A Study of the Fluid–Structure Interaction of the Plaque Circumferential Distribution in the Left Coronary Artery

Abstract

Atherosclerotic plaques within the coronary arteries can prevent blood from flowing to downstream tissues, causing coronary heart disease and a myocardial infarction over time. The degree of stenosis is an important reference point during percutaneous coronary intervention (PCI). However, clinically, patients with the same degree of stenosis exhibit different degrees of disease severity. To investigate the connection between this phenomenon and the plaque circumferential distribution, in this paper, four models with different plaque circumferential locations were made based on the CT data. The blood in the coronary arteries was simulated using the fluid–structure interaction method in ANSYS Workbench software. The results showed that the risk of plaque rupture was less affected by the circumferential distribution of plaque, and the distribution of blood in each branch was affected by the circumferential distribution of plaque. Low TAWSS areas were found posterior to the plaque, and the TAWSS < 0.4 Pa area was ranked from highest to lowest in each model species: plaque on the side away from the left circumflex branch, plaque on the side away from the heart; plaque on the side close to the heart; and plaque on the side close to the left circumflex branch. The same trend was also found in the OSI. It was concluded that the circumferential distribution of plaques affects their further development. This finding will be useful for clinical treatment.

1. Introduction

Worldwide, cardiovascular disease is the leading cause of death, accounting for approximately 30% of all deaths, which places a heavy burden on national economies [1,2]. Coronary atherosclerosis is one of the most common causes of cardiovascular disease. Atherosclerotic plaque in coronary arteries can block blood, leading to insufficient blood supply to the downstream tissues and organs, which can contribute to cardiovascular problems, including coronary heart disease and myocardial infarction [3,4]. Coronary atherosclerotic plaque formation is due to the activation of the immune system when the endothelial cells are damaged and inflammatory responses occur, due to disturbances in blood flow status or some other factors. At the site of the damage, cholesterol is oxidized and, then, continuously taken up by macrophages. At the same time, the smooth muscle cells divide, and the intima begins to thicken to form intimal hyperplasia. Macrophages and intimal hyperplasia, together, form atherosclerotic plaques in coronary arteries, which then protrude into the inner lumen and eventually block the blood flow.

Clinically, it can be alleviated by medication, when the disease is mild. However, percutaneous coronary intervention (PCI) is required, when the disease is more severe. During PCI, surgeons rely on a coronary angiography and the fractional flow reserve (FFR) for treatment decisions. FFR is the gold standard for assessing the degree of stenosis and is defined as the pressure behind (or distal to) a stenosis relative to the pressure in front of the stenosis [5,6]. When the FFR value is 0.8, it means that a specific stenosis is causing a 20% drop in blood pressure. Usually, an FFR > 0.8 means that the stenosis is not severe, while an FFR < 0.8 means that the stenosis is more severe and requires further interventional treatment [2,7]. However, there is a clinical phenomenon in which patients with the same FFR (<0.8) value or the same degree of stenosis can show significant differences in the severity of their disease. This is suspected to be related to the circumferential distribution of the plaques. A coronary hemodynamic study was performed by a fluid–structure interaction (FSI) simulation in order to reveal the influence of the circumferential distribution of coronary atherosclerotic plaques on their continued development.

Since in vivo experiments are very difficult and costly to perform, numerical simulations, at a fraction of the cost, are an effective alternative scheme. In the past, computational fluid dynamics (CFD) was often applied to the numerical simulation of blood flow, where mechanical parameters such as fluid velocity and pressure could be easily obtained. However, the interaction between the blood and the vessel wall cannot be solved by CFD, which limits its accuracy in coronary blood flow simulation. Now, the FSI method is popular in the numerical study of the coronary blood flow, and this method can effectively deal with the interaction between the fluid domain and the solid domain [8]. It has been shown that the FSI provides more satisfactory results than CFD in the analysis of coronary hemodynamics [9,10].

