Published Online
on August 2, 2007

A more recent version of this article appeared on September 1, 2007

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Submitted on January 14, 2007
Revised on February 27, 2007
Accepted on February 28, 2007

Computation of Hemodynamics in the Circle of Willis

Martin Sandve Alnæs MSc; Jørgen Isaksen MD; Kent-André Mardal PhD; Bertil Romner PhD; Michael K. Morgan MD; and Tor Ingebrigtsen PhD^*

From the Simula Research Laboratory (M.S.A., K-A.M.), Oslo, Norway; the Department of Neurosurgery (J.I., T.I.), University Hospital of North Norway, Tromsø, Norway; the Department of Neurosurgery(B.R., T.I.), Institute for Clinical Medicine, University of Tromsø, Tromsø, Norway; the University Clinic of Neurosurgery (B.R), Neuroscience Centre, Rigshospitalet, Copenhagen, Denmark; and the School of Advanced Medicine (M.K.M.), Macquarie University, Sydney, Australia.

^* To whom correspondence should be addressed. E-mail: tor.ingebrigtsen{at}unn.no.

Background and Purpose—Wall shear stress (WSS) and pressure are important factors in the development of cerebral aneurysms. We aimed to develop a computational fluid dynamics simulator for flow in the complete circle of Willis to study the impact of variations in vessel radii and bifurcation angles on WSS and pressure on vessel walls.

Methods—Blood flow was modeled with Navier-Stokes equations as an incompressible newtonian fluid within rigid vessel walls. A model of the circle of Willis geometry was approximated as a network of tubes around cubic curves. Pulsatile inlet flow rates and constant outlet pressure were used as boundary conditions.

Results—The simulations confirmed that differences in vessel radii and asymmetric branch angles influence WSS magnitude and spatial distribution. High WSS occurred at locations where aneurysms are frequent and in anatomic variants known to be associated with an increased risk for aneurysm development.

Conclusions—Computational fluid dynamics analysis can be applied to the complete circle of Willis and should be used to study the pathophysiology of this complex vascular structure, including risk factors for aneurysm development. Further development of the method should include simulations with flexible vessel walls.

Key words: aneurysm • computational fluid dynamics • circle of Willis • hemodynamics • wall shear stress

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