A method of decomposing stabilograms into two components, termed rambling and trembling, was developed. The rambling component reveals the motion of a moving reference point with respect to which the body's equilibrium is instantantly maintained. The trembling component reflects body oscillation around the reference point trajectory. The concepts of instant equilibrium point (IEP) and discrete IEP trajectory are introduced. The rambling trajectory was computed by interpolating the discrete IEP trajectory with cubic spline functions. The trembling trajectory is found as a difference between the approximated rambling trajectory and the COP trajectory. Instant values of the trembling trajectory are negatively correlated with the values of the horizontal ground reaction force at a zero time lag. It suggests that trembling is strongly influenced by a restoring force proportional to the magnitude of COP deviation from the rambling trajectory and acts without a time delay. An increment in relative COP position per unit of the restoring force, in mm/N, was on average 1.4 ± 0.4. The contribution of rambling and trembling components in the stabilogram was ascertained. The rambling variability is approximately three times larger than the trembling variability.
Vladimir M. Zatsiorsky and Marcos Duarte
Marcos Duarte and Valdimir M. Zatsiorsky
Prolonged (>30 min) unconstrained standing (PUS) was studied in 10 young healthy subjects. The usual methods of stabilographic analysis assume a random center of pressure (COP) migration. This study was based on the opposite idea and showed that during PUS, specific and consistent patterns of the COP migration can be recognized by a computer algorithm. Three COP migration patterns were found: (a) shifting, a fast displacement of the average position of COP from one region to another; (b) fidgeting, a fast and large displacement and returning of COP to approximately the same position; and (c) drifting, a slow continuous displacement of the average position of COP. A software code was written and default parameter values were chosen for recognizing COP migration patterns. For 30-min PUS the following patterns were identified: Shifting was generally observed every 316 ± 292 sec in the anterior-posterior (a-p) direction with an average shift amplitude of 17 ± 15 mm, and every 199 ± 148 sec in the medial-lateral (m-1) direction with an average shift amplitude of 22 ± 38 mm. Corresponding time intervals for fidgeting were 59 ± 15 sec in the a-p direction and 49±16 sec in the m-1 direction. The average drift-to-drift interval was 319 ± 173 sec in the a-p direction and 529 ± 333 sec in the m-1 direction.
Vladimir M. Zatsiorsky and Marcos Duarte
The goal of this study was to explore the rambling-trembling decomposition in quiet standing. The center of pressure (COP) and the horizontal ground reaction force (Fhor) were registered in healthy subjects standing in an upright bipedal posture on a force platform. The COP positions at the instants when Fhor = 0 were identified (instant equilibrium points, IEP) for the anterior-posterior direction, then the COP time series, were partitioned into its components using 2 different techniques, rambling-trembling decomposition and gravity line decomposition. The two decomposition techniques provided very similar results. An unexpectedly large correlation between the trembling trajectory and the difference between COP and gravity line was found, r = 0.91 (range, 0.83 < r < 0.98). The correlation implies that the GL moves from an IEP to the subsequent IEP along a smooth trajectory that can be predicted by the spline approximation. A substantial negative cross-correlation at a zero time lag was observed between the trembling and the Fhor, -0.90 < r < -0.75. For the rambling trajectory, the coefficients of correlation with Fhor were low, -0.33 < r < -0.05. The data support the hypothesis that during quiet standing the body sways for two reasons: the migration of the reference point (rambling) and the deviation away from that point (trembling).
Janina M. Prado-Rico and Marcos Duarte
The goal of this work was to investigate body weight distribution during relaxed and quiet (constrained) standing tasks. Forty-one healthy, young adults performed relaxed and quiet standing tasks, and they stood with each leg on a separate force plate. The weight distribution asymmetry across time was computed as the difference between the right and left vertical force time series. The subjects presented a small average across time asymmetry during relaxed and quiet standing. However, during relaxed standing, the subjects alternated between postures, and, as a result, they were largely asymmetrical over time (instant by instant). Two unexpected results that the authors found for the relaxed standing task were that women were more asymmetrical over time than men and that there were two preferential modes of weight distribution.
Marcos Duarte and Sandra M.S.F. Freitas
We investigated the speed and accuracy of fast voluntary movements performed by the whole body during standing. Adults stood on a force plate and performed rhythmic postural movements generating fore and back displacements of the center of pressure (shown as online visual feedback). We observed that for the same target distance, movement time increased with the ratio between target distance and target width, as predicted by Fitts’–type relationships. For different target distances, however, the linear regressions had different slopes. Instead, a single linear relation was observed for the effective target width versus mean movement speed. We discuss this finding as a result of the pronounced inherent variability of the postural control system and when such a source of variability is considered, the observed relationship can be explained. The results reveal that the accuracy of fast voluntary postural movements is deteriorated by the variability due to sway during standing.
