This research cohort included 649 patients with intracranial aneurysms diagnosed and treated at the Department of Neurosurgery of our center from January 2016 to December 2020. This study was approved by the Ethics Review Committee of the First Affiliated Hospital of Zhejiang University School of Medicine. The whole cohort was randomly divided into a training set (n = 454) and a testing set (n = 195) by R language at a ratio of 7:3 prior to analysis. We retrospectively reviewed the medical records and imaging data in our database. The inclusion criteria were as follows: (1) saccular aneurysms confirmed on digital subtraction angiography (DSA), three-dimensional computed tomography angiography (CTA) or magnetic resonance angiography (MRA); (2) family members of patients who signed informed consent to cooperate with the clinical treatment procedures; (3) patients without surgical treatment in referral centers; and (4) age >18 years old. The exclusion criteria were as follows: (1) traumatic, infectious, fusiform, or dissecting aneurysms; (2) patients with moyamoya disease or vascular malformation; (3) absence of patients' important medical information; and (4) poor image quality or absence of important image records. The patient selection process is shown in Figure 1.

The patient's clinical variables were collected as follows: (1) The demographic characters included: gender and age. (2) Medical history included: hyperlipidemia, hypertension, diabetes mellitus, history of cerebrovascular disease, alcohol consumption, smoking, antiplatelet (chronic low-dose) and family history of SAH. (3) Aneurysm morphology included: maximum size of aneurysm (the largest distance within aneurysm sac) (Dhar et al., 2008), neck width of aneurysm, height of aneurysm (the maximum perpendicular distance of the dome from the neck plane) (Dhar et al., 2008), width of aneurysm (the maximum distance of dome perpendicular to perpendicular height) (Dhar et al., 2008), multiple aneurysms, location of aneurysm, bifurcation position and presence of secondary sacs. The locations of aneurysms in our research were divided into three categories according to the hazard ratio of aneurysm location in the UCAS study (Akio et al., 2012): (a) ICA, VA; (b) ACA, MCA, PCA,BA; (c) ACom, IC-PCom. (4) The morphological parameters included: aspect ratio (AR), bottleneck factor (BN) and mean arterial pressure-aneurysm neck ratio (MAPN). To obtain accurate and objective measurement results, the morphological characteristics of IAs in this study were measured from reconstructed 3D CTA or DSA. Without considering the patient information, two neurosurgeons independently evaluated the morphological characteristics before grouping; Any inconsistencies were resolved by the third chief neurosurgeon (with more than 10 years of experience). AR, BN, and MAPN were calculated by the ratio of aneurysm height to neck width, aneurysm width to neck width, and mean arterial pressure to neck width, respectively (Ryu et al., 2011). Mean arterial pressure was calculated from 1/3 systolic blood pressure (SBP) plus 2/3 diastolic blood pressure (DBP). The blood pressure value in this study was obtained by consulting the outpatient records or health check-up center records. The dome of aneurysm is defined as the farthest point to the aneurysm neck.

We exported the DICOMs files sliced from 3-D DSA (Philips) to the Mimics Medical software (v21, Materialize) for aneurysm model reconstruction. The procedures for the extraction of surface geometry data from Mimics, and subsequent volume grids were generated using Geomagics. According to the previous studies, boundary conditions of inlets significantly affects only the region close to the inlet, and differences in flow solution are minimal beyond two diameters distal to the inlet where the flow is fully developed. Since patient specific flow information were not available for the present study, steady flow stimulations were applied using CFX software program (version 15.0) (Ansys, Inc, Lebanon, NH) in our patient-specific models. In boundary condition settings, mean velocity of 0.27 m/s was implied for proximal ICA inlets, a static pressure of 10,000 Pa were implied for the distal outlets. The artery walls were set as rigid. Blood flow was modeled as an incompressible, constant, and Newtonian fluid, that described by the Navier-Stokes equations in 3D. The blood density was 1,060 kg/m3, and the blood dynamic viscosity was 0.004 kg/m-s (Perktold and Peter, 1989; Xiang et al., 2011). In this study, mesh was calculated in ICEM–CFD, Tetrahedral and wall prism elements consisting of ~2,000,000 meshes with the element size of 0.1 mm were created for each aneurysm model using the ICEM–CFD meshing tool.

The PHASES score (ranging from 0 to 22) was developed in a study based on Finnish, Japanese and Dutch populations to predict the risk of aneurysm rupture and is now commonly used in patient management (Greving et al., 2014). This score was composed of 6 parameters, including population, hypertension, age, aneurysm size, early SAH and aneurysm locations.

This score system derivate from the Unruptured Cerebral Aneurysm Study (UCAS) in Japan, including patients with unruptured cerebral aneurysmsenrolled between 2000 and 2004 at neurosurgical departments at tertiary care hospitals in Japan (Tominari et al., 2015). Different from the PHASES score, this score increases the morphological factors of aneurysms, risk factors include age, sex, hypertension, aneurysm size, aneurysm location and daughter sac of aneurysm.

A nomogram-risk model was generated based on the output variables processed by the binary logistic regression, which were initially selected and evaluated by univariate logistic regression. The discriminant performance of the model was measured by receiver operating characteristic (ROC) curves and the corresponding area under the curve (AUC). The applicability of the model was assessed by the Hosmer–Lemeshow test (P > 0.05 is considered a good fit), and the calibration diagram graphically illustrates the consistency between the predicted probability of rupture and the observed probability of rupture. In addition, the clinical net benefit of the model (a value of 0 indicates no benefit and a higher value indicates more benefit) was quantified, so as to demonstrate clinical effectiveness through decision curve analysis (DCA). R Studio software (version 4.2.0, Boston, MA, USA) for model generation, validation, and diagramming.

