Article Text

Original research
Geometric uncertainty in intracranial aneurysm rupture status discrimination: a two-site retrospective study
  1. Florian Hellmeier1,
  2. Jan Brüning1,
  3. Philipp Berg2,3,
  4. Sylvia Saalfeld3,4,
  5. Andreas Spuler5,
  6. Ibrahim Erol Sandalcioglu6,
  7. Oliver Beuing7,
  8. Naomi Larsen8,
  9. Jens Schaller1,
  10. Leonid Goubergrits1,9
  1. 1Institute of Computer-Assisted Cardiovascular Medicine, Charité – Universitätsmedizin Berlin, Berlin, Germany
  2. 2Laboratory of Fluid Dynamics and Technical Flows, University of Magdeburg, Magdeburg, Germany
  3. 3Research Campus STIMULATE, University of Magdeburg, Magdeburg, Germany
  4. 4Department of Simulation and Graphics, University of Magdeburg, Magdeburg, Germany
  5. 5Helios Klinikum Berlin-Buch, Berlin, Germany
  6. 6Department of Neurosurgery, University Hospital Magdeburg, Magdeburg, Germany
  7. 7Department of Radiology, AMEOS Hospital Bernburg, Bernburg, Germany
  8. 8Department of Radiology and Neuroradiology, University Medical Center Schleswig-Holstein (UKSH), Kiel, Germany
  9. 9Einstein Center Digital Future, Berlin, Germany
  1. Correspondence to Dr Jan Brüning; jan.bruening{at}


Objectives Assessing the risk associated with unruptured intracranial aneurysms (IAs) is essential in clinical decision making. Several geometric risk parameters have been proposed for this purpose. However, performance of these parameters has been inconsistent. This study evaluates the performance and robustness of geometric risk parameters on two datasets and compare it to the uncertainty inherent in assessing these parameters and quantifies interparameter correlations.

Methods Two datasets containing 244 ruptured and unruptured IA geometries from 178 patients were retrospectively analysed. IAs were stratified by anatomical region, based on the PHASES score locations. 37 geometric risk parameters representing four groups (size, neck, non-dimensional, and curvature parameters) were assessed. Analysis included standardised absolute group differences (SADs) between ruptured and unruptured IAs, ratios of SAD to median relative uncertainty (MRU) associated with the parameters, and interparameter correlation.

Results The ratio of SAD to MRU was lower for higher dimensional size parameters (ie, areas and volumes) than for one-dimensional size parameters. Non-dimensional size parameters performed comparatively well with regard to SAD and MRU. SAD was higher in the posterior anatomical region. Correlation of parameters was strongest within parameter (sub)groups and between size and curvature parameters, while anatomical region did not strongly affect correlation patterns.

Conclusion Non-dimensional parameters and few parameters from other groups were comparatively robust, suggesting that they might generalise better to other datasets. The data on discriminative performance and interparameter correlations presented in this study may aid in developing and choosing robust geometric parameters for use in rupture risk models.

  • neurology
  • neuroradiology
  • neurosurgery

Data availability statement

All data relevant to the study are included in the article or uploaded as supplementary information.

This is an open access article distributed in accordance with the Creative Commons Attribution Non Commercial (CC BY-NC 4.0) license, which permits others to distribute, remix, adapt, build upon this work non-commercially, and license their derivative works on different terms, provided the original work is properly cited, appropriate credit is given, any changes made indicated, and the use is non-commercial. See:

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Strengths and limitations of this study

  • This study provides location-specific estimates of the discriminative ability of a large set of geometric parameters for intracranial aneurysm rupture status assessment, while also considering uncertainty.

  • The analysis was performed on two independent datasets to assess robustness of the findings.

  • Even though the relative uncertainty in acquisition of each geometric risk parameter was evaluated based on more than 20 individual segmentations performed during the Multiple Aneurysms Anatomy Challenge, this evaluation was only performed on five aneurysms in total.


