Computation of hemodynamics in the circle of Willis.
OBJECTIVE
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.
Simula Research Laboratory, Oslo, Norway.
Martin Sandve
MS
Alnaes
Jørgen
J
Isaksen
Kent-André
KA
Mardal
Bertil
B
Romner
Michael K
MK
Morgan
Tor
T
Ingebrigtsen
D001783:Blood Flow Velocity; D002560:Cerebrovascular Circulation / Q000502:physiology*; D002941:Circle of Willis / Q000033:anatomy & histology / Q000502:physiology; D018056:Hemorheology; D006801:Humans; D008955:Models, Cardiovascular; D008959:Models, Neurological; D011673:Pulsatile Flow; D012039:Regional Blood Flow / Q000502:physiology*; D033081:Shear Strength; D013314:Stress, Mechanical