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.

Detecting task-relevant spatiotemporal modules and their relation to motor adaptation.

How does the central nervous system (CNS) control our bodies, including hundreds of degrees of freedom (DoFs)? A hypothesis to reduce the number of DoFs posits that the CNS controls groups of joints or muscles (i.e., modules) rather than each joint or muscle independently. Another hypothesis posits that the CNS primarily controls motion components relevant to task achievements (i.e., task-relevant components). Although the two hypotheses are examined intensively, the relationship between the two concepts remains unknown, e.g., unimportant modules may possess task-relevant information. Here, we propose a framework of task-relevant modules, i.e., modules relevant to task achievements, while combining the two concepts mentioned above in a data-driven manner. To examine the possible role of the task-relevant modules, we examined the modulation of the task-relevant modules in a motor adaptation paradigm in which trial-to-trial modifications of motor output are observable. The task-relevant modules, rather than conventional modules, showed adaptation-dependent modulations, indicating the relevance of task-relevant modules to trial-to-trial updates of motor output. Our method provides insight into motor control and adaptation via an integrated framework of modules and task-relevant components.

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.

Impaired feedforward control of movements in pianists with focal dystonia.

Learning accurate and fast movements typically accompanies the modulation of feedforward control. Nevertheless, it remains unclear how motor skill learning modulates feedforward control, such as through maladaptation of the sensorimotor system by extensive training (e.g., task-specific dystonia). Here, we examined the modulation of feedforward control through motor skill learning while focusing on the motion of piano playing at either a natural tempo or the fastest tempo. The current study compared the kinematics and keypress data among individuals in three groups: healthy and well-trained pianists (i.e., subjects with skill learning), non-musicians (i.e., subjects without skill learning), and patients with focal-hand dystonia (FHD) (i.e., subjects with maladaptation by skill learning). Compared to healthy pianists, patients with FHD showed impairment in some feedforward motion components that are relevant to classifying the two playing tempi. However, while focusing on motion components that are irrelevant to the tempo classification, patients with FHD showed movements comparable to those of healthy pianists. Furthermore, patients with FHD demonstrated significantly slower movement times than healthy pianists. Our results suggest that maladaptation by skill learning affects parts of feedforward control rather than its entirety. Nevertheless, the affected feedforward components are relevant to performing movements as fast as possible, which may underlie the speed dependence of dystonic symptoms.

Effort-dependent effects on uniform and diverse muscle activity features in skilled pitching.

How do skilled players change their motion patterns depending on motion effort? Pitchers commonly accelerate wrist and elbow joint rotations via proximal joint motions. Contrastingly, they show individually different pitching motions, such as in wind-up or follow-through. Despite the generality of the uniform and diverse features, effort-dependent effects on these features are unclear. Here, we reveal the effort dependence based on muscle activity data in natural three-dimensional pitching performed by skilled players. We extract motor modules and their effort dependence from the muscle activity data via tensor decomposition. Then, we reveal the unknown relations among motor modules, common features, unique features, and effort dependence. The current study clarifies that common features are obvious in distinguishing between low and high effort and that unique features are evident in differentiating high and highest efforts.

Competition Rather Than Observation and Cooperation Facilitates Optimal Motor Planning.

Humans tend to select motor planning with a high reward and low success compared with motor planning, which has a small reward and high success rate. Previous studies have shown such a risk-seeking property in motor decision tasks. However, it is unclear how to facilitate a shift from risk-seeking to optimal motor planning that maximizes the expected reward. Here, we investigate the effect of interacting with virtual partners/opponents on motor plans since interpersonal interaction has a powerful influence on human perception, action, and cognition. This study compared three types of interactions (competition, cooperation, and observation) and two types of virtual partners/opponents (those engaged in optimal motor planning and those engaged in risk-averse motor planning). As reported in previous studies, the participants took a risky aim point when they performed a motor decision task alone. However, we found that the participant's aim point was significantly modulated when they performed the same task while competing with a risk-averse opponent (p = 0.018) and that there was no significant difference from the optimal aim point (p = 0.63). No significant modulation in the aim points was observed during the cooperation and observation tasks. These results highlight the importance of competition for modulating suboptimal decision-making and optimizing motor performance.