A relevant part of the general population harbours one or more unruptured intracranial aneurysms (IAs), with the overall prevalence estimated around 3%.1 While most IAs do not rupture,2 the question of whether and when to treat them remains relevant due to the poor prognosis of ruptured IAs3 4 as well as the risk of intervention.3 5 Current American Heart Association/American Stroke Association guidelines list several modifiable and non-modifiable risk factors for IA growth and/or rupture, including IA location, growth rate, morphology, smoking status, alcohol consumption, hypertension, age, sex, previous IA, and family history.6 Attempts have been made to develop scoring systems to quantify rupture risk, growth risk, and/or support treatment decisions; these include the PHASES score by Greving et al,7 the UIATS by Etminan et al8, and the ELAPSS score by Backes et al.9 All three of these scores are based on clinically available data and all include geometric rupture risk parameters: IA size in case of the PHASES score,7 surface irregularity, size ratio, as well as aspect ratio in case of the UIATS8, and IA size as well as surface irregularity for the ELAPSS score.9 While these metrics were designed to support clinical decision making, performance on clinical data has been mixed,10–12 and improvements, particularly for patients harbouring multiple IAs, are desired by clinicians.13

The aim of this paper is to assess the ability of a broad number of proposed geometric risk parameters to differentiate between unruptured and ruptured IAs while also comparing their discriminative ability relative to the uncertainty encountered in determining them. Any acquisition of patient-specific IA geometries and subsequent use of these geometries to derive geometric risk parameters is affected by a number of uncertainty-introducing factors. These include the medical imaging acquisition itself, which is followed by image data preprocessing, segmentation, geometry reconstruction including postprocessing (eg, smoothing, checking of topology), and finally calculation of the geometric risk parameters. All these processing steps are associated with some errors, resulting in uncertainty, which negatively affects the ability of parameters to discriminate IA rupture status. Discrimination of rupture status on an individual IA level is, however, necessary if these parameters are to support the clinical decision-making process, including any decisions regarding treatment modalities. Previous studies found high variability in the uncertainty of different geometric risk parameters as well as differences in their ability to differentiate between ruptured and unruptured IAs.14–16 Furthermore, for geometric risk parameters with multiple alternative definitions, the specific implementation can affect the discriminative performance of the parameter itself and any derived parameters, as demonstrated by Lauric et al for parameters incorporating IA and neck size.17

The current study was performed to facilitate optimal selection of geometric rupture risk parameters by identifying geometric parameters, which are good discriminators while also exhibiting low uncertainty. The analysis is performed on two datasets processed by different research groups and is differentiated by anatomical region, in order to assess how the rupture status discrimination of the geometric parameters is affected by geometry processing as well as anatomical location. Additionally, correlation of the geometric risk parameters with each other is assessed.


Medical imaging data

IA geometries were retrospectively reconstructed and segmented from three-dimensional (3D) rotational angiography data acquired for routine clinical indications. Data were collected consecutively. The inclusion criteria of the datasets were imaging modality and the corresponding acquisition resolution. Cases with considerable segmentation artefacts such as close vessels that appear to be merged or holes in the segmented lumen were rejected from the analysis. 142 IAs were acquired in the Helios Klinikum Berlin-Buch (Berlin, Germany), 38 in KRH Klinikum Nordstadt (Hanover, Germany), 23 in the University Medical Center Schleswig-Holstein (UKSH) (Kiel, Germany) and 41 in the University Hospital Magdeburg (Magdeburg, Germany). Processing of the imaging data, including segmentation, was performed at two sites: Berlin, which processed 142 IAs from Helios Klinikum Berlin-Buch (dataset 1), and Magdeburg, which processed 102 IAs from KRH Klinikum Nordstadt, UKSH and University Hospital Magdeburg (dataset 2). Overall, 244 IAs from 178 patients were included, from which geometric risk parameters were subsequently calculated. Based on the PHASES score,7 aneurysm location was classified into four anatomical regions: internal carotid artery (ICA), middle cerebral artery (MCA), anterior region (all vessels anterior of the ICA/MCA) and posterior region (all vessels posterior of the ICA/MCA). The distribution of the individual IA locations and their assignment to the four anatomical regions are shown in table 1.

