Blood Flow Through the Circle of Willis — Simulation Example


Biomedical researchers have been relying on computational fluid dynamics to model and understand physical mechanisms behind formation and progression of cerebral disorders, such as aneurysms, atherogenesis and atherosclerosis in the cerebral arteries. The branch of medical science studying dynamics of blood flow inside a brain is called cerebral hemodynamics. A critical area of research in cerebral hemodynamics is blood flow through the Circle of Willis, a circulatory network of blood vessels supplying blood to the brain and surrounding tissues. This circular anatomical connectivity is located at the base of the brain and is the main distributor of oxygenated blood throughout it. Blood comes into the Circle of Willis through two symmetric internal carotid arteries (ICAs) and two symmetric vertebral arteries (VAs), which are joined together at the basilar artery (BA). Blood symmetrically leaves through the circle via the two middle cerebral arteries (MCAs), two anterior cerebral arteries (ACAs) and the two posterior cerebral arteries (PCAs), as shown in the figure.

Wall shear stress (WSS) exerted on the walls of the blood vessel due to the flow of blood is one of the main pathogenic factors leading to the development of cerebral aneurysms. The magnitude and distribution of the WSS in and around the Circle of Willis can provide an insight into the locations of possible aneurysm growth. The governing equations of cerebral hemodynamics are the Navier-Stokes equations in which the blood flow through a brain artery or a cerebral arterial network is considered incompressible and viscous. The viscosity of blood varies with the shear rate. In this example, we will simulate this behavior using the non-Newtonian Carreau model for viscosity.


In this simulation example, you will learn how to:

  1. Simulate the flow inside the Circle of Willis using Ansys Fluent
  2. Set up the Carreau model for blood
  3. Verify conservation of mass for a problem having multiple inlets and outlets
  4. Create and analyze pressure and wall shear stress contours
  5. Visualize flow using path lines

Please note that the geometry used in this example is a simplified representation of the Circle of Willis intended to be used for instructional purposes only, and does not represent an actual Circle of Willis or any patient-specific case. For simplicity, the flow rates used in this example are assumed to be steady. However, in an actual Circle of Willis, the flow rates are pulsatile in nature and reflect the cardiac rhythm of the subject.



Download the Mesh file needed for setting up the simulation and the associated Case & Data files here. Follow the instructions below to set up this simulation in Ansys Fluent starting with a Mesh file. In case you face any issues setting up or running the simulation, then please use the corresponding initial and final Case and Data files.


Alternate video link.

Results and Discussion

Let’s now analyze the simulation results and understand the physics of blood flow through the Circle of Willis.