Title:  Distinct Patterns of Hemi-Spatial Neglect:  A Multi-Lesioned Mathematical Model

Presenter:  Tony Sloan, M.D., Department of Family Medicine, University of Alabama

Left hemi-spatial neglect typically occurs after a right hemispheric stroke.  Patients with hemi-spatial neglect exhibit a range of bizarre but consistent behaviors on classic clinical tests.  Patients to some degree fail to attend to left hemi-space or to left sides of objects.  A multi-lesioned mathematical model, the Gestalt grouping-combined hemi-attentional-affine representational model, is used to show the existence of several distinct patterns of hemi-neglect behavior that exist empirically in the neuroscience literature.  Moreover, we establish the existence of several more distinct patterns of hemi-neglect behavior that have yet to appear in the empirical literature.  The space of external visuo-spatial stimuli is realized as the space, H([a,b] x P), of compact subsets of a strip, [a,b] x P, in the plane P².  A Gestalt grouping procedure decomposes a finite collection of stimuli into disjoint perceptual objects.  An internal representation of visuo-spatial stimuli is determined by the action of a group of isometries on H([a,b] x P).  A combined hemi-attentional system, given by a linear combination of a pair of normal distributions, is applied to the internal representation.  A lesion can be a representational error (related to the isometries), an attentional error (related to the combined hemi-attentional system), or a Gestalt grouping error.