In this study, a realistic 3D coronary artery model was created using a patient’s coronary CT imaging data. In order to investigate the influence of the circumferential distribution of plaques, four models with the same shape of plaques with different circumferential positions were constructed. Realistic boundary conditions from in vivo measurements were applied, taking into account the pulsating effects of the blood flow. A patient-specific 3D coronary artery FSI study was conducted considering vascular compliance. The novelty of this work is its investigation of the effect of the plaque circumferential distribution at different stages on the blood flow within the same coronary artery. The time-averaged wall shear stress (TAWSS) and the oscillatory shear index (OSI) were used to evaluate the risk of further plaque development.

2. Materials and Methods

2.1. Geometry and Materials

A real coronary model helps to guarantee the accuracy of the study results. In this study, the 3D model of coronary arteries was constructed according to coronary CT data. Since the left coronary artery is more prone to plaque growth than the right coronary artery, the left coronary artery was selected for modeling in this research [11]. Diagonal branches are often neglected in coronary artery analysis. However, it has been demonstrated that the presence of side branches alters the blood flow distribution [12], so the diagonal branches were retained in the coronary model in this study. The model was set with 50% stenosis, and plaques were manually added to the left main coronary (LM). The four coronary models with different circumferential distributions of plaque are shown in Figure 1. In Model 1, the plaque was located on the side away from the heart; in Model 2, the plaque was located on the side close to the heart; in Model 3, the plaque was located on the side close to the left circumflex branch (LCX); and in Model 4, the plaque was located on the side away from the LCX. Blood is considered to be an isotropic, incompressible, homogeneous, laminar, non-Newtonian fluid, and the blood density ${\rho }_f$ was taken to be 1060 kg/m³ [13]. Considering the shear thinning behavior of the blood, the Carreau viscosity model [14] was applicable, which is defined by Equation (1).

$$\mu ={\mu }_{\infty }+\left({\mu }_0-{\mu }_{\infty }\right){\left[1+{\left(\lambda \dot{\gamma }\right)}^2\right]}^{\frac{n-1}{2}}$$

(1)

where ${\mu }_0$ is the viscosity at a zero shear rate, 0.056 Pa·s; ${\mu }_{\infty }$ is the viscosity at an infinite shear rate, 0.0035 Pa·s; λ corresponds to the relaxation time, 3.313 s, $n$ is the power index, 0.3568; and $\dot{\gamma }$ $\mathrm{is}$ the shear-rate of strain, s⁻¹.

Because the purpose of this study was to investigate the effect of plaque location, plaque material properties had little influence on the conclusions, and the plaque was considered to be consistent with the vessel wall material property. The vessel wall was assumed to be an isotropic, homogeneous, nonlinear elastic material with a uniform thickness of 0.4 mm [15]. In this study, the 5-parameter Mooney–Rivlin hyperelastic model was used to represent the mechanical properties of the coronary vessels [16]. The present constitutive equations were as follows:

$$W=c_{10}\left(I_1-3\right)+c_{01}\left(I_2-3\right)+c_{20}{\left(I_1-3\right)}^2+c_{11}\left(I_1-3\right)\left(I_2-3\right)+c_{02}{\left(I_2-3\right)}^2+\frac{1}{d}{\left(J-1\right)}^2$$

(2)

where $W$ is the strain energy–density function, $I_1$ and $I_2$ are the first and second stress invariants, $c_{10}$ (−4.02 MPa), $c_{01}$ (4.321 MPa), $c_{20}$ (18.401 MPa), $c_{11}$ (−51.856 MPa), and $c_{02}$ (39.105 MPa) are the hyperelastic constants describing the deformation, d (2.434 MPa⁻¹) is the incompressible parameter, and $J$ represents the elastic volume ratio. The density of the vessel wall ${\rho }_w$ was taken as 1120 kg/m³.

2.2. Mesh and Boundary Condition

The fluid and solid domains were discretized into tetrahedral mesh cells, as shown in Figure 2. Too coarse a mesh size will lead to inaccurate simulation results, while too fine a mesh size will waste computational resources. Therefore, it was necessary to conduct a mesh independence study to ensure that the appropriate mesh size was adopted for the numerical calculation. The number of elements in the fluid domain were 382,634, 516,906, 837,725 and 1,276,453. The solution operation was performed under the same model and the same parameters, and the velocity of a point at the bifurcation of the left circumflex branch at the same moment in the simulation results was taken and compared with the WSS progression of a point at the bifurcation of the diagonal branch, as shown in Figure 3. Compared with the result with the finest mesh accuracy, the velocity and WSS with a mesh number of 837,725 differed from them by 0.15% and 0.32%, respectively, while the computing time was only 45% of the former. Therefore, the mesh numbers of 837,725 and 147,326 for the fluid domain and solid domain, respectively, were selected for the numerical calculation.

