Idiopathic intracranial hypertension (IIH) is a syndrome of unknown etiology characterized by elevated intracranial pressure (ICP). Although a stenosis of the transverse sinus has been observed in many IIH patients, the role this feature plays in IIH is in dispute. In this paper, a lumped-parameter model is developed for the purpose of analytically investigating the elevated pressures associated with IIH and a collapsible transverse sinus. This analysis yields practical predictions regarding the degree of elevated ICPs and the effectiveness of various treatment methods. Results suggest that IIH may be caused by a sufficiently collapsible transverse sinus, but it is also possible that a stenosed sinus may persist following resolution of significant intracranial hypertension.
Given an initial graph G, one may apply a rule R to G which replaces certain vertices of G with other graphs called replacement graphs to obtain a new graph R(G). By iterating this procedure, a sequence of graphs {R n (G)} is obtained. When each graph in this sequence is normalized to have diameter one, the resulting sequence may converge in the Gromov-Hausdorff metric. In this paper, we compute the topological dimension of limit spaces of normalized sequences of iterated vertex replacements involving more than one replacement graph. We also give examples of vertex replacement rules that yield fractals.
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