Neurointervention.  2014 Feb;9(1):1-8. 10.5469/neuroint.2014.9.1.1.

Considerations of Blood Properties, Outlet Boundary Conditions and Energy Loss Approaches in Computational Fluid Dynamics Modeling

Affiliations
  • 1Department of Radiology and Research Institute of Radiology, University of Ulsan, College of Medicine, Asan Medical Center, Seoul, Korea. dcsuh@amc.seoul.kr
  • 2School of Mechanical Engineering, Yonsei University, Seoul, Korea. joonlee@yonsei.ac.kr

Abstract

Despite recent development of computational fluid dynamics (CFD) research, analysis of computational fluid dynamics of cerebral vessels has several limitations. Although blood is a non-Newtonian fluid, velocity and pressure fields were computed under the assumptions of incompressible, laminar, steady-state flows and Newtonian fluid dynamics. The pulsatile nature of blood flow is not properly applied in inlet and outlet boundaries. Therefore, we present these technical limitations and discuss the possible solution by comparing the theoretical and computational studies.

Keyword

Computer simulation; Hydrodynamics; Computational fluid dynamics; Biological boundary condition; Cerebral arteries

MeSH Terms

Bays
Cerebral Arteries
Computer Simulation
Hydrodynamics*

Figure

  • Fig. 1 The three main considerations in circulatory system modeling: A. non-Newtonian properties of blood, B. outlet boundary conditions of the model, and C. additional energy loss due to vessel geometry.

  • Fig. 2 A. Wall shear rate predicted using the flow rate and radii common carotid, brachial, and femoral arteries reported by Stroev et al.[30] (Reprinted with permission) B. Viscosity calculated using shear rate from Carreau-Yasuda model ( = (1+(λη)a)(n-1)/a, µ0=0.0022 Paty c a=0.644, n=0.392, λ=0.110s) in common carotid, brachial, and femoral arteries compared to Newtonian viscosity[31].

  • Fig. 3 Comparison between the zero pressure boundary condition and the impedance boundary condition. Zero pressure boundary condition assumes that pressure at the outlet boundary is zero, as if bleeding were occurring, without considering any influences from the vessels outside of the simulation domain. However, in impedance boundary case, as shown at right, the term Z is adopted to demonstrate the wave reflection caused by the outer domain. By regarding the blood flow of the whole vascular system as if it were electrical current running through a circuit, and so adopting the impedance term to express resistance of vessel to blood flow, the wave reflection is successfully accounted for at the outlet of the simulation domain.

  • Fig. 4 The simulation of mean flow rate at the stenotic blood vessel with two different boundary conditions: the constant pressure and the impedance boundary condition [18]. (Reprinted with permission) A. Geometry of a bifurcated blood vessel with stenosis that reduces the cross sectional area by 75%. B. Flow distribution between normal and stenotic iliac vessels. Flow rate is calculated at the bottom end of each bifurcation. For the case of constant pressure boundary, the left branch of bifurcation with stenosis has a drastically different flow rate compared to the right branch, which is completely unrealistic. In the case of impedance boundary, however, the difference between the two branches is much smaller as the pressure from the outer domain has been applied properly.

  • Fig. 5 A. Schematic representation of a stream of fluid traversing a vessel from an initial position i to a final position f. Uniform flow experiences a sudden change in its cross-sectional area A and direction θ. The symbols Ai and Af each represent the cross-sectional area, and Vi and Vf represent the corresponding average velocities of flow. B. The relationship between geometrical energy loss and cross-sectional area ratio. Each line represents the degree of change in flow angle. Each dot represents the point where the loss becomes minimum at the listed angles (0°, 30°, 45°, 60°, 90°).[26, 28] (Reprinted with permission)

  • Fig. 6 A. Gradual change of cross-sectional area and magnitude the function of β for increasing values of N (# of changes) at = 1/10. B. Change in angle where there is no change in cross-sectional area. The graph at the bottom shows that a larger number of transitions causes the angle change to become more gradual resulting in lower 'loss factor'. Both cases have directional change of 60°[26]. (Reprinted with permission)


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