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Conference Paper 

Improvement of Aortic Valve Stenosis Classification in Patients 
Through Computational Fluid Dynamics Model

Ioannis Makropoulos, Dimitris Zantzas, Vasilis Gkoutzamanis and Anestis Kalfas*

Aristotle University of Thessaloniki, Polytechnic School, Department of Mechanical Engineering, Thessaloniki, Greece.

* Corresponding Author Email: akalfas@auth.gr

ABSTRACT

Aortic valve stenosis (AS) is a common and severe valvular disease where accurate assessment is essential for determining 
prognosis and treatment. Current echocardiographic methods mostly rely on the simplified Bernoulli (SB) equation, which ap-
proximates the peak pressure drop (ΔP), risking poor stratification, especially for low-flow low gradient patients. This study 
examines the capabilities of combining computational fluid dynamics (CFD) and imaging techniques for better stratification of 
AS patients. Patient-specific geometries of the aortic valve, ascending aorta, and left ventricular outflow tract were reconstructed 
from CT and echocardiography data during peak systole. Inlet velocity boundary conditions based on ultrasound data enabled 
transient flow simulations. Blood flow was modeled as laminar and Newtonian, with the geometry discretized for computational 
efficiency without loss of accuracy. Validation against echocardiography data showed a 4% deviation in velocity predictions. 
Results indicated that ΔP and maximum velocity (Vmax) are strongly influenced by aortic valve area size, while leaflet geometry 
affects flow jet location. The CFD model revealed that SB overestimates ΔP in non-severe AS, potentially leading to misclassifi-
cation. By combining CFD with precise imaging, detailed hemodynamic insights can be achieved, addressing the limitations of 
conventional methods and improving patient stratification for treatment.

Keywords—Aortic valve stenosis, Patient-specific modeling, Stenosis categorization, Leaflet effects, Pressure drop, Maxi-
mum velocity, Hemodynamic flow field, Computational fluid dynamics.            

Copyright © 2024. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY): Creative Commons - 
Attribution 4.0 International - CC BY 4.0. The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright 
owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduc-
tion is permitted which does not comply with these terms.

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79 J Global Clinical Engineering Vol.6 Special Issue 6: 2024

INTRODUCTION

Cardiovascular diseases are the leading cause of death 
worldwide (32% in 2019)1, and among them, aortic valve 
stenosis (AS) is one of the most serious. Initially, the 
aortic valve (AV) is one of the four valves of the heart, 
situated between the left ventricle (LV) and the ascending 
aorta (AA). This valve typically consists of three leaflets2, 
which open and close during the cardiac cycle due to the 
pressure difference between the LV and AA, ensuring the 
unidirectional flow of blood towards the AA. 

AS is typically attributed to the calcification of its 
leaflets, resulting in an increased workload on the LV. 
Specifically, due to the constriction of the cross-sectional 
area of the aortic valve area (AVA), the LV is required to 
generate higher pressure, thereby ensuring the appropri-
ate pressure drop between the LV and the AA to maintain 
the flow of mass at normal levels. The primary method 
used for categorizing, i.e., assessing, the severity of AS is 
the non-invasive echocardiography. The key parameters 
utilized in this measurement include the maximum 
measured velocity, calculated AVA and pressure drop.2 
Specifically, the pressure drop is estimated using the 
simplified Bernoulli equation (SB, ΔPSB = 4 × VVC

2 mmHg, 
where Vvc represents the velocity at the vena contracta, 
i.e., the maximum velocity). Furthermore, it has been 
demonstrated that this equation tends to overestimate 
the actual pressure drop3, which could potentially impact 
patient assessment. The direct measurement of pressure 
drop can be achieved through invasive catheterization; 
however, this procedure carries inherent risks. 

Accurate patient categorization is of vital importance, as 
from the moment AS symptoms appear, the annual survival 
rate decreases by 25%.4 Therefore, in recent years, there 
has been an increased demand for more effective assess-
ment of individuals with AS and a deeper understanding 
of the flow field along the aortic valve. In this context, 
the goal of this research is to construct a computational 
fluid dynamics (CFD) model for simulating the flow along 
the aortic valve, utilizing real patient data. Additionally, 
another objective is to conduct a comprehensive analysis 
of the impact of aortic valve stenosis on the flow field. In 
this manner, this research aims to analyze the flow along 
the aortic valve for various constriction configurations, 

thereby enhancing our understanding of the phenomenon 
and facilitating future investigations in the quest for an 
additional index that will serve as a supportive tool in 
patient categorization. 

