Computation of hemodynamics in eccentric coronary stenosis: A morphological parametric study

Abstract

BACKGROUND:

Flow recirculation occurs in eccentric coronary stenosis, which can lead to adverse outcome. The complex local geodesic patterns of eccentric stenosis are critical factors in determining the flow characteristics in post-stenotic flow.

OBJECTIVE:

The main objective of this study is to relate the relationship between the detailed morphological parameters in eccentric coronary stenosis and the post-stenotic flow characteristics.

METHODS:

Several idealized eccentric coronary stenosis models with variable morphological parameters are created to conduct a series of computational fluid dynamics analysis. The impact of four specific lesion morphological parameters, eccentricity index (EI), diameter stenosis (DS), stenosis length (SL) and shape of lesion, are investigated.

RESULTS:

When EI is small ( $<$ 0.33), the length of recirculation zones would increase as EI increase; while when EI is large ( $>$ 0.33), it would decreased as EI increase; Larger magnitude of retrograde flow occurs in models with smaller EIs. Both the recirculation zone length and maximum shear rate increase significantly as DS increases. Increase of SL will lead to increase of recirculation zone length. Higher maximum shear rate and larger recirculation zone are observed in models with sharper stenosis shape.

CONCLUSIONS:

Except DS, the detailed geometry patterns (EI, SL and shape of the stenosis) also have great impact on post-stenotic flow behaviors in eccentric coronary stenosis.

Keywords

Eccentric coronary stenosis computational fluid dynamics analysis morphological parameters post-stenotic flow characteristics

1. Introduction

Atherosclerotic plaques in coronary arteries have great impact on blood flow patterns and will result in local physiological perturbances such as recirculation, which can lead to detrimental biological and clinical sequelae [1, 2, 3]. Recirculation zones will cause stasis and provide an optimal environment for procoagulant factor mixing and promoting activation of the coagulation system [4, 5]. High shear rate are also observed in severe coronary stenosis, which can result in abnormal platelet and leukocyte activation [6, 7].

Figure 1.

Eccentric coronary stenosis models and boundary conditions. (A) Idealized models and morphological parameters: EI, DS and SL. (B) Four shape of the eccentric coronary stenosis models (for trapezoid-shaped models, the wall length of the upper base is set to be 1/3 of the stenosis length). (C) Normalized boundary velocity waveform used at the inlet.

A lot of researchers have carried out their work on flow behaviors in different-shaped stenosis [8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18]. Among these studies, concentric (about the center of the artery) shaped stenosis has been widely studied. However, eccentric lesions are most commonly observed in coronary stenosis [19]. Flow patterns in concentric shaped stenosis are quite different from those in eccentric ones [20, 21]. It is also reported that eccentric lesions are more likely to be observed in patients with cardiovascular symptoms [22, 23]. Mates et al. have studied the impact of eccentric lesions on flow pressure drops [24]. Yong and Tsai have demonstrated that eccentric show strong influence on flow characteristics [20, 21]. Recently, by using the computational fluid dynamics (CFD) method, Javadzadegan et al. demonstrated that the lesion eccentricity could affect the flow recirculation and shear rate to a great extent [25]. However, the unsteady flow condition was not included in their computational model, which makes the flow behavior in stenosis section more complex. To overcome this limitation, a transient particle image velocimetry experiment was performed to relate the correlation between Reynolds number and eccentricity effect [26].

From the brief review of literature, the impact of detailed morphological parameters of eccentric coronary stenosis on post-stenotic flow characteristics has not been investigated. Therefore, the main objective of this study is to relate the relationship between the detailed morphological parameters in eccentric coronary stenosis and the flow characteristics. Since pressure drop is relatively independent of stenosis geometry (primarily dependent upon the minimum area of the stenosis) [24], here we will concentrate on blood flow patterns in recirculation zones. Several idealized coronary stenosis models with variable morphological parameters are created to conduct a series of morphological parametric studies. The impact of four specific lesion morphological parameters, eccentricity index (EI), diameter stenosis (DS), stenosis length (SL) and shape of lesion, are investigated by using the CFD approach.

Figure 2.

Streamlines for models with different EIs at $t=$ 0.66 s. Shear rates are labeled at the streamlines. The DS, SL and shape of the stenosis are kept constant for the four models (DS $=$ 70%, SL $=$ 2D and with a cosine shape).

