Study on Cerebral Aneurysms: Rupture Risk Prediction Using Geometrical Parameters and Wall Shear Stress With CFD and Machine Learning Tools

Machine Learning and Applications: An International Journal (MLAIJ) Vol.5, No.4, December 2018
DOI:10.5121/mlaij.2018.5401 1
STUDY ON CEREBRAL ANEURYSMS: RUPTURE
RISK PREDICTION USING GEOMETRICAL
PARAMETERS AND WALL SHEAR STRESS WITH
CFD AND MACHINE LEARNING TOOLS
Alfredo Aranda and Alvaro Valencia
Department of Mechanical Engineering,
Universidad de Chile, Beauchef 851, Santiago 8370456, Chile.
ABSTRACT
We modeled an SVM radial classification machine learning algorithm to determine the ruptured and
unruptured risk of saccular cerebral aneurysms using 60 samples with 6 predictors as the gender, the age,
the Womersley number, the Time-Averaged Wall Shear Stress (TAWSS), the Aspect Ratio (AR) and the
bottleneck of the aneurysms, considering real cases of patients. We reconstructed computationally each
geometry from an angiography image to realize a CFD simulations, where the TAWSS was computed by
CFD analysis. A cross validation method was used in the training sample to validate the classification
model, getting an accuracy of 92.86% in the test sample. This result may be used to help in medical
decisions to avoid a complicated operation when the probability of rupture is low.
KEYWORDS
Machine Learning, CFD, cerebral aneurysm simulations, SVM, aspect ratio, computational applications.
1. INTRODUCTION
Millions of data are generated every day, and machine learning algorithms are used more
frequently in many areas. In biology science is essential may be able to predict and reduce risk
factors when a phenomenon (that may cause death[1]) is difficult to measure. An intracranial
cerebral aneurysm is an abnormal dilation of an artery caused by a weakness in the wall (a
reduction in the tunica media, i.e., muscular middle layer of the artery wall due to certain
hemodynamic factors [2]), and it is located in the subarachnoid space at the base of the brain [3].
These are typically classified based on its form and position in the main artery into terminal,
lateral, or bifurcation aneurysm [4]. High-blood pressure, smoking, family history, stress out and
a previous aneurysm are main factors that may increase the risk of an aneurysm or its rupture.
Clinical studies regarding the behavior of hemodynamic parameters such as wall shear stress
(WSS) or the interior velocity field within the aneurysm may be occasionally difficult to measure,
and indeed be able to predict whether its rupture. In contrast, a complete aneurysm hemodynamic
[5]and prediction studies are possible via Computational Fluid Dynamics (CFD) reconstructing
cerebral aneurysm models, and then implementing Machine Learning algorithms[6]using data
generated for each simulation and the geometrical parameters. Hemodynamic stresses are
considered as important factors affecting the development of aneurysms because they are directly
related with aneurysm rupture risks [7][8]. Similarly, geometrical parameters (combinations

