Abstract
Purpose
To construct a classification model of rupture status and to clarify the importance of morphologic variables and hemodynamic parameters on rupture status by applying a machine learning (ML) algorithm to morphologic and hemodynamic data of cerebral aneurysms.
Materials and Methods
Between 2011 and 2019, 226 (112 ruptured and 114 unruptured) cerebral aneurysms in 188 consecutive patients were retrospectively analyzed with computational fluid dynamics (CFD). A random forest ML algorithm was applied to the results to create three classification models consisting of only morphologic variables (model 1), only hemodynamic parameters (model 2), and both morphologic variables and hemodynamic parameters (model 3). The accuracy of rupture status classification and the importance of each variable or parameter in the models were computed.
Results
The accuracy was 77.0% in model 1, 71.2% in model 2, and 78.3% in model 3. The three most important features were projection ratio, size ratio, and aspect ratio in model 1; low shear area ratio, oscillatory shear index, and oscillatory velocity index in model 2; and projection ratio, irregular shape, and size ratio in model 3.
Conclusion
Classification models of rupture status of cerebral aneurysms were constructed by applying an ML algorithm to morphologic variables and hemodynamic parameters. The model worked with relatively high accuracy, in which projection ratio, irregular shape, and size ratio were important for the discrimination of ruptured aneurysms.
Supplemental material is available for this article.
© RSNA, 2020
Summary
A machine learning algorithm was applied to morphologic and hemodynamic data of cerebral aneurysms, and a classification model of rupture status with relatively high accuracy was constructed, in which projection ratio, irregular shape, and size ratio were important for discrimination.
Key Points
■ A classification model of rupture status was developed with machine learning, in which a random forest algorithm was adopted.
■ The accuracy of the model was 78.1%, which was higher than that of experienced neurosurgeons’ judgment.
■ Consideration of hemodynamics allowed more accurate model construction.
Introduction
In recent years, machine learning (ML) has been used in various fields and is developing rapidly. Research using an ML approach is also increasing in clinical medicine, which is remarkable in diagnostic radiology (1,2). ML algorithms are classified into two broad categories: supervised and unsupervised algorithms. In supervised learning, pairs of inputs and outputs are given to the algorithm, which finds a way to generate the output from the input (3); this technique enables prediction of results, classification of various data, and detection of errors from data and is beginning to be applied to medical fields. In contrast, in unsupervised learning, only the input is known and no known output is provided to the algorithm; this is often used for the better understanding of the data in exploratory settings (3).
Computational fluid dynamics (CFD) has been applied to evaluate the pathogenesis of cerebral aneurysms. Although several hemodynamic parameters including wall shear stress have been developed for a better understanding of rupture status, rupture risk, and growth of aneurysms (4–15), the extent of contribution of each hemodynamic parameter has not been fully examined. Morphology of aneurysms has also been reported to be associated with rupture status and risk, but the extent of contribution of each morphologic variable has not been clarified.
In this study, we applied a supervised learning algorithm to morphologic variables and hemodynamic parameters of cerebral aneurysms as the input, and the rupture status as the desired output, and aimed to develop a classification model of rupture status and to evaluate the importance of each morphologic variable or hemodynamic parameter on rupture status.
Materials and Methods
Study Population
Between 2011 and 2019, 226 (112 ruptured and 114 unruptured) cerebral aneurysms in 188 consecutive patients, which were diagnosed with three-dimensional CT angiography in Mie Chuo Medical Center and analyzed with CFD, were retrospectively evaluated in this study. All aneurysms were saccular aneurysms; arterial dissection or fusiform aneurysms were excluded. Ground truth for rupture status was established in a patient with subarachnoid hemorrhage that was diagnosed as follows by using plain CT: When only one aneurysm adjacent to the cisternal clots was identified with CT angiography without trauma, the aneurysm was judged to be ruptured; when one aneurysm not adjacent to the cisternal clots was identified without trauma, its rupture status was judged intraoperatively; when one aneurysm was identified with trauma, its rupture status was judged intraoperatively; and when two or more aneurysms were identified, the aneurysm that was confirmed intraoperatively to be ruptured was judged to be ruptured and the others to be unruptured. Aneurysms with neither subarachnoid hemorrhage nor symptoms were judged to be unruptured. The institutional review board granted approval for this study, and informed consent was obtained. All study protocols and procedures were conducted in accordance with the Declaration of Helsinki.
