The regulation of walking speed is easily achieved. However, the central nervous system (CNS) must coordinate numerous muscles in order to achieve a smooth and continuous control of walking speed. To control walking speed appropriately, the CNS may need to utilize a simplified system for the control of numerous muscles. Previous studies have revealed that the CNS may control walking via muscle synergies that simplify the control of muscles by modularly organizing several muscles. We hypothesized that the CNS controls the walking speed by flexibly modulating activation of muscle synergies within one gait cycle. Then, we investigated how the activation of muscle synergies depend on walking speeds using the center of activity (CoA) that indicates the center of the distribution of activation timing within one gait cycle. Ten healthy men walked on a treadmill at 14 different walking speeds. We measured the surface electromyograms (EMGs) and kinematic data. Muscle synergies were extracted using non-negative matrix factorization. Then, we calculated the CoA of each muscle synergy. We observed that the CoA of each specific synergy would shift as the walking speed changed. The CoA that was mainly activated during the heel contact phase (C1) and the activation that contributed to the double support phase (C3) shifted to the earlier phase as the walking speed increased, whereas the CoA that produced swing initiation motion (C4) and the activation that related to the late-swing phase (C5) shifted to the later phase. This shifting of the CoA indicates that the CNS controls intensive activation of muscle synergies during the regulation of walking speed. In addition, shifting the CoA might be associated with changes in kinematics or kinetics depending on the walking speed. We concluded that the CNS flexibly controls the activation of muscle synergies in regulation of walking speed.

It is well known that humans run with a fore-foot strike (FFS), a mid-foot strike (MFS) or a rear-foot strike (RFS). A modular neural control mechanism of human walking and running has been discussed in terms of muscle synergies. However, the neural control mechanisms for different foot strike patterns during running have been overlooked even though kinetic and kinematic differences between different foot strike patterns have been reported. Thus, we examined the differences in the neural control mechanisms of human running between FFS and RFS by comparing the muscle synergies extracted from each foot strike pattern during running. Muscle synergies were extracted using non-negative matrix factorization with electromyogram activity recorded bilaterally from 12 limb and trunk muscles in ten male subjects during FFS and RFS running at different speeds (5–15 km/h). Six muscle synergies were extracted from all conditions, and each synergy had a specific function and a single main peak of activity in a cycle. The six muscle synergies were similar between FFS and RFS as well as across subjects and speeds. However, some muscle weightings showed significant differences between FFS and RFS, especially the weightings of the tibialis anterior of the landing leg in synergies activated just before touchdown. The activation patterns of the synergies were also different for each foot strike pattern in terms of the timing, duration, and magnitude of the main peak of activity. These results suggest that the central nervous system controls running by sending a sequence of signals to six muscle synergies. Furthermore, a change in the foot strike pattern is accomplished by modulating the timing, duration and magnitude of the muscle synergy activity and by selectively activating other muscle synergies or subsets of the muscle synergies.

Living organisms dynamically and flexibly operate a great number of components. As one of such redundant control mechanisms, low-dimensional coordinative structures among multiple components have been investigated. However, structures extracted from the conventional statistical dimensionality reduction methods do not reflect dynamical properties in principle. Here we regard coordinative structures in biological periodic systems with unknown and redundant dynamics as a nonlinear limit-cycle oscillation, and apply a data-driven operator-theoretic spectral analysis, which obtains dynamical properties of coordinative structures such as frequency and phase from the estimated eigenvalues and eigenfunctions of a composition operator. Using segmental angle series during human walking as an example, we first extracted the coordinative structures based on dynamics; e.g. the speed-independent coordinative structures in the harmonics of gait frequency. Second, we discovered the speed-dependent time-evolving behaviours of the phase by estimating the eigenfunctions via our approach on the conventional low-dimensional structures. We also verified our approach using the double pendulum and walking model simulation data. Our results of locomotion analysis suggest that our approach can be useful to analyse biological periodic phenomena from the perspective of nonlinear dynamical systems.