2
between neck, width and height of the aneurysms) may be good factors in the behavior of the
aneurysm ruptures as well [9][10].
Relevant studies in machine learning techniques to predict the rupture risk of aneurysms have
been developed as computing capacity increases. Judy Shum et al. [11] found in a machine
learning for the assessment of AAA rupture risk study that the null hypothesis is rejected when
geometrical factors are considered predictors in a classify model. Qian et al. [12] also studied the
risk analysis of unruptured aneurysms using CFD and Energy Loss techniques, founding a useful
tool for the prediction. An important work was developed by Bisbal et al.[13] applying a data
mining approach to predict the rupture risk of aneurysms using hemodynamic, morphologic and
clinical features, however, the validation of the models was not presented. Monsalve-Torra et al.
[14] used a neural network algorithm to predict in hospital mortality in patients with abdominal
aortic aneurysm. In addition, there are recent studies that have proposed a complete methodology
to predict the risk of intracranial aneurysm ruptures using machine learning and image processing
techniques, taking clinical, demographical, environmental and medical data [15]. On the other
hand, a study found a first machine learning approach to establish the relationship between shape
features and ascending aortic aneurysm risk predicted from FE analysis using SSM, SVM and
SVR algorithms[9].Muluk et al. [16] predicted the aortic aneurysm rupture using only geometry
modeling considering 15 variables. In the same way, Mocco et al. [10] used the aneurysm
morphology to demonstrate and predict that these ones can be good predictors. Finally, recent
studies of Liu et al. [17]and Lee et al. [18]predicted the rupture risk using morphological
parameters and healthy behaviors with feed-forward artificial neural network and SVR,
respectively. The objective of this investigation is carried out a supervised machine learning
algorithm (SVM) using the least amount of statistic significant morphologic and hemodynamic
variables, simplifying the model and the compute-time of each iteration. This work is organized
as follow: Sect. 2 explain the simulation procedure and the tools to carry out all analysis. Sect. 3
presents and discusses the results. Sect. 4 draws conclusions.
2. METHODOLOGY
2.1. RECONSTRUCTION OF GEOMETRIES AND PROPERTIES
The models were generated by first performing aneurysm surgeries of the patients of Instituto de
Neurocirugía Asenjo (INCA), and then reconstructing 60 three-dimensional angiography images
on a 1:1 scale to obtain adequate geometries for the simulation software, ANSYS (see Figure 1).
In this investigation, 30 aneurysms were previously ruptured and other 30 were previously
unruptured.

3
Figure 1. (a) Three-dimensional angiography image from a patient of INCA (b) Reconstruction from the
three-dimensional angiography with boundary conditions (inlet and outlets) and the aneurysm geometrical
measurement (Neck, Width, and Height).
The geometrical dimensions of three aneurysms are shown in Figure 1. The AR (neck-to-dome
length/neck-width) was calculated for the entire cerebral aneurysm geometries, wherein AR
values from 0.63 to 5.28 were considered.
A laminar and incompressible fluid flow was considered using 𝜌 = 1065 𝑘𝑔/𝑚3
[19], [20] and
modeled by the conservation of mass and momentum or the Navier–Stokes equations. Blood was
considered as a non-Newtonian fluid, and the Carreau model was used to model the shear
thinning behavior of blood, as follows [21]:
𝜇𝑒𝑓𝑓(𝛾̇) = 𝜇𝑖𝑛𝑓 + (𝜇0 − 𝜇𝑖𝑛𝑓)(1 + (𝜆𝛾̇)2)
𝑛−1
2 (1)
where 𝜇𝑖𝑛𝑓 = 0.00345 𝑘𝑔/𝑚 ∙ 𝑠 (viscosity at infinite shear rate), 𝜇0 = 0.056 𝑘𝑔/𝑚 ∙ 𝑠 (viscosity
at zero shear rate), 𝜆 = 3.313 𝑠 (relaxation time), and 𝑛 = 0.3568 (power index) are the material
coefficients.
Respect to the mechanic behavior of the artery walls, we considered the simplification of the rigid
artery in all cases.
2.2. Boundary Conditions
It is important to mention that we reconstructed real aneurysms using angiography images and the
boundary conditions simulated the internal cardiovascular system of the brain and these ones
should be adjusted to maximize the real conditions, being an important role in the development of
the flow inside each artery. While, the inlet condition was used as a velocity profile, the outlet
conditions represented the blood pressure. The pressure difference was another important factor
that was assumed to be only a function of time, and it was generated by a pulse wave of a finite
velocity [22].
We used the Womersley velocity theory [21] to obtain the physiological flow conditions at the
artery inlet. The velocity profile was computed from the general Womersley solution (Eq. 2)

