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3D Numerical Simulation of a Cerebral Aneurysm
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*  3D Numerical Simulation of a Cerebral Aneurysm

Hemodynamic factors are important in the formation, growth, and rupturing of cerebral aneurysms. The effectiveness of the medical treatment for this condition is closely related to these factors. Most current clinical image studies don’t depict the hemodynamic forces that are exerted on the vessel walls of aneurysms. The goal of this study is to help clinicians treat patients with aneurysms using computational hemodynamic models. To that extent, we use cerebral aneurysm models of various types to simulate the flow fields and shear stresses on the vascular walls.

*  Materials and Methods

For this study, CFD simulations were performed using the ANSYS CFX to solve the Navie–Stokes equations with specified boundary conditions. The blood was assumed to be an incompressible isothermal Newtonian fluid with a density of 1080 kg/m3 and a viscosity of 3.88×10-3kg/m•s. The viscoelastic properties of the vessel wall were neglected and a rigid wall with a no-slip condition was applied. At the inlet, a pulsatile flow with a Womersley velocity profile was assumed with the typical MCA velocity obtained by transcranial Doppler scanning (mean velocity, 0.6 m/s).

In the aneurysm analysis, three different geometric models, each a tetrahedral mesh, were considered. There were about 400,000 tetrahedron elements and 200,000 nodes in each model (Fig.1). The total computing time needed in each case was about 9 hours using the NCHC’s IBM P690 supercomputer.

Fig. 1. Mesh of the aneurysm model
¡¶ Fig. 1. Mesh of the aneurysm model

*  Results

Case ¢¹ is a right middle cerebral artery aneurysm (Fig. 2-a). The aneurysms form in a zone of artery bifurcation and the blood flow hits the aneurysm wall in a large open space. Fig. 2-a illustrates how the swirling blood flow appears near the aneurysm wall.

Case ¢º is a right internal carotid artery bifurcation aneurysm (Fig. 2-b). There are two aneurysms in the figure. The middle one is small and the blood flow speeds up upon entering and becomes a spiral flow. This phenomenon causes the aneurysm to grow. The other aneurysm is larger than the middle one. The entering blood velocity in the larger aneurysm is relatively low and the flow rate is small.

Case ¢» is a right posterior communicating artery aneurysm (Fig. 2-c). The blood velocity is high at the neck of the aneurysm and it appears to be spinning into the aneurysm.

The wall shear stresses (WSS) for the above three cases are shown in Fig. 3. WSS on the aneurysm walls is smaller as compared with those in the other parts of the artery because both the blood velocity and flow rate in the aneurysms are small. But WSS is high on the wall of the aneurysm neck. WSS can affect the intima and reduce its thickness. If the thinned arterial wall is under the impact of the blood flow, an aneurysm can form and grow in this region.

Fig. 2. Flow field of the aneurysm model
¡¶ Fig. 2. Flow field of the aneurysm model

Fig. 3. WSS of the aneurysm model
¡¶ Fig. 3. WSS of the aneurysm model

*  Discussion

The result of numerical hemodynamic analysis is useful in observing the blood flow. If the flow rate and velocity entering the cerebral aneurysm are large, they may cause pressure on the coil that, in turn, deforms. For this reason, coil embolization is not suitable for the treatment of aneurysms in this zone. The results of this study indicate that CFDs can be useful in evaluating various possible types of intervention and making the optimal therapeutic choice.

*  References

[1] Christoph G., Jochen L., Scott G., and Herrmann Z., “Three-Dimensional Pulsatile Flow Simulation Before and After Endovascular Coil Emboization of a Terminal Cerebral Aneurysm”, journal of Cerebral Blood Flow & Metabolism, 21: 1464-1471, 2001.
[2] Chopard B., Ouared R., Ruefenacht D.A., and Yilmaz H., “Lattice Boltzmann Medoling of Thrombosis in Giant Aneurysms”, International Journal of Modern Physics C, 18(4):712-721, 2007.
[3] Bell D.N., Spain S., and Goldsmith H. L., “Adenosine diphosphate-induced aggregation of human platelets in flow through tubes. i. measurement of concentration and size of single platelets and aggregations.” Biophy, J., 56(5):817-828, 1989.
[4] Bell D.N., Spain S., and Goldsmith H. L., “ Adenosine diphosphate-induced aggregation of human platelets in flow through tubes. ii. Effect of shear rate, donor sex, and adp concentration.” Biophy, J., 56(5):829-843, 1989.
[5] Masaaki Moroi and Stephanie M. Jung. ”Integrin-mediated platelet adhesion”. Frontiers in Bioscience, 3:719-728, July 23 1998.



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