Feasibility Study of Substituting the FFR Invasive

Proceedings of the Fifteenth Annual Early Career Technical Conference The University of Alabama, Birmingham ECTC 2015 November 7 – 8, 2015 - Birmingham, Alabama USA

FEASIBILITY STUDY OF SUBSTITUTING THE FFR INVASIVE PROCEDURE WITH CFD ANALYSIS FOR ASSESSMENT OF HUMAN CORONARY ARTERY STENOSIS Mohamed M. Selim University of Alabama at Birmingham, Birmingham, AL, USA Arab Academy for Science and Technology and Maritime Transport, Alexandria, Egypt

Ankur Gupta Noninvasive Cardiovascular Imaging Program, Departments of Medicine and Radiology, Brigham & Women's Hospital, Boston, MA, USA DISCOVERFLOW study [2] by Koo et al., DeFACTO study [3] by Min et al. and NeXT study by Norgaard et al. [4] (CFD analyses in all studies were done by Heart Flow Inc.) showed the diagnostic accuracy of CFD measurements compared with invasive measurements to be 84% and 73% respectively using geometries obtained from the computed tomographic (CT) scans. Thus, simulation of blood flow through human arteries to predict the pressure drop is still under-reliable and needs more research to be improved. This study was unique from the prior published work in two key respects: i) the target patient population was those undergoing coronary angiogram – thus, the geometry was obtained from the cine-angiogram; ii) our goal was to create a reliable CFD model to predict this pressure drop rather than only testing the validity of one pre-defined model. Regarding blood viscosity models, clinical studies by Koo et al., Min et al. and Norgaard et al [2-4] modeled blood as Newtonian fluid. Several other studies have suggested that Non-Newtonian approximation may be more appropriate to measure pressure drop across coronary stenosis [5] and to estimate the magnitude of wall shear stress (WSS)[6-8]. However, these studies on non-Newtonian viscosity models in coronary arteries lacked verifying their results against experimental data from invasive measurements. In our study, the effects of Newtonian and non-Newtonian blood viscosity models on the accuracy of predicting the FFR across stenosis using CFD approach was investigated. Moreover, the predicted FFR was compared against the experimental data obtained from the invasive reference standard during cardiac catheterization. The blood flow through coronary artery stenosis was modeled as a laminar flow mimicking the normal blood flow at rest condition. due to the difficulty of modeling turbulent nonNewtonian flow [9,10]. One of the important steps in any simulation is selecting the appropriate and realistic boundary conditions. Generally, this case involves three types of boundary conditions, which are inlet, wall, and outlet boundary conditions. Arterial wall boundary was a no-slip boundary type that applies zero flow velocity for the blood layer in contact with the wall [6, 8]. Regarding the outlet boundary condition, a few studies have applied a constant pressure (atmospheric or near to atmospheric which approximates central venous pressure) [6, 11], some studies have used a traction free boundary condition at the outlet [12, 13]. Furthermore, a few studies [14, 15] implemented a complicated but more realistic outlet boundary condition using lumped parameter models. Since the traction

ABSTRACT During cardiac catheterization, in order to determine the physiological importance of a coronary stenosis, it is sometimes required to measure pressure drop across the stenosis by passing a pressure wire through it, which is known as the Fractional Flow Reserve (FFR) procedure. If the pressure drop is significant, the stenosis is relieved by stent deployment. This pressure measurement approach leads to a considerable increase in procedure time, in addition to subjecting patients to increased radiation and increased risk of procedure related complications. The main objective of this study is to assess the reliability of using Computational Fluid Dynamics (CFD) modeling principles to calculate the FFR accurately. Realistic three-dimensional geometries were constructed based on a patient-specific angiography images. Then CFD simulations were conducted and its results compared to the invasively measured FFR. Two different blood viscosity models were investigated: 1) Newtonian model and 2) non-Newtonian model. Both viscosity models well-predicted the FFR across the coronary artery. However, the obtained results showed that modeling blood flow as Newtonian versus non-Newtonian fluid has minimal effect on the predicted FFR as compared with invasive reference standard. INTRODUCTION Heart disease is a leading cause of death in both men and women. Coronary heart disease is the most common type of heart disease, killing more than 385,000 people annually and costs the United States $108.9 billion each year [1]. Coronary artery stenosis, or blockages in heart arteries, occurs due to plaque build-up called atherosclerosis. During coronary angiogram, in order to determine the physiologic importance of a coronary stenosis, it is sometimes required to measure the pressure drop across the stenosis by passing a pressure wire through it, called Fractional Flow Reserve (FFR) measurement. This invasive technique leads to increase in procedure time and patient exposure to radiation and procedure related complications. Computational Fluid Dynamic (CFD) simulation of blood flow through coronary arteries is considered a promising technique to obtain this pressure drop information without subjecting the patient to additional invasive risks. There are a very few published prospective clinical studies in English literature that have studied the potential of CFD in predicting this pressure drop on real patient-specific coronary anatomy in humans [2-4]. 1

