Nomograms for assessing the rupture risk of anterior choroid artery aneurysms based on clinical, morphological, and hemodynamic features

Background and purpose A notable prevalence of subarachnoid hemorrhage is evident among patients with anterior choroidal artery aneurysms in clinical practice. To evaluate the risk of rupture in unruptured anterior choroidal artery aneurysms, we conducted a comprehensive analysis of risk factors and subsequently developed two nomograms. Methods A total of 120 cases of anterior choroidal artery aneurysms (66 unruptured and 54 ruptured) from 4 medical institutions were assessed utilizing computational fluid dynamics (CFD) and digital subtraction angiography (DSA). The training set, consisting of 98 aneurysms from 3 hospitals, was established, with an additional 22 cases from the fourth hospital forming the external validation set. Statistical differences between the two data sets were thoroughly compared. The significance of 9 clinical baseline characteristics, 11 aneurysm morphology parameters, and 4 hemodynamic parameters concerning aneurysm rupture was evaluated within the training set. Candidate selection for constructing the nomogram models involved regression analysis and variance inflation factors. Discrimination, calibration, and clinical utility of the models in both training and validation sets were assessed using area under curves (AUC), calibration plots, and decision curve analysis (DCA). The DeLong test, net reclassification index (NRI), and integrated discrimination improvement (IDI) were employed to compare the effectiveness of classification across models. Results Two nomogram models were ultimately constructed: model 1, incorporating clinical, morphological, and hemodynamic parameters (C + M + H), and model 2, relying primarily on clinical and morphological parameters (C + M). Multivariate analysis identified smoking, size ratio (SR), normalized wall shear stress (NWSS), and average oscillatory shear index (OSIave) as optimal candidates for model development. In the training set, model 1 (C + M + H) achieved an AUC of 0.795 (95% CI: 0.706 ~ 0.884), demonstrating a sensitivity of 95.6% and a specificity of 54.7%. Model 2 (C + M) had an AUC of 0.706 (95% CI: 0.604 ~ 0.808), with corresponding sensitivity and specificity of 82.4 and 50.3%, respectively. Similarly, AUCs for models 1 and 2 in the external validation set were calculated to be 0.709 and 0.674, respectively. Calibration plots illustrated a consistent correlation between model evaluations and real-world observations in both sets. DCA demonstrated that the model incorporating hemodynamic parameters offered higher clinical benefits. In the training set, NRI (0.224, p = 0.007), IDI (0.585, p = 0.002), and DeLong test (change = 0.089, p = 0.008) were all significant. In the external validation set, NRI, IDI, and DeLong test statistics were 0.624 (p = 0.063), 0.572 (p = 0.044), and 0.035 (p = 0.047), respectively. Conclusion Multidimensional nomograms have the potential to enhance risk assessment and patient-specific treatment of anterior choroidal artery aneurysms. Validated by an external cohort, the model incorporating clinical, morphological, and hemodynamic features may provide improved classification of rupture states.


Introduction
The occurrence of anterior choroidal artery (AChA) aneurysms is relatively low, constituting only 2-5% of all cerebral aneurysms (1).While the incidence of rupture in AChA aneurysms is elevated within the realm of medical care (2), the PHASES score scale (considering population, hypertension, age, size, prior subarachnoid hemorrhage, and location) indicated relatively lower scores for these small aneurysms (3)(4)(5).Furthermore, earlier research showed that the majority of ruptured intracranial aneurysms (IAs) exhibit a diameter of less than 7 mm (6), with approximately 35-47% of all IAs being small and ruptured (7,8).Given these findings, a conservative monitoring approach for predominantly small AChA aneurysms may potentially expose patients to aneurysmal subarachnoid hemorrhage (SAH).This may suggest that the simple, all-position assessment models do not apply to AChA aneurysms characterized by small size.Simultaneously, a precise evaluation of unruptured AChA aneurysms holds the potential for significant socioeconomic benefits, mitigating the costs and hazards associated with unnecessary interventions.
Moreover, both endovascular and surgical interventions for unruptured intracranial aneurysms (UIAs) entail a risk of postprocedural complications, encompassing ischemic events, hydrocephalus, and neurological deficits (9).Intensive therapy may not yield significant benefits for patients with unruptured IAs, especially those with a low probability of lesion rupture (10).Therefore, the timely identification of AChA aneurysms exhibiting an elevated risk of rupture, coupled with prompt intervention to forestall potential disastrous outcomes, assumes paramount importance in the realm of medical treatment.
To the best of our knowledge, AChA aneurysms have received limited consideration in existing aneurysm risk assessment models and scoring systems (11)(12)(13)(14)(15)(16).Furthermore, there is a paucity of documented research on risk factors and assessment models specifically tailored for AChA aneurysm rupture.In recent years, nomograms have gained widespread acceptance as a predictive method for IAs (3,13), meeting the criteria for integrated models and advancing personalized healthcare (17).In our pursuit of establishing patient-specific nomogram models for AChA aneurysms, our research group diligently explored rupture risk factors through the analysis of clinical, morphological, and hemodynamic parameters.Additionally, we sought to develop user-friendly and multidimensional nomograms that align with clinicians' needs for high efficiency and accuracy in estimating the probability of AChA aneurysm rupture.