MATERIALS AND METHODS 

Data from computed tomography (CT) and echocar-
diography (Echo) of a patient were acquired. From the 
CT data, the corresponding three-dimensional geometry 
was constructed for maximum diastole and systole us-
ing discretization software (Retomo, 2024, BETA CAE 
Systems International AG, D4 Business Village Luzern 
Platz 4, 6039 Root, Switzerland) (Figure 1 (a)→(b)). 
Subsequently, different software (ANSA, Beta) was used 
for processing and the improvement of the mesh (Figure 
1 (b)→(c)). Additionally, the open AV’s geometry was 
not discernible in the CT data at peak systole, likely due 
to the rapid nature of systole and the thinness of the 
leaflets. In contrast, the closed AV was distinguishable 
at maximum diastole. For this reason, the geometry of 
the open AV was constructed after processing the closed 
AV, and the geometric dimensions were validated using 
the echo data (Figure 1 (c)). Specifically, the AVA cross-
section was nearly identical between the model and the 
echo (310 mm2). Subsequently, the enhanced geometries 
obtained at both maximum diastole and systole were inte-
grated within the left ventricular outflow tract (LVOT) to 
facilitate the prescribed motion of the LV (Figure 1 (d)). 
However, it was found in the literature that this motion 
does not significantly affect pressure drop.5. Therefore, 
the prescribed left ventricle motion was chosen to be 
removed in order to reduce computational costs, and a 
conduit was placed in its position. Additionally, a second 
conduit was added to the ascending aorta to minimize 
the effect of boundary conditions on the results. The total 
dimensions of the two conduits are shown in Figure 1 (d), 
measured from the AVA. 

To investigate the influence of AS and its valve leaflets 
on flow dynamics, a Python code was developed. This 
code, in conjunction with ANSA, facilitates the creation 
of various aortic valve geometries. Specifically, this code 
utilizes some basic geometric characteristics of the original 
valve and a user-defined percentage step. In this way, the 
desired AVA profiles are automatically generated in the 

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J Global Clinical Engineering Vol.6 Special Issue 6: 2024 80

form of curves. Figure 2 depicts the geometries of the AV 
constructed with different AVA values.

The flow simulation was conducted using computational 
fluid dynamics software (ANSYS Fluent, R3, 2019). The 
simulation was time-varying (transient), and the valvewas 
in the fully open position during systole. The time step 
chosen was 10−3 seconds (it was found that variations 
between 10−3 seconds and 10−4 seconds result in a 0.03% 
deviation, while exponentially increasing computational 
cost). Incompressible fluid with a density of 1060 kg/m3 
and Newtonian fluid with a dynamic viscosity of 0.004 
kg·m/s) were considered. The boundary condition for the 
inlet referred to mass flow, for which it was assumed to 
follow a sin waveform, generating 90 ml (stroke volume, 
SV) during systole, which had a duration of 0.35 seconds 
(both values were derived from the echo data). The outlet 
boundary condition corresponded to a pressure, which 
was assumed to remain constant at 120 mmHg.6 

An investigation was conducted to assess the impact 
of inflation layers and turbulence model on the relevant 
parameters, pressure drop (ΔP), and maximum velocity 
(Vmax) at peak systole. The pressure drop was calculated 
based on the difference in static pressure between the 
level 45 mm before the AVA and 90 mm after the AVA. 

It was observed that the inflation layers introduced a 
deviation of 7.8% and 3.8% in ΔP and Vmax, respectively. 
For the investigation of the turbulence model, the low 
Reynolds SST model was chosen based on the literature.7 
This model was used in conjunction with the volume 
mesh containing the inflation layers and produced ymax

