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

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.