Case presentations
Two men aged 60 s and 70 s years (Case 1 and 2, respectively) underwent a medical check-up of the brain, and unruptured intracranial aneurysms were identified. The aneurysm in Case 1 was 3.5 mm in diameter and located on the middle cerebral artery (MCA) bifurcation. For Case 2, the aneurysm was 3.8 mm in diameter and located on the anterior communicating artery (AcomA) with a dominant left A1 segment of the anterior cerebral artery. Due to the aneurysms being small and asymptomatic, they were elected to undergo follow-up with annual three-dimensional (3D) computed tomographic angiography (CTA). During the follow-up period, the aneurysms in Cases 1 and 2 had de novo bleb formation 1 and 2 years later, respectively. The bleb is defined as a small, definite protrusion on the aneurysm surface. This study was approved by the institutional review board, and all patients provided informed consent prior to the study.
Aneurysm modeling
3D CTA was performed using a multislice CT scan system (Aquilion multi 16, Toshiba Medical Systems, Otawara, Japan). Contrast-enhanced CTA utilized the following scan parameters: 0.75-s rotation; scanning pitch, 0.69; 120 kVp, 300 mA; and voxel size, 0.21 × 0.21 × 0.50 mm. An iodinated contrast agent (80–100 mL; Omnipark 300 Daiichi-Sankyo, Tokyo, Japan) was injected at a rate of 3.5 ml/s without saline solution. Following the contrast agent reaching the internal carotid artery, approximately 15 s after injection, the imaging commenced. Blood vessels were extracted and converted into standard triangulated surfaces using Amira version 5.6 software (Maxnet Co, Ltd, Tokyo, Japan). These 3D images were imported into ICEM CFD version 16.2 software (ANSYS Inc., Canonsburg, PA, USA) to assess vessel structure. For each aneurysm, the actual prebleb and postbleb models were created from 3D imaging data of aneurysms before and after de novo bleb formation, respectively. The virtual prebleb model was created by manually removing the bleb to smooth the wall surface of the aneurysmal dome (Fig. 1) on the basis of the consensus of three neurosurgeons (KM, KF, and IN).
Numerical simulations
The fluid domains of blood vessel models were created using the ANSYS ICEM CFD software, to create meshes comprising tetrahedrons and seven prism element layers near the surface wall in the boundary [11]. A 75-mm passage was added to the proximal plane of the vessel structure to generate a sufficient the inlet length [12]. The density and dynamic viscosity of blood were defined as 1100 kg/m3 and 0.0036 Pa, respectively, and were modeled as a Newtonian fluid. The wall of the blood vessel was defined as a rigid no-slip boundary condition. ANSYS CFX version 16.2 (ANSYS Inc.) was used to solve the pulsatile-flow governing Navier–Stokes equations [13,14,15]. The flow-rate waveform at the inlet was set to be 1.80 s, according to a report by Ford et al. [16]. Zero pressure was imposed at the outlets, and the boundary conditions applied to all models were the same [17]. The interval time for calculation was set to 0.005 s. Two cardiac cycles were simulated, and the results from the peak systole of the second cycle were used in the analysis [18].
Data analysis
The results of CFD analysis were visualized so that the aneurysm wall information and blood flow state in the aneurysm could be evaluated. The structure of the major intra-arterial flows was determined using flow velocity maps drawn on the cutting surface. Contour maps of hemodynamic parameters, including normalized pressure, normalized WSS, time-averaged wall shear stress (TAWSS) and OSI, and WSS vectors, were exhibited on the aneurysmal wall in vessel models. The pressure and WSS were normalized to the parent vessel values, generated from the same CFD simulation, to minimize dependency on the inlet conditions. For normalization, each value was divided by the average value on the inlet plane, 1 mm proximal to the aneurysm. The normalized analysis values were calculated using the following equation:
$$\mathrm{Normalized}\;\mathrm{Pressure}=\frac{\mathrm{Pressure}}{\mathrm{PressureAVE}(\mathrm{inlet})},\;\mathrm{normalized}\;\mathrm{WSS}=\frac{\mathrm{WSS}}{\mathrm{WSSAVE}(\mathrm{inlet})}$$
In this equation, PressureAVE (inlet) and WSSAVE (inlet) indicate the average pressure and the average WSS at the inlet plane, respectively. The relationship between the de novo bleb formation area and contour maps of the hemodynamic parameters and WSS vectors on the aneurysm wall were visually evaluated. In the CFD analysis of the actual and virtual prebleb models, we visually characterized hemodynamic features of the de novo bleb formation area by comparing them with those in the area without de novo bleb formation. Contour maps of the hemodynamic parameters and WSS vectors on the aneurysm wall were visually evaluated. According to the bleb location in the postbleb model, the de novo bleb formation area in the actual prebleb model was determined based on the consensus of three neurosurgeons (KM, KF, and IN).
Using the ANSYS CFX function of the point cloud, we evenly distributed points with a 0.5-mm distance on the surface of the whole aneurysm of the actual prebleb model (Fig. 2). Consequently, the number of distributed points was 146 (11 points in the de novo bleb formation area and 135 in the area without de novo bleb formation) in Case 1 (Fig. 2a) and 152 (8 points in the de novo bleb formation area and 135 in the area without de novo bleb formation) in Case 2 (Fig. 2b). Hemodynamic parameters were measured at the center of a boll mark which was the symbol of the distributed points (Fig. 2). The centers of divergent WSS vectors were 2 (1 in each area with and without de novo bleb formation) in both Cases 1 and 2. We statistically compared the hemodynamic values and the number of centers of divergent WSS vectors at points in the areas with and without de novo bleb formation.
Statistical analysis
Continuous data were reported as mean ± standard deviation for continuous variables. The Mann–Whitney U test and Fisher’ s exact test were used to analyze parameters, as appropriate. Statistical significance was indicated when p < 0.05. Statistical analysis was performed using SPSS (IBM SPSS Statistics 24, Chicago, IL, USA).