+
 

(t) < 1.7 < 5. Comparing the results between the lami-
nar and turbulent flow models, differences of less than 
0.8% were observed for both ΔP and Vmax. Therefore, the 
impact of the turbulence model appears to be minimal. 
Additionally, the accuracy provided by the introduction of 
inflation layers, relative to the additional computational 
cost, is considered negligible. For these reasons, and to 
reduce computational costs, the laminar flow model and 
the volume mesh without inflation layers were chosen. 
Additionally, before employing the two-volume meshes 
(one with inflation layers and one without), independent 
studies of the mesh were conducted. Specifically, for the 
volume mesh that was chosen for the simulations (without 
inflation layers), five different volume mesh sizes were 
examined: 0.4, 0.8, 1.6, 3, 9.6 × 105. Between the 4th and 
5th volume meshes, there was a difference of 1.53% in 
ΔP and 0.98% in Vmax, while between the 3rd and 4th vol-
ume meshes, the differences were 3.34% and 0.96% for 
ΔP and Vmax, respectively. The 4th volume mesh size was 
selected to reduce computational costs. The assumptions 
made regarding the mesh size, the choice of a volume 
mesh without inflation layers, and the use of laminar 
flow reduced the computational time for simulating the 
entire systolic cycle for one case from approximately 24 
hours to 5 hours. The simulations were conducted on a 
laboratory computer with 32 GB RAM, a 512 GB SSD, and 
an 11th Gen Intel(R) Core™ i7-1165G7 processor.

FIGURE 1. Representation of the methodology followed for 
the construction of the computational model. (dAA diameter 
of the ascending aorta)

FIGURE 2. Different AVA cross-sections. 

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81 J Global Clinical Engineering Vol.6 Special Issue 6: 2024

RESULTS

For the validation of the model, initially, a comparison 
of the results with the measurements from the examined 
individual’s echo was performed. The maximum velocity 
in the echo at the LVOT ranges from 1.13 to 1.22 m/s, 
while the corresponding velocity in the model is 1.27 
m/s. Therefore, a 4% deviation in velocity is observed. 
Furthermore, at the peak of systole, the pressure drops 
and the maximum velocity calculated from the model are 
2.79 mmHg and 1.63 m/s, respectively. Figure 3 presents 
the results of the AVA’s impact on ΔP and Vmax, as derived 
using the AV from Figure 2 and connected with spline 
curves.  In the same diagram, the estimated pressure drop 
from SB is also depicted. The dashed lines indicate the 
thresholds for severe aortic stenosis condition.3 

To investigate the effect of each valve’s geometry on 
the flow field, four different models with different AVAs 
were created (Figure 4). The first model represents the 
patient’s initial AVA and serves as the baseline for com-
parison with the other three, which sequentially incor-
porate a dysfunctional valve. These dysfunctional valves 
were intentionally designed to achieve nearly identical 
AVA cross-sectional areas in all three cases. Simulation 
results showed that all three different aortic valves did 
not significantly differ in terms of the increase in ΔP and 
Vmax. Specifically, the three dysfunctional AVs exhibited 
an average increase of +215% in ΔP and +125% in Vmax.

DISCUSSION 

The comparison made between the results and the 
echo data indicates that the model adequately predicts 
the flow field. Moreover, for a more comprehensive 
comparison, a comparison was conducted with patients 
from the literature5,8 who exhibited similar geometric 
and hemodynamic characteristics, including comparable 
AVA and stroke volume. From the comparison, deviations 
were observed, which can be attributed to the slight differ-
ences in these characteristics. For instance, Vmax literature 
= 1.33 m/s, whereas Vmax model = 1.63 m/s. The higher 
value in the model can be attributed to the smaller AVA 
and the greater maximum flow volume. Based on this 
analysis, the methodology utilized for constructing the 
three-dimensional model has demonstrated its effective-
ness in calculating the maximum velocity and pressure 
drop at peak systole. In Figure 3, the high values of ΔP for 
severe AS are attributed to the constant stroke volume 
of 90 ml, whereas this volume is affected in cases of AS. 

FIGURE 3. Effect of AVA cross-sections on flow characteristics.

FIGURE 4. Models and flow patterns for assessing the impact 
of leaflets on the flow field.

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J Global Clinical Engineering Vol.6 Special Issue 6: 2024 82

was revealed that in the patient’s initial model, the infla-
tion layers have a more pronounced effect on ΔP and 
Vmax compared to the turbulence model, while the layers 
themselves are considered to provide negligible additional 
accuracy compared to the computational cost they intro-
duced. Moreover, it was observed that all three leaflets 
exhibited a similar impact on ΔP and Vmax, emphasizing 
that these parameters are predominantly influenced by 
the size of the AVA, rather than the specific valve geometry. 
However, the valve’s geometry, specifically the leaflets, 
influences the flow pattern of the jet.