4
using a code in C++ and it was subsequently exported to the ANSYS Fluent software (the
Womersley solution equation is described in more detail in [21]).
𝑣(𝑟, 𝑡) =
2𝑄0
𝜋𝑎2 [1 − (
𝑟
𝑎
)
2
] + ∑
𝑄𝑛
𝜋𝑎2
[
1 −
𝐽0 (
𝛽𝑛𝑟
𝑎 )
𝐽0(𝛽𝑛)
1 −
2𝐽1(𝛽𝑛)
𝛽𝑛𝐽0(𝛽𝑛)
]
𝑒𝑖𝑛𝜔𝑡
𝑁
𝑛=1
(2)
With
𝛽𝑛 = 𝑖
3
2𝛼𝑛 = 𝑖
3
2𝑎√
𝑛𝜔
𝜈
(3)
where αn is the n-Womersley number, a is the artery radius of the inlet, n is the number of modes,
and ω is the angular frequency obtained from the period of the cardiac cycle. In our study, we
have chosen eight modes and an angular frequency of 7.703 s-1 (period of the cardiac cycle was
0.857 s) [23]. The Womersley solution depends on the Womersley number, and it is a measure of
the ratio of the momentum equation to the viscous part [21]. When αn is small, the unsteadiness is
not important, and the solutions become Poiseuille solutions that vary in magnitude, but not in
shape. If αn is large, the shapes of the profiles are not parabolic [21].
Figure 2a shows one of 60 blood velocity profile measurements delivered by INCA. We obtained
the time-averaged maximum velocity (TAMAX) following the results given by Li et al. [24] and
Blanco [25] for all artery-images using an R Studio tool[26]. We localized each RGB pixel of the
TAMAX line (a smooth line of the Figure 2a), then, we related the distance between a subtraction
of pixels and a subtraction of centimeters at the vertical
axis. An average was derived from all the velocity profiles and it was multiplied by the inlet area
of each geometry to yield the flow (Qi). Subsequently, a Fourier fitting of Qi was performed using
a fit function of RStudio to obtain the respective Fourier coefficients. Finally, the Fourier
coefficients were employed to calculate the Womersley velocity of each geometry.
Figure 2. (a) Blood velocity measurement from a patient of INCA. (b) Flow volume to employ in the inlet
condition.

5
We used a normal pulsatile pressure condition between 80 and 120 mmHg [27] (represented in
Figure 3), calculated through a three-element Windkessel model for the outlets. The purpose of
this model was to represent the realistic physiological flow patterns and pressure distributions in
the computational domain for the fluid [28].
Figure 3.(a) Equivalent pulsatilepressure computed by the (b) three-element Windkessel model.
2.3. Numerical Method and Setup of CFD
A mesh for each geometry must be considered to solve the transient Navier–Stokes equations by
considering a non-Newtonian fluid. In our case, we used a mesh of a density of 1500
elements/mm3
(shown in Figure 4), in which we studied the difference between the mean WSS at
the systole of the pulsatile blood flow with 250, 500, 1000, 2500, 3500, and 4500 elements/mm3
,
respectively. The maximum difference is displayed in Figure 5, and it is below 3% between 1500
and 4500 elements/mm3
. The criteria values selected for the time step and residual were 0.0001 s
and 0.001, respectively.
Figure 4. Type of grid using 1500 elements/mm3 for a case studied.

6
Figure 5. Comparison between the mesh results when the WSS at systole time was calculated using
different mesh densities. The difference of the computing time in ANSYS was almost ten times between
4500 and 1500 elements/mm3
.
The pressure implicit with splitting of operator (PISO) algorithm was used to solve the Navier–
Stokes equations using the spatial discretization of the least squares cell based on the gradient,
second-order pressure, and second-order upwind for the momentum. For the transient
formulation, the second-order implicit method was used.
We also calculated the Time-Averaged Wall Shear Stress (TAWSS) (Eq 4), where it was besides
averaged over the area of each aneurysm during a cardiac cycle T.
𝑇𝐴𝑊𝑆𝑆 =
1
𝑇
∫ |𝜏𝑤(𝑥
⃗, 𝑡)|
𝑇
0
𝑑𝑡 (4)
2.4. Statistic Test and Machine Learning Algorithm
In the prediction algorithm (optimization problem) we minimized a multiclass SVM model [29]
shown in Eq. (4)
𝑚𝑖𝑛𝜃 [𝐶 ∑ ∑ 𝑦(𝑖)
𝑐𝑜𝑠𝑡1(𝜃𝑇
𝑓(𝑖,𝑘)
) + (1 − 𝑦(𝑖)
)𝑐𝑜𝑠𝑡0(𝜃𝑇
𝑓(𝑖,𝑘)
) +
1
2
∑ 𝜃𝑗
2
𝑚
𝑗=1
𝑚
𝑖=1
𝑛
𝑘=1
] (4)
Where 𝐶 (=
1
𝜆
) is a regularization parameter to avoid the bias or variance, 𝑦(𝑖)
is the target, 𝜃𝑇
are
the unknow variables, 𝑥𝑗 are the features of the model, 𝑛 the quantity of the predictors and 𝑚
quantity of the training set. We used the Gaussian kernel, 𝑓(𝑖,𝑘)
= 𝑒𝑥𝑝 (−
‖𝑥𝑖−𝑥𝑗‖
2𝜎2 ), where
features are separated for a hyperplane in the transformed space.
Also, we employed an 80% of the data for training and 20% for testing the model where an
exhaustive cross-validation was used as a validation technique to avoid the problem of over-
fitting and it gives much more information about the algorithm performance. In addition, the
features considered in the model were the gender (14 males and 46 females), the age, the
Womersley number, the TAWSS, the RRT, the OSI, the AR and the Bottleneck (BNF).