In the numerical calculation of the coronary arteries, the velocity inlet and pressure outlet are often used as the boundary conditions [10,16,17]. In this work, the boundary conditions used real data from the coronary arteries, which reflected the pulsatility of the blood flow induced by cardiac systole [16]. The inlet boundary was adopted as the velocity inlet, the outlet boundary was adopted as the pressure outlet, and the cardiac period was 0.8 s, as shown in Figure 4.

Due to the small displacement change of the arterial wall at the inlet and outlet, the position of the inlet and outlet of the arterial wall was fixed, and the rest of the arterial wall was free to move. Meanwhile, the inner vessel wall was set as the fluid–structure interface, which was used to transmit and receive data from the fluid domain.

2.3. Fluid–Structure Interaction (FSI)

FSI is a branch of mechanics that combines computational fluid mechanics and computational solid mechanics, used to study the interaction between solid and fluid domains. During the numerical simulation of the coronary arteries, the pulsating blood flow causes periodic deformation or movement of the vessel wall, which in turn has an effect on the blood flow. The Arbitrary Lagrangian–Eulerian (ALE) is a common method for solving FSI problems, ensuring that the boundaries and interfaces between the fluid and solid domains are accurately traced during the iterative process.

In the fluid domain, the continuity equation and momentum equation are as follows:

$$\nabla ·\mathit{v}=0$$

(3)

$${\rho }_f\left(\frac{\partial \mathit{v}}{\partial t}+\left(\mathit{v}-{\mathit{v}}_{\mathit{g}}\right)·\nabla \mathit{v}\right)=-\nabla p+\nabla ·T$$

(4)

where the vector operator $\nabla =\mathit{i}\frac{\partial }{\partial x}+\mathit{j}\frac{\partial }{\partial y}+\mathit{k}\frac{\partial }{\partial z}$; $\mathit{v}$ is the fluid velocity vector, m/s; ${\mathit{v}}_{\mathit{g}}$ is the moving grid movement velocity, m/s; $p$ is the blood pressure, Pa; ${\rho }_f$ is the blood density, kg/m³; and $T$ is the stress tensor, Pa.

In the solid domain, the conservation equation derived from Newton’s second law is as follows:

$${\rho }_s\frac{{\partial }^2{\mathit{d}}_{\mathit{s}}}{\partial t^2}=\nabla ·{\mathit{\sigma }}_s$$

(5)

where ${\rho }_s$ is the vessel wall density, kg/m³; ${\mathit{d}}_{\mathit{s}}$ is the vessel wall displacement vector, m; and ${\mathit{\sigma }}_{\mathit{s}}$ is the stress tensor, Pa.

The governing equation for the fluid–structure interaction is:

$$\left\{\begin{array}{c}{\mathit{\sigma }}_s{\mathit{n}}_s={\mathit{\sigma }}_f{\mathit{n}}_f\\ {\mathit{v}}_s={\mathit{v}}_f\\ {\mathit{d}}_s={\mathit{d}}_f\end{array}\right.$$

(6)

where $\mathit{n}$ is the unit normal vector; $\mathit{v}$ is the velocity vector, m/s; $\mathit{d}$ is the displacement vector, m; and $s$ and $f$ represent the solid domain and fluid domain, respectively.