free assumption is relatively more accurate than a constant pressure at the outlet, and less complicated than using the lumped parameter models, it was used in this study. For the inlet boundary one of the following two methods could be used: 1) fully developed constant velocity inlet, or 2) constant (pulsatile) pressure inlet. The first method relies on the fact that the heart typically pumps a fixed blood mass flow rate to the coronary artery (~2% of heart output flow rate) [13]. Such assumption is not accurate, since the blood mass flow rate varies from one patient to another and the percentage of this flow rate that is going to the coronary artery is also not fixed. The second method relies on the fact that the inlet pressure in upstream of coronary artery vasculature that is located in ascending aorta is always aortic pressure [11]. Moreover, all patients get the pulsatile aortic pressure measured during heart catheterization. In this study, according to the conducted literature search, the following boundary conditions were used: 1. No-slip condition for the artery walls; 2. Constant atmospheric pressure (equivalent to central venous pressure) outlet boundary condition; 3. Pulsatile pressure inlet boundary condition. The interaction between the blood flow and the deformation of the arterial walls is a factor that could significantly affect the blood flow. It is still under debate whether neglecting this interaction would result in a misleading interpretation of the artery stenosis severity. Current literature on utility of Fluid-Structure Interaction (FSI) modeling for blood flow in human arteries is controversial. Study by Hasan et al. [16] concluded that using FSI solver has a little effect on flow parameters but other studies have concluded that the FSI model does have a noticeable effect on the flow behavior and it must not be ignored for the sake of simplicity [17, 18]. However, there is a lack of reliable studies that measuring experimentally the mechanical properties of arterial walls [19]. In this study, arterial walls deformations were not taken into account and all walls were assumed to be rigid. Biological risk factors such as diabetes, high blood pressure, high cholesterol and smoking contribute to the plaque formation in arteries. All the heart arteries are subjected to the same systemic risk factors for the development of blockages. However, the blockages occur only in some regions of the arteries and not in others. These regions tend to be vicinity of the branch points, outer wall of bifurcations and inner wall of curvatures [20]. The physical factors are likely contributing on top of the biological risk factors to develop plaque. One such factor that has been studied is wall shear stress [21]. It has been postulated that at regions of low wall shear stress, there is flow stagnation leading to increased local accumulation of cholesterol and inflammatory cells that contributes to plaque formation [21, 22]. In this study, wall shear stress distribution through the entire coronary artery was investigated and compared for Newtonian and non-Newtonian viscosity models. In this article, three-dimensional geometry of the coronary arteries was constructed using real-world fluoroscopic images taken during cardiac catheterization. The effect of blood viscosity models on the CFD simulation results was investigated. The differences in simulation results when using

blood as Newtonian versus non-Newtonian fluid are presented. Finally, the FFR across coronary stenosis is calculated from the simulation results and validated against the invasively measured pressure drop. To the authors’ knowledge, this would be the first study investigating the accuracy of different blood viscosity models for validating FFR across coronary stenosis against invasive reference standard. The methodological approach used was as follows, a threedimensional geometry of the coronary artery was constructed using multi-angle fluoroscopic images taken during cardiac catheterization in a patient who had pressure drop across coronary stenosis measured invasively. Based on the conducted literature search, appropriate boundary conditions, and blood viscosity, models were employed. CFD simulations were conducted on the discretized three-dimensional geometries. FFR was then be calculated from the simulation results and validated against the invasively measured value. Based on the differences in simulated results and invasive measurements, recommendations were made in order to decide which viscosity model gives better predictions. Figure 1 shows a schematic flowchart describing the conducted research plan.

Figure 1 Schematic flowchart of the conducted research plan MATERIALS AND METHODS Geometry Creation Several fluoroscopic (angiography) frames from different angles of the coronary artery were used in order to construct a valid three-dimensional geometry. Typically, only two fluoroscopic frame angles are sufficient to project the threedimensional geometry. However, due to arterial branches overlap, four frames were used in this study.. The proposed approach consists of two main steps: 1) image processing in order to detect the wall edges of each frame and reduce the noise and 2) projecting the edges into three-dimensional domain. First step of the image processing procedure was to apply different thresholds in order to detect the arterial wall edges. Second step was to give different colors and IDs for each continuous segment. Final step was to delete short segments and manually delete unneeded segments which were considered 2

as noise. Figure 2 illustrates the image processing procedure for one angle of the angiography frames.

