Influence of coronary bifurcation angle on atherosclerosis

Zhaomiao Liu · Shengwei Zhao · Yunjie Li · Feng Shen · Yipeng Qi · Qi Wang

Abstract Hemodynamics plays a crucial role in the development and progression of coronary atherosclerosis, which is prone to occur in branch bifurcation. An individual aortic-coronary artery model and three changed bifurcation angle models are constructed by Mimics and Freeform based on computed tomography angiography. The influence of different coronary bifurcation angles between left main (LM), left anterior descending (LAD), and left circumflex (LCX) on the blood flow field and related hemodynamic parameters are studied. It is shown that a wider bifurcation angle between LAD and LCX can cause a wider low-wall shear stress area, leading to atherosclerosis. Similarly, a decreased angle between LM and LAD is predisposed to prevent atherosclerosis. The results help to better understand the hemodynamic causes of atherosclerosis with various bifurcation angles in coronary arteries and to provide guidance for clinical assessment and prevention.

Keywords Atherosclerosis · Coronary artery · Bifurcation angle · Hemodynamics · Wall shear stress

1 Introduction

Coronary bifurcation lesions account for 15% —20% of percutaneous coronary interventions and are an important component of coronary artery disease [1]. In recent years, studies have increasingly focused on the effects of coronary anatomical features on the development and progression of atherosclerosis, and have shown that the coronary bifurcation angle has an important influence on the formation and distribution of coronary atherosclerotic plaques [2]. Accurate evaluation of the relationship between the coronary bifurcation angle and atherosclerosis is of great clinical significance for the prevention and treatment of coronary heart disease.

The left main coronary artery bifurcation is the first bifurcation of the left coronary artery [3, 4], which is significantly more important than other bifurcations. A left main bifurcation lesion directly threatens a patient’s life and health [5]. The location of left main lesions can be divided into ostium, midshaft and distal bifurcations, or some combination of these, at least 50% of which are bifurcation disease [3]. The work of Pflederer et al. [5] analyzed the natural distribution of the bifurcation angles by multidetector computed tomography (MDCT) and found average values of 80° ± 27° (left anterior descending (LAD)/left circumflex (LCX)), 46° ± 19° (LAD/first diagonal branch (Diag1)), 48° ± 24° (LCX/first obtuse marginal branch (OM1)), and 53° ± 27° (posterior descending coronar y artery (PDA)/right posterolateral branch (Rpld)), respectively. Because of different measurement methods and samples collected, different sizes of coronary bifurcation angles have been reported, which also indicates the diversity of coronary bifurcation angles.

At present, coronary heart disease is clinically diagnosed and treated by imaging methods. Computed tomography (CT) coronary angiography with high temporal and spatial resolution [6] can accurately provide coronary anatomical diagnostic information and is widely used. In studies by Konishi et al. [7], Cui et al. [8], Cademartiri et al. [9], and Ryotaro et al. [10], the authors investigated the relationship between coronary anatomy and atherosclerosis from a clinical perspective, which showed that the location of atherosclerotic plaques is not random. Anatomical morphology such as the bifurcation angle, left main length, diameter, and myocardial bridge of the coronary arteries could result in a special blood flow environment in specific areas, where it will increase the potential for atherosclerosis.

Fig. 1 Processing of different bifurcation models. a Original model obtained by CT data in Mimics (LM: left main, LV: left ventricle, RCA: right ventricle). b Case of changed bifurcation angle model B in Freeform

Table 1 Four groups of models with different bifurcation angles

Fig. 2 Sketch of inlet and outlet boundary of aortic-coronary artery model. A: aortic inlet, B: aortic outlet, a: left anterior descending artery, b: septal branch, c: diagonal branch, d: left marginal branch, e: left circumflex branch, f: right coronary branch, g: posterior descending artery, h: right marginal branch

In addition, Malcolm and Roach [11] conducted dye flow experiments to study glass model bifurcations with different angles and found that the boundary layer separated on lateral branches and increased with the decrease in branch flow, which may be a contributing factor to atherosclerosis. In another work, Chaichana et al. [12] found that there was a disturbance flow pattern in the left coronary artery model with a larger angle. Wall pressure decreased as the fluid flowed from the left main branch to the bifurcation region.

