Patterns of functional damage in neural network models of associative memory

Current understanding of the eects of damage on neural networks is rudi-mentary, even though such understanding could lead to important insights con-cerning neurological and psychiatric disorders. Motivated by this consideration, we present a simple analytical framework for estimating the functional damage resulting from focal structural lesions to a neural network model. The eects of focal lesions of varying area, shape and number on the retrieval capacities of a spatially-organized associative memory are quantied, leading to specic scaling laws that may be further examined experimentally. It is predicted that multi-ple focal lesions will impair performance more than a single lesion of the same size, that slit like lesions are more damaging than rounder lesions, and that the same fraction of damage (relative to the total network size) will result in sig-ni cantly less performance decrease in larger networks. Our study is clinically motivated by the observation that in multi-infarct dementia, the size of metabol-ically impaired tissue correlates with the level of cognitive impairment more than the size of structural damage. Our results account for the detrimental eect of the number of infarcts rather than their overall size of structural damage, and for the `multiplicative ' interaction between Alzheimer's disease and multi-infarct dementia