Paulo H. Marchetti, Maria I.V. Orselli, and Marcos Duarte
The aim of this study was to investigate the effects of unilateral and bilateral fatigue on both postural and power bipedal tasks. Ten healthy subjects performed two tasks: bipedal quiet standing and a maximal bipedal counter-movement jumping before and after unilateral (with either the dominant or nondominant lower limb) and bilateral (with both lower limbs) fatigue. We employed two force plates (one under each lower limb) to measure the ground reaction forces and center of pressure produced by subjects during the tasks. To quantify the postural sway during quiet standing, we calculated the resultant center of pressure (COP) speed and COP area of sway, as well as the mean weight distribution between lower limbs. To quantify the performance during the countermovement jumping, we calculated the jump height and the peak force of each lower limb. We observed that both unilateral and bilateral fatigue affected the performance of maximal voluntary jumping and standing tasks and that the effects of unilateral and bilateral fatigue were stronger in the dominant limb than in the nondominant limb during bipedal tasks. We conclude that unilateral neuromuscular fatigue affects both postural and power tasks negatively.
Desiree Camara Miraldo, Renato Naville Watanabe, and Marcos Duarte
This study describes an open data set of inertial, magnetic, foot–ground contact, and electromyographic signals from wearable sensors during walking at different speeds. These data were acquired from 22 healthy adults using wearable sensors and walking at self-selected comfortable, fast and slow speeds, and standing still. All data are publicly available in the Internet (https://doi.org/10.6084/m9.figshare.7778255). In total, there are data of 9,661 gait strides. This data set also contains files with the instants of the gait events identified using the foot–ground contact sensors and notebooks exemplifying how to access and visualize the data. This data set gives the opportunity to all interested researchers to work with such data, for example, making tests of algorithms for gait event estimation against a common reference, possible.
Stacey L. Gorniak, Marcos Duarte, and Mark L. Latash
We explored possible effects of negative covariation among finger forces in multifinger accurate force production tasks on the classical Fitts’s speed-accuracy trade-off. Healthy subjects performed cyclic force changes between pairs of targets “as quickly and accurately as possible.” Tasks with two force amplitudes and six ratios of force amplitude to target size were performed by each of the four fingers of the right hand and four finger combinations. There was a close to linear relation between movement time and the log-transformed ratio of target amplitude to target size across all finger combinations. There was a close to linear relation between standard deviation of force amplitude and movement time. There were no differences between the performance of either of the two “radial” fingers (index and middle) and the multifinger tasks. The “ulnar” fingers (little and ring) showed higher indices of variability and longer movement times as compared with both “radial” fingers and multifinger combinations. We conclude that potential effects of the negative covariation and also of the task-sharing across a set of fingers are counterbalanced by an increase in individual finger force variability in multifinger tasks as compared with single-finger tasks. The results speak in favor of a feed-forward model of multifinger synergies. They corroborate a hypothesis that multifinger synergies are created not to improve overall accuracy, but to allow the system larger flexibility, for example to deal with unexpected perturbations and concomitant tasks.
Luis Mochizuki, Marcos Duarte, Alberto Carlos Amadio, Vladimir M. Zatsiorsky, and Mark L. Latash
We investigated changes in postural sway and its fractions associated with manipulations of the dimensions of the support area. Nine healthy adults stood as quietly as possible, with their eyes open, on a force plate as well as on 5 boards with reduced support area. The center of pressure (COP) trajectory was computed and decomposed into rambling (Rm) and trembling (Tr) trajectories. Sway components were quantified using RMS (root mean square) value, average velocity, and sway area. During standing on the force plate, the RMS was larger for the anterior-posterior (AP) sway components than for the mediolateral (ML) components. During standing on boards with reduced support area, sway increased in both directions. The increase was more pronounced when standing on boards with a smaller support area. Changes in the larger dimension of the support area also affected sway, but not as much as changes in the smaller dimension. ML instability had larger effects on indices of sway compared to AP instability. The average velocity of Rm was larger while the average velocity of Tr was smaller in the AP direction vs. the ML direction. The findings can be interpreted within the hypothesis of an active search function of postural sway. During standing on boards with reduced support area, increased sway may by itself lead to loss of balance. The findings also corroborate the hypothesis of Duarte and Zatsiorsky that Rm and Tr reveal different postural control mechanisms.