Fig. 3 Sketch of aortic-coronary arteries models with different bifurcation angles. a Model A (angle A: 90°, angle B: 90°, angle C: 180°), b model B (angle A: 60°, angle B: 120°, angle C: 180°), c model C (angle A: 120°, angle B: 60°, angle C: 180°), d model D (angle A: 120°, angle B: 120°, angle C: 120°)

Fig. 4 Coupling process of the multiscale model

Fig. 5 Lumped parameter model. a Heart entrance, b aortic outlet and coronary trunk, c distal coronary artery branch

A lower wall shear stress gradient existed at the left bifurcation with larger angles. Similarly, Chiastra et al. [13] studied the effect of bifurcation angle on atherosclerosis in normal and narrow cases and found that low time-averaged wall shear stress was located at the ostium of branches. A larger range of low-wall shear stress (WSS) distribution exists in the case of smaller bifurcation angles. High oscillatory shear index (OSI) exposure to different bifurcation angles can be negligible. There was a slight increase in the low WSS area and a significant expansion area of high OSI in narrow cases. The work by Doutel et al. [14] found that a major factor leading to atherosclerosis was the expansion ratio, the relationship between the cross-sectional area of the outflow branches and the cross-sectional area of the trunk. Large areas oflow WSS showed high expansion. In addition, the size of the low WSS region was independent of the ratio of branch diameters.

Although imaging studies have yielded significant results, the anatomical information of the coronary arteries alone cannot fully reflect the coronary blood flow, and there are some limitations in the effects of hemodynamic parameters on atherosclerosis [15]. Computational fluid dynamics (CFD) [16—18] are used to analyze coronary artery bifurcations. Because of the complex relationship between coronary arteries and the aorta, investigations regarding the relationship between the bifurcation structure and coronary atherosclerosis are still insufficient.

Therefore, a three-dimensional (3D) individual model of aortic-coronary arteries based on CT angiography is constructed, with three other changed bifurcation angle models. The boundary conditions of numerical simulation are provided by a lumped parameter model. In this paper, the effects of different bifurcation angles on coronary atherosclerosis are studied by hemodynamic parameters [19—21] including blood flow velocity and WSS.

Fig. 6 a Mass flow rate of inlet and outlet of the aorta in a cardiac cycle. b Mass flow rate of coronary branches in a cardiac cycle

2 Establishment of individual models

A CT scan of the heart without coronary stenosis, with 285 images and a thickness of 0.5 mm, is selected as model A (angle A: 90°, angle B: 90°, angle C: 180°). An image of the aortic-coronary-left ventricular model is obtained by setting the segmentation threshold and region growth of the original DICOM file by Mimics 18.0 (Materialise, Belgium), as shown in Fig. 1a.

Fig. 7 Pressure boundary conditions in a cardiac cycle. Inlet: aortic inlet, outlet: aortic outlet. a—h coronary branches

Table 2 Mean flow rate of the inlet and different exits

The data are then stored in a file format (STL) and imported into Geomagic Freeform 2015 and Geomagic Studio v. 12 (3D Systems, USA) for cutting and smoothing, as shown in Fig. 1b. Angle A is the angle between LM and LCX, angle B is the angle between LAD and LCX, and angle C is the angle between LM and LAD. Figure 2 shows each branch and exit in the aortic-coronary model, and LAD is a continuation of the LM trunk, which is at right angles to the LM, roughly in the same plane. Thereafter, according to the statistical study [22], the bifurcation angle of LM is modified to the control group in Table 1, which corresponds to the physiological range. Model B (angle A: 60°, angle B: 120°, angle C: 180°), model C (angle A: 120°, angle B: 60°, angle C: 180°), and model D (angle A: 120°, angle B: 120°, angle C: 120°) are constructed as shown in Fig. 3b—d. Other features of the geometry (e.g. arterial diameter, cross-sectional shape, 3D orientation) remain constant during this process, as shown in Fig. 1b.

In order to ensure the accuracy of numerical simulation calculation, not only the three-dimensional structure of the left and right coronary vessels and their branches but also the 3D structure of the aortic vessel is preserved to ensure that the blood flow is in line with the real situation.

Fig. 8 Sketch of high-quality mesh in model A

Fig. 9 Global flow field at peak systole (0.35 s)

3 Numerical simulation method

3.1 Governing equations

The blood is considered laminar, isothermal, Newtonian, and incompressible, with a constant density of 1060 kg/m3and a constant viscosity of 0.0035 Pa·s. The arterial wall is rigid and has no slip and ignores the effect of gravity. Using Cartesian coordinates where x, y, and z represent components in three directions respectively, the blood flow satisfies the Navier—Stokes (N—S) equation and the continuity equation

Fig. 10 Global flow field at peak diastole (0.45 s)

where ρ represents blood density, vx,vy,vzis the fluid velocity component, μ is the dynamic viscosity, and P is the pressure.

