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NJIT Mathematical Biology Seminar

Tuesday, March 28, 2006, 4:00 pm
Cullimore Hall 611
New Jersey Institute of Technology

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An Optimization Principle for Determining Movement Duration

Ning Qian

Center for Neurobiology & Behavior and the Mahoney Center for Brain & Behavior Research
Columbia University

Movement duration is an integral component of motor control, but nearly all extant optimization models of motor planning pre-fix the duration instead of explaining it. Here we propose a new optimization principle that can predict movement duration. The model assumes that the brain attempts to minimize movement duration under the constraint of meeting an accuracy criterion. The criterion is task and context dependent but is fixed for a given task and context. The model determines a unique duration as a tradeoff between speed (time optimality) and accuracy (acceptable end-point scatter). We analyzed the model for a general linear motor plant, and obtained an equation for determining movement duration. By solving the equation numerically with specific plant-parameters for eye and arm, we found that the model can reproduce saccade duration as a function of the amplitude (the main sequence), and arm-movement duration as a function of the target-distance-to-size ratio (Fitts¡Ç law). Furthermore, the model predicts peak velocity of eye and arm movements. Finally, for a linear plant, the neural control signal predicted by our model is identical to that of the minimum-variance model set to the same movement duration; it is a smooth function of time (except at the end point), instead of the discontinuous bang-bang control found in the time-optimal-control literature. We conclude that one aspect of movement planning, as revealed by movement duration, is assigning an end-point accuracy criterion for a given task and context.