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Computational and Mathematical Methods in Medicine
Volume 8, Issue 3, Pages 205-223
Original Article

Modelling, Analysis and Calculation of Cerebral Hemodynamics

1Department of Mathematics, University of Pittsburgh, 301 Thackeray Hall, Pittsburgh, PA 15260, USA
2Department of Trauma and Orthopaedic Surgery, Merheim Medical Center, University of Witten-Herdecke, Ostmerheimerstr. 200, Cologne D-51109, Germany

Received 6 November 2006; Revised 14 May 2007; Accepted 20 June 2007

Copyright © 2007 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 CO2 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 (Pic). By contrast, the rat model does not manifest Hopf-bifurcations and thus does not predict the existence of periodic solutions with critical high Pic.

Therefore the model questions the relevance of rodent injury models to predict human physiology following TBI.