Doppler Ultrasound and Boundary Conditions

Time-variant velocities at the ascending aorta, right common carotid artery, left common carotid artery, LSA and ARSA were measured via Doppler ultrasound of the patients. At each measurement site, an appropriate ultrasound probe was employed (Supplementary Table 1; Supplementary Data Sheet 4). The upper edge of the velocity sonogram was extracted as the variation in the maximum velocity at the measured site (Figure 1G). The measurements were used to provide patient-specific velocity boundary conditions for the computational model. In the current study, Doppler ultrasound data were acquired before treatment and at 4 days after treatment. Therefore, Post-1 and Post-2 were given the same boundary conditions. Supplementary Figure 2 shows the velocity boundary conditions for Pre-1, Post-1 and Post-2 (Supplementary Data Sheet 4). The flow distribution ratio for each aortic arch branch, including the right common carotid artery, left common carotid artery, LSA and ARSA was computed on the basis of the Doppler ultrasound data, which was defined as the ratio of the branching flow to the inflow. Details of pulsatile waveforms of pressure at the celiac artery, superior mesenteric artery, renal arteries and outlets at iliac arteries were obtained from a previous study and used as pressure boundaries (11). In our previous study (12), measured pressure was compared with the data we used in this study, confirming the rationality of pressure boundary conditions.