Design and Simulation of Blocked Blood Vessel for Early Detection of Heart Diseases

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1 Proceedings of the 215 2nd International Symposium on Physics and Technology of Sensors, 8-1th March, 215, Pune, India Design and Simulation of Blocked Blood Vessel for Early Detection of Heart Diseases Apoorva Garje and Y.G. Adhav Department of Instrumentation and Control, MKSSS s Cummins College of Engineering for WomenPune, India Abstract In this paper, we present two-dimensional modeling and simulation of blood vessel using COMSOL Multiphysics. The rationale behind this study is that mathematical modeling and numerical simulation can lead to better understanding of the phenomena involved in vascular diseases. This study assumes that the fluid is laminar, non- Newtonian, viscous and compressible and the arterial wall is elastic. Parameters of blood vessel were assigned to the wall and parameters for fat deposits to the blockages. Blood is an example of a non-newtonian fluid applied to the model in the present simulations. Structural deformation and fluid dynamics are determined simultaneously. Keywords: COMSOL Multiphysics; blood vessel; fluid structure interaction; blockages; computational fluid dynamics I. INTRODUCTION Many cardiovascular diseases are closely associated with the flow conditions in the blood vessel. One major type of arterial disease is coronary artery disease (CAD), which is characterized by localized accumulation of cholesterol. CAD is an occlusion of the coronary arteries resulting in insufficient supply of blood and oxygen deprivation to the heart muscle. When the blockage of an artery is complete, it results in a heart attack, or in very severe cases, may result in death of the patient [1]. To overcome the problem, detailed knowledge associated with the disordered flow patterns is then important for the detection of localized arterial disease in its early stages. Early detection of the disease will enable to cure using medication rather than surgery. This study hypothesizes that a multiphysics simulation of both diseased and healthy arteries can be readily implemented in such a software package. Wall shear stresses and distension were examined to validate the models against literature. Ideally these models can be adapted to incorporate cardiovascular devices to predict their behavior before physical prototypes are created. In order to treat patients with CAD, more needs to be known about the progression of the disease and the effectiveness of potential treatments. Using a computer model to study disease progression and treatments is faster, simpler, safer, and less expensive than experimentation. Dhananjay Bodas* Nanobioscience, Agharkar Research Institute, GG Agarkar road, Pune India. dsbodas@aripune.org The goal of this work was to model blood flow in blood vessel, simulate the formation and growth of a blockage, and observe the resulting changes in blood flow characteristics. We have designed a model to simulate pressure along the surface of artery. It is a step further for diagnosis of heart disease well before it occurs. Earlier detection of blockages eliminates the need of angiography. Thus all heart problems can be solved earlier. The simulation encompasses micro fluidics interactions as well as it takes advantage of the Multiphysics capabilities of COMSOL. The following assumptions were made to allow for COMSOL implementation: the cardiac output is constant; the artery is elastic; all fluid properties are estimated; blood is a uniform non-newtonian fluid; follows laminar flow pattern [2]. The setup of the simulation allows parametric studies of the geometry. II. OVERVIEW A. Use of ComsolMultiphysics A multiphysics approach that incorporates the solid mechanical behavior of the artery as well as the fluid dynamic behavior of the blood passing through it would provide a more accurate prediction of in vivo behavior [3]. B. Simulation The simulations were carried out using a 2D laminar flow and solid mechanics. Fully coupled model for fluid structure interaction has been considered for time dependent solver. Parameters of blood vessel and fat deposits were assigned to the wall and blockages respectively. The underlining assumptions are that the blood flow is Laminar, non- Newtonian, viscous, compressible and the artery walls are elastic. The structural deformation and fluid dynamics are determined simultaneously. Normal physics controlled mesh was used, to allow FSI simulations to be performed. The blood flow motion is governed by the continuity equation and the Navier-Stokes equations, which can be expressed in vector notation as:. = ; (1) /15/$ IEEE 24

