Precise Fluid-Solid Simulation of Human Left Ventricle along with

Aortic Valve during Systole

02+$00$'$/,021)$5(' A, MOHAMMAD MEHDI ALISHAHI A,1,

MARZIEH ALISHAHI A

a School of Mechanical Engineering,

Shiraz University,

Shiraz, 71936-16548, IRAN

Abstract: This paper presents an accurate blood flow model with tissue deformation of the human left

ventricle, including the aortic valve. A two-way fluid-solid Interaction (FSI) algorithm is employed to

simulate the performance of the human left ventricle during systole. The initial geometry of the left

ventricle is extracted from CT scan images of a healthy person. The simulation results produced the

systolic anterior motion of the Left Ventricle (LV) identical with the CT scan images at later times during

systole. Besides, the numerical results for left ventricular volume change, maximum blood velocity at the

aortic valve, and its maximum opening are in good agreement with physiological data. Although no clear

image of the aortic valve is apparent in CT images, the FSI simulation predicted the maximum opening of

the aortic valve to be 4.38 cm2 which is consistent with physiological observation on a healthy individual.

As an application of the above algorithm, a model of Hypertrophic Cardiomyopathy (HCM) or septal wall

thickening disease is constructed and studied during systole. This simulation provides an understanding of

heart performance under HCM conditions. According to the simulation outcomes, the mitral valve

approaches the septal wall under HCM due to the change in pressure gradient and the drag force on the

mitral valve. This blockage of the LV blood passage by the mitral valve results in stagnation pressure loss

and weaker hearth pumping power. Therefore, the maximum opening of the aortic valve, in this case, is

2.28 cm2, which is much lower than the physiological range, indicating the drastic effect of HCM on the

performance of the aortic valve and systolic performance.

Keywords: CFD, Systole, Left ventricle, Aortic valve, Fluid-Solid interaction, Mitral valve.

Received: April 15, 2021. Revised: January 12, 2022. Accepted: January 22, 2022. Published: March 3, 2022.

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1 Introduction

Cardiovascular diseases are the most crucial

cause of death, about 17.9 million people, an

estimated 31% of all deaths worldwide.

Therefore, any attempt to provide a better

knowledge of how they affect the regular

operation of the heart is worthwhile. One of

the disciplines for such studies is the

biomechanical branch and specifically the

heart simulation. In the end, such the ability

to predict the malfunction of the diseased

heart would be invaluable for choosing a

cure strategy.

With the ongoing growth of computational

capacities, researchers are inclined to use

Computational Fluid Dynamics (CFD)

methods and especially Fluid-Solid

Interaction (FSI) to simulate blood flow in

different parts of the cardiovascular system

[1-3]. These methods are also employed to

investigate heart pumping function in a

simplified model of the Left Ventricle (LV)

along with the aortic valve using different

geometrical assumptions [4]. Watanabe et

al. [5] assumed a simplified geometry model

and investigated the ventricular volume

change due to different contractile-stimulus

using the FSI method. The computational

algorithm was based on the Eulerian-

Lagrangian finite element method, while the

dynamic meshing captured large

deformations. Moosavi et al. [6] constructed

an anatomical model of the LV and the

aortic sinus based on the real images of a

volunteer and carried out the numerical

simulations of blood flow in the model. The

computed results for aortic outflow were

compared with the data obtained by the

phase-contrast MRI, and an acceptable

agreement between the simulation results

and the physiological measurements was

reported. Lorenz et al. [7] presented a

cardiac model consisting of four cardiac

chambers, cardiovascular and coronary

arteries. This geometric heart model was

built based on data from 27 CT cores at the

end of the diastole. The model's accuracy

was measured based on the comparison with

different references.

There is also some research on more precise

aortic valve modeling. Kim et al. [8]

simulated the nonlinear structure of polymer

aortic valves with three leaflets using both

computational and experimental approaches.

They presented a structural model that can

predict the heart structure's transformation

with a maximum error of 10% during one

complete stage of heart contraction.

