Augmenting Prediction of Intracranial Aneurysms’ Risk Status Using Velocity-informatics: Initial Experience

Abstract

Our primary goal here is to demonstrate that innovative analytics of aneurismal velocities, named velocity-informatics, enhances IA rupture status prediction. 3D computer models were generated using imaging data from 112 subjects harboring anterior IAs (4–25mm; 44 ruptured and 68 unruptured). Computational fluid dynamics simulations and geometrical analyses were performed. Then, computed 3D velocity vector fields within the IA dome were processed for velocity-informatics. Four machine learning methods (support vector machine, Random Forest, generalized linear model, and GLM with Lasso or elastic net regularization) were employed to assess the merits of the proposed velocity-informatics. All 4 ML methods consistently showed that, with velocity-informatic metrics, the area under the curve and prediction accuracy both improved by approximately 0.03. Overall, with velocity-informatics, the support vector machine’s prediction was most promising: an AUC of 0.86 and total accuracy of 77%, with 60% and 88% of ruptured and unruptured IAs being correctly identified, respectively.

Introduction

Most intracranial aneurysms (IA) have a low risk of rupture; however, aggressive treatment of unruptured IAs may pose a risk of treatment complications to patients, which could be higher than the risk of IA rupture. That is why managing unruptured IAs has become a clinical dilemma [1–6]. Among research efforts that have been devoted to accurately identifying IAs with a high risk of rupture, “patient-specific” computational fluid dynamics [7, 8] (CFD; also known as computational hemodynamics) has emerged as a valuable tool.

Biologically, disturbed aneurismal flow (e.g., swirling flow) introduces cellular structural and functional changes that would interrupt their normal physiological morphology, cell-to-cell adhesion, mechanotransduction, and cellular genetic expression [9–11]. That motivates researchers to link flow disturbance to destructive vascular remodeling of IAs. However, compared with hemodynamic metrics derived from wall shear stress (WSS) and its variants or derivatives, quantification of aneurismal flow disturbance still requires more attention [12]. It is important to note that WSS is derived from near-wall velocity and may not be a good reflection of global flow disturbance. In contrast, hemodynamic metrics derived from velocity within the IA dome can quantify gross aneurismal flow disturbance, providing complementary information to WSS.

In this study, we introduced an innovative technique to extract mineable data from velocity data; we aim to estimate aneurysmal flow disturbance using the above technique. Specifically, leveraging a widely used Radiomic package PyRadiomics [13], the proposed method quantifies flow disturbance based on the directional consistency of the blood velocity field within an IA.

To make a distinction from Radiomics dealing with textural analyses of radiographic data, our technique handles computed velocity data using CFD and, thus, is named velocity-informatics. In the literature, Radiomics-extracted morphological features have been used to predict the prognosis of IA aneurysms treated by flow-diverting stents [14] and IA stability [15], respectively. However, applying textural analysis technology to quantify aneurismal flow disturbance has not been reported. Consequently, our innovative study design makes unique contributions to the characterization of IAs. In this study, the initial utility of the proposed velocity-informatics approach is to predict IA rupture status, and its performance is demonstrated by using a cohort of 112 IAs with known rupture status.

Patient Cohorts

All patient data were obtained from three sources: the University of Michigan Medical Center (USA), Changhai Hospital in Shanghai (China), and the Aneurisk open-source repository (http://ecm2.mathcs.emory.edu/aneuriskweb/index). The inclusion criteria include: (1) image quality is sufficient for image segmentation, morphological analysis, and establishing CFD models, (2) IA size is limited to between 4 and 25 millimeters, (3) there is no presence of a closely spaced second IA, and (4) IA is in the anterior circulation.

112 (44 ruptured and 68 unruptured) cerebral aneurysms were identified, and all aneurysms were saccular aneurysms: 39 located at the intracranial internal carotid artery (ICA), 52 located at the middle cerebral artery (MCA), and 21 located at the anterior cerebral artery (ACA). The IAs’ rupture statuses were known and gathered from the medical record.

This study was approved by the institutional ethics committees, and written informed consent was not required because this is a retrospective analysis of existing data.

Hemodynamic Analysis

The overall workflow of obtaining morphological and hydrodynamic parameters is shown in Fig. 1.

Figure 1:

The overall workflow to acquire anatomical/hydrodynamic/morphological parameters and perform machine learning-based assessments of IA rupture risk.