Table 1

Frequency and rupture status of individual IA locations by dataset

Geometric risk parameters

Historically, several geometric parameters for IA rupture risk assessment have been proposed. In order to have access to information on parameter uncertainty, the parameters chosen for this study were limited to a subset of the parameters reported in Goubergrits et al,14 a parameter uncertainty study performed on segmentation data obtained during the Multiple Aneurysms AnaTomy Challenge (MATCH) 2018.18 The major outcome of this study was the median relative uncertainty (MRU) of geometric parameters. Briefly, five aneurysms were segmented and reconstructed by 26 international research groups, which participated in the MATCH challenge. These segmentations were used to calculate the median and the 68.3% range between the 84.13th and the 15.87th percentile of all selected geometric parameters for each of the five aneurysms. The uncertainty range was selected with respect to the range of ±1 SD for normally distributed data reported in other studies. The uncertainty was defined as the uncertainty range divided by the median value and calculated for each geometric parameter. Finally, the average of all five aneurysms was calculated to define the MRU. For a detailed description of the parameters and the rationale for choosing the parameters, the interested reader is referred to Goubergrits et al.14 Briefly, most of the proposed geometric parameters describe aneurysm and/or aneurysmal neck size or shape or irregularity. These parameters were previously proposed as predictors for rupture risk. Table 2 lists the geometric parameters, their abbreviations and MRU values, as well as their respective references.

Table 2

List of the investigated geometric parameters, their descriptions, and median relative uncertainties (MRUs)

Since the diameter of the parent vessel was not available for all IAs studied, size ratio could not be calculated and was excluded. Furthermore, UI and convexity ratio (CR) as well as NSI and isoperimetric ratio (IPR) are directly related through Embedded Image and Embedded Image, respectively. CR and IPR were therefore not included in the analysis, in order to avoid redundancy. Geometric risk parameters were calculated from the IA geometries using MATLAB (version R2017b, MathWorks, Natick, USA), Python (version 3.7.1, Python Software Foundation, Delaware, USA) and ZIBAmira (version 2015.28, Zuse Institute Berlin, Berlin, Germany). The individual parameter values, IA location, and rupture status for each IA in this study, as well as the exact values of the interparameter correlation coefficients are provided as online supplemental file 1, online supplemental file 2 respectively.

Statistical analysis

Since most of the geometric risk parameters were non-normally distributed, as assessed by Q–Q plots and Shapiro-Wilk tests, the median was used to quantify central tendency and interquartile range (IQR) was used to quantify dispersion. Correlations were quantified using Pearson’s r with correlations Embedded Image referred to as strong, while those with Embedded Image and Embedded Image referred to as moderate and weak, respectively. Statistical analysis was performed using SPSS (version, IBM, Armonk, USA) and MATLAB.

The discriminative ability of the individual parameters was assessed by standardising the absolute difference between the medians of the ruptured and unruptured IAs with the weighted arithmetic mean of the IQRs of the two groups. This measure of effect size will be referred to as the standardised absolute group difference (SAD). Furthermore, the ratio of the SAD to the median relative uncertainty (MRU), a measure of the uncertainty associated with parameter calculation, from Goubergrits et al14 was calculated for all parameters and will be referred to as the group difference–uncertainty ratio (DUR). The equations for SAD and DUR are thus Embedded Image and Embedded Image, where Embedded Image, Embedded Image, and Embedded Image are the sample sizes, median values, and IQRs of the geometric parameters evaluated for ruptured (subscript r) and unruptured (subscript u) samples, while Embedded Image is the median relative uncertainty from Goubergrits et al,14 which is also listed in table 2. SAD and DUR may take any value ≥0 with higher values indicating stronger discriminative ability and a better ratio of discriminative ability to uncertainty, respectively. SAD and DUR values of zero would indicate no discriminative ability and the worst possible ratio of discriminative ability to uncertainty, respectively. Additionally, the correlation coefficients between the parameters were calculated. Analysis of SAD and DUR as well as the correlation coefficients was performed individually for each anatomical region and each dataset.

Patient and public involvement

Due to the purely retrospective manner of this study, no involvement of patients or the general public was considered.