Moreover, another research carried out by

Merryman et al. [9] studied the function of

the heart valves by estimating at least 3 ×

109 cycles for one person's life. Focused on

the biocompatibility of heart valves, i.e.,

bio-solid along with the bio-fluid

characteristics, the physiological function of

the aortic valve was well-documented.

Trung Bao Le et al. [10] investigated a real-

shaped LV with a simple aortic valve model,

two sheets that open and close, using the FSI

method. In this modeling, the mitral valve

was assumed to be completely open during

diastole and completely closed during

systole. The results showed an asymmetry in

the closure of aortic valve leaflets, which did

not match the physiological results.

Considering the material models available

for valve’s leaflet tissue, Sturla et al. [11]

assumed the mechanical response of the

aortic valve to be linear, and therefore

elastic material was an appropriate model.

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Employing the FSI method, it was shown

that the use of elastic material for valve

leaflets gives relatively good results

compared to experimental results. MC Hsu

et al. [12] developed a hyperelastic model of

a biological aortic valve placed at the

opening of the aorta. Two material models

were chosen for aortic valve tissue; Fung

and Venant-Kirchhoff models. It was

observed that the Venant-Kirchhoff model

produced relevant results. Using the FSI

method with the Venant-Kirchhoff model

for the aortic valve, the outcomes were

remarkably close to the measured in vivo

data.

The main objective of the current study is to

present and investigate a real-shaped model

of LV along with an aortic valve during

systole. The initial 3-dimensional geometry

is constructed based on CT scan images of a

healthy person to fulfill this purpose. Blood

is considered a Newtonian fluid, and the

hyperelastic Ogden model is chosen for

ventricular wall tissue and aortic valve

leaflets. The blood flow inside the LV and

ventricular wall tissue movement were

simulated using a two-way FSI algorithm,

and the obtained results are compared with

physiological data as a verification of the

modeling and the simulation. Thorough

apprehension of aortic valve plus LV

operation provide a more precise tool for

studying different diseases and could assist

heart valve pre-surgery evaluations. Along

this path, a model of septal wall thickening

disease, hypertrophic cardiomyopathy

(HCM), is also constructed and investigated

during the systole. HCM is a heart muscle

disease where the myocardium becomes

thickened, resulting in stiffer heart muscle.

If HCM occurs in the LV, it also will reduce

the ventricular volume up to 50% [13]. In

the case of HCM, the mitral valve leaflets

approach the septum wall and partially block

the blood flow into the aorta, and eventually,

the heart will lose its pumping ability. There

are two potential causes for such

phenomena; the change in pressure gradient

and drag force hypothesis [14] resulting in

total pressure loss in systolic performance.

In this paper, a simple form of HCM in LV

is modeled at the start of the systole, and the

resulting dislocation of mitral valve leaflets

and heart performance degradation is

investigated.

2 Physical Modeling

2-1 Left Ventricle Geometry

In this study, the geometry of the left

ventricle is extracted from CT scan images

of a healthy young male at the beginning of

systole. The CT scan images are taken by a

Philips Brilliance 64-slices CT scanner. The

images are captured in 21 phases, and each

phase contains 397 slices in three different

views. The first and last phases are identical.

The corresponding time and spatial

resolution are 38 ms and 0.42 mm,

respectively. The left ventricle geometry

was constructed from a CT angiography set

of images at the beginning of the systole

phase, using Mimics software. Figure 1

shows the CT images taken from one

volunteer at the beginning of the systole.

The red color represents the blood flow

region, and the violet color identifies the left

ventricle wall tissues.

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The smoothed left ventricle geometries and

the ventricular volume, which is the blood region at the beginning of systole, are shown

in figure 2.

(a)

(b)

Figure 2 Left ventricle geometry (a) solid region (b) fluid region.

The HCM model is constructed based on the

geometry of reference [14] and is shown in

figure 3. It is noteworthy that the flexible

mitral valve is modeled for HCM study in

order to examine the septum and mitral

valve interactions.

