Numerical simulation of pulsatile blood flow characteristics in a multi stenosed coronary artery

Abstract

BACKGROUND:

Coronary artery disease is reported as one of the most common sources of death all over the world. The presence of stenosis (plaque) in the coronary arteries results in the restriction of blood supply, which leads to myocardial infarction.

OBJECTIVE:

The aim of this study was to investigate the effect of multi stenosis on hemodynamics parameters in idealized coronary artery models with varying degrees of stenosis and interspace distance between the stenosis.

METHODS:

A finite volume-based software package (Ansys CFX version 17.2) was employed to model the blood flow. The hemodynamic stenosis parameters of blood, such as the pressure, velocity, and wall shear stress were obtained.

RESULTS:

The computed results showed that the pressure drop is maximum across the 90% area stenosis (AS). The pressure drop is increased as the distance between the proximal and distal stenosis is decreased across the proximal stenosis for the model P₇₀_D₇₀ during the systolic period of the cardiac cycle. A recirculation zone is formed behind the stenosis and is restricted by the occurrence of distal stenosis as the interspacing distance decreases, which could lead to further progression of stenosis in the flow-disturbed area. The wall shear stress was found to increase as the distance between the proximal and distal stenosis is increased across the distal stenosis. The maximum wall shear stress was found at 90% AS.

CONCLUSIONS:

In the clinical diagnosis, an overestimation of distal stenosis severity could be possible. Furthermore, the low wall shear stress zone in between the proximal and distal stenosis may help atherosclerotic growth or merge adjacent stenosis.

Keywords

Coronary artery atherosclerosis stenosis hemodynamic wall shear stress

1. Introduction

Changes in the normal behavior of blood flow in coronary arteries are caused by atherosclerosis. This disease is one of the leading causes of death, which reduces the coronary artery lumen because of the formation of stenosis (fats, cholesterol and other substances) on the inner walls of the coronary artery. Several studies have proposed that the relationship of the initiation and progression of stenosis is preferentially located at the bifurcation, branches and curvatures of vessels [1–5]. The variation in wall shear stress and disturbed flow changes cannot be measured directly in coronary arteries, however, computational fluid dynamic (CFD) analysis provides alternate ways to evaluate the shear stresses and diagnose the early development of stenosis [6,7]. Computational fluid dynamic models of stenotic flow have been developed through advanced computers and numerical methods in recent years [8,9]. The effect of various shapes of stenosis, different angle of curvatures, and bifurcation angles on hemodynamics parameters was reported by numerous studies [10–14]. In some previously published studies the blood flow behavior was assumed as laminar [15,16] and some studied turbulence transition and non-Newtonian effects of blood in idealized stenosed artery with single stenosis [17–20]. The flow behavior in the downstream region of idealized stenosed models was experimentally analyzed in several previous studies [21–23]. The effect of stenosis in a patient-specific left coronary artery model on hemodynamics parameters was simulated by Chaichana et al. [6]. The pressure gradient and flow velocity were calculated and compared in models with and without stenosis. They found that a high-pressure gradient exists at the stenosis and low velocity at the post-stenosis. The hemodynamic effect of various types of plaque configuration in the left coronary artery was studied by Chaichana et al. [24], in which velocity, wall shear stress and pressure gradient were calculated for the plaque configurations. The highest velocity and pressure gradient was found in a type of plaque configuration which involves the plaque position in all three left coronary branches. The influence of various degrees of stenosis on the pressure, velocity and wall shear stress in a real patient-specific left coronary artery model was investigated [25]. Some studies numerically investigated the pulsatile flows passing through a tandem stenosed vessel. They showed that the drop in pressure caused by multiple stenoses was the sum of the pressure drops for individual stenoses. It was also found that the interspacing distance between stenoses had a minor effect on pressure drop [26,27]. Therefore, in order to properly diagnose and treat cardiovascular disease in a series of stenosis, a detailed understanding of the hemodynamic is required. In the current study, an attempt is made to study the effect of stenosis severity and interspacing distance between the stenosis on hemodynamic parameters such as wall shear stress, pressure and velocity by computational fluid dynamics.