Data were analyzed with SPSS, version 23.0 (IBM, Armonk, New York). Continuous variables were reported as the mean ± standard deviation and compared between ruptured and unruptured outcomes using an unpaired T-test. Categorical variables were reported as a proportion and percentile and were analyzed using X² or Fisher's exact test, as appropriate. Univariate and multivariate logistic regression analyses were performed using ruptured as the outcome variable in the training cohort. Variables with a P-value ≤0.1 in univariate analysis were entered into binary logistic regression with stepwise backward selection.

The detailed processes of the selection and exclusion of the patients in the training cohort and testing cohort are shown in Figure 1. Finally, 454 patients were included in the training set, while 195 patients were included in the testing set.

In the training set, 192 (42.3%) patients were male, and 262 (57.7%) were female. The patients' ages ranged from 20 to 85, and ~12.3% of the patients were over 70 years old. There was no significant difference in age or gender between the rupture group and the unrupture group. The medical histories in the training set are summarized in Table 1. Diabetes mellitus, cerebrovascular disease, alcohol consumption, smoking and chronic history of low-dose antiplatelet were more common among those with ruptured intracranial aneurysms (P < 0.05).

In the testing set, 92 (47.2%) patients were male and 103 (52.3%) were female. Among these patients, the age range was 22–83 years, and ~15.9% of the patients were over 70 years old. There was no significant difference in age or gender between the rupture group and the unrupture group. The medical histories in the testing set are summarized in Table 1, which shows that diabetes mellitus, cerebrovascular disease, chronic history of low-dose antiplatelet therapy and family history of SAH were more common among those with ruptured intracranial aneurysms (P < 0.05).

The morphological features of the UIAs and ruptured IAs are shown in Table 1. Aneurysms were classified by maximum size: 442 were small (<7 mm), 116 were moderate (7–10 mm), 82 were large (10–20 mm) and 9 were giant (≥20 mm). Aneurysm size was significantly different between the ruptured and unruptured groups in the training set, but no significant differences were observed in the testing set. AR and BN also showed statistically significant differences between the ruptured group and the unruptured group in the training set, but such significant differences did not exist in the testing set, which may be caused by the small number of testing sets. There were statistically significant differences (P < 0.05) in neck width, MAPN, location of aneurysm, bifurcated aneurysm, and presence of secondary sacs between the ruptured and unruptured groups in both the training set and the testing set.

In Figure 2, the linear proportion relationship between MAPN and static pressure of intra-aneurysms was deduced by the Bernoulli equation. It shows that MAPN, a new parameter, can reflect the changes of blood pressure in the aneurysm cavity. The specific formula derivation process can be sawed in the Supplementary material. In the hemodynamic analysis of IAs, it was also found that MAPN was positively correlated with wall shear stress (WSS) and the pressure at the dome of aneurysm.

In the univariate analysis, the mean MAPN value of the rupture group was higher in both sets (P < 0.05). In Figure 3A, the AUC of the MAPN is 0.64, demonstrating that this new parameter has a certain diagnostic ability for aneurysm rupture. Its cutoff point value is −0.529 (0.534, 0.683). In Figure 3B, we compared the diagnostic ability of MAPN with AR and BN, and their AUC values were 0.64, 0.611 and 0.607, respectively, suggesting that MAPN is superior to AR and BN in the diagnosis of aneurysm rupture.

Thirteen variables (P < 0.05 in univariate analysis) were entered into multivariate logistic regression. Table 2 shows the diabetes mellitus (OR, 0.345; p = 0.025), cerebrovascular disease (OR, 0.290; p = 0.001), presence of secondary sacs (OR, 2.806; p < 0.001), BPN (OR, 1.057; p < 0.001), size of aneurysm and location of aneurysm are independent influencing factors for rupture of cerebral aneurysms (Table 2). The Hosmer–Lemeshow test reflects a satisfied degree of consistency between the predicted risk of the model and the actual risk (P = 0.695, Table 2). Significant differences were found in the subgroup analysis of diabetes, cerebrovascular disease and drug use, suggesting that there may be an interaction between these parameters (Supplementary material). Thus, diabetes and cerebrovascular disease were excluded from the construction of the final MAPN prediction model. As shown in Figure 4, the final MAPN prediction model included the presence of secondary sacs, size of aneurysm, location of aneurysm and MAPN.

The ROC curve and AUC value of each model in the training set and the testing set are shown in Figure 5. In the training set, the MAPN model showed the best performance, with an AUC value of 0.799 (95% CI, 0.756–0.840), and the AUC values of the UCAS score and the PHASES score were 0.763(95% CI, 0.719–0.807), and 0.741 (95% CI, 0.695–0.787), respectively. In the testing set, the MAPN model also performed well with an AUC value of 0.786 (95% CI, 0.721–0.851), and the AUC values of the UCAS score and the PHASES score were 0.755(95% CI, 0.688–0.822) and 0.750 (95% CI, 0.681–0.819), respectively. The calibration plot showed good overall agreement between the predicted risk and observed events. Decision curve analysis suggested that given any selected risk threshold, the MAPN model achieved more benefit than both the UCAS score and PHASES score. In addition, Table 3 also suggests that the MAPN model has higher sensitivity and accuracy in the diagnosis of aneurysm rupture.