7
Morphologic and hemodynamic parameters will be analyzed in an analysis of variance (ANOVA)
test to determine the statistical significance of each one, using a tolerance smaller than 0.05 [30].
3. RESULTS AND DISCUSSION
3.1. Simulation Results
The time-dependent WSS on the wall of each cerebral aneurysm was computed in all the
simulations (a case is showed in Figure 6), then, all hemodynamic parameters were computed and
a SVM algorithm was developed to determine the rupture risk of each aneurysm using an RStudio
script code. The WSS had a lower magnitude at the diastolic time than the systolic time, although
the temporary form was maintained. In each simulation results we noted that the WSS was mainly
located at the neck of the aneurysm (shown in Figure 7) due to the velocity vector inside of the
cerebral artery was approximately 90° with respect to the wall of a saccular aneurysm [31]
forming vorticities without being significant at the dome [32][33].
Figure 6. Mean WSS computed at an aneurysm for a normal pressure difference. We had considered the
second cycle of the given pulsatile blood in each solution.
Figure 7. (a) WSS and (b) velocity streamline computed at a systolic time from ANSYS software. The
WSS was localized at the neck of the aneurysm (AR = 2.88) where the flow was facing the wall.

8
3.2. Statistical Analysis
We analyzed the statistical significance of all parameters from CFD simulations and
morphological parameters through ANOVA statistic tests, where we selected the variables shown
in Table 1, satisfying the tolerance of P-value, and besides, we considered the smallest quantity of
them.
Table 1. Statistic of the predictors used on the predicted models.
Statistic WN TAWSS
[Pa]
Age AR BNF
Ruptured
(30 cases)
Min. 0.196 0.253 29.00 0.854 0.633
1st Qu. 2.687 0.365 52.00 1.294 1.187
Median 3.303 0.414 57.00 1.690 1.453
Mean 3.004 0.427 58.67 1.930 1.819
3rd Qu. 3.362 0.523 67.50 2.303 2.157
Max. 3.985 0.621 81.00 5.279 6.316
Unruptured
(30 cases)
Min. 1.404 0.462 30.00 0.634 0.574
1st Qu. 2.423 0.513 48.25 1.054 1.012
Median 2.963 0.721 57.50 1.341 1.176
Mean 2.871 0.736 56.10 1.388 1.372
3rd Qu. 3.285 0.828 64.25 1.551 1.645
Max. 4.104 0.967 76.00 3.860 2.854
All cases
(60)
F Value 5.521 8.361 5.361 9.968 4.215
P Value 0.00823 <0.001 0.00231 0.00263 0.0095
In Table 1, all quantities had higher value of the mean in the ruptured than in the unruptured
group, except TAWSS, in accordance with the results obtained by Xiang et al. [34] and [35]. We
also analyzed other morphological parameters such as Non-sphericity index (NSI), Aneurysm
Inclination Angle (AIA), volume and area of the aneurysm being less statistically significant than
AR and BNF, which is in good agreement with previous works [36]. Respect to the age and
gender variable of the patients, the p-value is smaller than the tolerance defined, being
statistically significant, following the results obtained by Li et al. [37].
3.3. Machine Learning Results and Discussion
An SVM with radial basis function kernel was trained with 46 samples, 6 predictors and 2
classes, being “unruptured” the positive class. To validate the model, a cross-validation
methodology was implemented with 10-folds, repeated 3 times. Then, the test set was used with
14 out-of-samples. The final values used for the model were σ = 0. 1456 and C = 0.5, being
92.86% in accuracy (showed in Fig. 8) and 0.6438 in Kappa.