2. Methodology

2.1. Tandem stenosis coronary artery model

The computational models of the idealized coronary artery are developed with different severities of stenosis with varying interspacing distances, as shown in Fig. 1(a). It consists of a cylindrical tube representing the coronary artery models with a narrowing to mimic the tandem stenosis. The geometry of the tandem stenosis models was developed by using Eq. ((1)) [12,28,29]. The percentage area stenosis (AS) was calculated by using Eq. ((2)). $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle {\displaystyle \frac{\tilde{{\eta}}(\tilde{z})}{a}}=1-{\displaystyle \frac{h}{a}}\sin {\pi}\left({\displaystyle \frac{\tilde{z}-d}{L}}\right),\quad d\leq \tilde{z}\leq d+L,\end{eqnarray}$ (1) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle \text{Area stenosis (AS)%}={\displaystyle \frac{({\pi}\times a^{2})-[{\pi}\times (a-h)^{2}]}{{\pi}\times a^{2}}}\end{eqnarray}$ (2) where $\tilde{{\eta}}(\tilde{z})$ is the radius of stenosis, “a” is the radius of an artery, $\tilde{z}$ is along the axis of the artery “h” is the maximum projection of the stenosis into the lumen.

Fig. 1.

Computational models developed and mesh generated by using hexahedral elements for simulation.

The diameter of the idealized coronary artery is 3 mm and the stenosis length has been fixed to 10 mm in all models. The distances between the proximal stenosis and distal stenosis (L) are 3 mm, 6 mm, and 10 mm considered. Nine different coronary artery models with a combination of various interspacing distances (3 mm, 6 mm, and 10 mm) and severities [proximal and distal area stenoses with 70% AS (P₇₀_D₇₀), proximal 70% AS, distal 90%AS (P₇₀_D₉₀) and proximal 90% AS, distal 70% AS (P₉₀_D₇₀)] are simulated. The 3D computational models were imported into the Ansys ICEM CFD version 17.2 (Ansys Inc., USA) [30] to create hexahedral meshes elements. Figure 1(a,b) shows the computational mesh generated by using hexahedral elements. A grid independent study was carried out, in order to obtain mesh independent results to determine the best results and to minimize computer running-time. Figure 2 shows the pressure drop along the length of the coronary artery for the various number of elements. As is evident from Fig. 2, the results obtained from a mesh element with 748804 elements are very near to those results obtained from 989874 elements. So, the mesh with 748804 elements was used to reduce computational time and cost.

Fig. 2.

Comparison of mesh independent study for different number of elements.

2.2. Computational blood flow modeling

In the current study, blood flow in a stenosed coronary artery was assumed to be incompressible and non-Newtonian. The governing equations used to describe the flow are the Navier–Stokes equations, Eq. ((3)) and continuity equation, Eq. ((4)) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle {\rho}\left({\displaystyle \frac{\partial v}{\partial t}}+v.{\nabla}v\right)={\nabla}.{\tau}-{\nabla}P\end{eqnarray}$ (3) $\begin{eqnarray} \displaystyle \text{} & \text{} & \displaystyle {\nabla}.v=0 & & \displaystyle \end{eqnarray}$ (4) where v = 3D velocity vector, t = represents time, 𝜌 = fluid density, P = Pressure and 𝜏 = viscous stress tensor. Since the blood flow was assumed as non-Newtonian behavior in the current study. The Bird-Carreau shear thinning model was used as given in Eq. ((5)) $\begin{eqnarray}\displaystyle {\mu}={\mu}_{\infty }+({\mu}_{0}-{\mu}_{\infty })[1+({\lambda}{\gamma})^{2}]^{(n-1)/2}. & & \displaystyle\end{eqnarray}$ (5) The parameters in Eq. ((5)) are written as 𝜆 = 3.313 s; n = 0.3568, 𝜇₀ = 0.56 Pa, 𝜇_∞ = 0.0345 Pa, and the density (𝜌) is assumed as 1050 kg/m³. The blood flow simulations were carried out by using the finite volume software CFX version 17.2 (Ansys Inc., USA).