Participants and study design
Our retrospective cohort study received approval from the ethical committee of the hospital; however, informed consent was waived.Before data collection, all patient information underwent anonymization.
We obtained cerebrovascular imaging and medical records of 120 consecutive patients with AChA aneurysms admitted to 4 medical units between May 2017 and November 2022.Based on their admission status, we classified the aneurysms as either ruptured or unruptured.Inclusion criteria were as follows: (1) patients diagnosed with an AChA aneurysm through emergency computer tomography angiography (CTA) followed by digital subtraction angiography (DSA); and (2) availability of complete clinical data and traceable medical history.Exclusion criteria included the following: (1) patients with subarachnoid hemorrhage (SAH) lasting over 24 h where vasospasm of parent vessels could not be ruled out; (2) individuals with dissecting, fusiform, infectious, traumatic, or multiple aneurysms; (3) patients whose Digital Imaging and Communications in Medicine (DICOM) data did not permit morphological measurements and hemodynamic calculations; and (4) AChA aneurysms with insufficient information and data.Ultimately, 98 AChA aneurysms (45 ruptured and 53 unruptured) from 3 hospitals contributed to the development of the nomograms, while an additional 22 cases (9 ruptured and 13 unruptured) from a fourth hospital were included for external validation.For more detailed information, refer to the flowchart (Figure 1).

Acquisition, reconstruction, and analyses of AChA aneurysm images
User-friendliness hinges on a commitment to openness and transparency throughout the entire process.In the image acquisition phase, original DSA images are procured from the Artis zee biplane angiographic system (VC14, Siemens, Munich, Germany) as 490 files in DICOM format.The procedure using MIMICS 21.0 software (Materialise NV, Leuven, Belgium) unfolds as follows: Data are imported via "New Project, " settings are adjusted through "Threshold" until blood vessels are distinctly displayed, the region of interest is selected in "Crop Mask" for 3D image reconstruction, and the resultant file is exported in STereoLithography (STL) format.AneuFlow™ software (V1.1.4.1, ArteryFlow Technology, Hangzhou, China) for measuring aneurysm morphology and hemodynamics encompasses three steps (18).First, the STL file is imported into the AneuFlow™ software, allowing doctors to obtain additional morphological parameters by manually identifying the aneurysm neck.The vascular model is segmented into two regions: the parent artery and the aneurysm.Second, the computational fluid dynamics (CFD) simulation module initiates hemodynamic analysis.The maximum mesh size is set at 0.16 mm with three layers of wall prism elements.The aneurysm model comprises 1.8-2.3 million tetrahedral elements post-meshing (19).An implicit unsteady solver with a firstorder upwind numerical scheme is employed.By resolving the Navier-Stokes governmental equations and assuming solid walls, AneuFlow™ software conducts laminar and incompressible blood flow simulations (density = 1,056 kg/m 3 and viscosity = 0.0035 poise).Pulsating velocity profiles from transcranial Doppler are imposed at the intake, and an open border with no dynamic pressure defines the outflow (20).Utilizing a time step of 0.001 s generates 800 solutions for 3 cardiac cycles.The last simulated cardiac cycle is utilized for post-processing hemodynamic parameters (4).Finally, morphological and hemodynamic outcomes are exported together.(BMI).Two clinical research coordinators meticulously acquired data from the hospital information system, ensuring its accuracy through verification by a neurovascular interventionalist.Importantly, all personnel involved remained blinded to patients' individual details.
Morphological parameters of aneurysms comprised the presence of a daughter sac, inflow angle, aspect ratio (AR), size ratio (SR), ellipticity index (EI), non-sphericity index (NSI), undulation index (UI), size, diameter of the parent vessel, surface area, and volume.An extensive description of morphological variables obtained for this study could be found in previous studies (21)(22)(23).
In this investigation, we meticulously recorded and computed four crucial hemodynamic parameters: normalized wall shear stress (NWSS), average oscillatory shear index (OSI ave ), low shear area (LSA), and relative residence time (RRT).Comprehensive insights into the calculation methods can be gleaned from the seminal works of Liu et al. ( 4) and Retarekar et al. (24).
The identification of the aneurysm neck was executed by two neurosurgeons, both uninformed about the patient's particulars.Any disparities in their assessments were expertly resolved through the intervention of a third neurosurgeon boasting two decades of experience in the neuro-interventional domain.

