Background Intracranial aneurysms (IAs) are vascular dilations on cerebral vessels that affect between 1%–5% of the general population, and can cause life-threatening intracranial hemorrhage when ruptured. Computational fluid dynamics (CFD) has emerged as a promising tool to study IAs in recent years, particularly for rupture risk assessment. However, despite dozens of studies, CFD is still far from clinical use due to large variations and frequent contradictions in hemodynamic results between studies.
Purpose To identify key gaps in the field of CFD for the study of IA rupture, and to devise a novel tool to rank parameters based on potential clinical utility.
Methods A Pubmed search identified 231 CFD studies for IAs. Forty-six studies fit our inclusion criteria, with a total of 2791 aneurysms. For included studies, study type, boundary conditions, solver resolutions, parameter definitions, geometric and hemodynamic parameters used, and results found were recorded.
Data synthesis Aspect ratio, aneurysm size, low wall shear stress area, average wall shear stress, and size ratio were the parameters that correlate most strongly with IA rupture.
Limitations Significant differences in parameter definitions, solver spatial and temporal resolutions, number of cycles between studies as well as frequently missing information such as inlet flow rates were identified. A greater emphasis on prospective studies is also needed.
Conclusions Our recommendations will help increase standardization and bridge the gaps in the CFD community, and expedite the process of making CFD clinically useful in guiding the treatment of IAs.
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Intracranial aneurysms (IAs) affect between 1%–5% of the general population.1 2 Subarachnoid hemorrhage, the most serious consequence of ruptured IAs, affects 27 000 people in the United States every year, with a mortality rate of up to 45%.1 Rupture risk assessment has become an important subject of research on IAs, since most aneurysms today are discovered incidentally. While epigenetic and geometric risk factors have been associated with rupture risk, it remains that a significant proportion of patients presenting with subarachnoid hemorrhage do not completely meet current criteria for rupture prediction.3 4 Please see for figure 1 schematic of a typical CFD workflow.
In recent years, computational fluid dynamics (CFD) has emerged as a promising tool to study the initiation, growth, and rupture5 of IAs by demonstrating how hemodynamic parameters, such as wall shear stress (WSS), influence each of these phenomena by virtue of their influence on aneurysm wall pathophysiology and remodeling.6 Predicting aneurysm rupture is arguably the most clinically useful application of CFD. Supporting treatment planning is another possible application. Numerous studies have shown that CFD can be a useful tool to discriminate between ruptured and un-ruptured aneurysms.5 7–9
While predominantly a research tool today, neuro-interventionists hope one day to use CFD to supplement geometric parameters to help guide clinical decision making regarding aneurysm management. This is because while geometric parameters are useful, they often do not adequately predict rupture risk. For example, aneurysm size is currently the most useful discriminant of whether or not to treat an unruptured aneurysm, with 7 mm commonly used as a threshold for treatment due to a landmark study published in the Lancet in 2003.10 However, size is not an adequate discriminant since small aneurysms account for a significant proportion of ruptures. At one center, 87.5% of ruptured aneurysms were found to be less than 10 mm.11 Thus, hemodynamic results may provide a useful tool to discriminate which small aneurysms to treat and which ones not to treat.
However, as of today, CFD has little utility for the clinical management of intracranial aneurysms due to huge variations in results from different studies, as well as frequent contradictory results.12 Kallmes has derisively described CFD as confounding factor dissemination in an editorial as a result of the frequent contradictions observed.12 To illustrate, for maximum point-wise WSS in the aneurysm sac, both high13 14 and low9 values compared with the un-ruptured group have been shown to correlate with rupture. Another key impediment to the clinical application of CFD studies is the vast number of different hemodynamic and geometric parameters introduced and/or used in different studies.
Data sources and study selection and other methods
Data sources and study selection
For this systematic review, the population consist of patients with intra-cranial aneurysms, the intervention is not applicable, the comparison is hemodynamic and geometric parameters between the ruptured and unruptured aneurysms, the outcome is aneurysm rupture, and the study design consists of CFD studies using patient-specific models. The PRISMA guidelines for systematic review have been followed. The keywords ‘CFD/Computational Fluid Dynamic/Computational Fluid Dynamics/Computer Simulation/Computational Hemodynamics AND Brain/Cerebral/Intracranial AND aneurysm AND Rupture’ were used in PubMed to yield a total of 231 results. The inclusion criterion for this systematic review was CFD studies that compared ruptured and unruptured groups of aneurysms from patient-specific aneurysm models. Case reports, studies with a sample size of only one or no aneurysm in the ruptured group, idealized or theoretical models, studies without unruptured controls, studies involving stents, studies not published in English and review studies were excluded. Out of the 231 studies, 19 review articles, 20 case studies, 24 idealized studies, 17 stent or device studies, 27 studies without ruptured controls, three studies without unruptured controls, and 75 studies involving technique development or evaluation were excluded. The remaining 46 studies were selected for this review. Please see Figure 2 for a flowchart describing the systematic review.