2.3. Boundary conditions

In the current study, an attempt is made to replicate the actual physiological behavior by modeling a three-dimensional idealized coronary artery. The numerical simulation was carried out by assigning a time-dependent parabolic velocity $\bar{u}$ at the inlet (Fig. 3) and a transient pulsatile pressure p(t) at the outlet (Fig. 3) with no slip condition applied at the wall. The velocity is a normalized velocity with respect to the peak temporal velocity $\bar{u}_{p-t}$ . The same inlet and outlet boundary conditions were used to solve all the models. The convergence was achieved with maximum 10⁻⁵ residual level. Flow velocity, pressure drop and wall shear stress (WSS) were computed in CFD-Post version 17.2 (Ansys Inc., USA).

Fig. 3.

Coronary flow wave form imposed at the inlet and time varying physiological pressure imposed at the outlet [41–43].

Fig. 4a.

Pressure drop for a series of stenoses during the cardiac cycle for peak systole (1.2 s) (a) 70% and 70%, (b) 70% and 90%, (c) 90% and 70%.

3. Results

The aim of the current study was to numerically simulate the effect of tandem stenosis and the interspacing distance between the stenosis on the hemodynamic parameters. The pulsatile data are represented by point I (t = 1.20 s) and II (t = 1.51 s) in the coronary flow waveform (Fig. 3) represents the peak systolic flow, and later distal respectively in the second pulse. Figure 4a and 4b compare the axial drop in pressure along the length of the artery for all the three models of tandem stenosis at I (t = 1.20 s) and II (t = 1.51 s) pulse time respectively. As is evident from Fig. 4a, the drop in pressure increases across the proximal stenosis as the interspace between the stenosis is decreases for model P₇₀-D₇₀. The pressure drop is highest for the models P₇₀-D₉₀ and P₉₀-D₇₀ as compared to the P₇₀-D₇₀ model during the period of the cardiac cycle. It is also found that the pressure drops increase with the decrease in the distance between the stenosis across the distal stenosis in the model P₉₀_D₇₀. Therefore, the upstream pressure reaches a serious value for the model P₉₀-D₇₀ stenosis as compared to the other two models leading to a non-physiological increase in the upstream pressure and systemic pressure. No substantial variance was observed in pressure across the distal stenosis for the models P₇₀-D₇₀ and model P₇₀-D₉₀ during the cardiac cycle. The reverse pressure was found across the proximal and distal stenosis throat in all the idealized coronary artery models. The flow across the stenosis region became narrow and the risk of constriction increased. In some cases, the coronary artery ruptured near the stenosis [31,32]. The changes in the coronary vessel wall due to the progression of stenosis lead to hemodynamic variations that in turn may lead to myocardial ischemia, cardiac arrhythmias, angina, or even death [33,34].

Fig. 4b.

Pressure drop for a series of stenoses during the cardiac cycle for later diastole (1.51 s) (a) 70% and 70%, (b) 70% and 90%, (c) 90% and 70%.

Figure 5a and 5b represent the centreline velocity along the length of the artery for all the three models of tandem stenosis at systolic I (t = 1.20 s) and diastolic II (t = 1.51 s) period of cardiac cycle respectively. The higher velocity was found across the crest of the stenosis and linearly decreases and the decreasing rates are nearly identical, regardless of the interspacing distance for all the models simulated. The maximum velocity was found at 90% AS for the systolic period of the cardiac cycle. A slight increase in the velocity was noted across the distal stenosis for the model P₇₀-D₇₀ during the systole as the interspacing distance between the stenosis increases, whereas no significant changes in the velocity were found for the other two models. During the diastolic period of the cardiac cycle, a slight decrease in the velocity was recorded as the distance between the stenosis was increased for the model P₇₀-D₇₀. Figure 6 shows the recirculation zone formed across the post-stenosis. These recirculation regions were suppressed as the length between the tandem stenosis was minimum (3 mm), whereas a recirculation region was extended more from the crest of the proximal stenosis when spacing between stenosis was maximum (10 mm).

