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.