Extraction and FSI modeling of Left coronary artery structure from patient s CTA images Safia Salim Dept. of Electronics & Communication College of Engineering, Kerala University Trivandrum. 695016 Email: safiasalim88@gmail.com Binu L.S. Asst Professor, Dept. of Electronics & Communication College of Engineering, Kerala University Trivandrum. 695016 Email: binuls@yahoo.com Abstract The aim of this study is to extract the left coronary artery from the Computed Tomography Angiography (CTA) images stored in DICOM (Digital Imaging and Communication in Medicine) format and also to study the various haemodynamic properties such as Wall Shear Stress (WSS), Pressure distribution,wall Pressure Gradient etc. The proposed approach uses 3D slicer 3.6.3 for the extraction of the artery and the Computational Fluid Dynamics (CFD) software ANSYS 13.0 for predicting the flow characteristics through the left coronary artery and also for simulating the haemodynamic properties. The extracted artery consists of Left Main (LM) coronary artery, Left Anterior Descending (LAD), and Left Circumflex (LCX) artery. Finite element analysis of Navier-Stokes flow equations treating blood as a non-newtonian, incompressible fluid is done. In most of the previous works simulations are done by assuming that the arterial walls are rigid, but in actual case it do have elasticity. Inorder to make the study more realistic, here the elasticity of the arterial wall is also considered. By the simulation, contour plots of various haemodynamic properties were obtained and studied. Key words: Left Main(LM),Left Anterior Descending(LAD),Left Circumflex(LCX), Wall shear Stress (WSS), Wall Pressure (WP), Wall pressure Gradient (WPG). I. INTRODUCTION The central organ of the cardiovascular system in the body is the heart and is mainly composed of muscle tissue known as myocardium. The muscle is hollow in structure and it pumps blood through vessels throughout the body by continuously contracting and relaxing. The two vascular trees arises from the ascending aorta above the aortic valve, the Left Coronary Artery (LCA) and the Right Coronary Artery (RCA). Cardiovascular disease (CVD) is the leading cause of death worldwide. Among various CVDs the most threatening is the Coronary Artery Disease(CAD). Of the various forms of CADs, atherosclerosis is the primary cause. The coronary arteries are those arteries which provides oxygenated blood to heart muscle cells, so any blockage in these arteries will affect the working of the entire human body. Atherosclerosis is thickening of arteries which cannot be found by normal scanning techniques. To investigate about these disease various studies and experiments need to be conducted on human heart, but it being an internal organ limits the scope. Numerical modeling and analysis of internal organs is necessary and is performed mostly through computational fluid dynamics. Diagnosis and investigation of the severity of various heart diseases are performed through medical imaging. Simulation of blood flow using image-based models and computational fluid dynamics has found widespread application to quantifying haemodynamic factors relevant to the initiation and progression of cardiovascular diseases and for planning interventions. Some of the important haemodynamic parameters considered are Wall Shear Stress(WSS), Pressure Gradient etc. Haemodynamics or blood dynamics is the study of properties and flow of blood. Among various haemodynamic parameters important one is Wall Shear stress(wss) which induces a micro environment of interaction (frictional force) between blood and the arterial wall. WSS is vector whose magnitude is proportional to the blood viscosity and flow velocity gradient normal to the surface, and which acts in a direction parallel to the local velocity. Due to viscosity, blood exerts a drag force proportional to the velocity gradient normal to its surface on the arterial wall, which is termed as wall shear stress. WSS is difficult to measure directly in vivo or in vitro so that it is generally computed from the local velocity at the wall. So WSS is an important determinant of the commencement of coronary heart diseases [1]. Plaque deposition normally occurs in the LCA, so studies are focussed on the left coronary artery. The left coronary artery (LCA) bifurcates after 5-10mm into the left anterior descending artery (LAD) and the left circumflex artery (LCX). The LAD and LCX supply in most cases the left atrium, the left ventricle and most of the cardiac septum with blood [2]. From the preceding literatures it can be seen that many of the researchers have either used a two dimensional model or a reconstructed part of the coronary artery (one of the branches) for the determination of wall shear stress [3-4]. Since the left coronary artery system consist of Left Main which is branched into LAD and LCX, it is important to have a three dimensional model for the numerical simulation of pulsatile blood flow. In the present work three dimensional model with branches are considered. Section II discusses the work proposed. Section III explains the method used in the computational processes.
