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Detecting task-dependent modulation of spatiotemporal module via tensor decomposition: application to kinematics and EMG data for walking and running at various speed

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) while 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 repertories 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 module, the temporal module, and the task-dependent modulation of those modules. Although previous methods attempted to quantify these aspects, they considered the modulation in only the spatial or temporal module. These limitations were possibly due 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 module, the temporal module, and the task-dependent modulation of these modules without such limitations. We further demonstrate that the tensor decomposition provides 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 module while recruiting proximal muscles in the corresponding spatial module. Author summary There are at least two fundamental questions in motor neuroscience and related research areas: 1) how does the central nervous system (CNS) control many joints and muscles and 2) how does the CNS generate numerous repertories of movement patterns. One possible answer to question 1) is that the CNS controls groups of joints or muscles (i.e., spatial modules) while providing time-varying motor commands (i.e., temporal modules) to the spatial modules rather than controlling each joint or muscle separately. One possible answer to question 2) is that the CNS modulates the spatial and/or temporal module depending on the required tasks. It is thus essential to quantify the spatial module, the temporal module, and the task-dependent modulation of those modules. Here, we demonstrate the effectiveness of tensor decomposition in quantifying the modules and those task-dependent modulations while overcoming the shortcomings inherent to previous methods. We further show that the tensor decomposition provides a new perspective on how the CNS switches between walking and running. The CNS modulated the peak timing in the temporal module while recruiting proximal muscles in the corresponding spatial module.