2 Where, u is the blood velocity, ρ is the density and σ is the stress applied [1]. III. MODEL PARAMETERS Model geometry consists of three domains. 1) The space through which the blood flows. 2) The elastic wall of artery and 3) The blockage i.e. cholesterol deposit on the wall. A. Material Properties Material properties used for simulations are: Blood - Density: 16 kg/m 3 ; Dynamic Viscosity:.5 Pa-s. Artery - Density: 1.6e3 kg/m 3; Poisson s Ratio:.49; Young s Modulus = 2e6 [MPa]. Cholesterol Deposit- Density: 15 kg/m 3; Poisson s Ratio =.11; Young s Modulus = 2[MPa]. B. Fluid Flow Blood was modeled as a non-newtonian fluid with a laminar flow having fluid properties of normal inflow velocity of 16.9cm/s. Furthermore, the fluid was assumed to be under compressible flow [4]. Boundary conditions of no slip were applied to the entire geometry. The areas of the inlet and outlet were fixed to allow consistent flow rate readings with changes in outlet pressure. C. Solid Mechanics A linear elastic material with Isotropic model is used for the arterial walls and cholesterol deposit. The Young s modulus and Poisson s ratio of each material were given as shown above. The solid conditions based on the stress and strain variables were used in model. IV. THEORETICAL MODEL A. Geometry Dimensions The semicircular blood vessel with dimensions 5 mm in diameter and 25 mm in length are considered as shown in Fig. 1. The three portions such as at inlet, center and outlet blockages were modeled with variation in height from 1%, 25%, 5%, 75% and 9% of 5mm i.e. 5, 125, 25, 375 and 45 μm respectively. Artery wall thickness was set to 5 μm. Similarly simulations of the artery for the model size of 1mm in diameter with blockage size of 1%, 25%, 5%, 75% and 9% i.e. 1, 25, 5, 75 and 9 μm respectively at inlet, center and outlet. Artery wall thickness was set to 1 μm. The simulation of the arteries of size 5mm and 1mm radius without cholesterol deposit was carried out for the characteristic comparison with natural artery. B. Physics The trio of laminar flow, solid mechanics and fluid structure interaction were used for the geometry build up. Initially properties for laminar flow of fluid were assigned the inner surface of artery. and outlet were assigned at third and eleventh boundary respectively. Artery Walls Arc Length a) Blockage b) c) Fig. 1. Model of a blocked blood vessel with diameter 5 mm and length 25mm The blockage modeled with dimensions of 5% i.e. 25 μm in radius at a) Center b) c) At solid mechanics physics node, properties of linear elastic material were assigned to arterial walls and blockage i.e. first, third and fourth domain respectively. Along with this, free, initial values, fixed constraint and prescribed displacement were modeled. After that, fluid structure interaction boundaries were assigned. flow rate of 16.9 cm/s was kept constant for all the simulations, in consonance with the value for blood flow in a human body. Time dependent analysis along with parametric sweep of pressure variation from to 9 Pa was carried out to observe variation of the velocity and stress using FSI simulation tool. 25

3 V. RESULTS The heart experiences the same pressure as the fluids needs to be pumped more due to constriction. The pressure increases as the thickness of the blockage increases. Fig. 2 shows the variation of surface velocity, pressure and stress profiles with respect to length of 5mm artery for 5% blockage at center. It can be clearly observed that stress increment at blockage point is more pronounced as the thickness of blockage increases. The velocity rises sharply due to the blockage, which is again pronounced due to the thickness of blockage. This clearly indicates a variation, which starts very early due to deposition on the arterial walls. The effect can be detected as the backpressure exerted on the heart, which can be significant. a) b) Fig. 3 shows the variation of velocity and stress profiles with respect to length of 5mm artery for 1%, 25%, 5%, 75% and 9% sizes of blockage at inlet, center and outlet. It can be seen that, as the size of blockage increases amount of stress generated on artery walls increases. The blockage, with size of 1%, 25% and 5% of the artery, generates more stress at inlet as compared to center and outlet. For blockage size of 75% and 9% the stress generation is approximately same at inlet, center and outlet. It indicates that, for larger thickness of blockage, stress generation profile is exponentially increasing for the given portions of artery. It can be observed that, the surface velocity magnitude is decreasing from center towards arterial wall. For 1% blockage, the velocity magnitude is higher at center and outlet, for 25% blockage velocity magnitude is highest at inlet, for 5% and 75% blockage velocity is highest at center, for 9% blockage the blood flow is completely blocked by blockage hence velocity magnitude is highest at inlet. Similar results were obtained for the arterial model of 1mm radius. The behavior of velocity magnitude differed between each case. For the 75% and 9% blockage models (Figure 4-e and Figure 4-f), the nature of stress generation was roughly the same. Fig. 4 shows the variation of velocity and stress profiles with respect to length of 1mm artery for 1%, 25%, 5%, 75% and 9% sizes of blockage at inlet, center and outlet. VI. DISCUSSION The first major part of this work investigated the influence of the initiation and increment of cholesterol deposit on the variation in velocity magnitude, pressure and stress in thirty idealized models. Back-pressure generation factor is of special interest since it is the only main factor that will be changed in case of any sudden arterial disease. Simulations were repeated for five sizes of blockage at three locations with nine values of pressure assigned to the outlet of the artery, covering the normal and abnormal (hypertension) blood pressures in human cardiac cycle. Figure 2 and 3 illustrates the high degree of similarity between stress profiles for 5 mm and 1 mm artery. It also shows the direct correlation between velocity magnitude and stress through increasing blockage size. These results suggest that the model is functioning properly with the blockage. c) Fig. 2. Surface profiles of Blood vessel with blockage of 5% at center a) Velocity magnitude b) Pressure Exerted due to blockage and c) Stress. 26