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

The central nervous system (CNS) achieves a stable gait at several speeds and modes while controlling diverse instability. An essential feature of a gait is the motion of the center of body mass (CoM). CoM motion is at larger risk for trespassing the base of support in the mediolateral direction than in the anteroposterior direction. How the CoM trajectory in the frontal plane changes depending on the speed or mode can thus provide insights about the neural control of stable gaits. Here, we reveal the speed- and mode-dependent modulations of the trajectory by utilizing a Lissajous curve. The current study clarifies that speed-dependent modulations are evident in walking. Between walking and running, there were significant mode-dependent modulations. In contrast, there were no significant speed-dependent modulations during running. Deviations from standard tendencies quantified via Lissajous curve fitting could be a sign of gait impairments and recovery after treatments.

Larger, but not better, motor adaptation ability inherent in medicated Parkinson's disease patients revealed by a smart-device-based study.

Generating appropriate motor commands is an essential brain function. To achieve proper motor control in diverse situations, predicting future states of the environment and body and modifying the prediction are indispensable. The internal model is a promising hypothesis about brain function for generating and modifying the prediction. Although several findings support the involvement of the cerebellum in the internal model, recent results support the influence of other related brain regions on the internal model. A representative example is the motor adaptation ability in Parkinson's disease (PD) patients. Although this ability provides some hints about how dopamine deficits and other PD symptoms affect the internal model, previous findings are inconsistent; some reported a deficit in the motor adaptation ability in PD patients, but others reported that the motor adaptation ability of PD patients is comparable to that of healthy controls. A possible factor causing this inconsistency is the difference in task settings, resulting in  different cognitive strategies in each study. Here, we demonstrate a larger, but not better, motor adaptation ability in PD patients than in healthy controls while reducing the involvement of cognitive strategies and concentrating on implicit motor adaptation abilities. This study utilizes a smart-device-based experiment that enables motor adaptation experiments anytime and anywhere with less cognitive strategy involvement. The PD patients showed a significant response to insensible environmental changes, but the response was not necessarily suitable for adapting to the changes. Our findings support compensatory cerebellar functions in PD patients from the perspective of motor adaptation.

Author Correction: Speed-dependent and mode-dependent modulations of spatiotemporal modules in human locomotion extracted via tensor decomposition.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

A data-driven approach to decompose motion data into task-relevant and task-irrelevant components in categorical outcome.

Decomposition of motion data into task-relevant and task-irrelevant components is an effective way to clarify the diverse features involved in motor control and learning. Several previous methods have succeeded in this type of decomposition while focusing on the clear relation of motion to both a specific goal and a continuous outcome, such as a 10 mm deviation from a target or 1 m/s hand velocity. In daily life, it is vital to quantify not only continuous but also categorical outcomes. For example, in baseball, batters must judge whether the opposing pitcher will throw a fastball or a breaking ball; tennis players must decide whether an opposing player will serve out wide or down the middle. However, few methods have focused on quantifying categorical outcome; thus, how to decompose motion data into task-relevant and task-irrelevant components when the outcome is categorical rather than continuous remains unclear. Here, we propose a data-driven method to decompose motion data into task-relevant and task-irrelevant components when the outcome takes categorical values. We applied our method to experimental data where subjects were required to throw fastballs or breaking balls with a similar form. Our data-driven approach can be applied to the unclear relation between motion and outcome, and the relation can be estimated in a data-driven manner. Furthermore, our method can successfully evaluate how the task-relevant components are modulated depending on the task requirements.

Speed-dependent and mode-dependent modulations of spatiotem-poral modules in human locomotion extracted via tensor decom-position.

How the central nervous system (CNS) controls many joints and muscles is a fundamental question in motor neuroscience and related research areas. An attractive hypothesis is the module hypothesis: the CNS controls groups of joints or muscles (i.e., spatial modules) by providing time-varying motor commands (i.e., temporal modules) to the spatial modules rather than controlling each joint or muscle separately. Another fundamental question is how the CNS generates numerous repertoires of movement patterns. One hypothesis is that the CNS modulates the spatial and/or temporal modules depending on the required tasks. It is thus essential to quantify the spatial modules, the temporal modules, and the task-dependent modulation of these modules. Although previous attempts at such quantification have been made, they considered modulation either only in spatial modules or only in temporal modules. These limitations may be attributable to the constraints inherent to conventional methods for quantifying the spatial and temporal modules. Here, we demonstrate the effectiveness of tensor decomposition in quantifying the spatial modules, the temporal modules, and the task-dependent modulation of these modules without such limitations. We further demonstrate that tensor decomposition offers a new perspective on the task-dependent modulation of spatiotemporal modules: in switching from walking to running, the CNS modulates the peak timing in the temporal modules while recruiting more proximal muscles in the corresponding spatial modules.