9
Figure 8. Combination between Sigma and Cost to compute the best accuracy to the SVM radial model.
In addition, we computed a confusion matrix for the test set where results are showed in Table 2
and the statistics parameters showed in Table 3.
Table 2. Confusion matrix for the test set using an SVM algorithm.
Prediction Unruptured Ruptured
Unruptured 7 1
Ruptured 0 6
Table 3. Statistics parameters for the validation of the model.
Statistic parameter Value
Accuracy 0.9286
P-Value <1e-4
95% CI (0.7613, 0.9982)
Kappa 0.8571
Sensitivity 1.0000
Specificity 0.8571
Positive predictive value 0.8750
Negative predictive value 1.0000
Xiang et al. [34], Qin et al. [38], Jing et al. [39] and Fan et al. [40], used the area under the ROC
curve evaluation (AUC), achieved to obtain an AUC over 70% and under 90% using
morphological, biological or hemodynamic predictors. On the other hand, Monsalve-
Torra[14]obtained a 95.1% in accuracy using a multilayer perceptron (MLP) algorithm, however,
57 attributes were used from 310 cases (without hemodynamic parameters), being a non-scalable
problem due to high calculation times and a possible overfit of the model. Lau et al. [41] obtained
a maximum accuracy of 92.03%, evaluating many biological predictors in a small dataset. In this
investigation, the adjusted model may predict an accuracy of 92.86% using easily measurable
predictors as the AR, the Bottleneck, the age, the gender the Womersley number and the TAWSS.

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Respect to the limitations of this study, computational fluid dynamic techniques in cerebral
aneurysms are a relatively new approach translating a well-established engineering technology
into clinical research, being a real-world approximation [42]. Boundary conditions have an
important role in any CFD problem, they are approximated by no-variation generalized
waveforms, quantifying hemodynamic differences between ruptured and unruptured aneurysms
[43]. However, physiologic waveforms may also vary due to physical efforts or emotional
excitement, resulting in a sudden change in blood pressure and TAWSS. We could also improve
the accuracy of the models, considering the most statistically significant morphological, CFD,
biological and fluid-structure interaction (FSI) variables, where in situations that involves the life
or death of people, we need to have an accuracy as close as possible to 100%. This is also
possible according as we increase the number of predictors in the model, as indicated by Kohavi
et al. [44], or using reinforced learning algorithms, however in both cases it would imply having
more patient data, being a very difficult task to fulfill, although undoubtedly, these results may be
used as support for neurosurgeons. Respect to the time-computing limitations (considering both
the CFD and training simulations), we may improve it using a deep learning approach to estimate
the TAWSS [45], and then, to use the results in a new model to predict the rupture risk.
4. CONCLUSIONS
Six predictors were used to model an SVM radial classification algorithm to determine the
ruptured and unruptured of saccular cerebral aneurysms using 60 samples. We simulated CFD
models to compute the TAWSS in the aneurysms considering real cases of patients where we
reconstructed each geometry from an angiography image. We assumed a rigid artery in all
simulations. In the machine learning model, we considered a training sample of 48 cases
randomly selected and a test sample of 12 cases. A cross validation method was used to validate
the model, getting an accuracy of 92.86%. This result will help in medical decisions to avoid a
complicated operation when the probability of rupture is low. All predictors may be easily
measurable, however, to simulate and compute the TAWSS may be slow, in consequence, to
obtain a result of the ruptured or unruptured prediction in a short time, it could be investigated
and modeled with a machine learning algorithm in a future investigation. Also, in a future work,
fluid-structure interaction simulations may be carried out to obtain a complete scheme and
outcomes from the arterial oscillation, and how some resulting force can be used such as predictor
of the machine learning models.
ACKNOWLEDGMENTS
AA would like to thank CONICyT PhD fellowship No. 21140180.
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