A diseased coronary artery has been modeled to study the implications of plaque morphology on the fluid dynamics. In our previous study, we have successfully classified the coronary plaques of 42 patients who underwent intravascular ultrasound (IVUS) into four-types (Type I, Type II, Type III, and Type IV) based on the plaque morphology. In this study, we demonstrate that, for the same degree of stenosis (height of the plaques), hemodynamics parameters are strongly dependent on the plaque shape. This study is the first one to clearly demonstrate that in addition to wall shear stress, presence of turbulence and location of transition from laminar to turbulence state are additional hemodynamics parameters to identify plaques vulnerable to rupture.

Coronary artery disease (CAD) is a progressive disease characterized by the accumulation of plaques on the artery walls. CAD is initiated by the deposition of fatty materials in the coronary artery resulting in the thickening and formation of streaks of plaque on the artery walls. During these early stages, the plaques are not of significant consequence to the flow dynamics, and the flow does not deviate from the laminar state present in a normal coronary artery [

As of today, the degree of stenosis has been a classical metric to define the extent of the disease for medical purposes. The stenoses are commonly assessed as a percentage of obstruction in the diameter of the lumen. It is a common practice to characterize the stenosis using the percentage obstruction or the height of the obstruction criterion. However, recent studies have clearly shown that the characteristic flow dynamics due to stenosis are strongly influenced by factors such as morphological structure of the stenosis developed, the pulsatile nature of the flow, and numerous others [

With advances in medical imaging, it is now possible to obtain a comprehensive view of the coronary anatomy to assess plaque morphology using imaging techniques such as intravascular ultrasound (IVUS), computed tomography (CT), X-ray angiography, and magnetic resonance imaging (MRI). Hence, there is a clear need for well-defined metrics in addition to plaque height in order to identify patient-specific point of transition from laminar to turbulent flow and also to identify patient-specific poststenotic behavior such as turbulence levels and exact locations where the flow relaminarizes. This information is of clinical relevance because it provides important clinical interpretation. Turbulence is of pathological importance because localized bursts of shear stress may erode already weakened endothelial patches from the arterial wall [

The focus of the present study is to conduct a fluid dynamic simulation in diseased coronary artery to predict the transition to turbulence state, if any. Beaumont et al. [

Fuzzy logic analysis of the plaque measurements for 42 patients has revealed four distinct patterns: (a) Type I (protruding), (b) Type II (ascending), (c) Type III (descending), and (d) Type IV (diffuse).

In this section we discuss the numerical methodology including assumptions, the construction of the 3D solid model, boundary conditions, validations, and verifications. The governing equations have been solved numerically using the commercially available software FLUENT 6.0. A 3D model of the artery is constructed using the plaque morphology from the IVUS. Refer to Beaumont et al. [

The length of the artery is assumed to be 72 mm in length, and the outer diameter and the inner diameter dimensions are obtained from the IVUS measurements. The plaque inlet was positioned at an axial distance of 40 mm from the inlet of the artery in order to allow the flow to develop naturally before entering the stenotic region; while the plaque exit, after using the 13 different, 1 mm spaced cross sections, was position at 52 mm from the inlet of the artery. For the patient-specific flow simulations, a physiological waveform flow was specified at the inlet of artery. The waveform specified is based on Womersley’s solution [^{3} and dynamic viscosity of 1.0 mPa·s. The assumption of Newtonian fluid is justified, as it is known that blood behaves as a Newtonian fluid in large arteries especially at high shear rates. The convergence criterion for all the residuals was manually defined as 10^{−7} in order to control the accuracy of the solution. The timestep size was chosen as 0.0002855 s with approximately 1160 timesteps per cardiac cycle. A timestep independency test is described in Section

Velocity waveform used as inlet boundary condition for all simulations.

Initially, the data obtained from the IVUS at four circumferential locations was imported into SolidWorks. Based on the data, the plaque height was measured from the outer wall. The data between these four points has been interpolated using spline interpolation. The procedure was repeated for the 13 cross sections along the length of the artery. It was ensured that the accurate shape of the plaque is represented after the spline interpolation. After modeling the stenosis, the geometry was imported into the ANSYS software where a coarse, medium, and fine mesh were created for a mesh independency test. The independency test results are described is Section

Tetrahedral coarse, medium, and fine meshes generated from 3D SolidWorks of the lumen for Type I.

The flow is started from initial laminar flow conditions. At the inlet, the flow Reynolds number is 200 based on the diameter of the artery. At the output constant pressure, boundary condition has been prescribed. A transition model is applied to capture the transition, if any, to turbulent state. For this purpose, the shear stress transport (SST) transition model has been applied. The SST transition model is based on the coupling of Menter’s

The experimental results of Ahmed and Giddens [

A mesh independence test was carried out using the SST transition model with realistic boundary conditions for Type I (protrusion). The boundary conditions will be further described. Results in terms of maximum axial wall shear stresses (WSS) and peak turbulence kinetic energy (TKE) at the peak systolic phase were analyzed. Initial flow simulations results were mesh independent after using a grid of 250,000 tetrahedral elements with elements concentrated near the wall where the velocity gradients were expected to be high. A very fine near wall resolution of the wall boundary cells along the length of the stenosis was ensured in order to satisfy the requirements of the turbulence and transition models. Therefore, a

Mesh independency test results comparing the maximum axial WSS and peak TKE values between different meshes for Type I: Bump.