Section IV deals with results obtained and its relation to the localization of plaque deposition. II. PROPOSED WORK The purpose of this study is to numerically analyze the haemodynamic parameter distribution over the left coronary artery. Main emphasis is put on to extract the left coronary artery from the medical images. import the extracted mesh file to computational fluid dynamics platform. perform numerical simulations on arterial geometry using pulsatile flow case. find the distribution of the haemodynamic parameters on the normal human LCA, particularly at the bifurcations. For simulation the CTA image of the human heart is used. CTA is an imaging method used to view the coronary blood vessels. To get the image modern multi-slice Computer Tomography (CT) scanners are used while a contrast agent is injected directly into an arm vein and is allowed to circulate throughout the body to the coronary arteries. CTA image is shown in fig(1) (dataset from Erasmus Medical Center, Rotterdam, Netherlands). A. Geometry III. MATERIAL AND METHODS The geometry of the left main coronary artery with LCX and LAD are obtained from the CTA images using SLICER 3.6.3. 3D Slicer is a widely-accepted application for medical image processing [5]. The Vascular Modeling Toolkit (VMTK) is a system for image-based modeling of blood vessels [6]. Both are open source software and freely available. The library of VMTK has already been integrated in 3D Slicer allowing the establishment of processing pipelines between VMTK and 3D Slicer modules. The Vascular Modeling Toolkit is a collection of libraries and tools for the 3D reconstruction, geometric analysis, mesh generation and surface data analysis for image-based modeling of blood vessels. By using VMTK we can navigate around a 3D volume; reconstruct the 3D surface of a vascular segment from CT or MR images; process a surface model to generate a mesh. From the CTA image the volume of interest (LCA with LAD and LCX) is obtained first. The 3D surface reconstruction of a vascular segment is done by Level Set Method. The initialization method used to create the model of the blood vessel is the colliding fronts. In this method two seeds are placed on the image. Two fronts are then propagated from the seeds (one front from each) with their speeds proportional to the image intensity. The region where the two fronts cross (or collide), defines the deformable model the initial representation of the vessel volume.this method can be repeated if the result is not satisfactory. At this point, we have our surface model and we want to generate a computational mesh. In most cases, the surface model has bumpy surfaces. Artificial bumps in the surface can result in spurious flow features and will affect the wall shear stress distribution, so one may want to increase surface smoothness before building the mesh. The smoothened surface are then clipped to provide opening for inlet and outlet. The resultant surface model is shown in fig(2). These steps were performed using VMTK Scripts. Diameters of extracted 3D geometry is Left Main Artery (LM) = 2.98mm Left Anterior Descending Artery (LAD) = 1.89mm Left Circumflex Artery (LCX) = 1.7mm Fig. 2. Extracted LCA with LAD & LCX The obtained dimensions matched with the biomedical datas [7]. B. Computational Grid ANSYS CFX uses an element-based finite volume method, which first involves discretizing the spatial domain using a mesh. The mesh is used to construct finite volumes, which are used to conserve relevant quantities such as mass, momentum and energy. Here we are concentrating on 3D mesh. All the geometric data obtained from 3D slicer were inputed into a pre-processing program ICEM CFD for grid generation. The mesh generator works by performing two fundamental steps, Surface Remeshing and Volume Meshing. Surface remeshing is performed under the assumption that the surface requires improvement before being used for CFD. In the surface remeshing step, the surface triangle edges are resized. After the surface has been remeshed the volume is filled with a combination of tetrahedral and prismatic elements. In this case Tetrahedral elements are used with size of 0.1. For grid generation 28213 grid nodes were utilized giving rise to 162125 computational tetrahedral (fig 3). C. Governing Equations and Boundary Conditions All the computational grid data were imported to Computational Fluid Dynamics solver ANSYS 13.0. Computational Fluid Dynamics (CFD) is a computer-based tool for simulating the behaviour of systems involving fluid flow, heat transfer, and other related physical processes. It works by solving the
