Computation of hemodynamics in the circle of willis

• Published in: Stroke (1970) Vol. 38; no. 9; pp. 2500 - 2505
• Main Authors: AINAES, Martin Sandve, ISAKSEN, Jørgen, MARDAL, Kent-Andre, ROMNER, Bertil, MORGAN, Michael K, INGEBRIGTSEN, Tor
• Format: Journal Article
• Language: English
• Published: Hagerstown, MD Lippincott Williams & Wilkins 01.09.2007
• Subjects: Biological and medical sciences; Blood Flow Velocity; Cerebrovascular Circulation - physiology; Circle of Willis - anatomy & histology; Circle of Willis - physiology; Headache. Facial pains. Syncopes. Epilepsia. Intracranial hypertension. Brain oedema. Cerebral palsy; Hemorheology; Humans; Investigative techniques, diagnostic techniques (general aspects); Medical sciences; Models, Cardiovascular; Models, Neurological; Nervous system; Nervous system (semeiology, syndromes); Neurology; Pulsatile Flow; Regional Blood Flow - physiology; Shear Strength; Stress, Mechanical; Ultrasonic investigative techniques; Vascular diseases and vascular malformations of the nervous system; Stroke; Nervous system diseases; computational fluid dynamics; Aneurysm; Cardiovascular disease; Cerebral disorder; Vascular disease; Central nervous system disease; wall shear stress; Shear stress; circle of Willis; Hemodynamics; Cerebrovascular disease
• ISSN: 0039-2499; 1524-4628
• DOI: 10.1161/strokeaha.107.482471

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. 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. 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. 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.