## 2 Materials and Methods
### Size Variation  
Since there is no definitive method to predict aneurysm growth due to the many factors that can affect the growing process, in this study, we used a method found in the literature. The employed algorithm was an adaptation of that described by [PERSON] in previously cited work. That algorithm was modified for use with T-spline bodies in Autodesk Fusion 360 and to decrease those ruptured aneurysms. Instead of using offsets, as was performed in the original procedure, here, for the scaling process, a scale factor \(s\) was used to expand the aneurysm parallel to its neck plane. \(s\) is defined as the ratio between equivalent aneurysm diameters after (\(D_{f}\)) and before (\(D_{i}\)) scaling:  
\[D_{f}/D_{i}=s \tag{1}\]  
It was assumed that the contours in which the aneurysm was sectioned were similar to the circumference. Accordingly, the following formula was used:  
\[D_{f}\approx D_{i}+2\Delta \tag{2}\]  
where the approximation is taken as equality. \(\Delta\) is the offset used by [PERSON] et al., i.e., \(\Delta=(\alpha-1)\). Then, the previous expression can be written as \(D_{f}=D_{i}+2(\alpha-1)\), and \(s\) can be defined as follows:  
\[s=(2\alpha-1) \tag{3}\]  
Expression (3) was used to show the growth of unruptured aneurysms. For ruptured aneurysms, \(s^{\prime}\) was used instead, defined as \(s^{\prime}=1/s\). The main steps of the algorithm are listed below:  
1. From the original geometry, the aneurysm was extracted to convert its main faces into a T-spline body. The neck plane was visually identified, and a point was placed at its center, through which a perpendicular axis \(V\) passed. 2. A factor \(\alpha_{max}=1.26\) was used for all the cases. As in the original algorithm, there is an \(\alpha\) parameter that begins at 0 when \(V=0\) and linearly varies up to \(\alpha_{max}\) for \(V>V_{max}/3\). \(V_{max}\) is the distance between the point at the center of the neck and the highest point of the aneurysm dome. The height of each contour on the T-spline body, approximately parallel to the neck plane, was measured and named \(V_{c}\). 3. Each contour was moved upwards for unruptured aneurysms and downwards for ruptured aneurysms in the quantity \(V_{c}\) (\(\alpha-1\)). Additionally, each contour was scaled with the factor \(s\) or \(s^{\prime}\) depending on the rupture status of the aneurysm, parallel to the neck plane. The moving and scaling processes were repeated for each contour line on the body. 4. When the process was completed, the T-spline body was converted into a surface. The top zone of the aneurysm was closed following the curvature of the surrounding faces, and the zone at the bottom of the aneurysm was closed with another surface. Then, the created surface bodies were joined and converted into a solid. Finally, the resultant scaled aneurysm was joined back to the artery. For lateral aneurysms only, a fillet was created on the neck to form an organic transition between the artery and the aneurysm. An example of the main steps followed is shown in Figure 2, where the algorithm is applied to UG-2. Since for unruptured geometries, neither the size at which the aneurysm would rupture nor how the structural and fluid parameters would change were known before performing the simulations, two larger variations were created. These are shown for both original geometries in Figure 3. In (a), size I geometries are shown, while in (b) and (c), sizes II and III are also shown. Here, and for the ruptured geometries, a lower number indicates a smaller aneurysm size. The ruptured geometry variations can be seen in Figure 4, where (a) is size IV, and (b), (c), and (d) are sizes III, II, and I. The algorithm was applied beginning from geometries (a) and (b) to obtain (b) and (c), respectively, whereas (d), which represents a recently initiated  
Figure 3: Unruptured geometries of sizes (**a.1,a.2**) I, (**b.1,b.2**) II, and (**c.1,c.2**) III.