REFERENCES

1. World Health Organization, Cardiovascular diseases (CVDs). 
Available online: https://www.who.int/news-room/
fact-sheets/detail/cardiovascular-diseases-(cvds).

2. Ring, L., Shah, B.N., Bhattacharyya, S., et al. Echocar-
diographic assessment of aortic stenosis: a practical 
guideline from the British Society of Echocardiogra-
phy. Echo Res Practi. 2021;8(1):G19–G59. https://doi.
org/10.1530/ERP-20-0035.

3. Baumgartner, H., Stefenelli, T., Niederberger, J., et al. 
“Overestimation” of catheter gradients by Doppler 
ultrasound in patients with aortic stenosis: a predict-
able manifestation of pressure recovery. J American 
Coll Cardiol. 1999;33(6):1655–1661. https://doi.
org/10.1016/s0735-1097(99)00066-2.

4. Carabello, B.A. and Paulus, W.J. Aortic Stenosis. Lancet. 
2009;373(9667):956–966. https://doi.org/10.1016/
S0140-6736(09)60211-7.

5. Hoeijmakers, M.J.M.M., Silva Soto, D.A., Waechter-Stehle, 
I., et al. Estimation of valvular resistance of segmented 
aortic valves using computational fluid dynamics. J 
biomech. 2019;94:49–58. https://doi.org/10.1016/j.
jbiomech.2019.07.010.

6. Weese, J., Lungu, A., Peters, J., et al. CFD-and Bernoulli-
based pressure drop estimates: a comparison using 
patient anatomies from heart and aortic valve segmen-
tation of CT images. Med Phys. 2017;44(6):2281–2292. 
https://doi.org/10.1002/mp.12203.

Therefore, the illustrated ΔP values correspond to the 
complete preservation of flow (SV = const) in the case 
of AS. Similar observations apply to Vmax. Additionally, 
in the same figure, a pronounced overestimation of SB 
is observed in individuals with non-severe AS.3 Overall, 
based on the chart in Figure 3, clinical researchers could 
be able to assess the severity of stenosis in the specific 
patient for whom the model was created. Additionally, 
they could examine potential stenosis cases that may 
arise in the future.

Therefore, by applying the methodology presented for 
constructing the CFD model and valves, clinical researchers 
could create corresponding diagrams for each patient under 
examination. This would lead to a more comprehensive 
understanding of each examined individual by medical 
researchers. However, for this analysis to be applicable in 
clinical research, it is imperative to utilize supercomput-
ers to minimize computational costs. Additionally, this 
methodology should be fully automated and thoroughly 
validated for accuracy across hundreds of patients. Based 
on the results obtained from the investigation of the leaf-
lets, it was found that all three leaflets affect ΔP and Vmax 
to a similar extent. Therefore, this leads to the additional 
conclusion that ΔP and Vmax are not as strongly dependent 
on the geometry of the aortic valve as they are on the 
size of the AVA. However, the geometry of the AV affects 
the flow field, as depicted in Figure 4, where the flow jet 
location is different in the four cases. Hence, the valve’s 
leaflets impact the location where the flow jet impinges 
on the AA, potentially contributing to the development 
of an aortic root aneurysm, as the impingement point in 
the ascending aorta can influence the Wall Shear Stresses.

 CONCLUSION

In this research, a methodology was presented for con-
structing a patient-specific computational fluid dynamics 
model for simulating blood flow along the aortic valve. 
It was found that the model construction methodology 
is sufficient for calculating ΔP and Vmax. Additionally, the 
code developed for automating the process of constructing 
various valves from the initial valve proved to be highly 
useful, as it can yield significant insights for future cases 
of more severe AS in the same patient. Furthermore, it 

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83 J Global Clinical Engineering Vol.6 Special Issue 6: 2024

7. Stewart, S.F.C., Paterson, E.G., Burgreen, G.W. et al. 
Assessment of CFD performance in simulations of 
an idealized medical device: results of FDA’s first 
computational interlaboratory study. Cardiovasc Eng 
Tech. 2012;3:139–160. https://doi.org/10.1007/
s13239-012-0087-5.

8. Yang, C.S., Marshall, E.S., Fanari, Z., et al. Discrepancies 
between direct catheter and echocardiography-based 
values in aortic stenosis. Catheter Cardiovasc Interv. 
2016;87(3):488–97. https://doi.org/10.1002/ccd.26033.

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https://doi.org/10.1002/ccd.26033

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