Morphologic Variables
Maximum size, projection length, neck width, aspect ratio, projection ratio, and size ratio were measured at stereolithography with ImageJ software (version 1.5.1; National Institutes of Health, Bethesda, Md) (8,16–18). Dome volume, dome area, and volume-to-ostium area ratio were measured by using CFX-Post (ANSYS CFX CFD, version 18.0; ANSYS, Canonsburg, Pa) (19). Geometric shapes of aneurysms were classified into a smooth type and an irregular type with a daughter sac or multiple lobes, which were evaluated with stereolithography by the two evaluators (S.T., A.Y.) (20–22). When the evaluation disagreed, the stereolithographic image was re-evaluated by both evaluators together to develop consensus.
Hemodynamic Parameters
Wall shear stress, normalized wall shear stress, oscillatory shear index, wall shear stress gradient, gradient oscillatory number, low shear area ratio, standardized pressure difference, oscillatory velocity index, neck pressure loss coefficient, neck energy loss, and flow velocity were computed at aneurysm dome regions (see detailed methods in Appendix E1 [supplement]) (8,12,14,15,23,24).
Intra-aneurysm flow patterns including flow complexity and stability were evaluated on the temporal movie of streamlines over the cardiac cycle by a single evaluator (S.T.): A complex flow pattern indicated flow separation or division inside an aneurysm, and an unstable flow pattern indicated that vortex structures moved, appeared, or disappeared (5–7).
Machine Learning
The Python programming language (version 3.6.5; Python Software Foundation, Wilmington, Del; https://www.python.org/) and its libraries, NumPy (version 1.14.3; https://www.numpy.org/), scikit-learn (version 0.19.1; https://scikit-learn.org/stable/), and matplotlib (version 2.2.2; https://matplotlib.org/), were used for all data processing. The programming code was executed in Jupyter Notebook (version 5.5.0; https://jupyter.org/) using a laptop computer with general performance (Intel Core i7 central processing unit [Intel, Santa Clara, Calif] with 2.2 GHz and 8 GB of RAM).
As a supervised ML algorithm, random forest was adopted, which is one of the ensembles of decision trees. Random forests were applied to the findings of morphologic and hemodynamic analyses as the input, with which three classification models were created as follows: model 1 with only morphologic variables, model 2 with only hemodynamic parameters, and model 3 with both morphologic variables and hemodynamic parameters. Age, sex, and location of aneurysms were also added to each model. The models were applied to rupture status as the desired output. In the model creation process, random states in random forests were determined according to the assessment of models using 0 to 99 in increments of one to achieve the highest accuracy in each classification model. The number of trees was also determined according to the assessment of models using 75 to 1025 trees in increments of 50 trees. The Gini impurity was applied to the function to evaluate the quality of a split. The number of features, which were morphologic variables and/or hemodynamic parameters, to consider when looking for the best split was set to the square root of the total number of parameters in each model (25). Leave-one-out cross-validation was used to assess generalization performance, in which a single data point was picked to be the test set and the remaining data points were used as the training set for each split (3).
The accuracy was computed by the number of correct classifications divided by the number of all samples (3). The importance of each feature was computed with the mean decrease in the Gini impurity (26,27). In three classification models, the confusion matrices were calculated on the basis of the predictions of the test set, and the accuracy of rupture status classification and the importance of each feature were calculated as the mean values for every split in the leave-one-out cross-validation.
Judgments of Rupture Status by Experienced Vascular Neurosurgeons
Two vascular neurosurgeons (S.S., H. Sakaida), with about 30 years of experience and blinded to the clinical history of patients, independently evaluated age, sex, location of aneurysms, and stereolithography and classified aneurysms into ruptured or unruptured aneurysms. The results were compared with those of ML analyses.
Statistical Analysis
Patient and aneurysm data were analyzed with SPSS Statistics version 24.0 (IBM; Armonk, NY). Student t test, Mann-Whitney U test, and Pearson χ2 test of independence were performed to evaluate statistical significance between ruptured and unruptured aneurysms. P values less than .05 were considered to indicate statistical significance. Interobserver variability for geometric shapes of aneurysms was quantified with the κ test.
Results
Patient characteristics, location of aneurysms, morphologic variables, and hemodynamic parameters of ruptured and unruptured aneurysms are shown in Table 1. Their raw data in comma-separated values format are presented in Appendix E2 (supplement). The κ value for geometric shapes of aneurysms was 0.670.
Table 1:
Characteristics of Ruptured and Unruptured Aneurysms
The programming code is presented in Appendix E3 (supplement). The execution time to determine the random state and number of trees was about 60 minutes and 50 minutes, respectively. The number of trees in the random forests was set to 125 in models 1 and 3 and 175 in model 2, with which the highest accuracy was achieved in each model. In the leave-one-out cross-validation, a split was repeated 226 times. The confusion matrices are shown in Table 2.