(a)

(b)

Figure 3 Four two-dimensional frames projection into three-dimensional domain Figure 4 illustrates the three-dimensional geometries of the stenotic artery and the normal artery with the stenosis region circled in yellow color.

(c) (d) Figure 2 Image processing steps: (a) original angiography frame, (b) detected edges after applying threshold, (c) different colors and ID assigned, (d) short segments deleted By performing this procedure on each angle frames and by knowing the angle of each frame, it is possible to project these two-dimensional geometries into a three-dimensional geometry. After the wall edges of the three-dimensional profile being successfully constructed, the centerline of these edges was used as a sweeping path of left coronary artery cross-section. Figure 3 demonstrates the projection of the four two-dimensional frames into the three-dimensional domain.

(a)

(b)

Figure 4 three-dimensional geometries: (a) stenotic artery and (b) normal artery Solution Methodology To simulate the behavior of blood flow through human arteries, it is assumed that blood is governed by the incompressible Navier-Stokes equations [6] (1) 𝜌𝑣 ∙ ∇𝑣 = −∇ ∙ 𝜏 − ∇𝑝

Since the fluoroscopic images showed a 50% diameter stenosis, the projected three-dimensional artery will be referred to as the stenotic artery in this manuscript. In order to be able to compare the pressure drop and the blood flow rate of the stenotic artery against these of a normal artery, another threedimensional geometry was created by modifying the stenotic artery to restore the stenosis region to its normal cross-section area. This new geometry will be referred to as the normal artery in this manuscript.

and the continuity equation ∇∙𝑣 =0

(2)

where v is the 3D velocity vector, p is the pressure,  is the blood density and  is the shear stress term. The governing equations are solved numerically using the finite volume scheme. A commercially available CFD package, namely Star-CCM+, was used to perform the analysis. In order to solve the governing equations successfully, a set of boundary conditions is required. The following section describes the definition of the boundary conditions.

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Physical Models and Boundary Conditions

RESULTS AND DISCUSSION An unstructured hexahedral volume meshes with prism layer were generated for both stenotic and normal artery. The stenotic artery volume mesh consists of 1,236,785 cells and the normal artery volume mesh consists of 1,194,589 cells. Figure 6 shows the generated volume mesh for the normal artery.

The main aim of this study is to compare the computationally obtained FFR against invasively obtained FFR for both Newtonian and non-Newtonian viscosity models. In both cases, blood flow was assumed to be laminar, constant density and unsteady. Based on the conducted literature, for the Newtonian model the blood viscosity was assumed to be 0.0345 Poise and for the non-Newtonian model the well-known Carreau model was used [5]. Carreau model effective viscosity is based on the following relation (3) 𝜇 = 𝜇 + (𝜇 − 𝜇 )[1 + (3.313𝛾̇ )2 ]−0.3216 ∞

0

∞

where 𝜇0 = 0.56 Poise, 𝜇∞ = 0.0345 Poise and 𝛾̇ is the shear strain rate. Regarding the boundary conditions, it is important to imply the proper boundary conditions in order to assure precise model that can accurately mimic the blood flow within the artery. A no-slip wall condition was assumed for the artery walls. For the inlet boundary, a pulsatile aortic pressure boundary condition was applied since the inlet pressure of the coronary artery is considered to be equal to the aortic pressure. Figure 1 shows the pulsatile inlet pressure profile versus cardiovascular cycle time.

Figure 6 Volume mesh of the normal artery The CFD simulations were run to obtain a total of four set of results. For both geometries, stenotic and normal, Newtonian and non-Newtonian results were obtained. In order to verify the change in viscosity due to the use of Carreau model, the dynamic viscosity distribution along both geometries were plotted in Figure 7. It is clear from the figure that viscosity is lower near the artery walls and higher further away from the walls. This satisfies the Carreau model relation, since the viscosity is inversely proportional to the shear strain rate and the shear stress is higher at the walls. Of note, all reported results in this section were visualized at solution time equal to 0.3 seconds which corresponds to the maximum aortic pressure through the cardiovascular cycle. Newtonian and nonNewtonian pressure distributions along stenotic and normal arteries are shown in Figure 8. As expected, the pressure distribution for the non-Newtonian model was at a slightly higher absolute pressure scale than that of the Newtonian model. Moreover, as can be seen from Figure 8, there was a slight pressure drop across the stenosis region in both Newtonian and non-Newtonian models. The velocity distributions were investigated through the stenosis region, Figure 9. As can be seen from Figure 9, the recirculation zone was slightly larger for the case of nonNewtonian model than that of the Newtonian model. Oscillatory flows in recirculation zones are associated with atheroma formation due to changes in local endothelial gene expression, cytoskeletal arrangement, wound repair, leukocyte adhesion, etc., [23]. This recirculation zone might be associated with plaque formation since the blood is relatively more stagnant within this zone.

