underlying model assumptions. The methods based on the double integration of horizontal force had better outcomes with tasks challenging such assumptions, with a maximal error in COM location of 15mm in the sit-up-sit-down. The method proposed by Shimba (J. Biomech. 17 (1984) 53) showed the best trade-off between sensitivity to body segment parameters and estimation performances given the ideal test conditions.     

Comparison of three methods to estimate the center of mass during balance assessment

Evaluation of postural control is generally based on the interpretation of the center of pressure (COP) and the center of mass (COM) time series. The purpose of this study is to compare three methods to estimate the COM which are based on different biomechanical considerations. These methods are: (1) the kinematic method; (2) the zero-point-to-zero-point double integration technique (GLP) and (3) the COP low-pass filter method (LPF). The COP and COM time series have been determined using an experimental setup with a force plate and a 3D kinematic system on six healthy young adult subjects during four different 30 s standing tasks: (a) quiet standing; (b) one leg standing; (c) voluntary oscillation about the ankles and (d) voluntary oscillation about the ankles and hips. To test the difference between the COM trajectories, the root mean square (RMS) differences between each method (three comparisons) were calculated. The RMS differences between kinematic-LPF and GLP-LPF are significantly larger than kinematic-GLP. Our results show that the GLP method is comparable to the kinematic method. Both agree with the unified theory of balance during upright stance. The GLP method is attractive in the clinical perspective because it requires only a force plate to determine the COP-COM variable, which has been demonstrated to have a high reliability.     

Center of mass motion in swimming fish: effects of speed and locomotor mode during undulatory propulsion

Studies of center of mass (COM) motion are fundamental to understanding the dynamics of animal movement, and have been carried out extensively for terrestrial and aerial locomotion. But despite a large amount of literature describing different body movement patterns in fishes, analyses of how the center of mass moves during undulatory propulsion are not available. These data would be valuable for understanding the dynamics of different body movement patterns and the effect of differing body shapes on locomotor force production. In the present study, we analyzed the magnitude and frequency components of COM motion in three dimensions (x: surge, y: sway, z: heave) in three fish species (eel, bluegill sunfish, and clown knifefish) swimming with four locomotor modes at three speeds using high-speed video, and used an image cross-correlation technique to estimate COM motion, thus enabling untethered and unrestrained locomotion. Anguilliform swimming by eels shows reduced COM surge oscillation magnitude relative to carangiform swimming, but not compared to knifefish using a gymnotiform locomotor style. Labriform swimming (bluegill at 0.5 body lengths/s) displays reduced COM sway oscillation relative to swimming in a carangiform style at higher speeds. Oscillation frequency of the COM in the surge direction occurs at twice the tail beat frequency for carangiform and anguilliform swimming, but at the same frequency as the tail beat for gymnotiform locomotion in clown knifefish. Scaling analysis of COM heave oscillation for terrestrial locomotion suggests that COM heave motion scales with positive allometry, and that fish have relatively low COM oscillations for their body size.     

Can sacral marker approximate center of mass during gait and slip-fall recovery among community-dwelling older adults?

Falls are prevalent in older adults. Dynamic stability of body center of mass (COM) is critical for maintaining balance. A simple yet accurate tool to evaluate COM kinematics is essential to examine the COM stability. The purpose of this study was to determine the extent to which the COM position derived from body segmental analysis can be approximated by a single (sacral) marker during unperturbed (regular walking) and perturbed (gait-slip) gait. One hundred eighty seven older adults experienced an unexpected slip after approximately 10 regular walking trials. Two trials, the slip trial and the preceding regular walking trial, monitored with a motion capture system and force plates, were included in the present study. The COM positions were calculated by using the segmental analysis method wherein, the COM of all body segments was calculated to further estimate the body COM position. These body COM positions were then compared with those of the sacral marker placed at the second sacral vertebra for both trials. Results revealed that the COM positions were highly correlated with those of the sacrum׳s over the time intervals investigated for both walking (coefficient of correlation R>0.97) and slip (R>0.90) trials. There were detectable kinematic difference between the COM and the sacral for both trials. Our results indicated that the sacral marker can be used as a simple approximation of body COM for regular walking, and to somewhat a lesser extent, upon a slip. The benefits from the simplicity appear to overweigh the limitations in accuracy.     