Mesh nodes | Maximum wall shear stress (Pa) | Difference in WSS (%) | Peak turbulence kinetic energy (m^{2}/s^{2}) |
Difference in peak TKE (%) |
---|---|---|---|---|

130000 | 47.312 | 0.11874343 | ||

2.07 | 2.50 | |||

250000 | 48.292 | 0.11578202 | ||

1.73 | 1.24 | |||

600000 | 49.128 | 0.11721252 |

Time step size independency test results comparing the peak TKE values for the 250 k mesh configuration for Type I: Bump.

Time step size (s) | Time steps per cycle | Peak turbulence kinetic energy (m^{2}/s^{2}) |
Difference in peak TKE (%) |
---|---|---|---|

0.001142 | 290 | 0.11099838 | |

2.27 | |||

0.000571 | 580 | 0.11351982 | |

1.99 | |||

0.0002855 | 1160 | 0.11578202 |

Additionally, a sensitivity test of the inlet turbulence intensity (Tu) was carried out by using the SST transition model. The experimental results of Ahmed and Giddens [

Figure

Turbulence intensity profiles at three axial positions: (a)

Figure

Axial velocity profiles of the idealized stenosed tube at different axial positions: (a)

The simulations have been performed for protrusions of Type I through Type IV (see Figure

First, the differences and similarities in the axial component of the mean velocity are analyzed during the peak systolic phase of the cardiac cycle. Figure

Axial mean velocity profiles plotted against wall-normal distance scaled by lumen height (

Similarly, the differences and similarities in the radial component of the mean velocity are analyzed during the peak systolic phase. Figure

Radial mean velocity profiles plotted against wall-normal distance scaled by lumen height (

Furthermore, the three mean velocity components have been averaged in the

Mean velocity profiles averaged in

Next, an analysis of flow parameters such as turbulence intensity (Tu), turbulence kinetic energy (TKE), and wall shear stresses (WSS) is presented. Such analysis is of importance because these parameters are true representations of the turbulent nature of the flow. First, the differences and similarities in the turbulence kinetic energy profiles for Type I through Type IV are analyzed during the peak systolic phase of the cardiac cycle.

Figure

Turbulence kinetic energy profiles plotted against wall-normal distance scaled by lumen height (

Turbulence intensity plotted against wall-normal distance scaled by lumen height (

Additionally, the viscous and turbulent wall shear stresses (WSS) at the wall along the length of the stenosis have been computed during the peak systolic phase. The viscous and turbulent components in the mean flow direction normal to the wall have been included. Figure

Variation of WSS (mean flow direction) along the wall at time corresponding to peak systole (

Patient-specific simulations with realistic physiological flow conditions are conducted to understand the effect of plaque morphology in altering the flow characteristics in diseased coronary artery. In our previous study Bhaganagar et al. [

In the present study, we extend to realistic physiological flow conditions by accounting for the unsteady flow conditions (systole/diastole) as well as the transition from laminar to turbulent state. We use transition model to predict the location of flow transition to turbulent state. Under these realistic flow conditions, we demonstrate for same degree of stenosis (35%), and both the mean flow conditions as well as the disturbed flow conditions are significantly type-dependent. For the purpose of analysis, we select several axial locations along the length of the artery. The locations correspond to

The mean velocity (time and phase averaged) profiles exhibits significant differences between the types. All the types except Type IV exhibit flow reversal at distal portion of the stenosis. Peak velocity for Types I, II, and III is around 1.5 m/s, and it is only 1.2 m/s for Type IV. The velocity profile loses its symmetry along the centerline for Types I, II, and III. However, the location of the peak mean velocity shifts to the upper half of the artery for Types II and III, whereas this shift is towards the lower half of the artery for Type I. Similar trend has been observed during peak systole where Type II and Type III have higher mean velocity compared to the other types. Next, we analyze the flow disturbances. In particular, we are interested in understanding the differences in the location of the transition to turbulence, total stresses, and intensities of turbulent fluctuations between the types. The flow undergoes a transition from laminar to turbulent state for Types I, II, and III, whereas the flow continues to be in laminar state for Type IV. The location of the transition varies between 47 and 51 mm depending on the type. The transition for Type III occurs at much proximal location compared to other types suggesting that flow alters at earlier location for this type.

Peak turbulence intensities are present for Type III, followed by Type II and Type I, respectively. The flow continues to be in a disturbed state close to the exit region for Type II and Type III, whereas the flow relaminarizes to laminar state beyond the distal location of the plaque for Type I. Type III also exhibits high WSS, followed by Type II and Type I, respectively.

Further, the peak viscous WSS values for Type I through Type III are well correlated with the locations where TKE generation starts to grow, thus suggesting that the sudden increment of viscous WSS at the wall is a true indicator of point of transition. This study clearly shows that, for the same degree of stenosis, (a) the presence of turbulence, (b) location of transition to turbulence, (c) turbulence intensity, and (d) region of turbulence are type-dependent. This study is of great significance to determine the risk of rupture of the plaques and thus identify the vulnerable plaques prone to rupture. It should be noted that transition to turbulence is just one of the several biomechanical factors that contribute to risk of rupture plaque (see Fukumoto et al.) [

The coauthors do not have a direct financial relation with the trademarks mentioned in the paper that might lead to a conflict of interests for the coauthors.

This material is based upon work supported by the National Science Foundation under Grant number HRD 0932339.