Fig. 1. A CTA image of the human heart showing coronaries (a) Coronal view showing RCA (b) coronal view showing LCA Fig. 3. meshed artery To solve the governing equations numerically, a set of boundary condition is required. No slip at the arterial walls. Since the heart contracts and relaxes throughout the day, the velocity profile entering the fluid domain is assumed to be a pulsatile waveform (fig 4) given by U = 0.3(1+0.75 sin( 2 pi y ) 0.75 cos( 4 pi y )) t t (3) The pulsatile flow is written in User Defined Excel format and is delivered to CFX set up to initialise the profile data. equation of fluid flow over a region of interest with specified conditions on the boundary of that region. In this simulation blood is assumed to be incompressible, non-newtonian fluid with density of 1058 kg/m 2 and with viscosity of 0.0035 kg/ms. The operating pressure were considered as 13330 Pa [8]. To give elasticity to the arterial walls Young s Modulus of 3.21 10 5 ± 2.11 10 5 Pa is given. The nature of the flow is assumed to be three dimensional, steady, laminar, isothermal, with no external forces applied. Continuum fluid flow is governed by Navier-Stokes equations. These equations represent the differential forms of three basic conservation principles of fluid flows. The first one of Navier-Stokes equations is the continuity equation, which is a statement of the conservation of mass. The second one is called the momentum equation, which arises from the conservation of momentum.the third equation is obtained by applying the conservation of energy to the fluid flow, and this equation is called the energy equation. The blood is assumed as non- Newtonian fluid governed by the continuity equation, and the Navier-stokes equation where u = Velocity Vector P = Pressure t = Time µ = Viscosity ρ = Density.u = 0 (1) ρ Du Dt = P + µ 2 u (2) Fig. 4. pulsatile flow Volumetric flow splits of 0.598 for LAD and 0.4072 for LCX. CFX is a finite volume technique, where the region of interest is divided into small subregions called control volumes. The equations are discretized and solved iteratively for each control volume. As a result, an approximation of the value of each variable at specific points throughout the domain can be obtained. A full picture of the behaviour of the flow is obtained in this way. CFD solver will do the above steps. Segregated solvers employ a solution strategy where the momentum equation are first solved, using a guessed pressure and an equation for a pressure correction is obtained. Because of the guess-and-correct nature, a large number iterations are typically required in addition to the need for judiciously selecting relaxation parameters for the variables. ANSYS CFX uses a coupled solver which solves the system. This solution
approach uses a fully implicit discretization of equations at any given time step. For steady state problems, the timestep behaves likes an acceleration parameter to guide the approximate solutions in a physically based manner to a steady-state solution. This reduces the number of iterations required for convergence to a steady state, or to calculate the solution for each time step in a time-dependent analysis. For a typical satisfactory convergence solution, a total of 200 time step were required. Convergence was achieved when all velocity component changes from iteration to iteration were less than 10 4. IV. RESULTS The Navier-Stokes finite element analysis of the left coronary artery gives the contours of various haemodynamic properties such as Wall Shear Stress (WSS), Wall Pressure (WP), Wall Pressure Gradient (WPG), Velocity Distribution etc. The contour plots of important haemodynamic properties are discussed below. A. Contours of WSS curvature, especially at the bifurcations giving rise to high WSS. WSS is given by τ w = µ u t n wall (4) where µ(kg/m s) is the dynamic viscosity, u t (m/s) the tangential to the wall velocity and n is the unit vector perpendicular to the wall. WSS is determined from velocity gradients. Any nonzero value of WSS denotes a non-uniform haemodynamic environment. In the case of LMCA bifurcation high WSS values tend to form a ring located at the origin of bifurcation [9]. When the area for the flow decreases velocity of flow increases, thereby increasing the WSS. So any disturbance in flow can be found out by measuring the WSS. In the figure 5 WSS ranges from 0 N/m 2 to 0.001047 N/m 2, with an average WSS of 0.00048737 N/m 2. Plaque deposition frequently occurs where low WSS occurs. B. Contours of Wall Pressure Flowing blood imposes haemodynamic stress at the blood arterial wall interface. This stress has two components, namely: the vertical to the wall acting pressure (WP) and the tangentially to the wall acting component WSS. Contour plot of Wall Pressure (WP) magnitude is shown in fig 6. Pressure and velocity are inversely related. Since LMCA have higher area compared to LAD and LCX, LMCA have high pressure (low Velocity) compared to LAD and LCX. WP ranges from 10938.2 N/m 2 to 17278.2 N/m 2, with an average WSS of 14405.3 N/m 2. Fig. 5. Contour plots of the WSS (N/m 2 ) magnitude distribution at the LMCA with LAD & LCX. All spatial WSS values are shown in filled contours coupled with iso-contour line form. These contours show the WSS magnitude. Contour labels appear in figure 5, range from 1 to 17, and correspond to the 17 color levels also shown in figure 5. The results indicate that on the Left Main Coronary Artery (LMCA) bifurcation, dominant low WSS values occur at regions opposite flow divider. Low WSS occur at regions opposite to the flow divider at either LMCA or proximal LAD or LCX regions. Velocity distributions get affected at high Fig. 6. Contour plots of the Wall Pressure (N/m 2 ) magnitude distribution at the LMCA with LAD & LCX.