Figure 1 shows SAD for all geometric risk parameters by anatomical region and dataset. Considering both datasets, the following parameters achieved the comparatively highest SAD for each anatomical region: curvature (HMC, MLN, HGC, GLN) and non-dimensional (AR, eAR, AVSV, AASA) parameters in the anterior region, curvature (HMC, HGC) and non-dimensional (NSI, AASA, EI) parameters in the ICA, non-dimensional (AR, eAR, BL, AVSV, AASA) parameters in the MCA, and size (H, Lmax, A, AMBS) and curvature (MSD, absGAA, GSD) parameters in the posterior region. Compared with the other anatomical regions, SAD was higher in the posterior region, and more parameters exhibited relatively high SAD. Looking at all anatomical regions combined, curvature (HMC, MLN, absGAA, HGC, GLN) and non-dimensional (AR, eAR, AVSV, AASA) parameters as well as one neck (Dneck,min) and one size (Hb) parameter show comparatively high SAD in both datasets. Furthermore, the differences between the two datasets become less pronounced when combining all anatomical regions. Moreover, this combined evaluation resulted in SAD being higher for the size parameters in site 2 compared with site 1. Here, it is worthwhile to note that the SAD of this combined assessment is not the average of the SAD of all four region-specific evaluations. Thus, pooling for some parameters can result in the absolute difference between the ruptured and unruptured groups to be close to zero, which results in SAD values close to zero as observed for the one-dimensional size parameters of the site 1 dataset.

Figure 1

Standardised absolute group difference (SAD) for each anatomical region and dataset.

Figure 2 shows DUR for all geometric risk parameters by anatomical region and dataset. Considering both datasets, the following parameters achieved the comparatively highest DUR for each anatomical region: non-dimensional (AASA, EI) and one curvature (MLN) parameter in the anterior region, non-dimensional (EI, AASA, NSI) parameters in the ICA, non-dimensional (AASA, EI) parameters in the MCA, and size (H, Lmax, Hmax, A), curvature (MAA, absMAA), and one non-dimensional (EI) parameter in the posterior region. Similar to SAD, DUR in the posterior region was overall higher and more parameters exhibited relatively high DUR, compared with the other anatomical regions. Looking at all anatomical regions combined, non-dimensional (NSI, AVSV, AASA, EI) and curvature (absMAA, MLN) parameters show comparatively high DUR in both datasets. As for SAD, the differences between the two datasets are less pronounced when looking at all anatomical regions combined.

Figure 2

Group difference–uncertainty ratio (DUR) for each anatomical region and dataset. ICA, internal carotid artery; MCA, middle cerebral artery.

Figures 3 and 4 show correlation coefficients between the geometric risk parameters by anatomical region for both datasets. The following general features are present in most data correlation plots: The size parameters (H, Lmax, Hmax, Dmax, Hb, A, ACH, AMBS, Aclosed, V, VCH, VMBS) are generally strongly correlated with each other. Similarly, the neck parameters (Dneck,min, Dneck,max, Pneck, Dneck,equiv, Aneck, Aneck,elliptical) are also generally strongly correlated with each other.

Figure 3

Pearson’s r for correlation between geometric risk parameters by anatomical region for dataset 1. ICA, internal carotid artery; MCA, middle cerebral artery.

Figure 4

Pearson’s r for correlation between geometric risk parameters by anatomical region for dataset 2. ICA, internal carotid artery; MCA, middle cerebral artery.

Within the non-dimensional parameter group, there are two distinct subgroups in most plots: one formed by AR, eAR, BF and BL and one formed by NSI, AVSV, AASA, UI and EI. Within the latter subgroup, several of the correlations are negative, but their magnitude is overall moderate to strong. The curvature parameters also form two subgroups: one formed by dimensional curvature parameters (MAA, absMAA, MDS, GAA, absGAA, GSD) and one by non-dimensional curvature parameters (HMC, MLN, HGC, GLN). With regard to correlations between parameter groups, there is generally moderate to strong correlation between the size and neck parameters. Additionally, the size and neck parameters are generally moderately correlated with the curvature parameters, the direction of the correlation being positive for the non-dimensional curvature parameters and negative for the dimensional curvature parameters.