Fig. 5a.

Axial velocity for a series of stenoses during the cardiac cycle for peak systole (1.2 s) (a) 70% and 70%, (b) 70% and 90%, (c) 90% and 70%.

Fig. 5b.

Axial velocity for a series of stenosis during the cardiac cycle for later diastole (1.51 s) (a) 70% and 70%, (b) 70% and 90%, (c) 90% and 70%.

Fig. 6.

Comparison of velocity fields in the P70_D70 model with interspacing distance L = 3 mm (upper) and L = 10 mm (lower).

The wall shear stress is a significant hemodynamic parameter that plays a vital role in predicting the location and progression of stenosis. The endothelial mechanotransduction and downstream signaling pathways depend on the direction of the wall shear stress [35]. The effect of severity of stenosis in tandem stenosis and the interspacing distance between the tandem stenosis is shown in Fig. 7a and 7b at various cardiac pulse times I (t = 1.20 s) and II (t = 1.51 s) respectively. The maximum wall shear stress was reported across the 90% area stenosis for the systolic period of the cardiac cycle. An increase in wall shear stress was found across the distal stenosis as the distance between the tandem stenosis was increased for the model P₇₀-D₇₀. For the other two models P₇₀-D₉₀ and P₉₀-D₇₀ an increase in wall shear stress was found across the 90% stenosis with no significant changes in wall shear stress as the interspace distances changed. A region of recirculation in between the proximal and distal stenosis was formed, which caused a low wall shear stress. The existence of a low wall shear stress zone in between these stenoses may help atherosclerotic growth, leading to the union of adjacent stenoses.

Fig. 7a.

Wall shear stress a for series of stenosis during the cardiac cycle for peak systole (1.2 s) (a) 70% and 70%, (b) 70% and 90%, (c) 90% and 70%.

Fig. 7b.

Wall shear stress for a series of stenosis during the cardiac cycle for later diastole (1.51 s) (a) 70% and 70%, (b) 70% and 90%, (c) 90% and 70%.

4. Discussion

The aim of the current study was to numerically investigate the effect of multi stenosis in series of tandem idealized coronary artery models on hemodynamic parameters. The present result provides further information about the influence of multi stenosis in series of tandem idealized models with varying interspace between them on the hemodynamic, hence it advances our understanding of initiation and development of atherosclerosis. In recent years advanced several clinical methods have been developed [4,36], such as multi slice computer tomography angiography and intravascular ultrasound, to distinguish between the anatomy of coronary artery and the unwanted deposition developed in the coronary arteries. These innovative medical imaging techniques provide the remodelling structures of wall but are limited to the analysis of the flow variation in the coronary arteries. In contrast, computational fluid dynamics provides the behaviour of blood flow and the rheological factors. In the clinical situation, the variation in pressure has been used as a deciding factor to assess the risk of severity of stenosis. The highest-pressure drop across the 90% AS leads to the obstructing blood flow to the myocardium consequently affecting the flow velocity as shown in models P₇₀-D₉₀ and P₉₀-D₇₀. In addition, the disturbed flow behind the stenosis leads to the progression of future stenosis. Since velocity is the main factor of local WSS and acts along the direction of local WSS, which means that flow velocity is low when the WSS is low. The recirculation region behind the proximal stenosis is suppressed as the distance between the stenosis is decreases, this leads to the distal stenosis exposed to low and oscillatory wall shear stresses, which could cause the developments of stenosis [37]. The presence of low wall shear stress in between the proximal and distal stenoses (Fig. 7a and 7b) may prime the atherosclerotic growth, leading to the combination of adjacent stenoses. The oxidation of low-density lipoprotein (LDL) on the intima layer (inner most layer of endothelial cells) increases because of the reactive oxygen species produced due to the low wall shear stress. The adhesion molecules such as vascular cell adhesion molecule-1 (VCAM-1) and intracellular adhesion molecule-1 (ICAM-1) is produced by local endothelial layer during the process of oxidation [38]. In the low wall shear stress region, the platelets are likely to adhere to the endothelium layer due to the increase in production of the adhesive molecules. This action further activates the platelets which produce growth factors such as TGF-β2 and vasoconstrictors like thromboxane A2 (TXA2). The activation of platelets is a vital role in the migration and proliferation of smooth muscle cells [39]. In short, the raise of wall shear stress is related to platelets activation and leads the damage of the endothelial layer, whereas the decrease in the wall shear stress is related to the nitric oxide and increase endothelin-1 production by endothelial cells, ensuing in the development and progression of new stenosis [40]. These results provide more detailed information about the behaviour of blood flow in multi stenosis in a series of tandem idealized coronary artery models and hence, it advances our understanding of the progression of atherosclerosis at various locations in the coronary artery.