Numerical simulations were performed in ANSYS Workbench commercial software. The finite volume method (FVM) was used in Fluent for the fluid mechanics computations, the finite element method (FEM) was used in Transient Structural for the structural mechanics analysis, and System Coupling was used for the coupling between both. The SIMPLE algorithm was used for the coupling of the pressure–velocity terms. The Second Order Implicit Euler Scheme and the Second Order Upwind Scheme were adopted for achieving the temporal and spatial discretization of the equations, respectively. For each coronary model, transient flow simulations were performed for three cardiac cycles, and the results of the last cardiac cycle were used for hemodynamic analysis in order to eliminate the effect of the flow instability at the beginning of the calculation. The total number of steps per cardiac cycle was 160, and the time step was set to 0.005 s. The solution calculation was completed in each time step until the residuals of the coupled system were less than the specified residuals. In this work, the residual was set as 10⁻⁵.

3. Results and Discussion

3.1. Von Mises Force (VMS)

The VMS is a mechanical parameter used to reflect the internal stress distribution of a structure [18], which is defined as follows:

$$\mathrm{VMS}=\frac{1}{\sqrt{2}}\sqrt{{\left({\sigma }_1-{\sigma }_2\right)}^2+{\left({\sigma }_2-{\sigma }_3\right)}^2+{\left({\sigma }_3-{\sigma }_1\right)}^2}$$

(7)

where ${\sigma }_1$ is the first principal stress, Pa; ${\sigma }_2$ is the second principal stress, Pa; and ${\sigma }_3$ is the third principal stress, Pa.

The VMS value at the plaque has an effect on plaque rupture; the larger the value, the greater the risk of plaque rupture. In order to compare the effect of the circumferential distribution of the plaque on the risk of plaque rupture, the VMS at the plaque section was taken for postprocessing, as shown in Figure 5. It can be observed from the figure that a large VMS was exhibited both in front of and behind the plaque, while the VMS was small on the plaque. Due to the different responses of the vessel wall and the plaque to the force, cracks are most likely to occur at the junction between the plaque and the vessel wall, that is, at the fibrous cap, leading to plaque rupture.

The role of the VMS was further determined by the quantification of the VMS for one cardiac cycle, which is shown in Figure 6. It was observed that the distribution of the maximum VMS was consistent across the models, indicating that the risk of plaque rupture was the same in each model. Therefore, it can be concluded that the circumferential distribution of plaques has little effect on plaque rupture.

3.2. Flow Rate

The results of the mass flow rate distribution in each model were summarized from the simulation, as shown in Figure 7. The changes in blood flow over time in the LCX, LAD, and DB branches during a complete cardiac cycle are recorded in Figure 7a, Figure 7b, and Figure 7c, respectively. From the observation data, it was not difficult to find that regardless of the plaque distribution model, the flow changes in each branch during systole and early diastole were almost the same, and there was no obvious change. However, the flow rate fluctuated significantly at the outlet in the late diastole. The changes in branch flow in the late diastole of each model were compared. In Model 1, the flow rate was relatively moderate at the LCX and LAD branches, while the flow rate was relatively high at the DB branch. In Model 2, the flow rate was relatively high at the LCX branch, while the flow rate was relatively low at the LAD and DB branches, and the flow rate at the DB branch was significantly lower than the other models. In Model 3, the flow rate distribution was diametrically opposed to Model 2, with a lower flow rate at the LCX branch and a higher flow rate at the LAD and DB branches. In Model 4, the flow rate was relatively low at the LCX and LAD branches, while the flow rate was relatively moderate at the DB branch.

The average flow rate of each branch in the different models is summarized in

Table 1. Blood flow rate of each branch in different models.

	Model 1	Model 2	Model 3	Model 4
flow rate at LCX (g/s)	0.4113	0.4249	0.4016	0.4092
flow rate percentage at LCX (%)	32.73	33.82	31.89	32.66
flow rate at DB (g/s)	0.1915	0.1832	0.1944	0.1892
flow rate percentage at DB (%)	15.24	14.58	15.44	15.10
flow rate at LAD (g/s)	0.6536	0.6484	0.6632	0.6543
flow rate percentage at LAD (%)	52.02	51.60	52.67	52.23

. About half of the blood flow came out of the LAD, with most of the rest coming out of the LCX and a small portion out of the DB. The distribution of blood in the left coronary artery was consistent with the clinically observed data [15]. We observed the average flow of each branch and the percentage of the branch flow to the total flow. The flow of a branch in the late diastole determined the average flow of the branch. Intuitively, the location of the plaque had an impact on the distribution of the blood flow in each branch. When the plaque was close to the side of the heart, the blood flow distribution was significantly different from that of other plaques, and the difference in flow distribution between plaques at the other locations was not significant. When the plaque was on one side of the heart, blood flow to the LCX branch increased, while blood flow to the DB and LAD decreased compared to the other plaque locations.