Previous research has assessed the impact of uncertainty on geometric risk parameters in a limited fashion. Ma et al19 examined the influence of random noise on the calculation of 14 geometric risk parameters, finding curvature parameters more susceptible to random noise than size, neck, and non-dimensional parameters. Others have examined the influence of imaging modality20 and CT angiography reconstruction kernel21 on geometric risk parameters. Regarding image acquisition, Ramachandran et al20 have examined the influence of imaging modality while O'Meara et al21 and Berg et al22 have focused on the reconstruction kernel’s effect on geometric and haemodynamic risk parameters, respectively. The current study as well as the earlier uncertainty study based on the MATCH challenge14 were both based on 3D rotational angiography imaging, which is the routine imaging modality in both centres involved in this study. Other sensitivity and uncertainty aspects of computational fluid dynamics approaches to IAs have been explored, for example, by Cebral et al,23 Sarrami-Foroushani et al24, and Schneiders et al.25 To the authors’ knowledge, there is, however, no comprehensive publication relating discriminative performance and uncertainty of geometric risk parameters, while also providing detailed data on their correlation with each other.

Looking at the parameter groups examined in this study, the following findings can be made: the size and neck parameters measuring areas (A, ACH, AMBS, Aclosed, Aneck, Aneck,elliptical) and volumes (V, VCH, VMBS) generally do not achieve high DUR, despite having SAD similar to the size and neck parameters measuring length (H, Lmax, Hmax, Dmax, Hb, Dneck,min, Dneck,max, Pneck, Dneck,equiv). The cause is the higher uncertainty encountered in determining the higher dimensional parameters when compared with the one-dimensional parameters.14 This suggests that higher-dimensional size parameters tend to be less robust and thus less suitable for use in practical risk models than one-dimensional size parameters. Like Lauric et al,17 there are instances of noticeable differences in the discriminative performance of parameters capturing the same aspect of IA geometry, for example, for the neck size parameters. The non-dimensional parameters exhibit comparatively high SAD and DUR, except for BL and UI, which exhibit lower discriminative ability and/or higher uncertainty in their calculation. The curvature parameters show substantial variability in SAD and DUR depending on the anatomical region and the parameter, with MLN performing comparatively well overall. It is notable that the posterior region tends to exhibit higher SAD and DUR than the other regions, indicating more pronounced geometric differences between ruptured and unruptured IAs in this region. Regarding the differences in SAD and DUR between datasets 1 and 2, it is likely that differences in the patient collectives, subsample sizes, and reconstruction techniques are the main causes. The latter could in the future be tackled by machine learning-based segmentation methods, which can reduce operator-induced uncertainty. Examples of such methods have previously been presented, for example, in the context of the CADA challenge.26

Regarding the correlation patterns, there is substantial similarity between all analysed anatomical regions and datasets. Parameters tend to be most strongly correlated with other parameters from the same parameter group, except for the non-dimensional and curvature parameters, which form two subgroups each. This is reasonable, given that the parameters within each parameter group capture similar aspects of IA geometry. For the size and neck parameter groups, this is obvious, since they both capture aspects of IA and neck size, respectively. The two distinct correlation subgroups within the non-dimensional parameter group are likely caused by the underlying parameter subgroups capturing different aspects of aneurysm shape. While the parameters of the first subgroup (AR, eAR, BF, BL) are simply ratios of one-dimensional size parameters, the second subgroup (NSI, AVSV, AASA, UI, EI) is formed by parameters relating aneurysm area and/or volume to geometric reference objects, for example, the minimal bounding sphere or convex hull. The negative correlation between AVSV and AASA with the other parameters from the second subgroup is due to the parameter definitions, which cause AVSV and AASA to increase with increasing sphericity, while the other parameters tend to decrease with increasing sphericity. The curvature parameters also form two subgroups, with the first subgroup consisting of the dimensional parameters quantifying the mean or dispersion of IA surface curvature (MAA, absMAA, MSD, GAA, absGAA, GSD) and the second subgroup consisting of non-dimensional, scale invariant curvature parameters (HMC, MLN, HGC, GLN). Since the former parameters intrinsically decrease with IA size, while the latter parameters increase with IA size, the negative correlation of the two subgroups with each other makes sense. It should be noted that the positive correlation of the non-dimensional curvature parameters with IA size is not an intrinsic property of the non-dimensional parameters themselves, since they are designed to be scale invariant. It rather indicates that curvature and irregularities of the IA surface increase in larger IAs.