2. Methods

2.1 Eccentric coronary stenosis models

The idealized eccentric coronary stenosis sections are modeled as 3D pipes. The diameter of the arteries is set as 3 mm. The four morphological parameters are illustrated in Fig. 1A and B. EI is defined as [27]:

$\displaystyle\textit{EI}=\frac{(\text{Maximum wall thickness}-\text{Minimum % wall thickness})}{\text{Maximum wall thickness}}$ (1)

0 represents no eccentricity and 1 represents highest eccentricity. DS is calculated as:

$\displaystyle\textit{DS}=1-\frac{D_{s}}{D}$ (2)

where $D_{S}$ is the diameter of the stenosis and $D$ is the diameter of the parent artery [26]. Idealized models with the EI of 0.00, 0.33, 0.67 and 1.00, the DS of 40%, 50%, 60% and 70%, the SL of 1, 2, 3 and 4 diameters, and the stenosis shape of cosine-shaped, triangle-shaped, trapezoid-shaped and rectangle-shaped are created in this study. The inlet and outlet length of the arteries are extended by 30 mm and 70 mm, to minimize the effect of boundary conditions.

2.2 Boundary conditions

Pulsatile flow waveform was applied as velocity inlet boundary condition. The inflow profiles were based on the work of Boutsianis et al. [28]. The cardiac period and mass flow rate were normalized to 0.8 s and 0.9 g/s, respectively. The normalized flow rate was shown in Fig. 1C. The Womersley velocity profiles based on the specific inflow profiles wave were prescribed at the inlet. A zero relative pressure condition was applied at the distal end [29]. Furthermore, a no-slip wall boundary condition was imposed on the arterial wall.

2.3 Computational method

CFD analysis was performed using the commercial CFD software ANSYS FLUENT V13 (ANSYS Inc.). The numerical scheme in ANSYS FLUENT V13 was based on the finite-volume method. Blood was modeled as an incompressible Newtonian fluid. Dynamic viscosity was set to 3.5 cP and density $\rho$ was 1050 kg/m ${}^{3}$ . Mesh independence was judged by comparing the computed velocities (for each case, the computed velocity profiles for the finally chosen mesh differed by less than 1% from those for doubled mesh resolution). The solutions were run for three cardiac cycles and only the results of the third cardiac cycle were employed for further analysis.

Figure 3.

Axial velocity profiles for models with different EIs at 1, 2, and 3 diameters downstream of the stenosis section (indicated by plane 1, plane 2 and plane 3). The profiles at three different phases of the cardiac cycle ( $t=$ 0.16 s, 0.46 s and 0.66 s, indicated by different colors) are provided.

Figure 4.

Streamlines for models with different DSs at $t=$ 0.66 s. Shear rates are labeled at the streamlines. The EI, SL and shape of the stenosis are kept constant for the simulated models (EI $=$ 1.00, L $=$ 2D and with a cosine shape).

3. Results

3.1 Models with different EIs

Blood flow in four models with different EIs are simulated and the streamlines at early diastole (0.66 s) for four different EIs are shown in Fig. 2. Shear rates are also labeled at the streamlines. The DS, SL and shape of the stenosis are kept constant for the four models (DS $=$ 70%, SL $=$ 2D and with a cosine shape). For all models, separation is observed at downstream to the throat section and the blood flow reattached at some distal location. High shear rates occur at the throat section and the maximum of observed shear rates are 3.47 (10 ${}^{4}$ s ${}^{-1}$ ) (EI $=$ 0.00), 3.38 (10 ${}^{4}$ s ${}^{-1}$ ) (EI $=$ 0.33), 3.37 (10 ${}^{4}$ s ${}^{-1}$ ) (EI $=$ 0.67) and 3.60 (10 ${}^{4}$ s ${}^{-1}$ ) (EI $=$ 1.00). As EI increase, shear rate decreased near the opposite wall of the throat section. It is notable that the recirculation zone length is decreased as EI increases. Figure 3 gives the axial velocity profiles (at three phases of the cardiac cycle: end diastole (0.16 s), middle systole (0.46 s) and early diastole (0.66 s)) at three different locations downstream of the stenosis section (1, 2, and 3 diameters downstream of the stenosis section). The axial velocity profiles are more skewed in models with higher EI. Retrograde flow is present in all three locations and its magnitude is higher at Plane 2 and Plane 3. The maximum velocity of the retrograde flow is observed in models with EI $=$ 0.33.