(c)

(d)

Figure 1 Different views of left ventricle (a) Front view (b) Top view (c) Side view (d) 3D view.

Mitral inlet

Aortic outlet

(a)

(b)

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Figure 3 Left ventricle geometry for HCM model (a) solid region (b) fluid region.

2-2 Aortic Valve Geometry

The aortic valve has a complex structure, but

due to the rapid opening and closure, proper

medical images of the valve could not be

extracted from CT images. Therefore, aortic

valve geometry is constructed with the aid

of CAD software, enclosed by boundaries of

CT scan images, and based on physiological

information. The dimensions of different

parts of the reconstructed aortic valve are

shown in figure 4.

(a)

(b)

(c)

Figure 4 Aortic valve model (a) and (b) front view (c) top view.

After reconstruction of the aortic valve, it

was integrated with the left ventricles in

CAD software. The left ventricular

geometry and added aortic valve are shown

in figure 5.

25mm

Sinuses of

Valsalva

15mm

41.9mm

Sinotubular

Junction

Leaflets

25.63m

22.63m

10.55mm

Aortic

leaflets

Mitral valve

Thickened

Septum

Mitral

(a)

(b)

Aorta

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Figure 5 Left ventricle geometries with the aortic valve (a) solid domain (b) fluid domain.

2-3 Material Models

Blood is modeled as an isothermal,

incompressible and Newtonian viscous fluid

with density of 1060 Kg/m3 and a dynamic

viscosity of 0.00345 Pa.s [15-16]. Blood

flow is assumed to be laminar [6, 17].

During systole and diastole, the heart

muscles undergo large deformations;

therefore, the hyperelastic material model is

the best choice to simulate these behaviors.

For the sake of simplicity, the material of

the aortic valve and left ventricular wall is

assumed to be homogenous, isotropic, and

hyperelastic. This study uses the Ogden

model for the hyperelastic strain energy

function for the aortic valve and left

ventricular wall. According to Ogden model,

the strain energy is defined as;

  





  





 󰇛󰇜

Where  and  are time dependent

variables,  is the material compressibility

parameter and  is principal stretch. The

initial shear modulus,  and initial bulk

modulus  are;













The corresponding parameters of the stress-

strain relation were previously evaluated

using the uniaxial experiment data [18-19]

and shown in table 1. The left ventricular

tissue and aortic valve densities are,

respectively, 1050 and 1040 kg/m3 [20].

Table 1. Ogden model parameters.

i=3

i=2

i=1

modelOgden rder O

-2.814E-06

1.49E-06

4.56E-06

(Pa-1)

7.61

7.62

7.59



(2)

(1)

Aortic valve

(a)

(b)

81.89

81.88

(Pa)

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3 Numerical Modeling

This study applies the iterative segregated

method to solve the structure and fluid

equations using ANSYS software

separately. The coupling of fluid and solid

domains is carried out based on the two-way

FSI method [21]. Accordingly, the latest

results computed from one part of the

coupled system are transmitted to the other

part, and these communications are

iteratively continued until the desired

convergence criterion is reached. The whole

simulation is carried out for a total physical

time of 0.3 s, covering the whole systolic

period.

3-1 Governing Equations

The turbulent flow field of blood in LV is

described by the 3D Navier-Stokes

equations;



󰇍



 

(3)



󰇍



 󰇛

󰇍



󰇜

󰇍



 

󰇍



(4)

Where 

󰇍



is the velocity vector, p is the

pressure,  and  are the density and the

viscosity of blood, respectively. The

equations (1) and (2) are solved by a

transient, pressure based, finite volume

algorithm.

3-2 Boundary Conditions (BC)

During the systole of a healthy heart, the

mitral valve is closed to prevent backflow to

the atrium while the aortic valve is open.

