Speed- and mode-dependent modulation of the center of mass trajectory in human gaits as revealed by Lissajous curves

Guidelines for balancing the number of trials and the number of subjects to ensure the statistical power to detect variability - Implication for gait studies

Variability is one of the most crucial outcomes in human movement studies: variance and standard deviation of various parameters have been reported in numerous studies. However, in many of these studies, the numbers of trials and subjects have been intuitively determined and not justified with statistical considerations. Here, we investigated the impact of the numbers of trials and subjects on statistical power, based on the assumption that results per trial follow a normal distribution, using mathematical analysis and numerical simulation. An inverse-like relationship was observed between the number of trials and subjects required to ensure the statistical power for detecting differences in variance between subject groups or conditions. For instance, assuming a 1.2-times difference in population variance between pre-and post-training sessions as an alternative hypothesis, our simulation demonstrated that combinations of the number of subjects and trials, such as measuring 100 trials from each of 12 subjects under each condition, or measuring 20 trials from each of 60 subjects, can guarantee an 80 % of statistical power. Planning research based on such mathematical considerations will enable meaningful statistical interpretations in studies focusing on movement variability, such as gait studies.

Speed-dependent modulations of asymmetric center of body mass trajectory in the gait of above-knee amputee subjects

How to achieve stable locomotion while overcoming various instabilities is an ongoing research topic. One essential factor for achieving a stable gait is controlling the center of body mass (CoM). The CoM yields more instability in the mediolateral direction. Examining speed-dependent modulations of the CoM trajectories in the frontal plane can provide insight into control policies for achieving stable locomotion. Although these modulations have been studied while assuming symmetric CoM trajectories, this assumption is generally incorrect. For example, amputee subjects demonstrate asymmetric CoM trajectories. Here, we investigated speed-dependent modulations of asymmetric CoM trajectories in above-knee amputee subjects using Fourier series expansion. Despite the asymmetric CoM trajectories in amputee subjects, the framework of Fourier series expansion clarified that amputee subjects showed the same speed-dependent modulations as non-amputee subjects whose CoM trajectories were symmetric. Specifically, CoM trajectories became narrower in the mediolateral direction and broader in the superoinferior direction as walking speed increased. The speed-dependent modulations of CoM trajectories had a functional role in improving dynamic stability, and faster walking speeds provided greater dynamic stability on both prosthetic and non-prosthetic sides. Although the asymmetry of foot contact duration and CoM trajectory decreased as walking speed increased, step width and the asymmetry of dynamic stability between prosthetic and non-prosthetic sides remained constant across the walking speed, which corresponded to the predictions by our framework. These findings could offer a better strategy for achieving stable walking for amputee subjects.

Transition between individually different and common features in skilled drumming movements

Why do professional athletes and musicians exhibit individually different motion patterns? For example, baseball pitchers generate various pitching forms, e.g., variable wind-up, cocking, and follow-through forms. However, they commonly rotate their wrists and fingers at increasingly high speeds via shoulder and trunk motions. Despite the universality of common and individually different motion patterns in skilled movements, the abovementioned question remains unanswered. Here, we focus on a motion required to hit a snare drum, including the indirect phase of task achievement (i.e., the early movement and mid-flight phases) and the direct phase of task achievement (i.e., the hit phase). We apply tensor decomposition to collected kinematic data for the drum-hitting motion, enabling us to decompose high-dimensional and time-varying motion data into individually different and common movement patterns. As a result, individually different motion patterns emerge during the indirect phase of task achievement, and common motion patterns are evident in the direct phase of task achievement. Athletes and musicians are thus possibly allowed to perform individually different motion patterns during the indirect phase of task achievement. Additionally, they are required to exhibit common patterns during the direct phase of task achievement.

Stabilization Strategies for Fast Walking in Challenging Environments With Incomplete Spinal Cord Injury

Gait rehabilitation following incomplete spinal cord injury (iSCI) often aims to enhance speed and stability. Concurrently increasing both may be difficult though as certain stabilization strategies will be compromised at faster speeds. To evaluate the interaction between speed and lateral stability, we examined individuals with (n = 12) and without (n = 12) iSCI as they performed straight walking and lateral maneuvers at Preferred and Fast treadmill speeds. To better detect the effects of speed on stability, we challenged lateral stability with a movement amplification force field. The Amplification field, created by a cable-driven robot, applied lateral forces to the pelvis that were proportional to the real-time lateral center of mass (COM) velocity. While we expected individuals to maintain stability during straight walking at the Fast speed in normal conditions, we hypothesized that both groups would be less stable in the Amplification field at the Fast speed compared to the Preferred. However, we found no effects of speed or the interaction between speed and field on straight-walking stability [Lyapunov exponent or lateral margin of stability (MOS)]. Across all trials at the Fast speed compared to the Preferred, there was greater step width variability (p = 0.031) and a stronger correlation between lateral COM state at midstance and the subsequent lateral foot placement. These observations suggest that increased stepping variability at faster speeds may be beneficial for COM control. We hypothesized that during lateral maneuvers in the Amplification field, MOS on the Initiation and Termination steps would be smaller at the Fast speed than at the Preferred. We found no effect of speed on the Initiation step MOS within either field (p > 0.350) or group (p > 0.200). The Termination step MOS decreased at the Fast speed within the group without iSCI (p < 0.001), indicating a trade-off between lateral stability and forward walking speed. Unexpectedly, participants took more steps and time to complete maneuvers at the Fast treadmill speed in the Amplification field. This strategy prioritizing stability over speed was especially evident in the group with iSCI. Overall, individuals with iSCI were able to maintain lateral stability when walking fast in balance-challenging conditions but may have employed more cautious maneuver strategies.