Table 2:
Confusion Matrices in Models 1–3
The mean values of the accuracy of rupture status classification were 77.0% in model 1, 71.2% in model 2, and 78.3% in model 3. The sensitivity and specificity of rupture status classification were 77.7% and 76.3% in model 1, 69.6% and 72.8% in model 2, and 78.6% and 78.1% in model 3, respectively. The importance of each feature in each model is shown in Figures 1–3, in which the three most important features were projection ratio, size ratio, and aspect ratio in model 1; low shear area ratio, oscillatory shear index, and oscillatory velocity index in model 2; and projection ratio, irregular shape, and size ratio in model 3. In total, 13 aneurysms were misclassified in model 1 and correctly classified in model 3 (Table 3), whereas 10 aneurysms were misclassified in model 3 and correctly classified in model 1.
Figure 1:
Graph shows importance of each feature in model 1 with only morphologic variables. VOR = volume-to-ostium area ratio.
Figure 3:
Graph shows importance of each feature in model 3 with both morphologic variables and hemodynamic parameters. FV = flow velocity, GON = gradient oscillatory number, LSAR = low shear area ratio, NEL = neck energy loss, NPLc = neck pressure loss coefficient, NWSS = normalized wall shear stress, OSI = oscillatory shear index, OVI = oscillatory velocity index, SPD = standardized pressure difference, VOR = volume-to-ostium area ratio, WSS = wall shear stress, WSSG = wall shear stress gradient.
Table 3:
Characteristics of 13 Aneurysms That Were Misclassified in Model 1 and Correctly Classified in Model 3
Figure 2:
Graph shows importance of each feature in model 2 with only hemodynamic parameters. FV = flow velocity, GON = gradient oscillatory number, LSAR = low shear area ratio, NEL = neck energy loss, NPLc = neck pressure loss coefficient, NWSS = normalized wall shear stress, OSI = oscillatory shear index, OVI = oscillatory velocity index, SPD = standardized pressure difference, WSS = wall shear stress, WSSG = wall shear stress gradient.
The accuracy of two experienced neurosurgeons’ judgments were 72.6% and 73.5%. In total, 34 aneurysms were misclassified by both neurosurgeons, among which 14 aneurysms were correctly classified in model 1 (Fig 4).
Figure 4:
Stereolithography shows 14 aneurysms that were misclassified by both neurosurgeons and correctly classified in model 1. A, True ruptured aneurysms. B, True unruptured aneurysms.
Discussion
In this study, the accuracy in model 1 with only morphologic variables was higher than that in model 2 with only hemodynamic parameters. The findings indicate that morphology of cerebral aneurysms is still important in judging rupture status in the current era of developing CFD analysis. However, model 3 with both morphologic and hemodynamic parameters classified rupture status most accurately, which showed that adding consideration of hemodynamics to morphologic analysis brings more accurate classification of rupture status.
The five most important features in model 3, which were projection ratio, irregular shape, size ratio, low shear area ratio, and oscillatory shear index, corresponded with important features in models 1 and 2. They were almost the same as the morphologic variables or hemodynamic parameters that were reported to have correlation with rupture status or risk in previous reports: In morphology, aneurysms with irregular shapes such as aneurysms with a daughter sac or multiple lobes and those with higher aspect ratio, size ratio, and volume-to-ostium area ratio have been reported (4,16,17,19–22,28,29). In hemodynamics, low wall shear stress, high oscillatory shear index, high oscillatory velocity index, high neck energy loss, and low-neck pressure loss coefficient have been reported (4,8–15,24). Although projection ratio is defined as the ratio of projection length (which is the length between the middle point of neck width and the farthest aneurysm surface point) to the neck width (18) and its relationship to rupture status has not been studied, it was the most important feature in models 1 and 3. Low shear area ratio was the most important feature in model 2, and several reports have described its value in rupture status discrimination and rupture prediction (30–33).
Among 13 aneurysms that were misclassified in model 1 and correctly classified in model 3, six were true ruptured aneurysms, in which median values and interquartile ranges of aspect ratio and projection ratio were near to those in all unruptured aneurysms, which may be why the true ruptured aneurysms were classified as unruptured ones in model 1. However, median values and interquartile ranges of low shear area ratio, oscillatory shear index, and oscillatory velocity index were near to those in all ruptured aneurysms, which may have served the correct classification in model 3 as additional effects of consideration of hemodynamics. Similarly, seven true unruptured aneurysms had lower median values and interquartile ranges of low shear area ratio, oscillatory shear index, and oscillatory velocity index than all unruptured aneurysms, which may have served as additional effects in model 3. In contrast, 10 aneurysms were correctly classified in model 1 and misclassified in model 3, and thus, overall effects of hemodynamics brought an increase in three accurate classifications.