Statistical analysis
Continuous variables were summarized as either median (interquartile range) or mean ± standard deviation, while categorical data were expressed as percentages.Normality tests were conducted on the continuous variables within the training set.Subsequently, our team explored group differences utilizing the Student's t-test or Mann-Whitney U test for continuous variables and the chi-square test or Fisher's exact test for categorical data.Logistic regression models, encompassing both univariate and multivariate analyses, were executed to identify independent variables associated with AChA aneurysm rupture.A backward stepwise selection approach was employed, where univariate analysis parameters with a significance level of p < 0.2 were incorporated into the multivariate regression models.Following the exclusion of parameters exhibiting a variance inflation factor (VIF) exceeding 4.0, those with the minimum Akaike information criterion (AIC) were selected to formulate nomogram models.Additionally, additive and multiplicative interaction analyses were performed on these factors during model construction.Model 1 integrated clinical, morphological, and hemodynamic (C + M + H) characteristics, while Model 2 included solely clinical and morphological (C + M) variables.Homogeneity between the training and external validation sets was assessed with a significance threshold set at p = 0.05.
The discriminative efficacy of the nomograms and the external validation set was elucidated through the associated area under the curve (AUC) and the receiver operating characteristic curve (ROC).Calibration plots illustrated the congruence between the predicted rupture and the observed outcomes.Moreover, the clinical utility of the model was substantiated via decision curve analysis (DCA), quantifying the model's net benefit (higher values indicative of greater therapeutic efficacy) (25).Internal validation involved resampling with 1,000 bootstrap samples.The performance of model 1 was compared to that of model 2 in terms of AUC value, sensitivity, specificity, positive predictive value (PPV), negative predictive value (NPV), and accuracy.The DeLong test was employed to compare the AUC values of the two ROC curves.Additionally, integrated discrimination improvement (IDI) and net reclassification index (NRI) were computed to measure improvements in assessment and assess clinical utility.
A significance level of p < 0.05 (two-tailed) was deemed statistically significant in all conducted tests.Statistical analyses and graphical representations were conducted using R version 4.1.3. 1 Adherence to the TRIPOD guidelines was observed in this research (26).

Nomogram variable screening
Following univariate logistic regression analysis (p < 0.2), 16 variables were retained for further examination in the context of AChA aneurysm rupture assessment.These variables encompassed smoking, aneurysmal family history, the presence of a daughter sac, AR, SR, EI, NSI, UI, size, diameter of the parent vessel, surface area, volume,

Construction and performance of nomogram models
To assess the likelihood of rupture in AChA aneurysms, we developed two binary logistic regression models incorporating   2 provides a detailed visualization of both models using multidimensional nomograms.
Based on the observations in the training set, the external validation set revealed that model 1 (AUC = 0.709; 95% CI,  S3).The calibration plots for 2 models were generated based on 1,000 iterations of bootstrap sampling.The results presented in Figures 3B,C, 5 illustrate a significant alignment between the observed state of instability and the predicted risk of rupture evaluated through nomograms.Notably, the calibration plots reveal a higher level of consistency in the external validation set than in the training set.Additionally, Figures 3D, 6 display DCA curves, indicating that model 1 (C + M + H) exhibited superior performance and was deemed suitable for guiding more advantageous clinical decisions.