Therefore, the mitral valve is assumed as the

wall boundary condition with no flow

through in the present study. At the aortic

outlet, two different types of BC are used to

compare and evaluate the simulation results

with scan images. The first boundary

condition is the velocity BC, and the other is

the pressure BC at the aortic valve. Two

outlet BCs are the time-dependent

physiological velocity and physiological

pressure described respectively by Sagawa

et al. [22] and Fielden et al. [23]. Other

researchers widely used these relations for

blood flow simulation inside the aorta.

Figure 6 shows the physiological charts for

average pressure and average velocity

during systole.

Figure 6 The physiological charts during systole; (a) Average pressure BC [22] (b) Average velocity BC [23].

120

0 0,1 0,2 0,3

Pressure(mm-Hg)

Time(s)

0,2

0,4

0,6

0 0,1 0,2 0,3

Velocity(m/s)

Time(S)

(b)

(a)

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The inner surfaces of the ventricular wall

and the fluid surface in contact with this

wall are assigned as fluid-structure

interaction BC. The summary of the

boundary conditions is demonstrated in

figure 7. The same BCs are defined for the

HCM model.

The FSI boundary condition can be

described as;

 

(5)

 

(6)

In the above equations,  and  are fluid

and solid displacements, and and  are

fluid and solid stress tensors, respectively.

(a)

(b)

Figure 7 The boundary conditions; (a) solid boundary conditions (b) fluid boundary conditions

3-3 Computational Grid

For FSI modeling, the computational grids

are generated for fluid and solid domains,

and grid independence analysis was carried

out separately. The unstructured grids are

constructed for both solid and fluid regions.

The fluid grid consists of prismatic and

tetrahedral elements. The prismatic elements

are built near the wall surface to capture the

flow details in this region. The discretized

equations are solved for

each cell of the

computational grid. Three different grids in

both domains are generated to ensure that

the obtained results are independent of the

computational grid. Two surfaces are

defined in the fluid domain, one near the

apex and another near the aortic valve, to

study the grid independence of fluid domain

solution (figure 8). Figure 9 shows the grid

independence results regarding area-

weighted velocity computed on the

described planes at time 0.12 s.

Outlet BC:

 Pressure BC

 Velocity BC

Wall BC

Fluid-Solid

Interaction BC

Fix support BC

(Aorta outlet)

Fix support BC

(Mitral opening)

Fluid-Solid

Interaction BC

Free BC

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(a)

(b)

Figure 9 Mesh independency analysis based on average velocity changes on (a) plane 1 (b) plane 2.

Three grids with 143227, 299640, and

427667 elements are built to determine the

optimal spatial mesh resolution. According

to figure 9, the results of the three grids are

identical, which means that the obtained

solution is independent of the fluid grid.

Also, in two grids with more elements, the

results are closer to each other. The average

difference in velocity magnitudes between

the model with 299640 elements and the

model with 427667 elements is less than

1%. Therefore, the grid with 427667

elements is selected for further study. It

should be noted that at the end of the

systole, the speed on planes 1 and 2 is not

zero, which is due to the incomplete aortic

valve closure.

Grid independence analysis is also

performed for the solid domain. Therefore,

three different solid grids were generated

with 107699, 151689, and 226413 elements.

The results for the solid domain are

presented in Table 2 for different numbers

of elements for the LV wall tissue and aortic

valve.

Table 2. Mesh study of the solid domain for the physical model.

Maximum deformation

of aortic valve (mm)

Maximum heart muscle

deformation (mm)

Number of aortic valve

elements

Number of heart

muscle elements

5.88

20.612

41583

66161

6.05

20.625

63425

88264

6.08

20.628

115291

111122

0,2

0,4

0,6

0,8

0 0,1 0,2 0,3

Velocity(m/s)

Time(s)

mesh 143227 mesh 299640 mesh 427667

0,1

0,2

0 0,1 0,2 0,3

Velocity(m/s)

Time(s)

mesh 143227 mesh 299640 mesh 427667

Plane 1

Plane 2

Figure 8 Position of planes used for grid

independence analysis.

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A similar grid independence analysis is also

carried out for the HCM model. Three grids

for the fluid domain are constructed; 80939,

190217, and 291154 elements. The results of

the grid with 190217 elements are

independent of grid size, and it is considered

for further simulations.