The influence of the circumferential distribution of plaques on the velocity was further analyzed, and the streamline distribution of each model during the peak contraction period was obtained after postprocessing, as shown in Figure 8. Since the circumferential distribution of the plaque will change the magnitude and direction of blood flow velocity, in addition to the velocity at the LAD and LCX sections, the section velocity at the LM was also obtained, as shown in Figure 9. The maximum velocities, mean velocities, and velocity standard deviations for the three cross-sectional locations during peak systole and late diastole are summarized in

Table 2. Velocity values of each section during the peak systole and late diastole.

Time	Parameter	Model 1	Model 2	Model 3	Model 4
peaksy stole	LM. average velocity (cm/s)	4.63	4.97	4.50	4.79
	LM. maximum velocity (cm/s)	24.31	25.64	26.87	23.81
	LM. standard deviation (cm/s)	5.74	6.12	6.15	5.98
	LCX. average velocity (cm/s)	9.52	9.66	9.19	9.25
	LCX. maximum velocity (cm/s)	27.19	28.93	26.70	27.11
	LCX. standard deviation (cm/s)	7.58	7.84	7.42	7.48
	LAD. average velocity (cm/s)	5.45	5.75	5.93	5.44
	LAD. maximum velocity (cm/s)	18.49	18.60	19.95	17.79
	LAD. standard deviation (cm/s)	4.95	4.93	5.33	4.77
latedia stole	LM. average velocity (cm/s)	12.35	12.75	12.25	12.47
	LM. maximum velocity (cm/s)	51.43	53.65	56.34	50.06
	LM. standard deviation (cm/s)	13.45	13.87	14.14	13.99
	LCX. average velocity (cm/s)	21.20	23.23	19.45	21.83
	LCX. maximum velocity (cm/s)	56.02	62.17	52.27	60.26
	LCX. standard deviation (cm/s)	16.13	17.60	14.89	16.53
	LAD. average velocity (cm/s)	14.75	15.75	15.72	13.34
	LAD. maximum velocity (cm/s)	47.27	46.44	48.32	46.06
	LAD. standard deviation (cm/s)	13.37	12.68	14.90	12.45

. It can be observed that the flow velocity increased sharply at the plaque, and there was a clear vortex behind the plaque. For convenience of observation, the plaque area was enlarged and rotated at a certain angle in the figure.

It can be observed from Figure 8 and Figure 9 that during the peak systolic period the velocity distribution at the LM section was greatly affected by the circumferential position of the plaque. The narrowing of the blood flow channel was due to the presence of the plaque, which caused an increase in the blood flow velocity. In the different models, the maximum speed was inconsistent, and there were obvious differences. The different distribution locations of the plaques led to different sizes of the vortices behind the plaques. At the LCX section, the velocity distribution trends in the section were basically the same, but the magnitudes of the velocities were different. The reason for this phenomenon is that before the blood flow enters the LCX branch, the speed of the blood flow is different due to the different levels of energy consumption in the vortex region. The same interpretation can be found at the LAD section. However, this explanation does not apply to model 3, in which the velocity was small at the LCX section but large at the LAD section. In model 3, the vortex area behind the block not only consumed the kinetic energy of the fluid but also hindered the flow of the fluid into the LCX, which led to more blood flowing into the LAD; so, in the LAD section, the blood flow velocity in model 3 was significantly higher than other models. In the late diastole, the blood velocity increased significantly, and the velocity distribution in each section was basically consistent with the peak systolic period. However, the greater blood flow velocity resulted in a larger area of low velocity near the vessel wall, especially in the LAD section, which is easily observed from Figure 8. In Table 2, the maximum and average velocities quantify the information in Figure 9, and the standard deviation reflects the difference in velocity gradients at the cross-section.