C. Contours of Wall Pressure Gradient Another dominant haemodynamic factor is coronary artery pressure flow field. Low velocity as well as low wall shear stress contributes to atherosclerosis. Furthermore, geometrical particularities of a given coronary artery configuration also contributes to the haemodynamic behaviour. Thus, the analysis of Wall Pressure Gradient (WPG) is of importance [10]. The stress development within the arterial wall is a direct effect of the induced pressure flow field. WPG is given by W P G = where p is the static pressure. ( p x )2 + ( p y )2 + ( p z )2 (5) TABLE I CONTOUR VALUES OF WSS, WP, WPG Orientation WSS(N/m 2 ) WP(N/m 2 ) WPG(kg/m 2 s 2 ) LMCA (228.19 155.74 19.9236) 0.000219171 15919.4 63.2972 (214.539 157.718 22.7487) 0.000212047 16096.9 63.1208 (219.945 134.935 19.2683 0.000296127 16194.2 144.511 (221.623 134.35 29.7809) 0.000206533 16263 150.356 (228.715 142.977 24.7035) 0.000223963 15568.9 60.7631 LAD (226.902 136.942 19.2075) 0.000351086 15343.3 287.509 (229.154 129.393 20.2458) 0.000550188 14298 92.4019 (232.126 118.328 21.744) 0.000604895 13453.3 450.385 (225.007 127.115 25.9611) 0.000671696 12557.2 579.512 (226.151 119.504 25.4255) 0.000591129 13754.6 245.521 (229.173 109.133 27.4365) 0.000582841 13713.8 347.805 LCX (218.919 126.645 25.8171) 0.000699093 12948.4 810.736 (217.888 118.592 25.5016) 0.000572077 14091.9 120.55 (212.263 130.565 25.0644) 0.000572077 15168.4 266.304 (210.354 120.705 27.076) 0.000655228 13888.9 415.955 (208.053 109.393 28.8788) 0.000611302 13308.7 235.425 TABLE II CONTOUR VALUES OF WSS, WP, WPG Fig. 7. Contour plots of the WPG (kg/m 2 s 2 ) magnitude distribution at the LMCA with LAD & LCX. All spatial WPG values are shown in filled contours coupled with iso-contour line form. These contours show the WPG magnitude. Contour labels appear in figure 5, range from 1 to 11, and correspond to the 11 color levels also shown in figure 7. A highly non-uniform haemodynamic environment occurs if WPG are not uniformly distributed. High WPG co-exist with low WPG values. Spatial flow accelerations and decelerations are largely influenced by the wall pressure distribution. At all LCA bifurcations, high WPG values are always accompanied by low WPG ones. High values occur right at the flow dividers. Here WPG ranges from 0.780873 kg/m 2 s 2 to 2836.53 kg/m 2 s 2, with an average WSS of 248.326 kg/m 2 s 2. The values of parameters such as WSS, WP, WPG etc at LMCA, LAD and are shown in Table I. The results obtained here matched with various pathological studies [11-13], as shown in Table II. From the parameters discussed above, characteristics of the left coronary artery can be fully studied. Any variations in Orientation WSS(N/m 2 ) WP(N/m 2 ) WPG(kg/m 2 s 2 ) LMCA (228.19 155.74 19.9236) 0.000219271 15616.1 61.75 (214.539 157.718 22.7487) 0.000213 16156.6 63.1298 (219.945 134.935 19.2683 0.000351 16194.8 143.511 (221.623 134.35 29.7809) 0.000216533 16245.4 149.247 (228.715 142.977 24.7035) 0.0002456 14568.21 63.671 LAD (226.902 136.942 19.2075) 0.00035215 1424.9 288.61 (229.154 129.393 20.2458) 0.00052152 13291.99 90.41 (232.126 118.328 21.744) 0.00065221 13441.29 455.31 (225.007 127.115 25.9611) 0.0005977 11657.196 569.77 (226.151 119.504 25.4255) 0.00049985 13654.2 240.11 (229.173 109.133 27.4365) 0.0005754 12713.1 340.125 LCX (218.919 126.645 25.8171) 0.000799093 12849.4 799.514 (217.888 118.592 25.5016) 0.0004258 14119.9 119.11 (212.263 130.565 25.0644) 0.00054322 15162.2 261.21 (210.354 120.705 27.076) 0.00065288 13868.9 410.99 (208.053 109.393 28.8788) 0.0005811 13306.7 230.258 the blood flow and also the sites prone to atherosclerotic lesion can be found out from the values of haemodynamic parameters. High WSS, give rise to high Wall Shear Stress Gradient (WSSG), inhibit coagulation and migration of leukocytes. On the contrary, low wall shear stress values favours opposite effects, thereby contributing to atherosclerosis. Atherogenic blood flow particles usually migrates towards low pressure regions. The parameter values will give the physicians an idea regarding the placement of stents to reduce or remove the plaque deposition. ANSYS CFX also provides the provision to animate the blood flow through arteries. The streamlined flow is shown in figure 8. It is also possible to take a plane or slice of the artery and study the various parameters. The plane developed is shown in figure 9.