Moreover, three time-steps, 0.0002 s, 0.0005

s, and 0.001s, were chosen to study the time

step independence of the simulation

outcomes. It was observed that the

simulation results with the time-step 0.0002

s were appropriate.

4 Result and Discussions

4-1 Solid Domain

The time variation of different parameters

related to the aortic valve and myocardium

tissue are shown in figure 10. At each node,

the deformation is calculated in three

Cartesian directions, and the maximum

value of the resultant deformations in the

entire geometry is reported as the maximum

deformation at any given time (figure 10a

and 10c). Based on figure 10, the

deformation profile of the aortic valve is

almost similar to the output velocity profile

(figure 9a). The maximum deformation of

the aortic valve occurred at 0.12 s, at the

same time where the output velocity is

maximum (figure 9a). The following fact

can explain it; as the aortic valve continues

opening and its deformation increases to a

maximum, the output velocity increases too

and reaches a maximum without any time

lag. However, the aortic valve opening

happens in the numerical model due to the

velocity or pressure BC at the outlet. It is

noteworthy that the deformation of the aortic

valve gradually decreases after this

maximum (figure 10a) while the velocity

drop is steeper (figure 9a) due to relaxation

of the heart muscle that is clearly shown in

figure 10d, after t=0.12 sec. Note that the

early stage of systole, i.e., isovolumetric

compression that happens quite quickly, is

not precisely modeled here, although the

steep pressure rises before t=9.5 millisecond

(figure 6a) somehow takes this effect into

account.

(a)

(b)

0,0 0,1 0,2 0,3

Max Def.(mm)

Time(s)

0,0 0,1 0,2 0,3

Max Stress(KPa)

Time(s)

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(c)

(d)

Figure 10 (a) Maximum deformation of the aortic valve (b) Maximum Tension in Aortic Valve Tissue (c) Maximum

deformation of myocardium tissue (d) Maximum tension in myocardium.

According to figure 10a, the deformation is

almost zero at the end of the systole in

accordance with zero velocity at the aortic

valve. Note that a closed valve position

might accompany zero outflow. However,

negative cell volume may occur in the grid

in the event of complete closure of the aortic

valve. The proper precautions are taken to

avoid this erroneous situation in the current

study. At the start of the systole period, this

problem is handled by initializing the flow

field with a negligible velocity.

The blood volume in the left ventricle for

the specific person during systole was

obtained by Mimics software. To valid the

numerical outcomes, they should be

compared with the measured data of the that

individual whose CT scan images are used

for this research. The for numerical

simulations and measured data for blood

volume changes in the left ventricle are

shown in figure 11. According to figure 11,

the ventricular volumes decrease

monotonically in accordance with

physiological predictions for both

simulations with different BCs. This is in

line with the increasing deformation of

myocardium tissue shown in figure 10c and

stress relaxation in figure 10d. Moreover,

the trends of the simulation curves in figure

11 show a good agreement with the

physiological data and the experimental data

of the specific case.

Figure 11 The outlet BC effect on the computed left ventricular volume change

Secondly, as shown in figure 11, there is a

slight difference between the computed

systolic volume of LV with velocity BC and

pressure BC. Meanwhile, the difference of

these two simulations with physiological

0,0 0,1 0,2 0,3

Max Def.(mm)

Time(s)

0,0 0,1 0,2 0,3

Max Stress(KPa)

Time(s)

110

130

0 0,05 0,1 0,15 0,2 0,25 0,3

Volume(ml)

Time

Left ventricle volume - Pressure boundary condition

Left ventricle volume - physiological data

Left ventricle volume - velocity boundary condition

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data is more sensible, 10% maximum which

tends to be smaller at the end of systole.

However, the actual LV shape variation

during systole is different for these two

BC’s, explained later.