As illustrated in Fig. 1, “patient-specific” geometries were first derived from 3D rotational angiography or 3D digital subtraction angiography data. Then, CFD model creation was performed using in-house Python scripts integrated into Vascular Modeling ToolKit (VMTK) [16]. An open-source mesh generator, TetGen (Version 1.4.2), integrated into VMTK, was utilized to generate unstructured 3D tetrahedral meshes. Each 3D volumetric mesh contains tetrahedral elements with six boundary prism layers at the vessel wall. Typically, our model sizes ranged from 1.5–2.0 million, with the average mesh size as 0.0022 mm³. Our mesh sensitivity study demonstrated that our mesh density was appropriate (see Supplementary Materials).

Finally, a commercial CFD simulation solver, FLUENT (v20.0, Ansys Inc., PA, USA), was implemented to solve Navier–Stokes equations. Specifically, we solved the unsteady Navier-Stokes equations numerically for laminar flow. Blood was modeled as an incompressible, Newtonian fluid with 0.004 Pa·s and 1040 kg/m³ dynamic viscosity and mass density, respectively. Pressure and momentum were spatially discretized using second-order and second-order upwind schemes in FLUENT (Ansys Inc., PA, USA), respectively. The temporal discretization was done using a second-order implicit scheme in FLUENT (Ansys Inc., PA, USA). In FLUENT, the pressure-velocity coupling was set to be resolved using the classic SIMPLE algorithm. As patient-specific flow waveforms were unavailable, an averaged pulsatile flow waveform measured from healthy subjects using magnetic resonance imaging [17] was used as the inlet boundary condition. Each case’s waveform was scaled to standardize to a mean physiological flow rate of 280 mL/min at the internal carotid artery. At the outlets, zero-pressure boundary conditions were prescribed.

Detailed protocols are previously published and can be found elsewhere [18–20]. The above-mentioned CFD workflow was verified with both phase-contrast magnetic resonance angiography (PC-MRA) [21, 22] and ultrasound Doppler [23] for aneurysmal flow.

Geometric Analysis

Most morphological parameters have been used in a recent publication [20], except for Voronoi diagram characteristic curve points that were first proposed by Berkowitz [24]. A brief introduction of the Voronoi diagram and its characteristic curve is given below for completeness. As illustrated in Figure 2, an aneurysm volume can be decomposed with many overlapping spheres of varying sizes. Those spheres are known as maximal inscribed spheres (MIS). Of note, small MISs (see the green spheres in Figure 2(a)) often correspond to small-sized protrusions. If we remove a fraction of those MISs (from the smallest to the largest ones), the “summed” aneurysm volume will gradually shrink, as shown in Figure 3. This curve is known as the Voronoi Diagram characteristic (VDC) evolution curve. In the beginning, when small MISs are removed from the above-mentioned “volume summation” process, the reduction of the “summed” aneurysm volume is small. As larger spheres (typically close to the largest MIS) are removed, the “summed” aneurysm volume will sharply reduce. Because different aneurysms have different distributions of the MISs (see Figure 2(b)), the shape of this VDC evolution curve will be different.

Figure 2:

(a) An illustration example showing an aneurysm can be summed together by many overlapping spheres of varying size. (b) a histogram showing a distribution of radii of those overlapping spheres ranging from 1.1mm to 18.7mm. In (a), the aneurysm is shown by a transparent white surface, while green and yellow colors represent small and large spheres, respectively.

Figure 3:

Voronoi diagram characteristics (VDC) curves for three selected intracranial aneurysms

In Figure 3, given a more spherical aneurysm (aneurysm A), the “ summed “ volume reduction drops off slowly as the cutoff ratio increases. In contrast, reducing the residual aneurysm volume is considerably faster in two less spherical aneurysms (i.e., aneurysms B and C). This observation rationalized our use of the VDC curve to improve the differentiation of intracranial aneurysms. To do so, we define NRV_x as the normalized residual volume when the cutoff ratio is x/10. Thus, our machine learning methods can use a sequence of geometrical parameters NRVx for IA characterization.

Velocity-informatic Analyses of Directional Velocity Information

As shown in Figure 4, starting from a three-dimensional (3D) CFD-simulated velocity field at the peak systole phase in and around an IA, a published IA segmentation algorithm by our group [25] was used first to isolate the vector velocity field with the aneurysm dome. Then, all identified vector velocity values in the unstructured grid were resampled (through interpolations) to a uniform (computing) grid with a voxel size of 0.2 × 0.2 × 0.2 mm³. In the second step (Figure 4b), the direction of each velocity vector was mapped onto an equally partitioned unit sphere with 360 pieces [26]. More specifically, if a velocity vector direction aligns the best with a partition zone vector, the velocity vector should be associated with that particular partition zone. As a result, each velocity vector in the uniform grid mentioned above could be associated with one of 360 partitions on the unit sphere (Fig. 2c). We treated those velocity associations as a three-dimensional 8-bit image and named this image a directional velocity field/image (Figure 4d). A more illustrative description can be found in the Appendix. We found that the number of partitions used on the unit sphere did not influence velocity-informatics features, as long as the number of partitions was sufficiently large (e.g., > 256; see Supplementary Materials).