Optimizing motor decision-making through competition with opponents.

Although optimal decision-making is essential for sports performance and fine motor control, it has been repeatedly confirmed that humans show a strong risk-seeking bias, selecting a risky strategy over an optimal solution. Despite such evidence, the ideal method to promote optimal decision-making remains unclear. Here, we propose that interactions with other people can influence motor decision-making and improve risk-seeking bias. We developed a competitive reaching game (a variant of the "chicken game") in which aiming for greater rewards increased the risk of no reward and subjects competed for the total reward with their opponent. The game resembles situations in sports, such as a penalty kick in soccer, service in tennis, the strike zone in baseball, or take-off in ski jumping. In five different experiments, we demonstrated that, at the beginning of the competitive game, the subjects robustly switched their risk-seeking strategy to a risk-averse strategy. Following the reversal of the strategy, the subjects achieved optimal decision-making when competing with risk-averse opponents. This optimality was achieved by a non-linear influence of an opponent's decisions on a subject's decisions. These results suggest that interactions with others can alter human motor decision strategies and that competition with a risk-averse opponent is key for optimizing motor decision-making.

Decomposing motion that changes over time into task-relevant and task-irrelevant components in a data-driven manner: application to motor adaptation in whole-body movements.

Motor variability is inevitable in human body movements and has been addressed from various perspectives in motor neuroscience and biomechanics: it may originate from variability in neural activities, or it may reflect a large number of degrees of freedom inherent in our body movements. How to evaluate motor variability is thus a fundamental question. Previous methods have quantified (at least) two striking features of motor variability: smaller variability in the task-relevant dimension than in the task-irrelevant dimension and a low-dimensional structure often referred to as synergy or principal components. However, the previous methods cannot be used to quantify these features simultaneously and are applicable only under certain limited conditions (e.g., one method does not consider how the motion changes over time, and another does not consider how each motion is relevant to performance). Here, we propose a flexible and straightforward machine learning technique for quantifying task-relevant variability, task-irrelevant variability, and the relevance of each principal component to task performance while considering how the motion changes over time and its relevance to task performance in a data-driven manner. Our method reveals the following novel property: in motor adaptation, the modulation of these different aspects of motor variability differs depending on the perturbation schedule.

Influence of switching rule on motor learning.

Humans and animals can flexibly switch rules to generate the appropriate response to the same sensory stimulus, e.g., we kick a soccer ball toward a friend on our team, but we kick the ball away from a friend who is traded to an opposing team. Most motor learning experiments have relied on a fixed rule; therefore, the effects of switching rules on motor learning are unclear. Here, we study the availability of motor learning effects when a rule in the training phase is different from a rule in the probe phase. Our results suggest that switching a rule causes partial rather than perfect availability. To understand the neural mechanisms inherent in our results, we verify that a computational model can explain our experimental results when each neural unit has different activities, but the total population activity is the same in the same planned movement with different rules. Thus, we conclude that switching rules causes modulations in individual neural activities under the same population activity, resulting in a partial transfer of learning effects for the same planned movements. Our results indicate that sports training and rehabilitation should include various situations even when the same motions are required.

Detecting the relevance to performance of whole-body movements.

Goal-directed whole-body movements are fundamental in our daily life, sports, music, art, and other activities. Goal-directed movements have been intensively investigated by focusing on simplified movements (e.g., arm-reaching movements or eye movements); however, the nature of goal-directed whole-body movements has not been sufficiently investigated because of the high-dimensional nonlinear dynamics and redundancy inherent in whole-body motion. One open question is how to overcome high-dimensional nonlinear dynamics and redundancy to achieve the desired performance. It is possible to approach the question by quantifying how the motions of each body part at each time point contribute to movement performance. Nevertheless, it is difficult to identify an explicit relation between each motion element (the motion of each body part at each time point) and performance as a result of the high-dimensional nonlinear dynamics and redundancy inherent in whole-body motion. The current study proposes a data-driven approach to quantify the relevance of each motion element to the performance. The current findings indicate that linear regression may be used to quantify this relevance without considering the high-dimensional nonlinear dynamics of whole-body motion.

