J. Med. Biol. Eng. DOI 10.1007/s40846-015-0058-z

ORIGINAL ARTICLE

Numerical Simulation of Coronary Artery Stenosis Before and After Stenting Gang Li1 • Rui Hu2 • Feng Gao3,4

Received: 25 September 2014 / Accepted: 28 January 2015 Ó Taiwanese Society of Biomedical Engineering 2015

Abstract This study simulates the effect of stenting in an image-based coronary model. Three-dimensional models of the coronary artery were created from computed tomography images of a coronary artery stenosis patient before and after stent implantation, and a realistic aortocoronary differential pressure was imposed at the inlet of the computational vessels. The results show that the stent increased the flow rate several fold compared to that for the stenosis artery model, and that the hemodynamic values returned to near normal levels in the coronary artery model fitted with a stent. The results confirm that stenting significantly improves the hemodynamics of the artery. Keywords Numerical simulation  Coronary artery stenosis  Stent  Aorto-coronary differential pressure

& Feng Gao [email protected] 1

Cardiology Division in Geriatric Institute, Hebei General Hospital, 348 Heping West Road, Shijiazhuang 050051, Hebei, China

2

Clinical Laboratory, The Second Hospital of Hebei Medical University, 205 Heping West Road, Shijiazhuang 050000, Hebei, China

3

Department of Mechanical Engineering, Faculty of Engineering and Technology, Tokyo University of Science, 2641 Yamazaki, Noda 278-8510, Chiba, Japan

4

Department of Biomedical Engineering, Materialise Japan, Sakae-cho 8-1, Kanagawa-ku, Yokohama 221-0052, Kanagawa, Japan

1 Introduction Coronary artery disease is the most prevalent form of cardiovascular disease and is the largest subset of this mortality. Endovascular stenting has been applied extensively in coronary, renal, and peripheral vascular systems. The use of intravascular stents tends to lower the complication rate. It has been found that the magnitude of the shear stress is of secondary importance to the spatial and temporal fluctuations of atherosclerosis [1]. In vivo testing performed by Vernhet et al. [2, 3] and Rolland et al. [4] shows that endovascular stenting induces a large modification of the arterial compliance. Computational cardiovascular fluid mechanics is one of the most popular research areas in computational mechanics [5– 7]. The geometric configuration of vascular segments greatly affects the resulting flow patterns. Computed tomography (CT) is emerging as a potential technique for the non-invasive, high-resolution evaluation of coronary arteries [8]. CT and magnetic resonance imaging allow three-dimensional (3D) anatomy to be imaged with high resolution and low invasiveness. Image processing methods can be applied to these images to reconstruct 3D models that reproduce the geometry of the vascular walls. With proper boundary conditions, the reconstructed models can be used to perform computational simulations of local hemodynamics. This approach has been implemented with interesting results [9–12]. Image-based analysis of the flow in the coronary artery with a stent involves computational challenges, mostly related to the need to have a good spatial representation of the stent. Many studies have utilized image-derived arterial geometries for the analysis of stents [13–15]. Flow through the coronary artery is of great interest. Volume flow may be improved after stent implantation, but fixed inlet flow cannot simulate the changes of flow rate due to stenting.

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The present study quantifies the effect of stenting on the hemodynamics of an image-based coronary stenosis under a realistic aorto-coronary differential pressure gradient. The geometry and flow conditions are based on patientspecific data to simulate the hemodynamics and to enhance the potential application of computational fluid dynamics (CFD) prediction to clinical surgical planning.

2 Materials and Methods 2.1 Realistic Human Coronary Artery Models A patient with coronary artery stenosis was involved in this study. The patient, 65 years old and female, presented with unstable angina. Coronary angiography revealed luminal obstruction in the middle segment of the left anterior descending coronary artery. The patient was medicated with 300 mg of clopidogrel and 200 mg of acetylsalicylic acid on the day the angiography was carried out. On the following day, she underwent the implantation of a XIENCE V stent (Abbott Vascular, Santa Clara, CA, USA), with the right femoral artery used as the access via. The patient underwent 64-slice CT scanning both prior to the intervention and after the implantation to obtain CT images. A pair of images of the coronary artery before and after implantation of the stent is shown in Fig. 1. These data served as the input to generate 3D geometry models of pre- and post-interventional coronary artery. The patient’s individual coronary geometry was obtained by converting medical image data into image-based 3D surfaces and a volume representation. The construction process of the patient-specific model involves the following