This is expectable since by defining a

specific time variation of velocity at a

constant sectional area such as the aorta, i.e.,

velocity BC, we define the ventricle volume

change; hence the relative agreement of

velocity BC and the physiological

predictions was seen. However, one expects

more realistic results for pressure BC due to

more freedom for flow field allowed by such

BC.

Figure 12 demonstrates the aortic valve

deformations during systole for simulations

with applying pressure BC. The CT scan

images from [24] are also added for

comparison. The overall agreement is

apparent.

In Figure 13, LV deformations during

systole with outlet pressure BC are shown,

which can be compared with the

corresponding CT scan images collected in

this study. Different views are provided in

order to have a better comparison. Initial LV

shapes in all views, at t=0 Sec., are exactly

the same as the CT images, and at later

times differences between numerical and CT

images show the simulation discrepancies.

According to the CT scan image of figure

13a, in addition to movements of the left

ventricle muscle (mainly upward) that

enhances blood pumping, a thickening of

myocardium muscle, especially in the lower

parts of the ventricle, is clearly seen. These

effects are mainly due to stimulant electrical

currents that are not modeled in this study.

The agreement between the simulation

results and the CT images in all views for

time t=0.12 s is good and worsens at later

time-steps. The overall agreement of the

images is acceptable, and the main

difference is the abnormal side contraction

of the simulation images that might be

caused by the absence of the vertical

movement and thickening of the LV tissue,

as mentioned above. Also, left ventricle

systolic anterior motion is depicted in

simulation results. Horizontal vectors

represent this motion left and right in figure

13. This difference in ventricle shape after

the start of systole perhaps shows the

importance of electrical response modeling

of the heart tissue, which is absent in the

present study.

Model (a)

CT Scan images

Figure 12 Comparison of deformation of the aortic

valve for the performed simulation and CT scan

images [24].

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(a)

Simulation of the first

ventricle-pressure B.C

CT Scan images of first

ventricle

Simulation of the first

ventricle-pressure B.C

CT Scan images of first

ventricle

Time= 0 s

Time= 0.12 s

Time= 0.24 s

Time= 0.3 s

(b) Isometric view

Time= 0 s

Time= 0.12 s

Time= 0.24 s

Time= 0.3 s

Time= 0 s

Time= 0.12 s

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Time= 0.24 s

Time= 0.3 s

(d) Front view

Time= 0 s

Time= 0.12 s

Time= 0.24 s

Time= 0.3 s

Figure 13 Comparison of LV deformation based on simulation and CT scan images from different views.

4-2 Fluid Domain

Table 3 lists the computed hemodynamic

parameters of LV along with the related

physiological data [25-26]. All the computed

parameters lie in the normal ranges.

Table 3. Comparison of hemodynamic parameters of left ventricle with physiological values.

Present study-

Pressure B.C-

First ventricle

Present study-

velocity B.C-

First ventricle

Physiological range

End-systolic volume (ml)

76.485

73.102

58.1 ± 30.1

Stroke-volume (ml)

62.166

65.92

55-100

Cardiac output (l/min)

4.74

5.017

4-8

End-diastolic volume (ml)

138.621

134.2 ± 39.9

Ejection fraction %

44.85

47.42

58.1 ± 11.9

The maximum blood velocity at the outlet

for a healthy aortic valve is smaller than 2

m/s, and the maximum cross-sectional area

at the outlet of the aortic valve is 3.9 ± 1.2

cm2 [27]. Regarding the velocity at plane 1

in figure 9a and the area ratio of the

maximum opening of the aorta valve at

t=0.12 s to the outlet area, the maximum

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velocity of 1.607 m/s occurs at the aorta

valve, which is in the normal physiological

range. As shown in figure 14a, the mean

velocity at the exit of the aortic valve is

similar to the physiological reference chart

[27]. The only difference is in the magnitude

of maximum velocity. Although based on

the criteria that the maximum velocity

should be less than 2 m/s [27], the

simulation results are acceptable. The

maximum velocity at the output of the

domain, which is the same as the ascending

aorta, is presented in figure 14b.