Fig. 8. Streamlined flow through arteries, showing variation of Pressure. Fig. 9. Plane showing variation of Pressure. pathophysiology of atherosclerosis. This study shows that the regions which are anatomic sites predisposed for atherosclerotic development shows low WP,WPG,WSS at bifurcations in regions opposite flow dividers. REFERENCES [1] Sahid Smith, Shawn Austin, G. Dale Wesson, Carl A. Moore, Calculation of Wall Shear Stress in Left Coronary Artery Bifurcation for Pulsatile Flow Using Two-Dimensional Computational Fluid Dynamics, 28th IEEE EMBS Annual International Conference 2006. [2] Daniel Hahn. Coronary Artery Centerline Extraction in 3D Slicer using VMTK based Tools. Ruperto Carola University of Heidelberg, Germany February 2010. [3] Jin Suo, John Oshinski, Don Giddens, Flow patterns and wall shear stress distribution at atherosclerotic prone-sites in human left coronary artery, Proceedings of the 26th Annual International Conference of the IEEE EMBS, USA.Sept 1-5,2004. [4] Byoung Kwon Lee, Hyuck Moon Kwon, Computed Numerical analysis of the Biomechanical effect on Coronary atherogenesis using human hemodynamic and dimensional variables, Yonsei Medical Journal, Vol.39, No.2, pp167-174, 1988. [5] S. Pieper, M. Halle, and R. Kikinis, 3d slicer, In Proc. IEEE International Symposium on Biomedical Imaging: Nano to Macro, pages 632-635, 15-18 April 2004. [6] L. Antiga, M. Piccinelli, L. Botti, Ene-Iordache B., A. Remuzzi, and D.A. Steinman, 3An image-based modeling framework for patient-specific computational hemodynamics, Med Biol Eng Comput, 46(11):1097-1112, Nov 2008. [7] N. Bnard1, R. Perrault1, D. Coisne, Blood flow in coronary artery : numerical fluid dynamics analysis, Proceedings of the 26th Annual International Conference of the IEEE EMBS San Francisco, CA, USA September 1-5, 2004. [8] Anayiotos, A., Fluid Dynamics at a Complaint Bifurcation Model, Ph.D. thesis. Georgia Institute of Technology, Atlanta 1990. [9] Johannes V. Soulis, Thomas M. Farmakis, George D. Giannoglou, George E. Louridas Wall shear stress in normal left coronary artery tree, Journal of Biomechanics 39 (2006) 742-749. [10] George D. Giannoglou, Johannes V. Soulis, Thomas M. Farmakis, Wall pressure gradient in normal left coronary artery tree, Medical Engineering & Physics 27 (2005) 455464. [11] Giannoglou GD, Soulis JV, Farmakis TM, Farmakis DM, Louridas GE, Haemodynamic factors and the important role of local low static pressure in coronary wall thickening., Int J Cardiol 2002;86:27 40. [12] Nagel T, Resnick N, Dewey CF, Gimbrone MA, Vascular endothelial cells respond to spatial gradients in fluid shear stress by enhanced activation of transcription factors, Arterioscler Thromb Vasc Biol 1999;19:182534. [13] Zarins CK, Giddens DP, Bharadvaj BK, Sottiurai VS, Mabon RF, Glagov S, Carotid bifurcation atherosclerosis. Quantitative correlation of plaque localization with flow velocity profiles and wall shear stress,circ Res 1983;53:50214. V. CONCLUSION The left coronary artery with branches LAD and LCX have been successfully extracted. The geometry has been numerically analyzed to study various haemodynamic properties (Wall shear Stress, Wall Pressure, Wall pressure Gradient etc) using ANSYS CFX. The Computational Fluid Dynamics (CFD) solves the governing Navier-Stokes equations, providing the 3D non-newtonian haemodynamic solution of the human left coronary artery. Because of the LCA and its branching geometry irregularities, the physiological blood flow is highly complex and non-uniform. Flow disturbances are intensified in regions where the geometry drastically changes. Numerical analysis of blood flow in arterial segments is of paramount importance in understanding the biomedical