Turning in a Bipedal Robot

We report the development of turning behavior on a child-size bipedal robot that addresses two common scenarios: turning in place and simultaneous walking and turning. About turning in place, three strategies are investigated and compared, including body-first, leg-first, and body/leg-simultaneous. These three strategies are used for three actions, respectively: when walking follows turning immediately, when space behind the robot is very tight, and when a large turning angle is desired. Concerning simultaneous walking and turning, the linear inverted pendulum is used as the motion model in the single-leg support phase, and the polynomial-based trajectory is used as the motion model in the double-leg support phase and for smooth motion connectivity to motions in a priori and a posteriori single-leg support phases. Compared to the trajectory generation of ordinary walking, that of simultaneous walking and turning introduces only two extra parameters: one for determining new heading direction and the other for smoothing the Center of Mass (COM) trajectory. The trajectory design methodology is validated in both simulation and experimental environments, and successful robot behavior confirms the effectiveness of the strategy.     

Forward and Backward Inference in Spatial Cognition

This paper shows that the various computations underlying spatial cognition can be implemented using statistical inference in a single probabilistic model. Inference is implemented using a common set of ‘lower-level’ computations involving forward and backward inference over time. For example, to estimate where you are in a known environment, forward inference is used to optimally combine location estimates from path integration with those from sensory input. To decide which way to turn to reach a goal, forward inference is used to compute the likelihood of reaching that goal under each option. To work out which environment you are in, forward inference is used to compute the likelihood of sensory observations under the different hypotheses. For reaching sensory goals that require a chaining together of decisions, forward inference can be used to compute a state trajectory that will lead to that goal, and backward inference to refine the route and estimate control signals that produce the required trajectory. We propose that these computations are reflected in recent findings of pattern replay in the mammalian brain. Specifically, that theta sequences reflect decision making, theta flickering reflects model selection, and remote replay reflects route and motor planning. We also propose a mapping of the above computational processes onto lateral and medial entorhinal cortex and hippocampus.     

Dynamic Stability and Risk of Tripping during the Timed Up and Go Test in Hemiparetic and Healthy Subjects

Background

The Timed Up and Go (TUG) test is often used to estimate risk of falls. Foot clearance and displacement of the center of mass (COM), which are related to risk of tripping and dynamic stability have never been evaluated during the TUG. Accurate assessment of these parameters using instrumented measurements would provide a comprehensive assessment of risk of falls in hemiparetic patients. The aims of this study were to analyze correlations between TUG performance time and displacement of the COM and foot clearance in patients with stroke-related hemiparesis and healthy subjects during the walking and turning sub-tasks of the TUG and to compare these parameters between fallers and non-fallers.

Methods

29 hemiparetic patients and 25 healthy subjects underwent three-dimensional gait analysis during the TUG test. COM and foot clearance were analyzed during the walking and turning sub-tasks of the TUG.

Results

Lateral displacement of the COM was greater and faster during the walking sub-tasks and vertical displacement of the COM was greater during the turn in the patients compared to the healthy subjects (respectively p<0.01 and p<0.05). Paretic foot clearance was greater during walking and displacement of the COM was slower during the turn in the patients (p<0.01). COM displacement and velocity during the turn were correlated with TUG performance in the patients, however, vertical COM displacement was not. These correlations were significant in the healthy subjects. There were no differences between COM parameters or foot clearance in fallers and non-fallers.

Discussion and Conclusion

Hemiparetic patients are less stable than healthy subjects, but compensate with a cautious gait to avoid tripping. Instrumented analysis of the TUG test appears relevant for the assessment of dynamic stability in hemiparetic patients, providing more information than straight-line gait.     