Figure 4:

A graphic illustration of the procedures involved. Our procedures convert a CFD-simulated aneurismal velocity vector field (d) into a 3D image named directional velocity image (d). The directional velocity image can be directly used for velomic analysis using PyRadiomics. The velocity vector field is color-coded by its velocity magnitude (0–626 mm/s) and partition zone IDs (0–359), respectively.

Once the 3D directional velocity image became available, an open-source Pyradiomics package [13] was used to calculate velocity-informatic parameters in the third step. It is important to note that the Pyradiomics package was applied to a directional velocity image instead of a radiographic image. To make this point clear, we hereafter refer to resultant parameters obtained from the Pyradiomics package as velocity-informatic parameters.

We investigated all velocity-informatic parameters (>200) available through the Pyradiomics package related to first-order statistics, gray level co-occurrence matrix (GLCM), gray level run length matrix (GLRLM), gray level size zone matrix (GLSZM), neighboring gray-tone difference matrix (NGTDM), and gray level dependence matrix (GLDM).

Machine Learning Methods, Training, and Assessments

Four established machine learning (ML) algorithms (support vector machine [SVM], generalized linear model [GLM], Random Forest [RF], and Lasso and elastic-net regularized generalized linear model [GLMNet]) were selected to demonstrate added values for the proposed velocity-informatic variables for predicting IAs’ rupture status. All analyses were done using an open-source statistical analysis package (R Studio, Version 4.13, https://www.rstudio.com/).

Once all data were obtained (see Fig. 1), the entire dataset was first randomly split into a training set (102 cases) and a testing set (10 cases) by a 9 to 1 ratio for each realization. Optimal hyper-parameters for each model were auto-tuned during the training of 10-fold cross-validation. The ML models were finally tested on the testing dataset to conclude the analysis of each realization. This process was repeated 100 times to ensure that statistically stable results were achieved. The performance of 4 ML methods was assessed by computing the prediction accuracy and AUC on the testing samples.

Summary of Parameters Used in Machine-learning-based Characterization of IAs

This established workflow described above in Figure 1 generated two anatomical features, nine hemodynamic parameters, and thirteen morphological variables. Seven key velocity-informatic parameters obtained through the proposed velocity-informatic analysis (Figure 4) are briefly introduced in Table 1, and a complete list of all available computed features in Pyradiomics can be found online (https://pyradiomics.readthedocs.io/en/latest/).

Table 1:

A summary of anatomical features, hemodynamic parameters, and velocity-informatic and morphological variables.

Types	Parameters	Descriptions
Anatomical parameters	Aneurysm Location Aneurysm Type	Location of the aneurysm Type of the aneurysm
WSS-related and flow vortex parameters	Systole STAWSS	Spatio-temporal averaged wall shear stress at the peak systole
	Systole WSSMin	Minimum wall shear stress at the peak systole
	Systole WSSMax	Maximum wall shear stress at the peak systole
	SA OSI	Spatially-average of the oscillatory shear index
	Std OSI	One standard deviation of the oscillatory shear index
	TA LSA 2	Temporally averaged low shear area less than 0.4 Pa
	TA LSA Std 2	One standard deviation of temporally averaged low shear area less than 0.4 Pa
	Systole TADVO	Temporally averaged degree of volume overlap during the systole phase
	Systole DVOStd	One standard deviation of the degree of volume overlap during the systole phase
Morphological parameters	Bulbous	Presence of bulbous
	Aneurysm Volume	Volume of the aneurysm
	Aneurysm Height	Height of the aneurysm
	Sac Max Width	Maximum width of the aneurysm sac
	Size Ratio Height	The size ratio between aneurysm height and parental artery diameter
	Size Ratio Width	The size ratio between aneurysm width and parental artery diameter
	Aspect Ratio Star	An aspect ratio of the intracranial aneurysm
	Vessel Diameter	Diameter of the parental vessel connected to the aneurysm
	Ostium Minimum	The maximal ostium diameter
	Ostium Maximum	The minimal ostium diameter
	Aneurysm Area	Area of the aneurysm
	Ostium Area	Area of the ostium
	NRV1~NRV10	Points on the Voronoi diagrams characteristic curve
Velocity-informatic Parameters	Difference Average	A measure of the relationship between occurrences of pairs with similar intensity values and occurrences of pairs with differing intensity values.
	Difference Entropy	A measure of the randomness/variability in neighborhood intensity value differences.
	Informational Measure of Correlation	A measure of the complexity of an image texture
	Inverse Difference Moment	A measure of the local homogeneity of an image.
	Inverse Difference	A measure of the local homogeneity of an image.
	Inverse Variance Zone Percentage	A measure of the coarseness of the texture by taking the ratio of the number of zones and number of voxels in the IA dome.