(a)

(b)

Figure 14 Velocity profiles (a) at the exit of the aortic valve (b) at the ascending aorta.

4-3 HCM Results

As mentioned earlier, under HCM condition

the mitral valve leaflets approach towards

the septum wall. As the leaflets move within

a certain vicinity of the wall, some negative

volume elements occur in the neighboring

region. The HCM simulations are carried

out for the beginning of the systole up until

0.3s to avoid this computational error. A

significant parameter is named “coaptation-

to-septal distance” and is defined as the

shortest distance between the coaptation

point at the end-systole and the

intraventricular septum. Figure 15 shows

this distance and the geometry of the left

ventricle with the two valves added.

Figure 15 The coaptation-to-septal distance region and the geometry used for HCM simulation

Ventricular volume change is plotted for all

the simulations in figure 16 to compare

HCM results with the healthy condition.

0,5

1,5

0 0,1 0,2 0,3

Velocity(m/s)

Time(s)

Velocity profile at the exit of the aortic valve [25]

Velocity profile at the exit of the aortic valve - current

simulation

0,2

0,4

0,6

0 0,1 0,2 0,3

Velocity(m/s)

Time(s)

Velocity profile at the entrance of the aorta tube [25]

The velocity profile at the entrance of the aortic tube -

current simulation

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Figure 16 The left ventricular volume change for HCM condition.

Considering the whole cardiac cycle, the

cardiac output for the HCM condition would

be 2.123 lit/min, which is much less than the

physiological value under healthy condition,

i.e., 4-8 lit/min. Figure 17 shows the 3D

streamlines for laminar flow under HCM

condition.

t=0.01s

t=0.04s

t=0.08s

t=0.12s

Figure 17 3D streamlines for HCM condition

In order to study the interaction of the

septum wall and mitral valve for the HCM

case, figure 17 is presented. According to

figure 17, the streamlines should rotate to

pass the mitral valve and through the narrow

110

130

0 0,05 0,1 0,15 0,2 0,25 0,3

Volume(ml)

Time(S)

Healthy Left Ventricle

Hypertropic Cardiomyopathy

Physiologic Volume

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region between the mitral valve leaflets and

the septum wall (coaptation-to-septal

distance). This kind of flow exerts a drag

force on the mitral valve, which will make

the anterior leaflet move towards the septum

wall during the systolic anterior motion.

Based on the figure 18 and compared with a

healthy heart, the reduction in the cross-

section area and the decrease of the local

pressure along with the presence of the drag

force on the posterior leaflet and the lower

pressure on the anterior leaflet of a flexible

valve bring about more blockage of the LV

blood passage by the mitral valve.

Consequently, the flexible mitral valve

blockage results in stagnation pressure loss

and weaker heart-pumping performance.

Therefore, low local pressure and lower

stagnation pressure after the mitral valve

produce an adverse pressure gradient toward

the aorta and may even cause reverse flow.

This reverse flow is detected in simulation

results at t = 0.12s.

For HCM simulation, the maximum area of

the aortic valve is 2.228 cm2 and occurs at t

= 0.1s, while for healthy condition, the

maximum area of the aortic valve occurs at

the same time and is equal to 3.9±1.2 cm2.

Moreover, the maximum velocity at the

aorta inlet is 1.27 m/s and 0.414 m/s for

healthy and HCM conditions, respectively.

The comparison shows that under the HCM

condition, the blood velocity at the aorta's

inlet and the aortic valve's maximum

openness lie outside the physiological

ranges.

t=0.02s

t=0.04s

t=0.06s

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t=0.1s

t=0.14s

t=0.16

t=0.3s

Figure 18 pressure contour around the coaptation-to-septal distance region for HCM condition