Predicted threshold against backward balance loss in gait

The purpose of this study was to determine the minimum forward center of mass (COM) velocity required to prevent backward loss of balance in gait as function of the initial COM position. We hypothesized that these threshold values would be different from those previously published for standing because of the postural differences between gait and standing. To investigate this issue, we constructed a seven-link, nine-degree-of-freedom biomechanical model and employed dynamic optimization to estimate these threshold values under two initial postural conditions: (1) the posture at the beginning of swing phase (i.e., at toe-off), and (2) symmetric bipedal standing. In particular, for a range of possible COM positions posterior to the base of support (BOS), simulated annealing was used to search for the minimum velocity that could carry the COM into the BOS and avoid backward loss of balance. We found that the stability boundary against backward balance loss in walking had a similar overall trend as that previously published for standing. In general, the minimal COM velocity necessary to prevent a backward loss of balance in walking was greater than that in symmetric bipedal standing, and the difference could approach 30% or more when the COM started 0.5 and 1.0 foot-lengths behind the BOS. These discrepancies suggest that simpler biomechanical models, while being more efficient and easier to employ, may not always be adequate for exploring stability limits of humans.     

An Iterative Variable-timestep Algorithm for Molecular Dynamics Simulations

A method for performing variable-timestep molecular dynamics integration is described, in which an iterative algorithm is used to select the largest timestep consistent with the desired simulation accuracy. Accuracy in this context is defined in terms of energy conservation, rather than trajectory correctness. Specifically, a timestep-independent measure of the rate of "diffusion" of the total energy is used. This variable timestep approach is compared to fixed-timestep integration for three different hydrocarbon systems (polyethylene, liquid benzene and ethylene), which are modeled with a reactive bond-order potential. These systems represent both equilibrium and highly non-equilibrium systems at temperatures ranging from 298 to 2500 K. The variable-timestep method is found to be approximately twice as computationally efficient as fixed-timestep integration for the non-equilibrium sputtering of polyethylene, and the two methods were competitive for the equilibrium systems. The algorithm requires the specification of two parameters controlling the rates of timestep growth and decay, but it is found that one set of values is appropriate for all three systems studied, and there is reason to believe that the parameters are transferable to other systems. The algorithm was developed specifically for simulations involving disparate timescales, such as are encountered with the reactive bond-order model used here, but it should also prove beneficial for a wide range of molecular dynamics applications.     

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.     

CT Scanning Imaging Method Based on a Spherical Trajectory

In industrial computed tomography (CT), the mismatch between the X-ray energy and the effective thickness makes it difficult to ensure the integrity of projection data using the traditional scanning model, because of the limitations of the object’s complex structure. So, we have developed a CT imaging method that is based on a spherical trajectory. Considering an unrestrained trajectory for iterative reconstruction, an iterative algorithm can be used to realise the CT reconstruction of a spherical trajectory for complete projection data only. Also, an inclined circle trajectory is used as an example of a spherical trajectory to illustrate the accuracy and feasibility of this new scanning method. The simulation results indicate that the new method produces superior results for a larger cone-beam angle, a limited angle and tabular objects compared with traditional circle trajectory scanning.     

Tethering human immunodeficiency virus type 1 preintegration complexes to target DNA promotes integration at nearby sites.

Integration of retroviral cDNA in vivo is normally not sequence specific with respect to the integration target DNA. We have been investigating methods for directing the integration of retroviral DNA to predetermined sites, with the dual goal of understanding potential mechanisms governing normal site selection and developing possible methods for gene therapy. To this end, we have fused retroviral integrase enzymes to sequence-specific DNA-binding domains and investigated target site selection by the resulting proteins. In a previous study, we purified and analyzed a fusion protein composed of human immunodeficiency virus integrase linked to the DNA-binding domain of lambda repressor. This fusion could direct selective integration in vitro into target DNA containing lambda repressor binding sites. Here we investigate the properties of a fusion integrase in the context of a human immunodeficiency virus provirus. We used a fusion of integrase to the DNA binding domain of the zinc finger protein zif268 (IN-zif). Initially we found that the fusion was highly detrimental to replication as measured by the multinuclear activation of a galactosidase indicator (MAGI) assay for infected centers. However, we found that viruses containing mixtures of wild-type integrase and IN-zif were infectious. We prepared preintegration complexes from cells infected with these viruses and found that such complexes directed increased integration near zif268 recognition sites.     