Abbreviations are listed as follows: Systole STAWSS -- Spatially and temporally averaged wall shear stress during peak systole, Systole WSSMin -- wall shear stress minimum during peak systole, Systole WSSMax -- wall shear stress maximum during peak systole, Mean OSI -- spatially averaged oscillatory shear index, Std OSI -- one standard deviation of the oscillatory shear index, TA LSA 2 -- time-averaged low shear area less than 0.4 Pa, TA LSA Std 2 -- one standard deviation of time-averaged low shear area less than 0.4 Pa, Systole TADVO – time-average degree of overlap between flow vortex cores during systole, Systole DVOStd -- one standard deviation of the time-average degree of overlap between flow vortex cores during systole, Size Ratio Height -- Size ratio between aneurysm height and parent vessel diameter, Size Ratio Width -- size ratio between aneurysm width and parent vessel diameter, and NRV_x -- the normalized residual volume when the cutoff ratio is x/10 (see Figure 3).

Baseline Predictive Models and Dimension Reduction

Given a large number of parameters available, following good practices in ML, a multiple-step dimension reduction strategy was used to control the number of parameters in the subsequent ML-based predictive modeling to prevent overfitting and increasing computing time. First, the Wilcoxon rank sum test was performed to remove parameters with a p-value above 0.8. Second, using anatomical and morphological parameters (see Table 1), the GLM function in R was utilized for three ML methods: SVM with a linear function, GLMnet, and GLM as linear classifiers, to find the baseline models (i.e., feature combination). Since RF is a tree-based model, a stepwise feature selection technique was utilized to find a baseline model. Third, the feature importance function in R (R Studio, Version 4.13, https://www.rstudio.com/) was used to rank the top 20 parameters in the remaining hemodynamic and velocity-informatic parameter pool. Fourth, to improve the prediction performance, stepwise feature selection methods were used to adjust parameters empirically. More specifically, we used forward and backward feature selection to add or subtract parameters from the baseline model for each ML model. Meanwhile, the correlation coefficient was calculated in any step to avoid multiple highly correlated features (i.e., correlation coefficient >0.9). This parameter adjustment procedure terminated when 100 variants were reached for each ML method.

Results

Statistical Analysis

All identified geometric, hemodynamic, anatomical, and velocity-informatic variables (see Table 1) were analyzed using the Wilcoxon rank-sum test to investigate whether a statistically significant difference exists between the ruptured and unruptured groups.

Thirty-two parameters that are statistically significant in terms of differentiating ruptured and unruptured IAs are shown in Table 2. Of note, the total number of velocity-informatic parameters with statistically significant differences was 173. Only 14 most important parameters based on feature importance ranking are shown in Table 2 to keep our presentation concise.

Table 2:

IA morphological, hemodynamic (WSS and flow vortical characteristics), anatomical, and velocity-informatic variables tested in predictive modeling. Parameters are listed as Mean ± one standard deviation. Features marked with an asterisk indicate significant differences between ruptured and unruptured IAs: non-parametric Wilcoxon rank-sum test, p < 0.05. Only variables with p-values less than 0.35 are displayed in the table below. Abbreviations used in this table can be found in the caption of Table 1.

