Tans-scale Coupling in Multi-scale Simulation

The physics and mathematics involved in modeling of components of cardiovascular system is very different from that in many other engineering problems. For example, the blood flows in vessels with a deformable boundary (the viscoelastic walls of the vessel) that may require modeling of fluid and tissue interaction and for smaller arteries, the non-Newtonian nature of the blood requires special constitutive models. To make the problem computationally manageable, minor arteries such as arterioles, venules and capillaries need to be truncated, which require equivalent outflow boundary conditions at truncated positions. Although the blood flow simulations in deforming large vessels (such as coronary, carotid, femoral or iliac arteries) require the solution of 3-D Navier-Stokes equations, the truncated part of the cardiovascular system can be modeled by lumped parameter models. Thus, appropriate coupling algorithms are required for integrating the 3-D CFD simulations with 1-D fluid and tissue interaction models, and lumped parameter models. Furthermore, not only the flow at the inlet boundary of an artery is pulsatile, but also the inflow and outflow boundaries can switch roles (i.e., an inlet boundary can turn into an outflow boundary, and vice versa) in a cardiac cycle. Additionally, the auto-regulation mechanism in the arteriolar bed needs to be modeled to account for the flow resistance due to truncation. Multi-scale and multi-model coupling algorithms are therefore needed to solve the cardiovascular flow problems [1-3]. We employ the approach outlined in References [1-3] to compute the flow fields and pressure distributions in arteries with vascular stenosis, stents and bypass-grafts. References [1] Formaggia, L., Nobile, F., Quarteroni, A., and Veneziani, A., “Multi-Scale Modeling of the Circulatory System: A Preliminary Analysis,” Comput. Vis. Sci., 2, 75-83, 1999. [2] Quarteroni, A., Tuveri, M., and Veneziani, A., “Computational Vascular Fluid Dynamics: Problems, Models, and Methods,” Comput. Vis. Sci., 2, 163-197, 2000. [3] Quarteroni, A., Ragni, S., and Veneziani, A., “ Coupling Between Lumped and Distributed Models for Blood Flow Problems,” Comput. Vis. Sci., 4, 1111-1124, 2001. 1 Corresponding Author. Email: [email protected]; Phone: 314-935-6091; Fax: 314-935-4014