A Mathematical Model to Simulate Intracranial Pressure and Unified Interpretation of Several Disease Entities

Abstract

BACKGROUNDMany clinical phenomena related to cerebrospinal fluid(CSF) and intracranial pressure (ICP) are often contrary to common sense and difficult to explain by classical theory. Such as slit ventricle syndrome, normal intracranial pressure hydrocephalus / low pressure hydrocephalus, paradoxical herniation, and so on. Many authors have different theories about them but cant have an unified explanation. OBJECTIVEWe try to simulate the above CSF disorders and ICP conduction with a mathematical method, and make theoretical interpretations to them. METHODSWe introduced a mathematical model based on several well-accepted hypothesesto simulate human CSF physiology and propose that ICP curve should be an U-shaped curve (especially, we introduce the hypothesis that CSF also play a role of decompression). Maple software was used to draw charts according to our formula. We use the theory and intuitive charts to explain those illnesses one by one. RESULTSThe formula: ICP = {middle dot} MAP - {delta} {middle dot} V {middle dot} {middle dot} MAP + {theta} {middle dot} V{beta} {middle dot} {middle dot} MAP + C, and corresponding diagrams was conducted. CONCLUSIONThis mathematical model is a supplement to the classical Monro-Kellies theory, the curve and coordinate system can be used to analyze different pathophysiological states and give a reasonable unified explanation to them.