120 110 Aortic 100 Pressure (mmHg) 90

80 70 0

0.2

0.4

0.6

0.8

Time (Seconds)

Figure 1 Pulsatile inlet pressure profile versus time For the outlet boundary, a traction-free boundary condition is assumed. Traction-free boundary assumes that there is no pressure acting on the transverse direction of the flow and pressure is only acting on the longitudinal direction. In other words, the blood flow is derived only by its momentum. Hence, the pressure can be calculated based on the following relation 1 𝜕𝑣𝑛 (4) −𝑝 + ( ) ( )=0 𝑅𝑒 𝜕𝑛 where p is the pressure, Re is the flow Reynold’s number, and n represents the normal direction of the velocity field v [12, 13]. The blood density was assumed to be constant at 1025 kg/m3. Implicit unsteady solver was used with time step of 0.001 seconds and five inner iterations. The total time of the cardiovascular cycle is 0.811 seconds which led to 811 time steps per each cardiovascular cycle. The simulation was set to be run for two complete cycles.

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(a)

The resulted FFR-CFD was compared against the invasively measured FFRinv. Table 1 shows the mass flow rate obtained computationally for each case and the calculated FFRCFD. FFR of 1.0 means that the stenosis region has no effect on the blood flow and the same amount of blood is being delivered by the artery as that of a normal artery. FFR of 0.0 means that the stenosis region is completely blocking the blood flow and no blood is being delivered. The specific artery that has been analyzed in this study had FFRinv of 0.95 which means that the stenosis has a minimal effect on the blood flow [23]. The CFD results predicted FFR of 0.98 when Newtonian viscosity model was used while FFR of 1.0 when non-Newtonian viscosity model, namely Carreau model, was used.

(b)

Figure 7 Dynamic viscosity distribution: (a) stenotic artery and (b) normal artery (a)

Furthermore, the wall shear stress was investigated. Figure 10 shows the wall shear stress distribution for Newtonian and non-Newtonian models. No significant difference was noted between both models. In this study, the Fractional Flow Reserve (FFR) was calculated based on the mass flow rate difference between the stenotic artery and the normal (non-stenotic) artery. Thus, the mass flow rate through the stenotic branch of the coronary artery was obtained for Newtonian and non-Newtonian models. The FFR is calculated based on the following equation 𝑆𝑡𝑒𝑛𝑜𝑠𝑖𝑠 𝑀𝑎𝑠𝑠 𝐹𝑙𝑜𝑤 𝑅𝑎𝑡𝑒 (5) FFR 𝐶𝐹𝐷 = 𝑁𝑜 𝑆𝑡𝑒𝑛𝑜𝑠𝑖𝑠 𝑀𝑎𝑠𝑠 𝐹𝑙𝑜𝑤 𝑅𝑎𝑡𝑒

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(b)

Figure 9 Velocity vectors distribution through the stenosis region, (a) Newtonian and (b) non-Newtonian; recirculation zone marked in red dotted line

(a)

(b)

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Figure 10 Wall shear stress distribution through the stenosis region: (a) Newtonian and (b) non-Newtonian Table 1 Mass flow rate for each case and FFR calculation Case

(c)

Stenotic Newtonian Normal Newtonian

(d)

Stenotic non-Newtonian Normal non-Newtonian

Figure 8 Pressure distribution: (a) stenotic Newtonian, (b) stenotic non-Newtonian, (c) normal Newtonian, (d) normal non-Newtonian

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Mass Flow Rate (g/s) 5.0 5.1 5.2 5.2

𝐅𝐅𝐑 𝐂𝐅𝐃

𝐅𝐅𝐑 𝐢𝐧𝐯

𝐅𝐅𝐑 𝐢𝐧𝐯 𝐅𝐅𝐑 𝐂𝐅𝐃

0.98

0.95

0.969

1.0

0.95

0.950

CONCLUSION Realistic three-dimensional geometry models of left coronary artery with a stenosis and without a stenosis were constructed using fluoroscopic coronary cine-angiograms. The three-dimensional geometry was created to mimic the realistic artery; however, it is not an exact geometry. The obtained results showed that modeling blood flow as Newtonian versus non-Newtonian fluid has minimal effect on the Fractional Flow Reserve across the stenosis as compared with invasive reference standard. Both models are considered to be in a good agreement with the invasively measured Fractional Flow Reserve. However, more stenotic arteries need to be computationally modeled in order to reach more concreate conclusions. From a hemodynamics point of view, using nonNewtonian viscosity model resulted in slightly higher pressure distribution and slightly larger recirculation zone within the stenosis region.

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