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The etiology, and hence most effective treatment, of cerebral vasospasm remains unknown, thus this devastating sequela to subarachnoid hemorrhage continues to be responsible for significant morbidity and mortality. Based on abundant and diverse clinical and laboratory observations, we hypothesize that vasospasm and its subsequent resolution result from a short-term chemo-dominated turnover of cells and matrix in evolving vasoconstricted states that produces a narrowed lumen and thicker wall, which is stiffer and largely unresponsive to exogenous vasodilators, and a subsequent mechano-dominated turnover of cells and matrix in evolving vasodilated states that restores the vessel toward normal. There is, however, a pressing need for a mathematical model of arterial growth and remodeling that can guide the design and interpretation of experiments to test this and competing hypotheses. Toward this end, we present a new biochemomechanical framework that couples a 2-D model of the evolving geometry, structure, and properties of the affected arterial wall, a 1-D model of the blood flow within the affected segment, and a 0-D model of the biochemical insult to the segment. We submit that such a framework can capture salient features of the time-course of vasospasm and its potential resolution, as illustrated numerically in part II of this paper.

Biochemomechanics of Cerebral Vasospasm and its Resolution: I. A New Hypothesis and Theoretical Framework