# Numerical Simulation of Red Blood Cell-Induced Platelet Transport in Saccular Aneurysms
## 3 Results and Discussions
### Blood Flow and Platelets Migration in Aneurysms
#### 3.2.2 Bulging Saccular Aneurysm  
Figure 4b shows the geometry of the bulging saccular aneurysm having a neck, which is twice the size of the bulbous saccular aneurysm. Figure 7 shows the platelet concentration field, the RBCs volume fraction field, and the velocity field in the bulging saccular aneurysm. The difference between the fields in two different aneurysms is obvious. First, for the velocity and streamlines distribution, the vortexes in the bulging saccular aneurysm is not obvious and only exists in the region near corner A (see Figure 7d for the position of corner A). Compared with Figure 5a,b, it is shown that at the dimensionless time point of \(\tau=100\), the accumulation of the platelets and the RBCs in the bulging saccular aneurysm are much greater than in the bulbous saccular aneurysm. Following the previous case, we also look at the dynamics of the platelets and RBCs migration in the bulging saccular aneurysm at different dimensionless time points. In comparison to Figure 6, Figure 8 shows that the initial mixing of the cells occurs much more quickly than the bulbous saccular aneurysm. This can be explained by the relatively weak circulation in the bulging saccular aneurysm. This velocity field also causes the cells to transport out of the aneurysm, therefore decreasing the dwell time. This has the additional effect of reducing the steady-state concentration of the platelets in the bulging saccular aneurysm, although the initial mixing is faster. To further exemplify this, Figure 9a and b indicate the platelets concentration fields in the bulbous saccular aneurysm and the bulging saccular aneurysm at \(\tau=5000\) when the flow fields have changed little over time. We can clearly see that the accumulation of the platelets in the bulbous saccular aneurysm is obviously higher. This is illustrated quantitatively in Figure 9c which shows the platelets concentration profiles along the center line of the aneurysms (lines \(A\)-\(A\) as defined in Figure 9a,b) at \(\tau=500\) and \(\tau=5000\). Figure 6: (**a**) The distributions of the platelets concentration in the bulbous saccular aneurysm at different dimensionless time steps. The unit of the scale bar is \(1\times 10^{14}\)/m\({}^{3}\). (**b**) The distributions of the RBCs concentration in the bulbous saccular aneurysm at different dimensionless time steps. Figure 7: The distribution of, (**a**) the RBCs concentration, (**b**) the platelets concentration, (**c**) the velocity and (**d**) the streamlines of the whole blood in the bulging saccular aneurysm after simulating for \(\tau=100\). The units of the scale bars in (**b–d**) are \(1\times 10^{14}\)/m\({}^{3}\), m/s and m/s. The effect of flow rate (Reynolds number) is illustrated in Figure 10 (at \(\tau=5000\)) in the bulbous and bulging saccular aneurysms. When the Reynolds number increases, the platelets concentration near the wall of the upstream vessel increases, which is known to be attributed to the transport of RBCs towards the core [21]. As a result, the near-wall enrichment layer of platelets flows into the aneurysm. For the aneurysm with the small neck, the RBC gradient is preserved, which constrains the platelets to remain within the aneurism. On the other hand, the wide neck of the bulging aneurism permits the RBC gradient to dissipate, hence reducing its constraining effect, and permitting platelets to escape, particularly at the downstream region (See Figure 10a,b). This disparity is emphasized with an increasing Reynolds number. Figure 11 quantitatively illustrates this effect. As Re increases, the platelets concentration increases monotonically, but not proportionately. However, the concentration patterns are similar. Figure 8: (**a**) The distributions of the platelets concentration in the bulging saccular aneurysm at different dimensionless time steps. The unit of the scale bar is \(1\times 10^{14}/\mathrm{m}^{3}\). (**b**) The distributions of the RBCs concentration in the bulging saccular aneurysm at different dimensionless time steps.