Bayesian geodesic path for human motor control.

Despite a near-infinite number of possible movement trajectories, our body movements exhibit certain invariant features across individuals; for example, when grasping a cup, individuals choose an approximately linear path from the hand to the cup. Based on these experimental findings, many researchers have proposed optimization frameworks to determine desired movement trajectories. Successful conventional frameworks include the geodesic path, which considers the geometry of our complicated body dynamics, and stochastic frameworks, which consider movement variability. The former succeed in explaining the kinematics in human reaching movements, and the latter succeed in explaining the variability in those movements. However, the conventional geodesic path framework does not consider variability, and the conventional stochastic frameworks do not consider the geometrical properties of our bodies. Thus, how to reconcile these two successful frameworks remains unclear. Here, I show that the conventional geodesic path can be interpreted as a Bayesian framework in which no uncertainty is considered. Hence, by introducing uncertainty into the framework, I propose a Bayesian geodesic path framework that can simultaneously consider the geometric properties of our bodies and movement variability. I demonstrate that the Bayesian geodesic path generates a mean movement trajectory that corresponds to the conventional geodesic path and a variability of movement trajectory, thus explaining the characteristic variability in human reaching movements.

A balanced motor primitive framework can simultaneously explain motor learning in unimanual and bimanual movements.

Certain theoretical frameworks have successfully explained motor learning in either unimanual or bimanual movements. However, no single theoretical framework can comprehensively explain motor learning in both types of movement because the relationship between these two types of movement remains unclear. Although our recent model of a balanced motor primitive framework attempted to simultaneously explain motor learning in unimanual and bimanual movements, this model focused only on a limited subset of bimanual movements and therefore did not elucidate the relationships between unimanual movements and various bimanual movements. Here, we extend the balanced motor primitive framework to simultaneously explain motor learning in unimanual and various bimanual movements as well as the transfer of learning effects between unimanual and various bimanual movements; these phenomena can be simultaneously explained if the mean activity of each primitive for various unimanual movements is balanced with the corresponding mean activity for various bimanual movements. Using this balanced condition, we can reproduce the results of prior behavioral and neurophysiological experiments. Furthermore, we demonstrate that the balanced condition can be implemented in a simple neural network model.

Development of a Portable Motor Learning Laboratory (PoMLab).

Most motor learning experiments have been conducted in a laboratory setting. In this type of setting, a huge and expensive manipulandum is frequently used, requiring a large budget and wide open space. Subjects also need to travel to the laboratory, which is a burden for them. This burden is particularly severe for patients with neurological disorders. Here, we describe the development of a novel application based on Unity3D and smart devices, e.g., smartphones or tablet devices, that can be used to conduct motor learning experiments at any time and in any place, without requiring a large budget and wide open space and without the burden of travel on subjects. We refer to our application as POrtable Motor learning LABoratory, or PoMLab. PoMLab is a multiplatform application that is available and sharable for free. We investigated whether PoMLab could be an alternative to the laboratory setting using a visuomotor rotation paradigm that causes sensory prediction error, enabling the investigation of how subjects minimize the error. In the first experiment, subjects could adapt to a constant visuomotor rotation that was abruptly applied at a specific trial. The learning curve for the first experiment could be modeled well using a state space model, a mathematical model that describes the motor leaning process. In the second experiment, subjects could adapt to a visuomotor rotation that gradually increased each trial. The subjects adapted to the gradually increasing visuomotor rotation without being aware of the visuomotor rotation. These experimental results have been reported for conventional experiments conducted in a laboratory setting, and our PoMLab application could reproduce these results. PoMLab can thus be considered an alternative to the laboratory setting. We also conducted follow-up experiments in university physical education classes. A state space model that was fit to the data obtained in the laboratory experiments could predict the learning curves obtained in the follow-up experiments. Further, we investigated the influence of vibration function, weight, and screen size on learning curves. Finally, we compared the learning curves obtained in the PoMLab experiments to those obtained in the conventional reaching experiments. The results of the in-class experiments show that PoMLab can be used to conduct motor learning experiments at any time and place.