Discussion
Rupture risk assessment of AChA aneurysms plays a pivotal role in the medical management of those yet to rupture.Through a training set encompassing 98 cases, we identified 4 contributors (smoking, SR, NWSS, and OSI ave ) for constructing nomogram models.Subsequently, two models were devised and juxtaposed to discern the rupture probability of AChA aneurysms.In this study, clinical features independent of morphological and hemodynamic factors were identified as significant determinants of aneurysm rupture (27).Specifically, smoking emerged as a distinct risk factor for AChA aneurysm rupture.Notably, Juvela (28) integrated smoking into the PHASES rating scale, enhancing its efficacy in assessing long-term rupture risks in UIAs.Consistent with our findings, a case-control analysis of 4,701 individuals with 6,411 aneurysms demonstrated that smokers faced a heightened risk of rupture compared to non-smokers (29).Additionally, while hypertension (30), earlier SAH (11), and familial history of aneurysm (31) were commonly recognized as risk factors for UIAs, our study did   not find these variables to be statistically significant, potentially due to the limitations of our sample size.Notably, morphological parameters of aneurysms have been empirically linked to their propensity for rupture (32).SR encompasses the combined influence of the aneurysm and adjacent arteries, denoting the ratio of aneurysmal height to the average diameter of the parent artery (21).A substantial cohort, comprising 854 ruptured aneurysms and 180 UIAs, divulged that SR, rather than aneurysmal size, plays a pivotal role in predicting rupture status, especially in small aneurysms (<5 mm) (33).Furthermore, the investigations by Xiang et al. (34) and Yuan et al. (35) supported our findings, revealing a robust correlation between high SR and aneurysmal rupture.Interestingly, previous studies observed disparate cutoff values for SR, potentially attributable to variations in study design, particularly single-site methodologies.Our study evidenced that the ruptured group exhibited higher values for AR, EI, NSI, UI, size, and the presence of a daughter sac than the unruptured group, aligning with previous research (32).Despite SR being the sole morphological feature integrated into our models, it does not negate the significance of the seven other contributors in the rupture of AChA aneurysms.
The morphology and hemodynamics of aneurysms are intricately connected, with poor morphology exacerbating the process of aneurysmal growth and rupture by influencing hemodynamics (34).The impact of wall shear stress (WSS) on aneurysm growth and rupture remains a subject of debate.In a retrospective analysis of 210 aneurysms, it was suggested that ruptured aneurysms exhibit an increased WSS (36).In contrast, Xiang et al.     4) categorized the rupture risk concerning the stability of IAs in the anterior circulation.The C-indices for the models (C + M + H), (C + M), and PHASES scores were 0.94, 0.89, and 0.68, respectively.Our current investigation identified similar risk factors as previous studies but exhibited variable efficacy, potentially attributable to the exclusive focus of our models on AChA aneurysms.
Machine learning has played a pivotal role in the extensive identification and assessment of rupture risk in IAs.Through a comprehensive analysis of various algorithms, Ou et al. (14) and Xiong et al. (15) have substantiated that the predictive accuracy of machine learning significantly surpasses that of logistic regression models and scoring systems.Conversely, a multicenter study conducted in China revealed that traditional logistic regression is not inferior to machine learning algorithms in multidimensional models for predicting the rupture status of unruptured IAs (42).Therefore, it is essential to undertake a comparative analysis of several models for AChA aneurysms and carefully select the optimal model for subsequent external validation.This approach is indispensable for fostering continual improvement in predicting the rupture risk of AChA aneurysms in the future.

Limitations
In conducting this preliminary exploratory study on the assessment of AChA aneurysm risk, several limitations persist.First, the study is retrospective, and future endeavors should involve the advancement of predictive models through a multicenter prospective cohort to enable personalized evaluation of the rupture risk associated with AChA aneurysms.Second, the occurrence of instantaneous morphological and hemodynamic changes before aneurysm rupture poses a formidable challenge in capturing these changes at their pre-ruptured state in clinical practice.Additionally, a previous study indicated that morphological changes before and after the rupture of the majority of IAs were not statistically significant (43).Third, the absence of patient-specific data for CFD simulation with the software may hinder the widespread application of assessment models in realworld scenarios.Fourth, the small sample size could introduce selection bias and result in low specificity.Although there were 98 cases in the internal training set and 22 in the external test set, representing considerable numbers for AChA aneurysms, the sample sizes remained statistically small.Finally, the employed statistical methodologies lacked novelty, and machine learning algorithms were not incorporated.Collaborative efforts with artificial intelligence engineers are underway to develop interpretable algorithms suitable for application to small datasets.

Conclusion
We have developed and validated two assessment models to evaluate the risk of rupture in AChA aneurysms.Model 1 (C + M + H) exhibited superior accuracy, calibration, and clinical utility, whereas model 2 (C + M) possessed the advantage of time efficiency.These nomogram models represent valuable tools for conducting personalized risk assessments of unruptured AChA aneurysms.

FIGURE 1 Flowchart
FIGURE 1 Flowchart of study design.AChA aneurysms enrolled from May 2017 to November 2022 established both the training and validation cohorts, which were adopted to develop the nomogram models; 98 and 22 cases were adopted for nomogram construction and external testing.Discrimination, calibration, and clinical utility were illustrated by ROC, calibration plots, and DCA, respectively.Moreover, we performed the DeLong test, NRI, and IDI to compare the performance of two nomogram models.AChA, anterior choroid artery; CTA, computed tomographic angiography; DSA, digital subtraction angiography; SAH, subarachnoid hemorrhage; DICOM, digital imaging and communications in medicine; NRI, net reclassification index; IDI, integrated discrimination improvement; C + M + H, clinical, morphological, and hemodynamic features; C + M, clinical and morphological features, SR, size ratio; NWSS, normalized wall shear stress; OSI ave , average oscillatory shear index.

