Norihiko Watanabe [1] Analysis of the non-Newtonian effect Figure 1 shows the schematic view of a model of a stenotic vessel. Using this model, we carried out a computation. Figure 2 shows the pressure distribution and stream lines of a steady flow having a Reynolds number of 1000. In this case, even when Watanabe’s viscosity, which reflects the non-Newtonian effect (refer to Eq.1 in [2]), was included in the simulation, no significant change was observed in the wall shear stress, as shown in (Fig. 3). Further, even in the case of pulsatile flow, the difference in the shear stress between Newtonian and non-Newtonian fluids was small (Fig. 4). This reveals that it is not necessary to include the non-Newtonian effect, when the Reynolds number is not low. Fig. 1 Boundary fitted grid system used for the present computation Fig 2. Pressure distribution and stream lines in the vicinity of the stenotic region (steady flow). Fig. 3 Shear stress exerted on the center line of the stenotic region (steady flow). Fig. 4 Shear stress exerted on the center line of the stenotic region (pulsatile flow). [2] Weak coupling method for fluid-structure interaction problem Fig. 5 The deformation behavior of a stenotic region due to the pulsatile flow. (Click to see the behavior in detail.) We adopted a weak coupling method for an approximate analysis of blood flowing through a blood vessel with a stenotic region. In this method, the blood flow and vessel regions are analyzed separately, and the velocity and force are exchanged at the boundary between the blood flow and the vessel. Figure 5 shows an animation of the deformation behavior of a blood vessel with a stenotic region in the case of a pulsatile flow, with an average Reynolds number of 1000, through a vessel having the same shape as that used for the computation of non-Newtonian flow. In this example of calculation, we chose moderate material properties as compared with those in the actual vessels in human beings since the aim of the calculation was to test whether the coupling method functioned appropriately.