5. Conclusion

In the present study, influence of severity (70% AS and 90% AS) of tandem stenosis and interspacing distance (3, 6 and 10 mm) on the flow characteristics in tandem stenosis was numerically investigated. The finite volume-based software CFX version 17.2 (Ansys Inc., USA) was used to model the blood flow. The highest-pressure drop was found across the 90% AS for irrespectively of interspacing distance. The more pressure drop was noted as the interspacing distance decreases between the stenosis for the model P₇₀-D₉₀. The region of flow behind the distal stenosis is solely influenced by the flow characteristics behind the proximal stenosis. The recirculation region is suppressed as the interspacing length is decreased between the stenosis. The wall shear stress increases as the distance between the stenosis is increased for the model P₇₀-D₇₀. The maximum wall shear stress was noted across 90% AS for the systolic period of cardiac cycle.

Footnotes

Acknowledgement

The author extends his appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through the research groups program under grant no. R.G.P.2/74/41.

Conflict of interest

The author has no conflict of interest to declare.

References

Asakura

and Karino

, Flow patterns and spatial distribution of atherosclerotic lesions in human coronary arteries, Circ. Res. 66(4) (1990), 1045–1066.

Chaichana

Sun

and Jewkes

, Computation of hemodynamics in the left coronary artery with variable angulations, J. Biomech. Eng. 44(10) (2011), 1869–1878.

Fuster

, Lewis A. Conner Memorial Lecture. Mechanisms leading to myocardial infarction: Insights from studies of vascular biology, Circulation 90(4) (1994), 2126–2146.

El-Ghobashy

El-Garf

and Abdo

, Arterial aneurysms in Behçet’s disease patients: Frequency, clinical characteristics and long-term outcome, Egypt. Rheumatol. 41(4) (2019), 309–312.

Zarins

C.K.

Giddens

D.P.

Bharadvaj

B.K.

Sottiurai

V.S.

Mabon

R.F.

and Glagov

, Carotid bifurcation atherosclerosis. Quantitative correlation of plaque localization with flow velocity profiles and wall shear stress, Circ. Res. 53(4) (1983), 502–514.

Chaichana

Sun

and Jewkes

, Computational fluid dynamics analysis of the effect of plaques in the left coronary artery, Comput. Math. Meth. Med. 2012 (2012).

Shanmugavelayudam

S.K.

Rubenstein

D.A.

and Yin

, Effect of geometrical assumptions on numerical modeling of coronary blood flow under normal and disease conditions, J. Biomech. Eng. 132(6) (2010), 061004.

Fazli

Shirani

and Sadeghi

M.R.

, Numerical simulation of LDL mass transfer in a common carotid artery under pulsatile flows, J. Biomech. 44(1) (2011), 68–76.

Razavi

Shirani

and Sadeghi

M.R.

, Numerical simulation of blood pulsatile flow in a stenosed carotid artery using different rheological models, J. Biomech. 44(11) (2011), 2021–2030.

10.

Ahamad

N.A.

