1How the central nervous system (CNS) controls many joints and muscles is a fundamental question 2 in motor neuroscience and related research areas. An attractive hypothesis is the module hypothesis: 3 the CNS controls groups of joints or muscles (i.e., spatial modules) while providing time-varying motor 4 commands (i.e., temporal modules) to the spatial modules rather than controlling each joint or muscle 5 separately. Another fundamental question is how the CNS generates numerous repertories of movement 6 patterns. One hypothesis is that the CNS modulates the spatial and/or temporal modules depending 7 on the required tasks. It is thus essential to quantify the spatial module, the temporal module, and 8 the task-dependent modulation of those modules. Although previous methods attempted to quantify 9 these aspects, they considered the modulation in only the spatial or temporal module. These limitations 10 were possibly due to the constraints inherent to conventional methods for quantifying the spatial and 11 temporal modules. Here, we demonstrate the effectiveness of tensor decomposition in quantifying the 12 spatial module, the temporal module, and the task-dependent modulation of these modules without such 13 limitations. We further demonstrate that the tensor decomposition provides a new perspective on the 14 task-dependent modulation of spatiotemporal modules: in switching from walking to running, the CNS 15 modulates the peak timing in the temporal module while recruiting proximal muscles in the corresponding 16 spatial module.
17Author summary 18 There are at least two fundamental questions in motor neuroscience and related research areas: 1) how 19 does the central nervous system (CNS) control many joints and muscles and 2) how does the CNS 20 generate numerous repertories of movement patterns. One possible answer to question 1) is that the 21 CNS controls groups of joints or muscles (i.e., spatial modules) while providing time-varying motor 22 factors inherent to joint angle and electromyographic (EMG) data (i.e., spatial and temporal modules), 54 there can be limitations to considering more than three factors such as spatial modules, temporal modules, 55 and the task-dependent modulations of those modules. For example, with matrix decomposition, the task-56 dependent modulation of the temporal module between two tasks has been discussed under the constraint 57 of the same spatial module; on the other hand, the modulation of the spatial module has been discussed 58 without considering the temporal module. These constraints can thus provide diverse and non-unified 59 perspectives on the task-dependent modulation of the spatiotemporal modules.
60Here, we demonstrate the effectiveness of tensor decomposition in extracting the spatial module, the 61 temporal module, and the task-dependent modulations of the spatiotemporal modules. Tensor decompo-62 sition is a generalized version of matrix decomposition. By constructing tensor data that combine matrix 63 data in the third dimension, tensor decomposition e...