The following conclusions can be drawn from the flow, velocity streamlines, and cross-sectional velocity: the presence of plaque causes the blood flow velocity to rise sharply at the plaque, and a vortex forms behind the plaque. The existence of vortices lowers the kinetic energy of the fluid, and at the same time hinders the movement of the fluid in this direction. The plaques are distributed in different circumferential positions, and vortices of different shapes and degrees are generated behind them. Under the combined action of the plaque and the eddy current, plaques at different circumferential positions in coronary arteries cause changes in the blood flow and velocity in each branch. Due to the different parts of the heart supplied by blood in the corresponding coronary branch (the LCX supplies the left edge of the left ventricle to the apex of the heart, the LAD supplies part of the anterior ventricular septum, most of the left and right ventricles, and part of the left bundle branch, and the DB supplies the anterior wall of the left ventricle), differently distributed plaques may cause different degrees of heart disease.

3.3. Wall Shear Stress (WSS)

It is well known that the WSS is associated with the occurrence and development of intimal hyperplasia and atherosclerotic plaques. Smaller WSS areas are prone to plaque growth, while larger WSSs can cause plaque rupture. The degree of WSS oscillation during the cardiac cycle is related to the endothelial cell damage. The higher the degree of oscillation, the greater the risk of endothelial damage. The WSS distribution of each model at the peak systolic period is shown in Figure 10.

No matter where the plaques were located, there was a large WSS in front of the plaque, a small WSS behind the plaque, a large WSS at the LCX bifurcation, and a small WSS at the DB bifurcation. Combining the velocity streamlines in Figure 8, it is not difficult to see that there was a certain correlation between the WSS and the blood flow velocity of the blood vessel wall. The WSS value was consistent with the variation trend of the velocity. Behind the plaque, the eddy current caused the blood flow to be disordered and the flow velocity was low, forming a low WSS area. At the LCX bifurcation, the blood flow impacted the top of the bifurcation and caused a high WSS there. When entering the DB, the blood flow rate was further reduced due to the existence of the bifurcation, forming a low WSS area. Comparing between different models, there were obvious differences in the low WSS area behind the plaque, which was the result of the combined effect of the vortex behind the plaque and the separation of the blood flow. The WSS distributions at the DB forks were similar, and there was no significant difference. In order to further compare the distribution of the WSS among each model, a representative position in the model was taken to quantify the change in WSS in the complete cardiac cycle, as shown in Figure 11.

At the shoulder of the LCX bifurcation, that is, point 1, the variation trend of the WSS under different models was similar, but the WSS value was different. The WSS values were sorted from high to low; the highest were model 2 and model 4, and their WSS changes were almost the same; the second was model 1; the lowest was model 3, which was significantly different from the other models. At the apex of the LCX bifurcation, that is, point 2, the trend of the WSS changes was similar to that at point 1. The difference was that the amplitude of the WSS was larger here, and the maximum amplitudes from model 1 to model 4 were 26.54 Pa, 22.79 Pa, 37.36 Pa, and 21.84 Pa, respectively. In addition, no matter which model, the WSS at point 2 was the largest among the four points, which was caused by the impingement and shunting of blood here. At the front-end side branch of LAD, namely point 3, the WSS fluctuation was significantly stronger than in the other models, but the WSS value at this point was the smallest among the four feature points. Here, the low and oscillatory WSS was due to the combination of plaque, eddy currents, and shunts that the blood experienced before entering the site. At the shoulder of the DB bifurcation, that is, point 4, the WSS trend of each model was similar, and there was only a slight fluctuation in the time period of 2.1 s to 2.2 s. It is not difficult to observe the changes in the WSS at the four characteristic points. In the early stage of the cardiac cycle, the difference in the WSS value in the different models was small; however, in the late stage of the cardiac cycle (2.0 s ~ 2.4 s), the difference in the WSS value was significant. This phenomenon was the result of the combined effect of the blood flow velocity and outlet pressure. The WSS increased with the increasing flow rate and decreased with the increasing outlet pressure. In the early part of the cardiac cycle, the blood flow velocity was lower and the pressure was higher, while the latter part was the opposite. To further analyze the distribution of the WSS in the cardiac cycle, the time-averaged wall shear stress (TAWSS) was obtained after postprocessing, as shown in Figure 12.