Category	Variable	Ruptured IAs	Unruptured IAs	P-value
	*Sac Volume (mm3)	149.92 ± 194.775	280.73 ± 355.14	0.002
	*Sac_max_width (mm)	6.54 ± 3.07	7.79 ± 3.03	0.011
	Size Ratio_height (mm)	3.51 ± 1.98	2.95 ± 1.39	0.186
Morphology	*Aspect_Ratio*	1.77 ± 0.76	1.72 ± 1.35	0.037
	*Parent Vessel Diameter (mm)	2.09 ± 0.76	2.77 ± 0.86	<0.001
	*Aneurysm Surface Area (mm2)	114.41 ± 97.32	176.04± 154.06	0.007
	*Ostimum Area (mm2)	14.58 ± 11.12	25.29 ± 20.33	<0.001
	*Ostimum_min (mm)	1.63 ± 0.58	2.15 ± 0.68	<0.001
	*Ostimum_max (mm)	2.52 ± 0.96	3.10 ± 1.04	0.001
	*Bolnus	21/44	20/68	0.050
	*NRV2	0.94 ± 0.03	0.95 ± 0.02	0.013
	*NRV3	0.90 ± 0.05	0.92 ± 0.05	0.018
	*NRV4	0.84 ± 0.09	0.88 ± 0.07	0.013
	*NRV5	0.76 ± 0.20	0.84 ± 0.09	0.007
	*NRV6	0.68 ± 0.25	0.79 ± 0.17	0.004
	*NRV7	0.53 ± 0.34	0.67 ± 0.29	0.005
	*NRV8	0.38 ± 0.36	0.53 ± 0.38	0.008
	*NRV9	0.17 ± 0.31	0.36 ± 0.40	0.007
	*NRV10	0.07 ± 0.23	0.25 ± 0.37	0.005
	Height (mm)	6.60 ± 2.67	7.80 ± 4.00	0.166
Anatomical	*Location			0.001
Parameters	MCA	15/44	37/68
	ICA	13/44	26/68
	ACA	16/44	5/68
	*IA Type			0.050
	Side-wall	23/44	48/68
	Bifurcation	21/44	20/68
Velocity-informatic Parameters	*GLCM.Difference Average	1.77 ± 0.24	1.53 ± 0.25	<0.001
	*GLCM.Difference Entropy	1.30 ± 0.67	0.94 ± 0.408	<0.001
	*GLCM.Imc2	0.97 ± 0.018	0.98 ± 0.008	<0.001
	*GLCM.Imc1	0.97 ± 0.018	0.98 ± 0.008	<0.001
	*GLCM.Idm	0.99 ± 0.003	0.99 ± 0.002	<0.001
	*GLCM.Idn	− 0.43 ± 0.08	− 0.51 ± 0.08	<0.001
	*GLCM.Id	0.67 ± 0.07	0.73 ± 0.06	<0.001
	*GLRLM.LongRunEmphaasis	1349.54 ± 535.07	1126.24 ±450.46	<0.001
	*Fisrtorder.Entropy	2.51 ±0.42	2.142 ± 0.327	<0.001
	*GLRLM.RunEntropy	3471.66 ± 3943.51	3996.43 ± 2770.26	<0.001
	*GLRLM.RunPercentage	2.43 ± 1.53	4.60 ± 3.56	<0.001
	*GLSZM.ZonePercentage	214267.98 ± 395532.06	12281.70 ± 2866315.92	<0.001

Model Assessment

The best predictive model and its performance are summarized in Table 3 for each ML method. The accuracy and AUC of each ML model were estimated, along with their confidence intervals (with a 95% confidence level).

Table 3:

A summary of prediction performance of 4 ML methods (average of 100 iterations). The (relative) performance enhancements are provided by the underlined numbers in the squared brackets. Each ML model with Velocity-informatics includes base variables and additional variables.

SVM (Baseline Variables: Aneurysm Location, Parent Vessel Diameter, Ostium min, NRV2)
Without Velocity-informatics		With Velocity-informatics (Additional Variables: IMC2, GLCM.DE, GLRLM.LongRunEmphaasis)
AUC	0.82(0.81–0.82)	AUC	0.86 (0.86–0.87) [0.04]
Mean Accuracy	72.60%	Mean Accuracy	76.90% [2.3%]
Mean Ruptured Accuracy	45.10%	Mean Ruptured Accuracy	60.00% [14.9%]
Mean Unruptured Accuracy	90.10%	Mean Unruptured Accuracy	88.10% [−2.0%]
GLM (Baseline Variables: Aneurysm Location, Parent Vessel Diameter, Ostium min, NRV2)
Without Velocity-informatics		With Velocity-informatics (Additional Variables: GLCM.DE, GLRLM.LongRunEmphaasis, GLCM.DA, GLSZM.ZP )
AUC	0.79 (0.79–0.80)	AUC	0.82 (0.82–0.83) [0.03]
Mean Accuracy	73.70%	Mean Accuracy	80.00% [6.30%]
Mean Ruptured Accuracy	54.25%	Mean Ruptured Accuracy	68.00% [13.75%]
Mean Unruptured Accuracy	86.66%	Mean Unruptured Accuracy	88.00% [1.34%]
GLMNet (Baseline Variables: Aneurysm Location, Parent Vessel Diameter, Ostium min, NRV2)
Without Velocity-informatics		With Velocity-informatics (Additional Variables: IMC2, GLCM.DE, GLRLM.LongRunEmphaasis)
AUC	0.80 (0.79–0.80)	AUC	0.83 (0.83–0.84) [0.03]
Mean Accuracy	72.10%	Mean Accuracy	76.40% [4.30%]
Mean Ruptured Accuracy	55.00%	Mean Ruptured Accuracy	57.00% [2.00%]
Mean Unruptured Accuracy	83.50%	Mean Unruptured Accuracy	89.33% [5.83%]
RF(Baseline Variables: Aneurysm Location, Parent Vessel Diameter, Ostium min, NRV2)
Without Velocity-informatics		With Velocity-informatics (Additional Variables: Id, GLCM.DE, GLRLM.LongRunEmphaasis, GLSZM.ZP)
AUC	0.75 (0.74–0.76)	AUC	0.78 (0.77–79) [0.03]
Mean Accuracy	71.50%	Mean Accuracy	74.30% [2.80%]
Mean Ruptured Accuracy	60.25%	Mean Ruptured Accuracy	60.50% [0.25%]
Mean Unruptured Accuracy	71.50%	Mean Unruptured Accuracy	83.50% [12.00%]