Observers (experienced neurosurgeons) evaluated aneurysm morphology from stereolithography in conjunction with patient’s age, sex, and location of the aneurysms and judged rupture status by adding their past experiences. Although evaluation points of the observers were considered to correspond with features in model 1, the accuracy in model 1 was higher than that of observers’ judgments. This fact indicates the characteristics of ML well, in which a simple program with a large collection of features of ruptured and unruptured aneurysms is enough for an algorithm to classify rupture status better than human experts (3).
In the world of ML, there are some benchmarks for evaluating the availability of accuracy of algorithms such as the classification of Modified National Institute of Standards and Technology dataset. However, there does not exist a shared cerebral aneurysm imaging database, so it is difficult to create benchmarks of rupture status classification algorithms. In addition, it is also difficult to compare the accuracy of our ML models with previous studies because the shapes of aneurysms or angioarchitecture are different among the studies. Therefore, we used the results of human experts as benchmarks.
In clinical practice, we sometimes encounter cases of aneurysm in which the judgment of rupture status is difficult but important to determine the treatment strategy. For instance, when a patient with subarachnoid hemorrhage has right and left middle cerebral artery aneurysms whose shapes are similar with a uniform distribution of cisternal clots, it may be impossible to identify which aneurysm is ruptured. However, the decision of the surgical side is required, and if the aneurysm of one side is found to be unruptured in the surgery, an additional surgery of the opposite side becomes necessary, which may increase the risk of treatment. If our ML classification models are applied to such aneurysms, then the models can identify a ruptured aneurysm more accurately than experienced vascular neurosurgeons, which may reduce unnecessary treatment and its additional risk. In another instance, when a patient admitted after head injury has both subarachnoid hemorrhage and an aneurysm adjacent to the cisternal clots, it is difficult to decide whether subarachnoid hemorrhage has occurred as a result of head injury or aneurysm rupture. As with the above case, if the ML models could identify the rupture status correctly, then we can avoid an unnecessary risky surgery of an unruptured aneurysm in an acute posttraumatic phase. However, in this case, more accurate models need to be developed because the clinical decision is whether a patient should undergo the surgery.
There were some limitations in this study. First, more patients are required to allow models to have more sufficient quality. Although it is hard to determine a proper sample size in ML analyses, which differs according to the quality of input data, efforts are needed to increase sample size and to confirm that classification accuracy and its stability have reached a plateau regardless of an increase in sample size (34). Second, classification models were constructed based on data from a single institution; therefore, further validation using independent data is necessary for generalization of results and implementation in clinical practice. Third, other commonly used ML algorithms such as an artificial neural network or support vector machines may have developed more accurate classifications (35). However, they require thorough tuning of parameters in the algorithms to obtain good results (3). In contrast, a random forest algorithm performs well without careful tuning of the parameters or preprocessing of the input data (3). Additionally, it is relatively easy to interpret the relationship between input and output in a random forest algorithm because the importance of the features is calculated with the Gini impurity. Fourth, morphologic variables were measured by human evaluators so that interobserver variability needs to be considered; maximum size, projection length, neck width, aspect ratio, projection ratio, and size ratio may have lower variability because their measurement criteria have been well established, with measurements being performed with three-dimensional stereolithographic images. Shapes of aneurysms may have higher variability, whose κ values have been reported as 0.680–0.818 (20,22,24), because the objective and detailed criteria for classification of shapes do not exist. Fifth, although morphologic analysis of aneurysms depended on geometric measurement and evaluation, an artificial neural network approach using raw CT data may excel in the detailed and accurate assessment of morphology. Sixth, CFD is a simulation performed through some modeling processes, in which blood was assumed to be Newtonian fluid, boundary conditions were not patient specific, and elasticity of the arterial wall was not considered. Seventh, for many radiologists, neurosurgeons, and radiologic technologists, it is not easy to perform CFD analysis in clinical practice. We CFD researchers need to address the promotion of automation and clinical application of CFD analysis. Finally, the findings in this study should be confirmed in a prospective study.
In conclusion, we developed classification models of rupture status by applying an ML algorithm to morphologic and hemodynamic data of cerebral aneurysms. The model worked with relatively high accuracy, in which projection ratio, irregular shape, and size ratio were important features.
APPENDIX
Supported by Scientific Research from Japan Society for the Promotion of Science (17K10825, 18K16556).
Disclosures of Conflicts of Interest: S.T. disclosed no relevant relationships. F.I. disclosed no relevant relationships. A.Y. disclosed no relevant relationships. S.S. disclosed no relevant relationships. H. Sakaida disclosed no relevant relationships. M.T. disclosed no relevant relationships. N.K. disclosed no relevant relationships. H. Suzuki disclosed no relevant relationships.
Abbreviations:
- CFD
- computational fluid dynamics
- ML
- machine learning
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