3.2 Models with different DSs

To demonstrate the effect of DS in eccentric stenosis, the streamlines of four models with different DSs at early diastole (0.66 s) are shown in Fig. 4. The EI, SL and shape of the stenosis are kept constant for the simulated models (EI $=$ 1.00, L $=$ 2D and with a cosine shape). From the results, the recirculation zone length is significant increased as DS increases. The maximum of observed shear rates increased more than five folds as DS increases from 40% to 70% (the maximum of observed shear rates are: 0.63 (10 ${}^{4}$ s ${}^{-1}$ ) (DS $=$ 40%), 1.09 (10 ${}^{4}$ s ${}^{-1}$ ) (DS $=$ 50%), 1.89 (10 ${}^{4}$ s ${}^{-1}$ ) (DS $=$ 60%), 3.60 (10 ${}^{4}$ s ${}^{-1}$ ) (DS $=$ 70%)). Figure 5 gives the axial velocity profiles (at three phases of the cardiac cycle: end diastole (0.16 s), middle systole (0.46 s) and early diastole (0.66 s)) at 1, 2 and 3 diameters downstream of the stenosis section. From the results, the magnitudes of both forward and backward maximum axial velocity are increased as DS increases. For models with a 40% stenosis, retrograde flow only observed in Plane 1 and two phases (end diastole and early diastole) in Plane 2.

Figure 5.

Axial velocity profiles for models with different DSs at 1, 2, and 3 diameters downstream of the stenosis section (indicated by Plane 1, Plane 2 and Plane 3). The profiles at three different phases of the cardiac cycle ( $t=$ 0.16 s, 0.46 s and 0.66 s, indicated by different colors) are provided.

Figure 6.

Streamlines for models with different SLs at $t=$ 0.66 s. Shear rates are labeled at the streamlines. The EI, DS and shape of the stenosis are kept constant for the four models (EI $=$ 1.00, DS $=$ 70% and with a cosine shape).

3.3 Models with different SLs

To demonstrate the impact of SL in eccentric stenosis, the streamlines at early diastole (0.66 s) for models with different SLs are shown in Fig. 6. The EI, DS and shape of the stenosis are kept constant for the four models (EI $=$ 1.00, DS $=$ 70% and with a cosine shape). From the results, flow patterns are more complex in models with small SLs. Vortex was observed in both pre- and post- stenosis regions in model with a 1D SL. The recirculation zone length increases as SL increase. The maximum of observed shear rates were: 3.44 (10 ${}^{4}$ s ${}^{-1}$ ) (SL $=$ 1D), 3.60 (10 ${}^{4}$ s ${}^{-1}$ ) (SL $=$ 2D), 3.49 (10 ${}^{4}$ s ${}^{-1}$ ) (SL $=$ 3D), 3.18 (10 ${}^{4}$ s ${}^{-1}$ ) (SL $=$ 4D). Figure 7 gives the axial velocity profiles (at three phases of the cardiac cycle: end diastole (0.16 s), middle systole (0.46 s) and early diastole (0.66 s)) at 1, 2 and 3 diameters downstream of the stenosis section. The maximum axial velocity would increase as SL increase, and this phenomenon was more pronounced at early diastole. It is also noticeable that both the area and magnitude of the retrograde flow is much larger for models with a 1D SL at Plane 1 and Plane 2.

3.4 Models with different shapes

Streamlines for models with different stenosis shapes at early diastole (0.66 s) are shown in Fig. 8. The EI, DS and SL are kept constant for the four models (EI $=$ 1.00, DS $=$ 70% and SL $=$ 2D). For stenosis with a triangle shape, flow separation occurs at throat section. It has a smallest recirculation zone length, but largest regions of vortex. Vortex was observed in both pre- and post- stenosis regions in model with a rectangle-shaped stenosis. The maximum of observed shear rates were: 3.17 (10 ${}^{4}$ s ${}^{-1}$ ) (Cosine), 3.60 (10 ${}^{4}$ s ${}^{-1}$ ) (Triangle), 3.70 (10 ${}^{4}$ s ${}^{-1}$ ) (Trapezoid), 3.85 (10 ${}^{4}$ s ${}^{-1}$ ) (Rectangle). Figure 9 gives the axial velocity profiles (at three phases of the cardiac cycle: end diastole (0.16 s), middle systole (0.46 s) and early diastole (0.66 s)) at 1, 2 and 3 diameters downstream of the stenosis section. The maximum of axial velocity is larger in rectangle and trapezoid stenosis. The magnitude of the retrograde flow is much larger for models with a triangle stenosis at $t=$ 0.66 s.

