An Optimization Principle for Determining Movement Duration

by Dr. Ning Qian, Associate Professor, Columbia University, USA.

 :  13 May 2005 (Fri)
 :  11:00am - 12:00noon
Venue  :  Room 3008, 3/F (Lifts 3), HKUST.

Movement duration varies across tasks and with other parameters such as movement amplitude and end-point accuracy. It is thus an integral component of motor control. However, nearly all extant optimization models of motor planning pre-fix the movement 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 demanded by the task and context, in the presence of signal-dependent noise. 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 linear motor plant, and obtained a closed-form equation for determining movement duration. By solving the equation numerically with plant parameters for eye and arm, we found that the model can reproduce experimentally observed saccade duration as a function of the amplitude (the main sequence), and experimentally observed arm movement duration as a function of the ratio of the amplitude to the target size (Fitts' law). In addition, we show analytically that for arm movements, the duration is only a function of the ratio of the amplitude to the target size, instead of a function of each variable separately. Furthermore, the model predicts the peak velocity as a function of the saccade amplitude and arm-movement distance. Finally, the 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 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 to a given task and context.

Ning Qian obtained his PhD in Biophysics from Johns Hopkins University in 1990. He worked in Dr. Terry Sejnowski's lab on predicting protein secondary structure with artificial neural networks, and on applying Nersnt-Planck equation to model ionic concentrations and electrical activities in neuronal processes. He then obtained a McDonnell-Pew postdoctoral fellowship and joined Dr. Richard Andersen's lab in the Department of Brain & Cognitive Sciences at MIT. There, he studied the problem of transparent motion perception using a combination of psychophysical, physiological, and computational techniques. In 1994, Dr.Qian became an assistant professor in the Center for Neurobiology & Behavior at Columbia University. Since 2001, he has been a tenured associate professor at Columbia. He was a Sloan Research Fellow from 1997 to 2000. For more than 10 years, Dr. Qian's research has been focused on constructing physiologically realistic models of stereovision, motion processing, and visual perceptual learning. Over the recent few years, he has also been working on computational models of motor control. He hopes to combine his experiences in vision and motor research to address issues in sensorimotor integration in the near future.


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