As described in Table 1, DA – difference average, DE – difference entropy, DV – difference variance, Id – inverse difference, Idm – inverse difference moment, ZP – zone percentage.

As shown in Table 3, the predictive accuracy of all 4 ML models falls into a relatively narrow range (AUC: 0.75 ~ 0.82 [without velocity-informatics] and 0.78 ~ 0.86 [with velocity-informatics]). With the inclusion of velocity-informatic variables, the prediction performance improved: on average, AUC and overall accuracy increased 0.03 and 4%, respectively. Most notably, on average, we were able to improve the average prediction accuracy for ruptured and unruptured IAs by 7.75% and 4.3%, respectively.

The ROC curves from 4 ML methods with and without the proposed velocity-informatic variables and their AUCs can be seen in Figure 5.

Figure 5:

ROC curves averaged from 100 runs of cross-validation support vector machine statistical characterization. Characterization model outcomes for 4 ML methods (a) without and (b) with the proposed velocity-informatic variables. 95% confidence intervals of AUCs are provided in the parentheses.

Discussion

In this work, we added novel velocity-informatics to quantify aneurismal flow disturbance, contributing to the predictive modeling of IA’s rupture status. Overall, our results (Table 3 and Fig. 3) demonstrated that including velocity-informatics can improve the prediction outcome (AUC and total prediction accuracy). It is interesting to note that, with the velocity-informatics, the SVM and GLM models can more accurately identify ruptured IAs (approximately by 14%), while maintaining a comparable prediction accuracy for unruptured IAs. In contrast, the RF model improved the prediction accuracy in the unruptured category (by approximately 12%). This is a notable improvement as compared to prediction models without velocity-informatics.

We also performed stratified k-fold cross-validation to generate folds with a fixed ratio between labels (i.e., ruptured/unruptured, IA location [MCA, ACA, and ICA]) in any folds, following identical steps described in the Methods section. As shown in Table 4, the improvements after adding velocity-informatic parameters were comparable (i.e., on average, AUC and overall accuracy increased 0.03 and 4.2%, respectively).

Table 4:

A summary of prediction performance of 4 ML methods (average of 100 iterations) using stratified k-fold cross-validation. The (relative) performance enhancements are provided by the underlined numbers in the squared brackets. Each ML model with Velocity-informatics includes base variables and additional variables.

SVM (Baseline Variables: Aneurysm Location, Parent Vessel Diameter, Ostium min, NRV2)
Without Velocity-informatics		With Velocity-informatics (Additional Variables: IMC2, GLCM.DE, GLRLM.LongRunEmphaasis)
AUC	0.78(0.77–0.78)	AUC	0.81(0.80–0.81) [0.03]
Mean Accuracy	70.20%	Mean Accuracy	74.30% [4.1%]
Mean Ruptured Accuracy	51.00%	Mean Ruptured Accuracy	54.75% [4.75%]
Mean Unruptured Accuracy	88.30%	Mean Unruptured Accuracy	87.33% [−0.97%]

GLM (Baseline Variables: Aneurysm Location, Parent Vessel Diameter, Ostium min, NRV2)
Without Velocity-informatics		With Velocity-informatics (Additional Variables: GLCM.DE, GLRLM.LongRunEmphaasis, GLCM.DA, GLSZM.ZP)
AUC	0.79(0.79–0.80)	AUC	0.82(0.82–0.83) [0.03]
Mean Accuracy	72.80%	Mean Accuracy	75.80% [3.00%]
Mean Ruptured Accuracy	50.25%	Mean Ruptured Accuracy	66.50% [16.25%]
Mean Unruptured Accuracy	87.85%	Mean Unruptured Accuracy	82.00% [−5.85%]

GLMNet (Baseline Variables: Aneurysm Location, Parent Vessel Diameter, Ostium min, NRV2)
Without Velocity-informatics		With Velocity-informatics (Additional Variables: IMC2, GLCM.DE, GLRLM.LongRunEmphaasis)
AUC	0.79(0.79–0.80)	AUC	0.81(0.80–0.81) [0.02]
Mean Accuracy	72.00%	Mean Accuracy	74.00% [2.00%]
Mean Ruptured Accuracy	51.00%	Mean Ruptured Accuracy	53.00% [2.00%]
Mean Unruptured Accuracy	86.00%	Mean Unruptured Accuracy	88.50% [2.50%]