3.2 Boundary conditions

Since the coronary system is an integral part of the human blood circulation system, it is necessary to consider the overall interaction with the ascending aorta, the left ventricle, the capillary network downstream of the coronary arteries, and the like. An effective research method to solve this complex boundary condition is to introduce a lumped parameter model [23—25] and combine the 3D model with a zero-dimentional (0D) model to form a multi-scale calculation model [26], as shown in Fig. 4. P represents pressure and Q represents the flow rate.

Fig. 11 Streamline diagram of different bifurcation angles models at 0.35 s

Clinical experimental data show that the combination of the lumped parameter model and the CFD model can better simulate the cardiovascular hemodynamic parameters of patients, with the advantages of fewer parameters, and clear physical and computational significance [27]. It has been widely used to assist in the design and evaluation of surgical treatment of cardiovascular disease and to predict cardiovascular risk in potential patients [28, 29]. The centralized parameter model of the entry and exit boundary conditions introduced in this work is shown in Fig. 5. The component parameters refer to the results of Kim et al. [24], Zhen et al. [30], and Lan et al. [31].

In the lumped parameter model, R, L, and C are the resistance, the inductance, and the capacitance, respectively, which represent the resistance of the blood vessel, the inertia of the blood flow, and the compliance of the vessel separately.

Figure 5a shows the heart entrance model where the function of the heart valve is simulated by unilateral conductivity of diode. The reciprocal of time-varying capacitance represents the periodic change in ventricular volume contraction. Figure 5b display the aortic outlet model and coronary artery trunk model based on the circuit model of Kirchhoff’s law. Subscripts p and d represent vascular proximal and distal resistance, respectively. Figure 5c shows the distal coronary load model. The blood flow is restricted during systole in the coronary circulation due to the increased intramyocardial pressure caused by ventricular contraction. A pressure source called Pim is added in the distal coronary branch model, which represents the elastance function of different chambers.

Because the blood flow in coronary artery branches is dominated by the resistance of the downstream capillary network, the change in bifurcation angles could cause a slight increase in local resistance, Rd, in the coronary trunk model, as shown in Fig. 5b, but it is a small fraction of the total resistance of the coronary network. The distributions of mass flow in four models have no significant change.

Taking model A as an example, the entrance and exit boundary conditions obtained by the pumped parameter model are shown in Figs. 6 and 7. One cardiac cycle is 0.8 s. In this paper, five cycles are calculated, and the final one is selected as the result.

The mean flow rate and volume rate of the entrance and different exits are shown in Table 2. The ratio represents the relative sizes of mass flow rate between inlet and outlet, LAD, LCX, and RCA. The inlet volume rate of 4.53 L/min meets a normal person’s cardiac output. The outflow rate of LAD and LCX is close to clinical data [17].

Fig. 12 Streamline diagram of different bifurcation angle models at 0.40 s

3.3 Grid independence verification

Altair Hyper Mesh 12.0 is applied to generate a high-quality polyhedral mesh for the established aortic-coronary model, and the coronary branches are encrypted. Three different mesh numbers (110,865, 163,020, and 844,151) are used. The mean outlet pressures of the ascending aorta are 12,254 Pa, 12,596 Pa, and 12,685 Pa, respectively. The error in the middle mesh numbers is only 0.7% , which meets the accuracy requirement of calculation. An example of model A (angle A: 90°; angle B: 90°; angle C: 180°) is shown in Fig. 8.

4 Results and discussion

4.1 Influence of different bifurcation angles on flow field

The coronary arteries are mostly buried between the myocardial tissues and compressed by ventricular contraction during systole, resulting in reduced coronary blood flow. When ventricular compression is relieved, the coronary blood flow is restored. Figures 9 and 10 show the global flow field in model A at the peak period of 0.35 s and 0.45 s.