Figure 7.

Axial velocity profiles for models with different SLs at 1, 2, and 3 diameters downstream of the stenosis section (indicated by Plane 1, Plane 2 and Plane 3). The profiles at three different phases of the cardiac cycle ( $t=$ 0.16 s, 0.46 s and 0.66 s, indicated by different colors) are provided.

4. Discussion and conclusions

In this study, a CFD simulation was conducted to relate the impact of specific geodesic patterns of eccentric stenosis on the flow characteristics of the recirculation zones in coronary arteries. From the results, the geometry patterns have great impact on the velocity profiles at the stenosis section, and these changes in velocity profiles would further lead to changes in post stenotic flow behaviors.

As demonstrated, larger DS was associated with larger regions of recirculation in eccentric stenosis. Low shear rates was observed in the recirculation zone, providing a favorable environment for stasis-related thrombosis. As DS increase, high shear rates occurred at the throat section, which might lead to abnormal platelet activation. However, an important finding in our evaluation was that except DS, the detailed geometry patterns (EI, SL and shape of the stenosis) also had great impact on post-stenotic flow behaviors.

Figure 8.

Streamlines for models with different shapes at $t=$ 0.66 s. Shear rates are labeled at the streamlines. The EI, DS and SL are kept constant for the four models (EI $=$ 1.00, DS $=$ 70% and SL $=$ 2D).

Figure 9.

Axial velocity profiles for models with different shapes at 1, 2, and 3 diameters downstream of the stenosis section (indicated by Plane 1, Plane 2 and Plane 3). The profiles at three different phases of the cardiac cycle ( $t=$ 0.16 s, 0.46 s and 0.66 s, indicated by different colors) are provided.

EI is the most popular index to quantify eccentric stenosis. Previous study reported that eccentricity had minor impact on the shear rate at the throat wall, while as eccentricity increase, a significant decrease in shear rate at the opposite wall was observed [30]. Here, similar results were obtained in this work. Javadzadegan et al. reported a positive correlation between EI and recirculation zone length, and a PIV experiment was implemented to further validate their conclusion (positive correlation between EI and recirculation zone length) in transient condition [25, 26]. However, the other lesion morphological parameters (except EI), which played an important role in determining the recirculation zone length, were not kept the same among models with different EIs. From our results, the relationship between EI and post-stenotic flow behaviors are complex. When EI is small ( $<$ 0.33), the length of recirculation zones would increase as EI increase; while when EI is large ( $>$ 0.33), the length of recirculation zones would decreased as EI increase. Thus, whether higher EI enhanced the flow stasis is still unclear, and applying particle tracking approach may provide further information.

Increase of SL would lead to increase of recirculation zone length in eccentric stenosis. Similar phenomena were reported in bell-shaped concentric stenosis [31]. It is very interesting to note that flow patterns in recirculation zone became more complex when SL decreased to 1 diameter. This might be caused by a sharper inlet shape in model with a 1 diameter SL. The impact of sharpness of inlet shape on flow patterns could also be demonstrated by comparing different shapes of stenosis. Rectangle stenosis had a sharpest shape, leading to a largest recirculation zone length. While, triangle stenosis had a modest shape and led to a smallest recirculation zone length.

5. Limitations

We have to clarify that there are still some limitations. In this work, blood is modeled as Newtonian fluid and vessel wall is modeled as rigid wall. However, previous studies showed that these assumptions had minor impact on flow distributions in stenosis coronary arteries. Our work focused on the morphological parameters that fully characterize the geodesic patterns of eccentric coronary stenosis. Thus, idealized models were preferred to minimize the effect of patient-specific geometric variability. However, curvature and bifurcations, which often co-exist with eccentric stenosis, were ignored by using this approach. Nevertheless, the general concepts addressed from this work would still be applicable to the realistic eccentric coronary stenosis.

Footnotes

Acknowledgments

This work was supported in part by the National Science Fund of China under Grant 61601368, 61273250, the Natural Science Basic Research Plan in Shaanxi Province of China (2017JQ6012) and the Fundamental Research Funds for the Central Universities (No. 3102017jc11002).

Conflict of interest

None to report.

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