As shown in figure 18, the blood flow

initially moves to the aortic valve. It is

observed that during systole, the blood flow

behind the posterior leaflet of the mitral

valve moves it to the left ventricular wall

(septum). Streamline vectors in this form are

visible behind the posterior leaflet of the

mitral valve. The drag force on the mitral

valve causes it to move towards the septum

and reduces the distance between the

ventricular wall and the anterior leaflet of

the mitral valve. This distance is called

coaptation-to-septal distance. Another

prominent factor seen in the images of

figure 18 is the pressure gradient around the

mitral valve. Before the 0.12 second, as the

leaflets approach the septum, the pressure

after the mitral valve decreases. This

reduction in pressure after the mitral valve is

another factor that causes the anterior leaflet

of the mitral valve to move toward the

septum. The coaptation-to-septal distance is

reduced to the point that after the time 0.12 s

and the creation of stagnation pressure, the

flow begins to rotate after the mitral valve,

and the pressure gradient is reversed. At this

time, a reverse flow occurs.

5 Conclusion

The precise and correct simulation of the

human heart can be beneficial to estimate

the heart performance and cardiac output

under different in vivo conditions. In this

study, real CT scan images are used to

construct an actual shaped model of human

LV under the healthy and HCM disease

conditions. Using the FSI method, the blood

flow in LV and ventricular tissue and aortic

valve deformations are simulated during the

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systole period of the cardiac cycle for two

models; the healthy LV and HCM model.

The 3D grid is built for physical models, and

the discretized equations are solved for both

solid and fluid domains. The grid

independence analysis is performed for both

models. Also, the time independence of

numerical outcomes is investigated to ensure

obtained results' accuracy. Two simulations

with different BCs at the aortic outlet are

carried out for the healthy model. The

velocity and pressure outlet BCs are defined

based on the physiological charts. The

results for left ventricular volume change for

these simulations are approximately the

same and in accordance with available

physiological data of LV volume change

during systole. While these two models

produce similar approximate flow and solid

results for systole, another study for the

diastole phase of the LV showed different

results for the velocity (imprecise) and

pressure BC (precise) models. The

explanation would be the strong effect of the

heart electrical current on the deformations,

which is presented during systole and not

modeled in the present study, and the

absence of this effect in the diastole phase.

For the healthy model, numerical results

capture the systolic anterior motion of LV

identical to the CT scan images. The blood

streamlines in LV display the local pressure

variation near the aortic valve leaflets during

the anterior motion. The results for the solid

domain show the good accordance between

FSI results for LV shape deformation and

CT scan images. Besides, the FSI results for

the aortic valve leaflets deformation are

analogous with available CT scan images of

this valve during systole. The maximum

deformation of the aortic valve occurred at

the time of 0.12 s; simultaneously, the

output velocity is maximum, and the aortic

leaflet experiences the maximal opening.

The maximum opening surface of the aortic

valve is 4.38 cm2 which is consistent with

physiological observation on a healthy

individual.

For the HCM model, the maximum opening

of the aortic valve is 2.228 cm2, which is not

in the physiological range, indicating the

drastic effect of HCM on the performance of

the aortic valve. Moreover, the ventricular

volume change decreases significantly from

healthy to HCM condition. Compatible with

the pathological nature of the HCM, under

the severe malady, the LV loses its pumping

ability to send blood into the aorta.

Accordingly, the maximum blood velocity at

the aortic outlet for HCM condition is 0.414

m/s while this velocity is 1.27 m/s for the

healthy condition. The comparison indicates

that under the HCM disorder, the blood

velocity at the aorta's inlet and the aortic

valve's maximum openness lie outside the

physiological spans.

In conclusion, the FSI simulation can

undoubtedly lead to feasible results for LV

simulation when relevant physical and

numerical details are considered. More

complete heart models considering heart

electrical current and subsequent tissue

deformation would eventually provide the

necessary numerical tool for practical

applications.

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Contribution of individual authors

to the creation of a scientific article

Mohammad Monfared carried out the

simulation and writing down the manuscript.

Prof. Mohammad Mehdi Alishahi was the

academic supervisor who guided the

research.

Marzieh Alishahi wrote the final manuscript

and was responsible with editing process.

Sources of funding for research

presented in a scientific article or

scientific article itself

There is no specific source of funding for

this research.

2005.

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