Figures 11, 12, and 13 are the local flow streamlines in different bifurcation angle models at a specific time in a cardiac cycle (0.35 s, 0.40 s, and 0.45 s). It can be seen from Fig. 11 that the flow velocity in LM, as the total flow ofleft coronary, is higher than that of LAD and LCX, and the streamlines in LAD are denser than that of LCX. The streamlines are basically parallel to the blood vessel. However, the blood flow in LCX is obviously more disordered, because angle A is not a straight angle in the four models. Combining the three angles corresponding to the four models in Fig. 11, the confusion order of streamlines in the circumflex branch is model B(C), D and A. Angle B is 120° in both models B and D. Angle C is 180° in both models B and A. This indicates that angle A plays an important role in the streamline of LCX. When angle A is equal to angle B, it is more advantageous for the steady blood flow in LCX.

Fig. 13 Streamline diagram of different bifurcation angle models at 0.45 s

Fig. 14 TAWSS contours in model A. Additional details for circle A and perspective B in four models are shown in Figs. 15, 16

Fig. 15 TAWSS contours of different bifurcation angle models in circle A. The circles in models B and D show the enlarged area of low wall shear stress

Fig. 16 TAWSS contours of different bifurcation angle models in circle B. The circle in model D shows the disappeared area of low-wall shear stress

As shown in Fig. 12, the blood flow in the left coronary arteries decreases, especially in LAD at the period of 0.40 s. The streamlines in LAD become disordered, and a significant recirculation zone appears in the anterior descending branch. It is also interesting to note that when the blood becomes reflux, some in LCX flows into LAD.

As given in Fig. 13, the blood flow in the left coronary arteries increases at the period of 0.45 s. Compared with the time at 0.35 s, the streamlines are denser and more uniform, and the disordered streamlines in LCX disappear.

In addition, whether it is systolic or diastolic, there exists a particularly low-velocity zone at the location of the left coronary bifurcation, where platelet particles and blood cell particles are prone to be aggregated and solidified to form an embolus. Subsequently, they migrate and consolidate on a certain blood vessel wall near or downstream of the bifurcation, forming thrombosis, which is consistent with the research results of Chiastra et al. [13].

4.2 Influence of different branch angles on wall shear stress

One valid parameter used to characterize the impact of bifurcation angle on hemodynamic flow is calculated as timeaveraged wall shear stress (TAWSS), which is defined as

where T is the period of the cardiac cycle and τwis instantaneous WSS. It means the total shear stress exerted on the wall throughout a cardiac cycle.

The TAWSS contour in model A is shown in Fig. 14 as an example. It can be seen that the distribution of TAWSS is not uniform. In general, TAWSS in LM is higher than LAD and LCX. Since the four models have no narrow near the bifurcation, there is no high TAWSS area.

Comparing the four models in Fig. 15, models B and D have an obvious larger low TAWSS region (TAWSS ＜ 1 Pa) shown in the red circle at the bifurcation, respectively. The common point in models B and D is that angle B is 120°, while angle B in models A and C is 90° and 30°. This means that a wider angle between LAD and LCX is prone to atherosclerosis, which is consistent with clinical statistical studies [15].

Comparing the four models in Fig. 16, model D has an obvious smaller low TAWSS region (TAWSS ＜ 1 Pa) shown in the red circle on the outside of LAD. The difference between the four models is that angle C in model D is 120°, while that in the other three models is 180°. This indicates that the decrease in the angle between LM and LAD tends to prevent atherosclerosis.

5 Conclusion

The primary objective of this study is to investigate the effect of different bifurcation angles on the left coronary artery. The branch bifurcation is prone to low-wall shear stress areas, resulting in atherosclerosis. When the angle between the LAD and LCX is too large (above 90°), there is an obvious enlarged low-wall shear stress area at the bifurcation. When the angle between the LM and LAD decreases from a near line, the low-wall shear stress area decreases at the outside of LAD. One potential solution to prevent future atherosclerosis is to deploy a stent from LM to LCX that expands the angle between LM and LAD, while decreasing the angle between LM and LCX.

The main limitations of this study are that the elastic change in the blood vessel wall was not taken into account, and the fluid structure interaction (FSI) was not considered due to the complexity of 3D models.

The result regarding the distribution of wall shear stress influenced by different flow fields with different bifurcations is consistent with clinical statistics. This can help to gain a better understanding of the occurrence and development of atherosclerosis at the bifurcation angle of coronary arteries, as well as provide clinical evaluation and prevention of coronary artery disease.

Acknowledgements The authors are grateful for the support of the Specialized Research Fund for the Doctoral Program of Higher Education (Grant 20131103110025), the Key Program of Science and Technology Plan of Beijing Municipal Education Commission (Grant KZ201710005006), and the National Natural Science Foundation of China (Grant 81601557).