Current understanding of the effects of damage on neural networks is rudimentary, even though such understanding could lead to important insights concerning 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 effects of focal lesions of varying area, shape, and number on the retrieval capacities of a spatially organized associative memory are quantified, leading to specific scaling laws that may be further examined experimentally. It is predicted that multiple 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 significantly less performance decrease in larger networks. Our study is clinically motivated by the observation that in multi-infarct dementia, the size of metabolically impaired tissue correlates with the level of cognitive impairment more than the size of structural damage. Our results account for the detrimental effect 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.