From each of the studies selected, the number of patients in both the ruptured and unruptured groups, study type, boundary conditions, CFD solver brand and version, spatial resolution, temporal resolution, hemodynamic parameters, geometric parameters, and parameters that showed positive and negative correlation with rupture were recorded. A parameter that shows positive correlation with rupture indicates that in the study, higher values of the parameter is reported to be associated with rupture. Conversely, a parameter that shows negative correlation with rupture indicates that in the study, lower values of the parameter compared with the control is associated with rupture. Key systemic sources of biases are discussed in detail in the Discussions and limitations section.
The power score was devised as a method to rank the different hemodynamic and geometric parameters used in CFD studies in order to demonstrate how well each parameter correlates with rupture. This parameter-ranking tool is derived by looking at each of the 81 different parameters identified in the literature review, and recording the number of studies in which the parameter statistically significantly correlated positively with rupture and the number of studies in which the parameter statistically significantly correlated negatively with rupture. The power power score for each parameter is the difference in the two values described above.
The modified power score is determined by finding the absolute value of the difference between the sum of sample sizes for each parameter that correlated positively with rupture and the sum of samples that correlated negatively with rupture, and dividing that by the maximum difference of sums for all 81 parameters to normalize the value. This is likely an even more accurate measure of the clinical utility of each parameter to aneurysm rupture as it takes into account the sample sizes of the study.
These novel custom parameter-ranking tools were used instead of standard meta-analyses tools for several reasons, and will be discussed in detail in the Discussion and limitations section.
Data analysis and synthesis
The key results from the novel parameter-ranking tool are described in tables 1 and 2. The full table of parameter rankings, as well as the list of studies used in this study to derive the parameter ranking, can be found in the online supplementary materials. The parameters with the highest power scores were aspect ratio, low shear stress area (LSA), aneurysm size, minimum WSS, average WSS, size ratio, and oscillatory shear index (OSI). After adjusting for the sample size of the studies, the parameters with the highest modified power scores are aspect ratio, aneurysm size, LSA, average WSS, size ratio, and minimum WSS. Definitions of key parameters described in this paper are provided in Table 3.
Supplementary file 1
It is interesting to note that although average and maximum WSS are two of the most commonly measured parameters in CFD studies, they did not strongly correlate with rupture. They ranked fourth and 55th in the parameter ranking, respectively. It is also interesting to note that in both the power and the modified power scores, the two parameters that correlate the strongest with rupture were the geometric parameters of aspect ratio and aneurysm size. This may be due to the fact that the definitions for geometric parameters used from study to study are usually more consistent than the definitions of hemodynamic parameters. In addition, geometric parameters such as size and aspect ratio are simpler to derive since they do not require many complex steps such as segmentation and the use of a mesher, solver, and an array of boundary conditions as required by hemodynamic parameters, all of which are sources of variability between studies as demonstrated in this review. As a result, they are less prone to methodological variations between studies.
Definition and methodological variations
Out of the 46 studies used in this systematic review, a total of 81 different hemodynamic and geometric parameters were identified. Many studies introduced new parameters, and the sets of hemodynamic and geometric parameters used by individual studies, as well as the definitions for each parameter, often differed widely. For example, the definition for LSA, which is the area of the aneurysm sac exposed to WSS below some defined threshold, varied widely. This threshold ranged from less than 10% of the mean WSS of the parent artery,15 to less than 10% of the mean shear stress of the carotid siphon,16 to less than 1.5 Pa,17 to less than one SD below that of the mean WSS of the parent artery.18 Likewise, the definitions for maximum wall shear stress (MWSS) ranged from absolute MWSS at peak-systole,13 to absolute MWSS averaged over an entire cardiac cycle,17 to absolute point-wise MWSS with no-averaging specified.19 Lauric et al have found that variations in parameter definitions have significant effects on the predictive value of a parameter.20 The significant variations in definitions likely account for many of the discrepancies in results.