For a geometric risk parameter to be a good candidate for rupture risk prediction, it should generally have a high SAD, in order to be able to differentiate between ruptured and unruptured IAs. Additionally, DUR should be high, indicating low sensitivity of the parameter to the imaging, segmentation and calculation workflow, by which it is calculated. This is desirable because it allows models including such parameters to generalise well to other datasets. Finally, when choosing a set of parameters, data from the correlation analysis can be used to identify parameters that are not strongly correlated. Neyazi et al13 have previously used this method to derive a two-parameter rupture status prediction model from a set of 49 geometric and haemodynamic rupture risk parameters, identifying AR and the maximal relative residence time as the most suitable model parameters. Other attempts to identify suitable rupture status prediction models based on geometric risk parameters have been attempted, for example, Dhar et al15 and Zheng et al,27 but results have generally been inconsistent. Possible reasons for the discrepant findings regarding optimal parameter choice are the sample sizes used and the uncertainty inherent in the workflow by which the parameters are calculated. This may lead to the selection of less robust parameters that perform well on a given dataset but generalise less well to others. Based on the results of this study and considering SAD, DUR, as well as the correlation between geometric risk parameters, examples of more robust parameter choices could look as follows:

  • Hmax, Dneck,min, AR, AASA and MLN for the anterior region.

  • Lmax, Pneck, AR, AASA and HGC for the ICA.

  • Dmax, Dneck,min, eAR, AASA and HMC for the MCA.

  • Lmax, Dneck,min, BL, EI and absMAA for the posterior region.

  • Hb, Dneck,min, AR, AASA, and MLN if looking at all anatomical regions combined.

Overall, while individual size, neck and curvature parameters achieved good discriminative performance and robustness, the non-dimensional parameters tended to perform well as a group. This suggests that non-dimensional geometric risk parameters can provide comparatively good discriminative performance, while the non-dimensionalisation itself mitigates some of the uncertainty introduced through the workflow by which the parameters are calculated.14 Neither did we attempt to develop a novel aneurysm rupture risk prediction model, nor did we test earlier published models.16 28 We decided against this analysis due to the large variety of published proposed risk models. Such models as well as the propagation of the parameters’ uncertainty to the rupture risk assessment should be tested in a separate study. Finally, more elaborate models will also require further information such as hypertension status, earlier SAH as well as haemodynamic parameters, which were unavailable for this study.


IAs were grouped by anatomical region because IA location is an important determinant of rupture risk, as demonstrated by its weight in current risk scores.7–9 However, by analysing the datasets by anatomical region, some subsamples become quite small. Small sample size might affect the accuracy of the median and IQR estimates derived from these groups. This limitation is, however, partially mitigated by also analysing all anatomical regions combined and using two datasets, in order to get a more comprehensive picture of the risk parameters’ performance. The major focus of the study was the analysis of the performance and robustness of 37 geometric risk parameters. Thus, not all findings of this study could be assessed in depth. For example, we decided to group the aneurysms by anatomical regions as recommended by clinical scores, such as such as PHASES score.7 While we observed differences in both SAD and DUR based on the aneurysms’ location within the circulation, the underlying mechanisms for these differences cannot be assessed using the available data. However, Tykocki and Kostkiewicz29 found significant differences between some geometric parameters (parent artery size, size ratio, and aspect ratio) of aneurysms of the anterior and the posterior regions. They associated the difference in these parameters to different impacts on the intra-aneurysmal haemodynamics such as vortex formation and wall shear stress. Why these geometric parameters might result in different haemodynamic conditions and rupture risks must be investigated in a dedicated study. This is especially important as this study’s findings demonstrated differences in the SAD between locations and the cohorts and when all aneurysm locations were evaluated together.