three major steps: (1) non-invasive image acquisition, (2) imaging processing, and (3) 3D reconstruction to create a voxel-based volumetric image representation. The original digital imaging and communication in medicine (DICOM) data before and after stenting was transferred to a workstation with Mimics V17.0 (Materialise, Leuven, Belgium) for the generation of 3D reconstructed images. The coronary geometric image reconstruction also involves smoothing, contrast enhancement, and automatic edge detection. The Mimics 3D calculation feature was used to build up the coronary models (Fig. 2). After segmentation, 3D models were created using the Mimics 3D calculation module from the selected mask, and the 3D surface were exported to stereo lithography (STL), a commonly used format for computedaided design. The lengths of the two models were about 40 mm. The stenosis grade was 10–20 % for the patient before stenting and 80–90 % after stenting. The STL files for pre- and post-stenting models were imported into ADINA 8.9 (ADINA R & D, Inc., USA). ADINA creates the necessary points, body edges, and faces for defining finite element meshes, loads, and boundary conditions. The pre- and post-stenting models were generated with tetrahedral volume meshes using ADINA-F. Figure 3 shows the mesh models for the coronary artery before and after stenting. The pre- and post-stenting models are composed of 57,814 and 56,668 elements, respectively. Mesh sensitivity was tested on the two coronary artery models by monitoring the magnitude and location of the maximum velocity. Mesh sensitivity was tested by monitoring the magnitude and location of maximum velocity and pressure. A mesh density was accepted when the maximum difference in monitored parameters from a denser mesh was less than 5 %.

Fig. 1 CT images for coronary artery before and after stenting. The patient was 65 years old female, presented with unstable angina. Coronary angiography revealed luminal obstruction in the middle segment of the left anterior descending coronary artery. She underwent the implantation of a stent and the right femoral artery was the access via used. The patient underwent 64-slice CT-scanning both prior to the intervention (a) and after the implantation (b) to obtain CT images data

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Numerical Simulation of Coronary Artery Stenosis Before and After Stenting

Fig. 2 Coronary arterial bifurcation geometry before and after stenting. The sub-figure shows the stent shape and position

Fig. 3 Mesh models for coronary artery bifurcation (a) before and (b) after stenting

2.2 Governing Equations and Boundary Conditions The flow was assumed to be laminar Newtonian, viscous, and incompressible. The blood can be represented by an incompressible fluid governed by the Navier–Stokes equation: qv  rv ¼ r  s  rP and the continuity equation: rv¼0 where v is the 3D velocity vector, P is the pressure, q is the density, and s is the shear stress term. Average physiological hemodynamic conditions with steady flow were considered for the 3D numerical simulations. The blood was assumed to behave as a Newtonian fluid. The viscosity was set to 0.0035 Pa s and the density was set to 1060 kg/m3, corresponding to the standard values cited in the literature [16]. The Navier–Stokes equations provide differential expressions of the mass and momentum conservation laws. At the inflows, fully developed flow was prescribed in a rigid straight pipe. Vessel walls were assumed to be rigid, and no slip boundary conditions were applied at the walls. The model of arteries was subjected to an aorto-coronary differential pressure gradient waveform obtained from a canine coronary artery under resting baseline conditions [17] (Fig. 4).

Fig. 4 Inlet pressure waveform. In vivo aorto-coronary differential pressure gradient under resting baseline condition reproduced from [17]

The heart rate data were scaled to human level. A zero-pressure boundary condition was imposed at the outlet of the artery model. The inlet pressure was initialized at 5000 Pa to increase the likelihood of convergence. A fixed computational time step of 0.02 s was set for the transient simulations. The results obtained with various time step sizes were compared. The chosen time step size had no significant influence on the results. Five cardiac cycles were used for each simulation. A satisfactory criterion for convergence with respect to time step was set to 10-4. The computations were performed on a computer with a 64-bit 2.27-GHz Intel Xeon CPU and 48 GB of memory.

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3 Results and Discussion The velocity distributions in the cross-sections of all the coronary artery segments before and after stenting at peak systole are presented in Fig. 5. The velocity is small for the flow at the artery’s inlet. There is an increase in velocity at the stenosis before stenting, but at the branches the flow behavior is lower than 0.2 m/s. In the presence of a stenosis, a sharp velocity profile is obtained. A jet-like flow emerges from the constricted region, severely affecting the downstream flow field. After stent implantation, the flow recovers to its normal profile and the overall distribution remains higher than 0.2 m/s. The maximum flow rate of blood in the coronary artery after stent implantation is 1.5 m/s. The angiographic severity of coronary stenoses correlates with impaired coronary flow velocity reserve [18, 19]. Contour maps of the wall pressure at the coronary artery bifurcation before and after stenting at peak systole are shown in Fig. 6. There is a region of high pressure in the pre-stenting coronary artery model and it is situated upstream of the stenosis. For the coronary artery model after stent implantation, the pressure in the proximal region to stenosis was reduced. In the stenosis coronary artery, blood accumulated upstream of the plaque region. Hence, an increase of blood pressure was observed upstream of the plaque region in the coronary artery. After stent implantation, the blood pressure pattern was maintained in the normal range by the fitted stent in the stenosis region. After stent implantation, blood flow resistance decreases in the