RF (Baseline Variables: Aneurysm Location, Parent Vessel Diameter, Ostium min, NRV2)
Without Velocity-informatics		With Velocity-informatics (Additional Variables: Id, GLCM.DE, GLRLM.LongRunEmphaasis, GLSZM.ZP)
AUC	0.75(0.74–0.75)	AUC	0.79(0.78–0.79) [0.04]
Mean Accuracy	70.70%	Mean Accuracy	77.50% [6.80%]
Mean Ruptured Accuracy	60.25%	Mean Ruptured Accuracy	69.50% [9.25%]
Mean Unruptured Accuracy	71.50%	Mean Unruptured Accuracy	82.33% [10.83%]

As described in Table 1, DA – difference average, DE – difference entropy, DV – difference variance, Id – inverse difference, Idm – inverse difference moment, ZP – zone percentage.

To date, other studies [20, 27–29] have also connected gross aneurismal flow disturbance to IA rupture risk. Early research by Cebral et al. [27] qualitatively observed that “ruptured aneurysms were more likely to have complex flow patterns, stable flow patterns, concentrated inflow, and small impingement regions.” Later, Byrne et al. [29] quantitatively estimated aneurismal flow’s spatial complexity and temporal stability using quantities derived from vortex core lines and proper orthogonal decomposition. They found that the spatial complexity (area under the curve [AUC] = 0.905) and temporal stability (AUC = 0.85) were promising for characterizing IAs. A recent study by Varble et al. [30] reported that the (swirling) flow vortex core surface areas had no strong correlation to IA rupture status. Sunderland et al. [20] found that the inclusion of flow vortex core parameters slightly improved the prediction accuracy of IA rupture status.

Notably, three previous studies [20, 29, 30] analyzed the flow vortex regions within IAs and correlated them with the IA rupture status. However, using the flow vortex analysis has limitations. First, flow vortex regions are low-velocity sub-regions within the IA dome, as implied by the definition of flow vortex cores. Consequently, in theory, they could be sensitive to small changes in velocity. Recall that the utility of different CFD solvers and settings may introduce minor changes but influence the outcome of vortex analysis. Second, analyses derived only from low-velocity sub-regions make hemodynamic assessments incomplete. In this study, we found that adding one or both flow vortex core-related variables did not exhibit improved prediction performance (data not shown). Two flow vortex core-related variables were not good discriminators because their p-values were low (0.7~0.9). Our early work [20] using flow vortex core-related variables found some marginal improvements in 47 Middle Cerebral Artery Aneurysms, while a large study by Varble et al. [30] reported that there was no strong correlation between (flow) vortex surface area and IA rupture status. In this sense, our results are consistent with both early studies.

We believe that velocity-informatics parameters investigated in this study could better assess the overall flow disturbance; therefore, adding velocity informatics parameters improved our ability to predict IA rupture status. Of note, fourteen velocity-informatics variables strongly correlated with IAs’ rupture status (P-value < 0.001; see Table 2). Seven of those fourteen velocity-informatics variables (Table 2) were GLCM-based. GLCM calculates how often pairs of velocity directions with specific values and in a specified spatial relationship occur in the directional velocity image. Also, directional velocity entropy and GLSZM’s Zone Percentage (see Table 2) are significantly correlated to the IA rupture status. GLSZM is based on counts of groups (so-called zones) of inter-connected neighboring voxels with the same velocity directions. In short, velocity-informatics variables statistically estimate changes in velocity directions with the IA dome, which are sensitive indications of gross flow disturbance regardless of velocity magnitude. Also, velocity-informatics does not rely on velocity (spatial) gradients. In short, the proposed velocity-informatic does not have the two limitations of flow vortex core/line analysis mentioned above.

Our study also reveals that our ML prediction models have room for improvement, as our strongest models (in terms of AUC) identified only 60% of ruptured IAs (see Table 3). Many studies incorporate patient medical information: age, gender, family history (hemorrhage), smoking habits, hypertension, etc. [31–34]. Such information was not available for this work. Medical information could improve predictions when adapted to this study’s models.

Furthermore, in all four ML methods, WSS and its derivatives were not included in the best models (see Table 3) because those parameters negatively impacted our prediction performance. This observation is not surprising because both WSS extrema impart differing cellular changes linked to IA rupture [35], making accurate prediction models using WSS and its derivatives difficult. One potential improvement is to investigate spatial patterns of WSS instead of using WSS extrema. To our knowledge, spatial patterns of WSS have not been well explored in the literature.