Another potential limitation is the uncertainty values from Goubergrits et al,14 which were used to calculate DUR. These values were calculated on a sample containing MCA and posterior region IAs.14 While it does not seem particularly probable, it is possible that IA location and size might affect the uncertainty inherent in calculating the geometric risk parameters in a relevant manner, which in turn could influence DUR results. Accordingly, the generalisation of MRU values from the uncertainty study14 should be considered with caution, especially as those values were calculated only based on five aneurysms. A more fundamental limitations is the focus on geometric risk parameters. These parameters serve as proxies for the pathophysiological processes leading to IA rupture through the latter’s influence on the geometry of the IA surface. Due to their nature, geometric risk parameters cannot directly capture the haemodynamic, mechanical, or biochemical aspects of IA rupture. Nevertheless, they are among the most intensely researched types of IA rupture risk parameters, due to the comparative ease with which they can be calculated from clinical data.

All parameters included within this study have been discussed in previous literature as potential risk parameters. Note, however, that the list of parameters investigated in this study is not exhaustive. More proposed geometric parameters can be found in recent literature.30 The parameters investigated here are limited to a set of parameters investigated earlier in frames of the uncertainty study.14 Additionally, these parameters were constrained to parameters that can be calculated automatically.

Finally, the calculation of geometric parameters including the ostium plane depends on a sufficient reference plane selection. Recently, Berg et al31 quantified the potential effect of neck curve variations on haemodynamic predictions. These findings could be transferred to the cases included in this study in future work.

Due to the retrospective nature of this work, only the parameters’ capabilities to discriminate the rupture status could be assessed by comparing their respective values observed in ruptured or unruptured IA. To adequately assess the capabilities of any model using these parameters for rupture risk assessment, it has to be evaluated on a longitudinal cohort containing only UIA.


Based on datasets from two research groups, the present study provides location-specific estimates of the discriminative ability of a large set of geometric risk parameters for IA rupture status assessment, while also considering uncertainty. Additionally, correlation patterns between the parameters are identified. The presented data are potentially useful in evaluating geometric risk parameters for use in rupture risk models or when choosing input parameters for machine learning approaches to rupture risk prediction. It may also be helpful when designing future geometric risk parameters for clinical use.

Data availability statement

All data relevant to the study are included in the article or uploaded as supplementary information.

Ethics statements

Patient consent for publication

Ethics approval

This study involves human participants and was approved by Ethikkommission der Charité – Universitätsmedizin Berlin: EA2/222/19 and Ethikkommission der Med. Hochschule Hannover: NOVA Nr. 68/20. In this study, only surface geometries of intracranial aneurysms that were reconstructed from clinical routine data were used. Collection of informed consent was waived by the respective institutional review boards.


The authors kindly acknowledge PD Dr Belal Neyazi (Department of Neurosurgery, University Hospital Magdeburg) for his assistance during data acquisition as well as Adriano Schlief (Institute of Computer-assisted Cardiovascular Medicine, Charité – Universitätsmedizin Berlin) for his help in checking the topology and scaling of the intracranial aneurysm geometries.


Supplementary materials

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  • Contributors Roles according to CRediT (contributor roles taxonomy). Conceptualisation: LG, JS, FH, JB and PB. Methodology: FH, JS and LG. Resources: AS, IES, OB, NL, SS and PB. Investigation: JB, FH and JS. Formal analysis: FH. Funding acquisition: LG, PB and SS. Supervision: LG. Writing – original draft: FH, LG and JB. Writing – review and editing: PB, SS, AS, IES, OB, NL and JS. Guarantor: FH.

  • Funding This study was partly funded by the Federal Ministry of Education and Research in Germany within the Forschungscampus STIMULATE (grant number 13GW0473A) and the German Research Foundation (grant number SA 3461/2-1, BE 6230/2-1).

  • Competing interests None declared.

  • Patient and public involvement Patients and/or the public were not involved in the design, or conduct, or reporting, or dissemination plans of this research.

  • Provenance and peer review Not commissioned; externally peer reviewed.

  • Supplemental material This content has been supplied by the author(s). It has not been vetted by BMJ Publishing Group Limited (BMJ) and may not have been peer-reviewed. Any opinions or recommendations discussed are solely those of the author(s) and are not endorsed by BMJ. BMJ disclaims all liability and responsibility arising from any reliance placed on the content. Where the content includes any translated material, BMJ does not warrant the accuracy and reliability of the translations (including but not limited to local regulations, clinical guidelines, terminology, drug names and drug dosages), and is not responsible for any error and/or omissions arising from translation and adaptation or otherwise.