III.Results
III.1. Model of the geometry of the descending aorta in
3D
In this section, the first phase of our 5D model which consists of
defining the geometry of the descending aorta in 3D was proceeded. This
step states on the reconstruction of the aortic model from the TRICKS
sections. The Multiplanar reconstruction in Figure.6 is a crucial step
to carry out 3D reconstruction for the descending aorta presented in
axial plane in Fig.1 and Fig.2:
A threshold to the areas of interest that defines the active mask was
applied based a low limit and a high limit. The mask contains pixels
with a value between the two threshold limits. The upper and lower
thresholds are limited to the maximum and minimum intensity. The updates
according to the defined limits gives a reconstruction of the model of
the aorta in 3D based on the Multiplanar reconstruction of the TRICKS
cuts in Figure.3:
The refinements of the three-dimensional reconstructions obtained
depends essentially on the conditions and quality of acquisition of
cuts, thickness of the cuts, the distance between two successive
acquisition slices and the quality of the segmentation and the
reconstruction algorithm used. The final geometry is shown in Figure.4:
Mathematical modeling and simulation environment presentation is
detailed in (Wilhelm et al., 2016) with precision analysis for IGS
models in (Ray et al., 2017). The second phase consists of decomposing
this IGS model into 3 elements: body, inlet, outlet as shown in
Figure.5:
The geometry of the aorta has the following characteristics: length
along the x-axis = 3.6339e-002 length along the y-axis = 5.66596e-002 m,
length along the z-axis = 8.4559e-002 m with a total volume =
2.5915e-005 m³, number of nodes = 593223, and number of elements =
3168417². The number of faces of the body (wall) is equal to 449 with
total area of 5.6453e-003 m². The result of the mesh is presented in
Figure.6
III.2. Setting of the
solution
To solve the 2D Navier-Stokes equation the configuration of this fluid
solver was based on the pressure with absolute velocity formation in
stable time. Our fluid will be blood with density of 1056 (kg / m3) and
viscosity of 6 (kg / m3). Boundary conditions must be zero in the aortic
model. The execution of the laminar flow model defines velocities and
pressure in the viscous flow field (the Navier-Stokes equation) to solve
the displacement of the internal facet of the 3D model of the aorta.
In the momentum that governs fluid equations, velocity and pressure the
parameters are coupled. There are two main types of methods for solving
the discrete time equation algebraic equations: the coupled method and
the separate method. A coupled method is characterized by the
simultaneous solution of velocity and pressure parameters. Due to the
low computing efficiency and the large memory requirement, it has not
been widely applied in engineering problems. Coupled methods have been
widely used for calculating compressible flows, while separate methods
have been preferred for calculating incompressible flows. Unlike a
coupled solution, a separate method solves the velocity and pressure
fields separately or consecutively. It presents the advantages of
reducing the computer’s memory and computing time, making it more
efficient for analyzing incompressible environment simulation fluids as
it is indicated in our case for aortic stenosis modeling. (Wang et al.,
2018). The pressure analysis for our model is presented in Figure.7.
It could be concluded from this illustration that the pressure of the
entrance and exit is negligible compared to the body outside and inside
the model of the stenotic aorta. The pressure intersection (Pa) between
these 2 zones (inside and outside) of the wall at a critical point in
the position of 15 mm shows a remarkable overlap between the red and
blue part which explains why we can have a turbulence because of the
strength of the parietal wall exerted by the external and internal body.
The location of blood flow in a case of aortic dissection with a
complicated geometric feature, qualitatively and quantitatively, based
on the evolution of vortex structures and their interaction in the
narrowing region throughout a cardiac cycle can give an index on the
presence of a stenosis from 15mm length of the aortic segment.
The position of 15 mm there is a very high vortex magnitude which
reaches (800000 1 / s) as well as a mass of negative fluxes during the
first 6 iterations during solver calculation. This reflux shows that it
occludes in a segment of the aorta. These indices support the results
reported in the clinical assessment with isthmic extensor aortic
stenosis extended over 10 mm in length, reducing approximately 65% of
its lumen by 6mm in diameter, compared to what we estimated there is 15
mm wide aortic stenosis, a 5 mm error rate is detected.
III.3. Solution with
ANSYS-Fluent
CFD predicts the overall size of the stagnation and shunt zones, but
underestimates the length of the current line and the changes in speed
due to the flow in the aorta, a whole range of physics has been included
beyond simple structural simulations: fluid flow, electromagnetic,
thermal(Zaripov et al., 2018),(Tora & Dahlquist, 2015),(Hosseini &
Vahedi Tafreshi, 2012). However, the quality of the measurement needs to
be improved for quantitative validation of CFD results and the search
for flow effects such as tortuosity and laminar flow behavior. At the
same time, the results of the CFD simulations are interpreted not only
in terms of pressure drop but in all aspects of flow such as vector
orientation and velocity, current lines, areas of stagnation of blood
flow.(Schlanstein et al., 2015) . This concept of time-based flow is
considered in 3D modeling of the stenosing aorta to obtain the 5D format
as shown in Figure.8.
Due to the fiber of this model, the fluid flow is deflected, resulting
in a sinuous orientation of the flow lines which shows a
three-dimensional flow around the wall of the aorta, mainly directed
from the inlet to the outlet. The area of stenosis in the middle
indicated by lower speeds can be seen in Figure.9.
Focusing on the velocity in the stenosis part, we notice that the flow
field lines are delayed and decreased from 6.034 to 1.207 e001 to 1.810
e001 [ms-1]. What is interesting is the detection of a negative
pressure in the value narrowing zone is equal to -3.735 e005 [Pa] in
Figure.10.