## 4 Discussion
In model B0, the streamlines toward the LA and FA both passed through the vicinity of the catheter under the boundary condition of the syringe driver (Figure 10b,c). This blood flow delivered the agent into both the LA and FA even though the catheter tip was placed in the main trunk of the ECA. While in model A0, the flow field toward the peripheral region of the ECA was observed around the catheter tip. This flow delivered the agent into the MA (Figure 8b). These results suggest that the manual dye injection cannot reproduce the fluid field of the anticancer agent prescribed by the syringe driver in the actual phenomenon. In actual practice for patient A, clinicians may conclude that the agent flows into the LA-based on the findings of manual injection staining, even though the anticancer agent can be mainly deliveredinto the MA by a syringe driver. Besides, there is a possibility that the dye may flow into the ICA, which can cause cerebral disorders. Among the models that assumed SSIAC, models A1-A4 showed the inflow of anticancer agents into both the LA and FA, while the anticancer agent flowed into only FA in models B1-B3. This difference was thought to be caused by the characteristics of blood flow fields in two patients, which arose from the anatomical topography of the vessel. The angle between the common trunk and ECA and the angle between the FA and common trunk of patient B were smaller than those of patient A (Figure 2). Therefore, the blood flowed from the CCA toward the FA more directly than that of patient A (Figure 11d). Then, the catheter tip was covered by this blood flow in models B1-B3. As a result, the agent was transferred to only the FA by this blood flow field. Furthermore, the blood flow toward the LA was located further from the catheter tip than that toward the FA (Figure 11e). To deliver the anticancer agent into the LA, the catheter tip needs to be placed in the zone closer to the LA, or the anticancer agent should be injected at a higher velocity to allow the agent to reach the blood flow toward the LA. In contrast, in patient A, the common trunk branches had a larger angle against the ECA compared to that in patient B. Besides, the length of the common trunk is longer than that of patient B. Therefore, blood flow towards the LA and the FA both passed through the vicinity of the catheter tip in the common trunk, which allowed the anticancer agent to flow into both the LA and FA. These suggest that the distribution of the agent between the LA and FA in the ECA with the linguofacial trunk varies among patients due to the anatomical topology of vessels. Thus, clinicians should not assume that the anticancer agent is evenly distributed between the LA and FA but recognize that the distribution can be changeable even if the catheter is placed in the common trunk. Moreover, there is a possibility that the anticancer agent flows to only one branch of the common trunk, as observed in models B1-B3. WSS is related to vascular epithelial injury and arteriosclerosis. In models A0 and B0, the analyses assuming manual injection resulted in higher WSS at all walls than those in the analyses assuming syringe driver injection (Figures 12 and 13). In model B0, the WSS at the APA was 67.5 Pa, which exceeded the yield stress of the artery (37.9 Pa [21]). This indicates that manual injection of dye can cause acute epithelial injury in the carotid artery. When comparing the WSS values for CIAC and SSIAC, in model A1, the OA showed a higher WSS value than that in model A0 with the boundary condition of syringe driver injection. In model B1, the WSS showed a higher value at the APA than that in model B0 with the boundary condition of syringe driver injection. These results imply that SSIAC loads mechanical stress on the ECA branches that arise from the ECA, even apart from the tumor-feeding arteries. To our knowledge, no study follows the functional and morphological changes in patients' vessels after IAC.