Kamangar

and Badruddin

I.A.

, The influence of curvature wall on the blood flow in stenosed artery: A computational study, Biomed. Mater. Eng. 29(3) (2018), 319–332.

11.

Chen

and Lu

X.Y.

, Numerical investigation of the non-Newtonian pulsatile blood flow in a bifurcation model with a non-planar branch, J. Biomech. 39(5) (2006), 818–832.

12.

Kamangar

Badruddin

I.A.

Ahamad

N.A.

Govindaraju

Nik-Ghazali

Ahmed

N.J.

, The influence of geometrical shapes of stenosis on the blood flow in stenosed artery, Sains. Malays. 46(10) (2017), 1923–1933.

13.

Lorenzini

and Casalena

, CFD analysis of pulsatile blood flow in an atherosclerotic human artery with eccentric plaques, J. Biomech. 41(9) (2008), 1862–1870.

14.

Yao

Ang

K.C.

Yeo

J.H.

and Sim

E.K.

, Computational modelling of blood flow through curved stenosed arteries, J. Med. Eng. Technol. 24(4) (2000), 163–168.

15.

Boutsianis

Dave

Frauenfelder

Poulikakos

Wildermuth

Turina

, Computational simulation of intracoronary flow based on real coronary geometry, Eur. J. Cardiothorac. Surg. 26(2) (2004), 248–256.

16.

Liu

Huang

Ghista

D.N.

and Wong

K.K.

, Transient blood flow in elastic coronary arteries with varying degrees of stenosis and dilatations: CFD modelling and parametric study, Comput. Meth. Biomech. Biomed. Eng. 18(16) (2015), 1835–1845.

17.

M.X.

Beech-Brandt

J.J.

John

L.R.

Hoskins

P.R.

and Easson

W.J.

, Numerical analysis of pulsatile blood flow and vessel wall mechanics in different degrees of stenoses, J. Biomech. 40(16) (2007), 3715–3724.

18.

Moreno

and Bhaganagar

, Modeling of stenotic coronary artery and implications of plaque morphology on blood flow, Mod. Sim. Eng. 2013 (2013), 1–14.

19.

Nosovitsky

V.A.

Ilegbusi

O.J.

Jiang

Stone

P.H.

and Feldman

C.L.

, Effects of curvature and stenosis-like narrowing on wall shear stress in a coronary artery model with phasic flow, Comput. Biomed. Res. 30(1) (1997), 61–82.

20.

Varghese

S.S.

and Frankel

S.H.

, Numerical modeling of pulsatile turbulent flow in stenotic vessels, J. Biomech. Eng. 125(4) (2003), 445–460.

21.

Beratlis

Balaras

Parvinian

and Kiger

, A numerical and experimental investigation of transitional pulsatile flow in a stenosed channel, J. Biomech. Eng. 127(7) (2005), 1147–1157.

22.

Carew

E.O.

and Pedley

T.J.

, An active membrane model for peristaltic pumping: Part I—Periodic activation waves in an infinite tube, J. Biomech. 119(1) (1997), 66–76.

23.

Trip

Kuik

D.J.

Westerweel

and Poelma

, An experimental study of transitional pulsatile pipe flow, Phys. Fluids 24(1) (2012), 014103.

24.

Chaichana

Sun

and Jewkes

, Haemodynamic analysis of the effect of different types of plaques in the left coronary artery, Comput. Med. Imag. Graph. 37(3) (2013), 197–206.

25.

Kamangar

Badruddin

I.A.

Govindaraju

Nik-Ghazali

Badarudin

Viswanathan

G.N.

, Patient-specific 3D hemodynamics modelling of left coronary artery under hyperemic conditions, Med. Biol. Eng. Comput. 55(8) (2017), 1451–1461.

26.

Karayannacos

P.E.

Talukder

Nerem

R.M.

Roshon

and Vasko

J.S.

, The role of multiple noncritical arterial stenoses in the pathogenesis of ischemia, J. Thorac. Cardiovasc. Surg. 73(3) (1977), 458–469.