Our study has a few limitations. First, this study is a small retrospective analysis with only 112 IAs with known IA rupture status. Now, the feasibility has been established, and thus, our ongoing work includes expanding the study with additional cases and cases from an independent source for validation. It is important to note that a clinically more valuable tool would predict the rupture risk of unruptured IAs. Given the low rupture probability among IAs [1–6], we must collect a large volume of IAs’ data under continued imaging surveillance. However, such a public database is not available yet. We echo the plea by Bijlenga et al. [36]: Creating an aneurysm data bank is critically important and perhaps the only pathway to develop ML algorithms like ours further. Second, our ML results are probably not optimal. There are approximately 300 variables; thus, variable selection through an exhaustive search of all possible combinations is intractable and, therefore, was not attempted. GLM was used to generate a baseline model for itself, SVM, and GLMNet. We verified that baseline models developed for SVM and GLMNet by combining correlation analyses (i.e., creating a pool of uncorrelated variables) and stepwise adjustments were the same as those generated by the GLM. In the future, more automated variable selection schemes will be investigated. Third, this study used idealized flow waveforms based on magnetic resonance-based flow imaging from healthy human subjects, which might limit the realism of our hemodynamic analysis. In the future, patient-specific waveforms as inlet boundary conditions would better represent patient flow patterns.

Conclusion

Given the data investigated, we found that adding velocity-informatics from aneurismal velocity data can improve the overall characterization of an IA’s rupture status (AUC: 0.03 and Total Accuracy: 0.04). Notably, the proposed velocity-informatics can sizably enhance the prediction of ruptured IAs (approximately 13%) for SVM and GLM models. In contrast, the proposed velocity-informatic variable was able to noticeably improve the prediction of IAs’ rupture status for the RF model (12%). In our future work, we aim to extend our ML models to predict the rupture risk of IAs once surveillance imaging data of IAs become available.

Abbreviations

ACA

Anterior Cerebral Artery

AUC

Area Under the Receiver Operator Characteristic Curves

CFD

Computational Fluid Dynamics

DVO

Degree of Volume Overlap

GLCM

Gray Level Co-occurrence Matrix

GLDM

Gray Level Dependence Matrix

GLM

Generalized Linear Model

GLMNet

GLM with Lasso or Elastic-Net Regularization

GLRLM

Gray Level Run Length Matrix

GLSZM

Gray Level Size Zone Matrix

IA

Intracranial Aneurysm

ICA

Internal Carotid Artery

LSA

Low Shear Area

MCA

Middle Cerebral Artery = MCA

ML

Machine Learning

MIS

Minimal Inscribed Sphere

NGTDM

Neighboring Gray Tone Difference Matrix

NRV_x

Normalized Remaining Volume at x% of (MIS) sphere cutoff

OSI

Oscillatory Shear Index

OSI-Std

Oscillatory Shear Index Standard Deviation

RF

Random Forest

SA-OSI

Spatially Averaged Oscillatory Shear Index

STA-WSS

Spatially and Temporally Averaged Wall Shear Stress

SVM

Support Vector Machine

TA-DVO

Temporally Averaged Degree of Volume Overlap

TA-NOV

Temporally Averaged Number of Vortices

TA-WSSMax

Temporally Averaged Wall Shear Stress Maximum

TA-WSSMin

Temporally Averaged Wall Shear Stress Minimum

UI

Undulation Index

VDC

Voronoi Diagram Core

VMTK

Vascular Modeling ToolKit

VtV

Vortex Volume to AAA Volume

WSS

Wall Shear Stress

WSS-Std

Wall Shear Stress Standard Deviation

Appendix: Creation of a Directional Velocity Field

We use two-dimensional velocity fields shown in Figure 6 as two simplified but concrete examples. According to the directionality, each velocity vector can be mapped to one of 360 partitions onto a unit circle in a two-dimensional space. As a result, a laminar flow field will be mapped to a narrow range (see the right column of Figure 6(a)), whereas a disturbed flow’s (directional) mapping will be more uniformly distributed from 0 to 359 (see the right column of Figure 6(b)).

Figure 6:

Two two-dimensional examples of mapping a vector field to its distribution: (a) a laminar case and (b) a disturbed flow case.)

In the three-dimensional space, each velocity vector field can be mapped to a partitioned united sphere (instead of a partitioned unit circle). The equal partition of a unit sphere is well understood in the Applied Math literature, and a well-established method [26] was used in this study. If a velocity vector field is displayed in a three-dimensional uniform grid, we can easily obtain the proposed directional velocity field as a three-dimensional image (see Figure 6(d)).