Enormous variability was also observed in the spatial and temporal resolution of the CFD solvers used in different studies. The mesh resolution ranged from an average of 250 000 elements per model to 4 million elements per model.17 The temporal resolution varied by two orders of magnitude, from 0.01 s per time step to 0.0001 s per time step. Valen-Sendstad et al 21 have shown, for example, that low temporal and spatial resolution could lead to significant underestimations of results with ‘high resolution’ solvers leading to a WSS 30% higher and a MWSS 60% higher than those obtained using normal resolution solvers.
Another key limitation to the clinical utility of CFD is that the vast majority of current studies only used post-rupture geometries, instead of pre-rupture geometries. Out of the 46 studies used in this study, 41 were retrospective and used post-ruptured geometries. While it is true prospective studies are more difficult to perform, for reasons further specified in the Discussions and limitations section, this is an important limitation to the clinical utility of CFD studies, as a recent study has found that the aneurysm geometry changes significantly due to rupture.22 Furthermore, only four out of the studies used actual patient-specific boundary conditions, whereas the rest used generic boundary conditions from a healthy patient or the averages from previous studies. Lastly, most studies had a relatively small sample size: only 21 had sample sizes of 50 aneurysms or greater.
Furthermore, key methodological information was often missing from existing studies. For example, in 46% of studies (21/46), the specific inlet flow rates used could not be found in the paper. This often occurred when the authors stated that the inlet flow rate was based on that of a healthy patient measured such as using trans-cranial Doppler or phase contrast MRI, but the actual flow rate was not given. In four of the studies, instead of providing the flow rate, the authors scaled the flow rate so that the inlet WSS was the same across different aneurysms. In addition, also often missing was information on the number of cardiac cycles simulated (10/46), mesh spatial resolution (9/46), and solver temporal resolution (22/46). There are also significant variations in imaging modality and segmentation techniques identified in the studies included, which is a further source of error.23 24
Variations in results
The methodological variations described in the previous sections likely account for the large variations in the hemodynamic values observed between studies. For example, for anterior aneurysms, the MWSS of ruptured aneurysm ranged from 10.76 Pa25 to 55.64 Pa19 between studies, a variation of more than 400%. This is likely due to a combination of methodology and patient-to-patient variations. However, this is partly mitigated by the fact that results for individual studies were compared with the un-ruptured group in the study. In addition, some studies present absolute values of parameters, whereas others present values normalized to the parent artery, further introducing variability since the definition of parent artery WSS also varied across studies.
Discussions and limitations
This systematic review has found 81 different hemodynamic and geometric parameters used to predict rupture in IAs. The huge number of different parameters and the lack of consistency in the sets of parameters used among studies make the use and interpretation of CFD studies very difficult in clinical practice. As a result, comparing the results from different studies is often akin to comparing apples and oranges.
There are several reasons why a novel parameter-ranking tool was devised instead of relying on more traditional meta-analyses tools. First, many of the parameters found have only been used in one study, thus a tool that allowed such studies to be included in the ranking was needed. Second, since the values of the baseline un-ruptured controls for most parameters varied significantly from study to study, the results are not reliable enough to acquire relative risk reduction ratios or odds and hazards ratios from. As a result, the direction of the correlation with rupture as well as the sample size of each study were far more important than the effect size demonstrated in the studies. Once CFD studies become more well-established and less contradictory, traditional meta-analyses tools can be used to determine the effect sizes.
The fact that the sum of the top three parameter modified power scores was higher than the subsequent nine parameter modified power scores combined illustrates that not all parameters are equally useful in predicting rupture. Some parameters, such as LSA, aneurysms size, and oscillatory shear index, are far superior correlates of aneurysm rupture than others. In addition, there is no direct correlation between the frequency in which a parameter is used in previous studies and its potential in predicting rupture. For example, although average WSS and MWSS are the first and third most frequently used parameters in the literature, they are fourth and 55th, respectively, in the modified power score. Furthermore, many parameters, as shown in the Supplementary Information section, did not show any correlation with rupture. It is worth noting that the robustness of each modified power score is proportional to the number of studies included for the hemodynamic or morphological study in question, and will become more robust as the number of studies that assessed the parameter increase. Thus, an additional study would more strongly impact the results of a parameter in which a small number of studies have assessed the parameter.