Figure
Model 1 (C + M + H) showcased superior performance in both training and validation sets, excelling in discrimination, calibration, and clinical applicability in contrast to model 2 (C + M).The clinical and morphological parameters in model 2 (C + M) were conveniently accessible, enabling interventionalists to swiftly make initial assessments.The precision of model 1 (C + M + H) and the accessibility of model 2(C + M) might yield distinct advantages.

FIGURE 2
FIGURE 2Nomograms for AChA aneurysms regarding clinical, morphological, and hemodynamic candidates.Model 1 (A) was constructed by four independent factors: smoking, SR, NWSS, and OSI ave .Model 2 (B) was developed by two independent factors: smoking and SR.AChA, anterior choroid artery; SR, size ratio; NWSS, normalized wall shear stress; OSI ave , average oscillatory shear index.

FIGURE 3 ROC
FIGURE 3 ROC curves, calibration plots, DCA for model 1 (C + M + H) and model 2 (C + M) in the training set.In models 1 (C + M + H) and 2 (C + M), the AUC values were 0.795 (95% CI, 0.706 ~ 0.884) and 0.706 (95% CI, 0.604 ~ 0.808), respectively.(A) The horizontal and vertical axes illustrate, respectively, the evaluated and observed probabilities of aneurysmal rupture.The dashed lines reveal an ideal model's flawless prediction.The green lines show inner validation by 1,000 bootstrap resampling.The red lines demonstrate the performance of the nomogram model.(B,C) The horizontal and vertical axes represent the threshold for determining great risk and clinical net benefit, respectively.The blue and red lines represent the net benefits of Models 1 (C + M + H) and 2 (C + M), respectively.At Y = 0, the horizontal line represents no treatment, while the gray curve means thorough intervention.(D) ROC, receiver operator characteristic; DCA, decision curve analysis; C + M + H, clinical, morphological, and hemodynamic features; C + M, clinical and morphological features; AUC, area under curve; CI, confidence interval.

FIGURE 5
FIGURE 5 Calibration curves of model 1 (C + M + H) and model 2 (C + M) in the validation set.The calibration curve describes the calibration of the external validation set.The x-axis and y-axis represent the model estimated and actual values, respectively.The diagonal gray lines represent model-perfect assessments.The level of accuracy increases as the black line approaches the gray line.C + M + H, clinical, morphological, and hemodynamic features; C + M, clinical and morphological features.

FIGURE 6 DCA
FIGURE 6 DCA curves for model 1 (C + M + H) and model 2 (C + M) in the validation set.The green lines represent the net benefits of models 1 (C + M + H) and 2 (C + M) in the validation set.The horizontal line (Y = 0) and the gray curve indicate no treatment (treat-none) and radical intervention (treat-all), respectively.DCA, decision curve analysis; C + M + H, clinical, morphological, and hemodynamic features; C + M, clinical and morphological features.

TABLE 1
Clinical, morphological, and hemodynamic features of AChA aneurysms in the training set.

TABLE 2
Univariate and multivariate regression analyses of the training set.
above-presented results indicate that model 1, incorporating hemodynamic features, may effectively discern the rupture status of AChA aneurysms compared to model 2. Additionally, DCA curves reveal that model 1 (C + M + H) yields greater net benefits than model 2 (C + M) under both treat-all and treat-none strategies (Figures (40)ave emerges as another pertinent hemodynamic parameter in aneurysm rupture dynamics (34).Despite our findings indicating non-statistical significance, OSI ave found its place in the final models based on AIC minimum criteria.In a study focusing on PCoA aneurysms, OSIave demonstrated higher values in ruptured aneurysms than in unruptured counterparts, albeit lacking statistical significance (p > 0.05)(40).The patterns observed in AChA aneurysms mirror those in PCoA.Given our constrained sample size, leveraging extensive datasets for robust validation remains imperative in future investigations.Similar to our findings, a retrospective study involving 119 IAs found that high SR, low WSS, and high OSI ave were risk factors for the rupture of IAs.The derived regression equations yielded an AUC of 0.89 for the comprehensive model, incorporating hemodynamic parameters, marking the highest predictive accuracy (41).Moreover,Liu et al. (