The TAWSS can reflect the changes in the WSS during the whole cardiac cycle and is widely used in hemodynamic analysis [16,19]. The TAWSS distribution was similar to the WSS distribution during the peak systole. Regardless of the model, the regions with higher TAWSS values occurred upstream of the plaque and at the bifurcation of the circumflex, which was associated with higher flow velocity at these locations. A low TAWSS occurred behind the plaque and on the LAD side of the bifurcated shoulder. Since the TAWSS < 0.4 Pa region is considered to be the region that induces the development of atherosclerosis [19], the circular region in the figure enlarges the plaque location, and only the TAWSS < 0.4 Pa part is retained. It is not difficult to see that the circumferential distribution of plaques can lead to changes in the location of atherosclerotic regrowth areas. In Model 1 to Model 4, the areas of the TAWSS < 0.4 Pa were 22.58 mm², 18.64 mm², 23.52 mm², and 25.65 mm², respectively. Assessed by this parameter, the order of plaque further development risk from high to low is: when the plaque is located on the side away from the LCA; when the plaque is located on the side away from the heart; when the plaque is located on the side close to the heart; and when the plaque is located on the side close to the LCX.

3.4. Oscillatory Shear Index (OSI)

The OSI reflects the oscillatory behavior of the WSS throughout the cardiac cycle and is a dimensionless constant [20,21]. OSI values range from 0 to 0.5, with 0 representing no oscillation and 0.5 representing full oscillation [22]. An OSI > 0.2 is considered as an atherogenic region [23]. The OSI is defined as:

$$\mathrm{OSI}=\frac{1}{2}\left(1-\frac{\left|{\int }_0^{\mathrm{T}}\mathrm{WSSdt}\right|}{{\int }_0^{\mathrm{T}}\left|\mathrm{WSS}\right|\mathrm{dt}}\right)$$

(8)

where WSS is the instantaneous WSS (Pa) magnitude, and T (s) is the cardiac cycle time. The maximum OSI values in the different models are recorded in Figure 13. In models 1 to 4, the OSI values were 0.385, 0.340, 0.388, and 0.396, respectively. The largest OSI value was in model 4, and the smallest OSI value was in model 2. The OSI differences were insignificant in the different models except for the significantly smaller values in model 2. This finding suggests that the WSS oscillations were most severe when the plaque was located away from the LCX, followed by the plaque located close to the LCX and away from the heart side, and the oscillations were least severe when the plaque was located close to the heart side. The findings obtained by the OSI were the same as those of the TAWSS, which further validates the effect of the plaque circumferential distribution on the coronary blood flow.

4. Conclusions

The paper studied the effect of the circumferential distribution of coronary plaques on the further development of atherosclerosis. Based on coronary CT data, four three-dimensional coronary models with the same degree of stenosis but different plaque circumferential positions were established. Considering the pulsatile action of blood and the compliance of the vessel wall, the fluid–structure interaction method was used for the numerical simulation. The results of the study showed that the circumferential location of the plaque hardly changed the risk of plaque rupture. Plaques with different circumferential positions changed the direction of blood flow and caused eddies behind the plaques, which in turn altered the velocity of blood entering each branch and the flow of blood in the branches. Since each branch plays a different role in the heart, over time, this difference in flow distribution may have varying degrees of impact on heart disease. In the early stage of the cardiac cycle, the WSS did not change significantly due to the circumferential distribution of plaques; however, in the late cardiac cycle, when the blood flow velocity increased, the size and position of the vortex region after the plaque was affected by the circumferential distribution of the plaque, resulting in very different WSSs. Combined with the area of the TAWSS < 0.4 Pa and the OSI value, it is concluded that under the same degree of stenosis, when the plaque is located on the side away from the circumflex branch, the risk of further development of coronary atherosclerosis is the greatest, followed by the plaque located on the side away from the heart and the plaque located on the side of the circumflex artery. On the side closest to the heart, the least risky plaque is on the side of the circumflex artery. This conclusion can provide help for clinicians to make decisions during PCI treatment.