By focusing on a smaller number of parameters that correlate strongly with rupture, the scientific community can compare results from different experiments more easily and thus improve the clinical utility of CFD as a rupture prediction tool. While scientists should have the freedom to introduce new and potentially more valid parameters, a set of baseline parameters should be presented in all CFD studies to ensure consistency. Moreover, the findings from this study show that there are numerous and significant gaps in the methodologies of current CFD studies, such as the parameter definitions, and spatial and temporal resolutions used. These gaps are likely responsible for much of the enormous variability and frequent contradictions in results between different studies.
To overcome these gaps, we recommend the CFD community to ensure that definitions for hemodynamic and geometric parameters should be as consistent as possible between studies. This may be achieved by having experts in the field come together to agree on parameter definitions, especially for the most commonly used parameters as described in this paper. Second, it would be useful for the CFD community to agree on a minimum set of parameters to include in all future CFD studies. The parameters identified in this study that correlate the most strongly with rupture may be a useful starting point for this baseline set. These standards will not only expedite the validation of the most promising parameters, but will also pave the way for future meta-analysis studies to be done. An additional approach to increasing standardization could be the use of automated parameter characterization tools, such as those developed by Piccinelli et al and Rajabzadeh-Oghaz et al.26 27 Such tools will reduce the inter-user variability inherent to obtaining geometric and hemodynamic measurements.27 However, a key requirement of this approach is the thorough validation of such tools. Third, key methodological information on the solver type, inlet flow rates, number of cycles, solver temporal, and spatial resolutions should be provided in all studies. Last, future CFD studies should have stricter guidelines, and perhaps even requirements, on minimum solver temporal and spatial resolutions, as well as solver verification.
In addition to the standardization of definitions and methodology, there is an equally important need for prospective studies. This is because the aneurysm geometry changes significantly following rupture, thus a better understanding of pre-rupture geometries of ruptured aneurysms is crucial, especially if they are taken at multiple points in time to show the dynamics of aneurysm initiation. of ruptured aneurysms is crucial.22 Retrospective studies usually use post-rupture geometries that are likely much different from the pre-rupture ones. However, prospective studies are more difficult and expensive to conduct since they would require a much larger cohort of patients than retrospective studies given the annual rupture rate of intracranial aneurysms is 0.7%.28
The standardization of segmentation and CFD methodologies, as well as the use of meta-analysis tools, would expedite the translation of knowledge gained from prospective studies. In addition to prospective studies, studies with larger number of patients are important, since a large number of findings in current finds are not statistically significant partly due to the small sample size. To illustrate, only 21 existing studies identified in this review have sample sizes of more than 50. Furthermore, patient-specific boundary conditions could help increase the translational potential of CFD, at least, until robust parameters will be described and strongly correlated with rupture. Studies have shown using generic instead of patient-specific velocities can have significant effects on results, such as WSS, high WSS location, and inflow jet stability.29 The latest CFD challenges have demonstrated this variability, the impact of the segmentation on the hemodynamic parameters and, more critical, the failure of most of the CFD results to accurately predict the rupture using hemodynamic parameters.
Rupture risk evaluation is important clinically since most of the newly discovered unruptured IAs are small and lack robust assessment methods.30 31 Our study proposes a power score based on all the studies published currently. The ranked analysis is a useful guide for future studies and analysis, and describes the impact of each parameter as well as its significance.
Computational fluid dynamics is an emerging tool that could potentially guide the management of IAs, especially for smaller aneurysms. However, the heterogeneity and frequent contradictions in results is holding CFD back from clinical utility. This review addresses some of the key sources of the heterogeneity and contradictions, and proposes solutions to bridge the gaps in the CFD community. To our knowledge, this systematic review is the first holistic review of all previous CFD studies with multiple patients which assessed aneurysm rupture that ranked the geometrical and hemodynamic parameters. In addition, the proposed rank summarizes the correlation of hemodynamic and geometric parameters with aneurysm rupture based on the sum of results from previous studies, which could be used to assess the potential of each parameter as a rupture prediction tool.
Contributors LL devised the study, acquired and analyzed data, and contributed to the writing. DAS and VMP devised the study and contributed to the writing. OB analyzed data and contributed to the writing. CC and NMC contributed to the writing. All authors have read and approved the final manuscript.
Funding This work was supported by grant G-16-00012564 from the Heart & Stroke Foundation of Canada. VMP acknowledges the support of the Brain and Spine Research Group and the Medical Imaging Department at the University of Toronto. DAS acknowledges support from a Heart and Stroke Foundation Mid-Career Investigator award.
Competing interests None declared.
Patient consent Not required.
Provenance and peer review Not commissioned; externally peer reviewed.
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