Fig. 5 Comparison of velocity distribution in coronary artery bifurcation before and after stenting at peak systole

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vessel. Therefore, the wall pressure at the stent implantation site decreased. The distribution of wall shear stress at the coronary artery bifurcation before and after stenting at peak systole is shown in Fig. 7. The maximum wall shear stress is in the

Fig. 6 Comparison of wall pressure in coronary artery bifurcation before and after stenting at peak systole

Fig. 7 Comparison of wall shear stress in coronary artery bifurcation before and after stenting at peak systole (WSS: wall shear stress)

Numerical Simulation of Coronary Artery Stenosis Before and After Stenting Fig. 8 Flow rate throughout model during cardiac cycle (a) before and (b) after stenting

stenosis region and the highest wall shear stress is in the most severely stenotic segment. The maximum wall shear stress of the stenotic portion of the coronary artery was 0.024 Pa. After stent implantation, the distribution of wall shear stress in the coronary artery was overall increased. These results indicate that the stent increases wall shear stress most in the stenotic coronary artery. This finding contradicts a previous study that used the same inlet flow conditions. Ku et al. [20] found a significant positive correlation between low oscillating shear stress and wall thickness by measuring velocity using laser Doppler anemometry in an averaged Plexiglas model of the carotid bifurcation and intimal thickness in histological sections. With the development of numerical methods and the availability of computational resources, experiments have been progressively replaced by computational approaches, but are still used for computational model validation [11, 21]. In general, CFD methods allow flow patterns, particle residence times, and shear stress distributions to be obtained at a great level of detail and simulation parameters to be easily varied. Increasingly complex models of

arterial segments have been generated and studied [5–7, 22–24], leading to a deeper understanding of the influence of geometry, flow waveforms, viscosity, and wall distensibility on flow and shear stress patterns. Figure 8 shows the flow rate throughout the models during the cardiac cycle before and after stenting. The flow rate increased after peak systole due to the aorto-coronary differential pressure gradient. In the stenosis artery model, the flow rate was 0.028–0.032 ml/s. After stent implantation, the flow rate increased to 1.15–1.17 ml/s. The results show that the stent increased the flow rate several fold compared to that for the stenosis artery model. Most previous studies used the same inflow to investigate the hemodynamic effects of stents. However, a fixed inlet flow cannot simulate the increased flow rate. The present study thus used aorto-coronary differential pressure to simulate the effect of a stent on flow rate during the cardiac cycle. The effects of arterial movement and flexibility were not considered in this study. The movement and flexibility of vessels can influence velocity and flow rate. The wall of a coronary artery is assumed to be rigid. In arteries with

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severe stenosis, the high pressure proximal to a stenosis may expand the flexible wall to allow more volume to pass the stenosis. Zhao et al. [25] showed that wall compliance does not considerably influence the general characteristics of flow and wall shear stress in coronary arteries. Another limitation of this study is setting the same pressure gradient for both models. The geometric configuration of vascular segments greatly affects the resulting flow patterns, so the coronary velocity distribution is mostly affected by the coronary stenosis. It is expected that both influence the results quantitatively, but not qualitatively.

4 Conclusion This work simulated the hemodynamics of a stenotic coronary artery treated with a stent. The geometry and flow conditions were based on patient-specific data obtained before and after stent implantation, making the simulation more realistic and enhancing the potential application of CFD prediction to clinical surgical planning. This study is the first to investigate the hemodynamic changes of stent implantation based on patient-specific preand post-stenting models under a realistic aorto-coronary differential pressure gradient. The quantitative results of the hemodynamics simulation show that the stent increased flow rate several fold compared to that of the stenosis artery model. The wall shear stress and blood velocity were greater in the region of stenosis after stenting. The quantitative and qualitative hemodynamic changes after stentgraft implantation in a patient-specific model were demonstrated using a hemodynamics simulation. This study confirms that the stenting procedure significantly improves the hemodynamics of the artery. Future studies will address the effects of fluid structure interaction between blood flow and the coronary artery wall for stent implantation.

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