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Modelling, analysis and calculation of cerebral hemodynamics. (English) Zbl 1121.92019
Summary: Mathematical models of cerebral hemodynamics, applicable to humans and rats, have been developed and analysed with the purpose of reaching a deeper insight to which degree experimental results on rats can be extrapolated to humans and to clinical management of patients. These models include regulation mechanisms involving the small cerebral arteries and arterioles, flow autoregulation, as well as CO\(_{2}\) and NO reactivity. Bifurcation analysis was conducted on both models. The human model includes Hopf-bifurcations, which allow for the existence of periodic solutions with a time scale comparable to Lundberg’s plateau waves in intracranial pressure \((P_{\text{ic}})\). By contrast, the rat model does not manifest Hopf-bifurcations and thus does not predict the existence of periodic solutions with critical high \(P_{\text{ic}}\). Therefore the model questions the relevance of rodent injury models to predict human physiology following traumatic brain injury.
MSC:
92C35 Physiological flow
92C50 Medical applications (general)
93A30 Mathematical modelling of systems (MSC2010)
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