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Modeling Reaching Impairment After Stroke Using a Population Vector Model of Movement Control That Incorporates Neural Firing-Rate Variability

dreinken{at}uci.edu, Department of Mechanical and Aerospace Engineering and Center for Biomedical, Engineering, University of California at Irvine, Irvine, CA 92697, U.S.A.

Mario G. Iobbi

mario_iobbi{at}hotmail.com, Department of Physics and Center for Biomedical Engineering, University of California at Irvine, Irvine, CA 92697, U.S.A.

Leonard E. Kahn

L-kahn{at}nwu.edu, Sensory Motor Performance Program, Rehabilitation Institute of Chicago, Chicago, IL 60611, U.S.A., and Department of Biomedical Engineering, Northwestern University, Evanston, IL 60208, U.S.A.

Derek G. Kamper

d-kamper{at}nwu.edu, Sensory Motor Performance Program, Rehabilitation Institute of Chicago, Chicago, IL 60611, U.S.A., and Department of Physical Medicine and Rehabilitation, Northwestern University Medical School, Evanston, IL 60208, U.S.A.

Craig D. Takahashi

ctakahas{at}uci.edu, Department of Mechanical and Aerospace Engineering, University of California at Irvine, Irvine, CA 92697, U.S.A.

The directional control of reaching after stroke was simulated by including cell death and firing-rate noise in a population vector model of movement control. In this model, cortical activity was assumed to cause the hand to move in the direction of a population vector, defined by a summation of responses from neurons with cosine directional tuning. Two types of directional error were analyzed: the between-target variability, defined as the standard deviation of the directional error across a wide range of target directions, and the within-target variability, defined as the standard deviation of the directional error for many reaches to a single target. Both between- and within-target variability increased with increasing cell death. The increase in between-target variability arose because cell death caused a nonuniform distribution of preferred directions. The increase in within-target variability arose because the magnitude of the population vector decreased more quickly than its standard deviation for increasing cell death, provided appropriate levels of firing-rate noise were present. Comparisons to reaching data from 29 stroke subjects revealed similar increases in between- and within-target variability as clinical impairment severity increased. Relationships between simulated cell death and impairment severity were derived using the between- and within-target variability results. For both relationships, impairment severity increased similarly with decreasing percentage of surviving cells, consistent with results from previous imaging studies. These results demonstrate that a population vector model of movement control that incorporates cosine tuning, linear summation of unitary responses, firing-rate noise, and random cell death can account for some features of impaired arm movement after stroke.