# Neural population partitioning and a concurrent brain-machine interface for sequential motor function.

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Ziv Williams, Mar 17, 2014 Available from:- [Show abstract] [Hide abstract]

**ABSTRACT:**Object-manipulation tasks (e.g., drinking from a cup) typically involve sequencing together a series of distinct motor acts (e.g., reaching toward, grasping, lifting, and transporting the cup) in order to accomplish some overarching goal (e.g., quenching thirst). Although several studies in humans have investigated the neural mechanisms supporting the planning of visually guided movements directed toward objects (such as reaching or pointing), only a handful have examined how manipulatory sequences of actions-those that occur after an object has been grasped-are planned and represented in the brain. Here, using event-related functional MRI and pattern decoding methods, we investigated the neural basis of real-object manipulation using a delayed-movement task in which participants first prepared and then executed different object-directed action sequences that varied either in their complexity or final spatial goals. Consistent with previous reports of preparatory brain activity in non-human primates, we found that activity patterns in several frontoparietal areas reliably predicted entire action sequences in advance of movement. Notably, we found that similar sequence-related information could also be decoded from pre-movement signals in object- and body-selective occipitotemporal cortex (OTC). These findings suggest that both frontoparietal and occipitotemporal circuits are engaged in transforming object-related information into complex, goal-directed movements. © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.Cerebral Cortex 01/2015; DOI:10.1093/cercor/bhu302 · 8.31 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**Neuroscientific studies of the drawing-like movements usually analyze neural representation of either geometric (eg. direction, shape) or temporal (eg. speed) features of trajectories rather than trajectory's representation as a whole. This work is about empirically supported mathematical ideas behind splitting and merging geometric and temporal features which characterize biological movements. Movement primitives supposedly facilitate the efficiency of movements' representation in the brain and comply with different criteria for biological movements, among them kinematic smoothness and geometric constraint. Criterion for trajectories' maximal smoothness of arbitrary order n is employed, n = 3 is the case of the minimum-jerk model. I derive a class of differential equations obeyed by movement paths for which nth order maximally smooth trajectories have constant rate of accumulating geometric measurement along the drawn path. The geometric measurement is invariant under a class of geometric transformations and may be chosen to be an arc in certain geometry. For example the two-thirds power-law model corresponds to piece-wise con-stant speed of accumulating equi-affine arc. Equations' solutions presumably serve as candidates for geometric movement primitives. The derived class of differential equations consists of two parts. The first part is identical for all geometric parameterizations of the path. The second part is parametrization specific and is needed to identify whether a solution of the first part indeed represents a curve. Counter-examples are provided. Equations in different geometries in plane and in space and their known solutions are presented. A method for constructing trajectories based on primitives in different geometries is proposed. The derived class of differential equations is a novel tool for discovering candidates for geometric movement primitives. - [Show abstract] [Hide abstract]

**ABSTRACT:**Neuroscientific studies of execution of the drawing-like movements usually analyze neural representation of either geometric (eg. direction, shape) or temporal (eg. speed) features of trajectories rather than trajectory's representation as a whole. This work is about mathematical ideas behind splitting and merging geometric and temporal features which characterize biological movements. Movement primitives supposedly facilitate the efficiency of movements' representation in the brain and comply with different criteria for biological movements, among them kinematic smoothness and geometric constraint. Criterion for trajectories' "maximal smoothness" of arbitrary order $n$ is employed, $n = 3$ is the case of the minimum-jerk model. I derive a class of differential equations obeyed by movement paths for which $n$th order maximally smooth trajectories have constant speed. The speed is invariant under a class of geometric transformations. Equations' solutions presumably serve as candidates for geometric movement primitives. The speed here is defined as the rate of accumulating geometric measurement along the drawn path. The geometric measurement may be chosen to be an arc in certain geometry. For example the two-thirds power-law model corresponds to piece-wise constant speed of accumulating equi-affine arc. The derived class of differential equations consists of two parts. The first part is identical for all geometric parameterizations of the path. The second part is parametrization specific and is needed to identify whether a solution of the first part indeed represents a curve. Corresponding counter-examples are provided. Equations in different geometries in plane and in space and their known solutions are presented. The derived class of differential equation is a novel tool for discovering candidates for geometric movement primitives.