Temporal integration of movement: the time-course of motion streaks revealed by masking

Temporal integration in the visual system causes fast-moving objects to leave oriented 'motion streaks' in their wake, which could be used to facilitate motion direction perception. Temporal integration is thought to occur over ≈100 ms in early cortex, although this has never been tested for motion streaks. Here we compare the ability of fast-moving ('streaky') and slow-moving fields of dots to mask briefly flashed gratings either parallel or orthogonal to the motion trajectory. Gratings were presented at various asynchronies relative to motion onset (from -200 to +700 ms) to sample the time-course of the accumulating streaks. Predictions were that masking would be strongest for the fast parallel condition, and would be weak at early asynchronies and strengthen over time as integration rendered the translating dots more streaky and grating-like. The asynchrony where the masking function reached a plateau would correspond to the temporal integration period. As expected, fast-moving dots caused greater masking of parallel gratings than orthogonal gratings, and slow motion produced only modest masking of either grating orientation. Masking strength in the fast, parallel condition increased with time and reached a plateau after 77 ms, providing an estimate of the temporal integration period for mechanisms encoding motion streaks. Interestingly, the greater masking by fast motion of parallel compared with orthogonal gratings first reached significance at 48 ms before motion onset, indicating an effect of backward masking by motion streaks.     

Temporal changes in motor variability during prolonged lifting/lowering and the influence of work experience

Existing research indicates that repetitive motions are strongly correlated with the development of work-related musculoskeletal disorders (WMSDs). Resulting from the redundant degrees-of-freedom in the human body, there are variations in motions that occur while performing a repetitive task. These variations are termed motor variability (MV), and may be beneficial for reducing WMSD risks. To better understand the potential role of MV in preventing injury risk, we evaluated the effects of fatigue on MV using data collected during a lab-based prolonged, repetitive lifting/lowering task. We also investigated whether experienced workers used different motor control strategies than novices to adapt to fatigue. MV of the whole-body center-of-mass (COM) and box trajectory were quantified using cycle-to-cycle standard deviation, sample entropy, and goal equivalent manifold (GEM) methods. In both groups, there were significantly increased variations of the COM with fatigue, and with a more substantial increase in a direction that did not affect task performance. Fatigue deteriorated the task goal and made it more difficult for participants to maintain their performance. Experienced workers also had higher MV than novices. Based on these results, we conclude that flexible motor control strategies are employed to reduce fatigue effects during a prolonged repetitive task.     

Neural network estimation of balance control during locomotion

Gait patterns of the elderly are often adjusted to accommodate for reduced function in the balance control system and a general reduction in skeletal muscle strength. Recent studies have demonstrated that measures related to motion of whole body center of mass (COM) can distinguish elderly individuals with balance impairment from healthy peers. Accurate COM estimation requires a multiple-segment anthropometric model, which may restrict its broad application in assessment of dynamic instability. Although temporal-distance measures and electromyography have been used in evaluation of overall gait function and determination of gait dysfunction, no studies have examined the use of gait measurements in predicting COM motion during gait. The purpose of this study was to demonstrate the effectiveness of an artificial neural network (ANN) model in mapping gait measurements onto COM motion in the frontal plane. Data from 40 subjects of varied age and balance impairment were entered into a 3-layer feed-forward model with back-propagated error correction. Bootstrap re-sampling was used to enhance the generalization accuracy of the model, using 20 re-sampling trials. The ANN model required minimal processing time (5 epochs, with 20 hidden units) and accurately mapped COM motion (R-values up to 0.89). As training proportion and number of hidden units increased, so did model accuracy. Overall, this model appears to be effective as a mapping tool for estimating balance control during locomotion. With easily obtained gait measures as input and a simple, computationally efficient architecture, the model may prove useful in clinical scenarios where electromyography equipment exists.