27.

Rathish Kumar

B.V.

Yamaguchi

Liu

and Himeno

, A numerical study of an unsteady laminar flow in a doubly constricted 3D vessel, Int J. Numer. Meth. Fluids 38(12) (2002), 1159–1176.

28.

Dash

R.K.

Jayaraman

and Mehta

K.N.

, Flow in a catheterized curved artery with stenosis, J. Biomech. 32(1) (1999), 49–61.

29.

Kamangar

Kalimuthu

Anjum Badruddin

Badarudin

Salman Ahmed

N.J.

and Khan

T.M.

, Numerical investigation of the effect of stenosis geometry on the coronary diagnostic parameters, Sci. World J. 2014 (2014), 354946.

30.

Ansys Inc., Ansys CFX Introduction, 2012.

31.

Downing

J.M.

and Ku

D.N.

, Effects of frictional losses and pulsatile flow on the collapse of stenotic arteries, J. Biomech. Eng. (1997), 317–324.

32.

Tang

Yang

Kobayashi

and Ku

D.N.

, Steady flow and wall compression in stenotic arteries: A three-dimensional thick-wall model with fluid–wall interactions, J. Biomech. Eng. 123(6) (2001), 548–557.

33.

Corban

M.T.

Hung

O.Y.

Eshtehardi

Rasoul-Arzrumly

McDaniel

Mekonnen

, Myocardial bridging: Contemporary understanding of pathophysiology with implications for diagnostic and therapeutic strategies, J. Am. Coll. Cardiol. 63(22) (2014), 2346–2355.

34.

Lee

M.S.

and Chen

C.H.

, Myocardial bridging: An up-to-date review, J. Invasive Cardiol. 27(11) (2015), 521.

35.

Zhang

Gao

and Chang

, Helical flow component of left ventricular assist devices (LVADs) outflow improves aortic hemodynamic states, Med. Sci. Mon. Int. Med. J. Exp. Clin. Res. 24 (2018), 869.

36.

Gijsen

F.J.

Wentzel

J.J.

Thury

Lamers

Schuurbiers

J.C.

Serruys

P.W.

, A new imaging technique to study 3-D plaque and shear stress distribution in human coronary artery bifurcations in vivo, J. Biomech. 40(11) (2007), 2349–2357.

37.

Myers

J.G.

Moore

J.A.

Ojha

Johnston

K.W.

and Ethier

C.R.

, Factors influencing blood flow patterns in the human right coronary artery, Ann. Biomed. Eng. 29(2) (2001), 109–120.

38.

Jahangiri

Saghafian

and Sadeghi

M.R.

, Numerical simulation of hemodynamic parameters of turbulent and pulsatile blood flow in flexible artery with single and double stenoses, J. Mech. Sci. Technol. 29(8) (2015), 3549–3560.

39.

Gawaz

, Role of platelets in coronary thrombosis and reperfusion of ischemic myocardium, Cardiovasc. Res. 61(3) (2004), 498–511.

40.

Sadeghi

M.R.

, Numerical simulation of blood flow in vessels with arterial stenosis considering fluid structure interaction (Doctoral dissertation, Ph.D. Dissertation), Graduate School of Mechanical Engineering, Isfahan University of Technology, Iran.

41.

Banerjee

R.K.

Back

L.H.

Back

M.R.

and Cho

Y.I.

, Physiological flow analysis in significant human coronary artery stenoses, Biorheology 40(4) (2003), 451–476.

42.

Govindaraju

Viswanathan

G.N.

Badruddin

I.A.

Kamangar

Ahmed

N.S.

and Al-Rashed

A.A.

, A parametric study of the effect of arterial wall curvature on non-invasive assessment of stenosis severity: Computational foluid dynamics study, Curr. Sci. (2016), 483–491.

43.

Konala

B.C.

Das

and Banerjee

R.K.

, Influence of arterial wall-stenosis compliance on the coronary diagnostic parameters, J. Biomech. 44(5) (2011), 842–847.