4 a) 5 mm; 1% c) 5 mm; 5% Center b) 5 mm; 25% d) 5 mm; 75% e) 5 mm; 9% Figure 3: Variation in velocity and stress profile of 5 mm diameter artery with 2-9% blockages a-e. a) 1 mm; 1% c) 1 mm; 5% Center b) 1 mm; 25% d) 1 mm; 75% e) 1 mm; 9% Figure 4: Variation in velocity and stress profile of 5 mm diameter artery with 2-9% blockages a-e. 27

5 The blood velocity dropped before the blockage, get compressed and sharply increased after the blockage. It generates lot of pressure on the arterial wall. As the size of blockages increased, the back-pressure and stress are more pronounced. At each time point there is a characteristic drop in pressure across the artery related to velocity magnitude. Significant back-flow was observed near the blockage point just after the maximum velocity point, as can be seen in Figure 2-a. From the graphs, it can be observed that, the backpressure effect is more pronounced for blockage at inlet, it is obvious since it directly affects the blood flow from heart pump. As arterial blockage location moves away from the inlet, back-pressure effect is not pronounced. Compared to 5 mm artery, the variation in stress and velocity can be clearly seen for 1mm artery. In this simulation, the results obtained indicate that the blockage can be predicted at very early stages. Using current technologies, it is difficult and expensive to determine the location of blockages in living patients. However it has to be noted that the stress test, angiography cannot detect the blockage of small size, the detection range is limited for 9%. The blockage affects the blood flow characteristics in the artery, it is more pronounced for smaller blockages at center. According to the clinical point of view, stress profile is more essential. When blood force distribution acts on the boundary surfaces, higher stress occurs at the inlet and outlet and rapidly drops the pressure causes reversing of its direction. When the blockage size is increased, higher stress occurs at the blockage area, which means the blood flow could be closure leading to higher pressure drop and increasing the center-line velocity at higher rate. That results in decreasing compliance effect. More importantly, it is possible to detect in which artery the blockage exists. Being able to accurately predict that blockage is near or far away from the heart, incorporating the actual percentage of blockage. By observing the pressure contour and stress profile detection of blockages can be done. The multidisciplinary nature of these models allows many phenomena to be observed or incorporated, providing for more accurate simulations of arteries and techniques used to treat their diseases. CONCLUSION Several multiphysics models of a blocked blood vessel were successfully created. The model achieved the design goals. It produced a realistic representation of blood flow in the artery with and without a blockage that matched other computational models and clinical experiments. This simulation is concerned with the blood flow interaction with arterial vessels and the fat deposit blockages, under laminar flow conditions. Two-dimensional human coronary arteries with dimensions 5mm and 1mm are simulated; similar detection can be performed for capillary model in micron size. It was observed that, the effect of pressure is more pronounced at 1mm artery compared to 5 mm. At younger age, the arteries are more elastic, hence the effect of similar blockage is not pronounced. As the arteries goes on hardening in adults, it affects the blood flow and blood pumping. Arterial blockage location greatly affects the blood flow and pumping. If the blockage is formed at inlet, it directly produces the backpressure on heart pump, as you go away from the inlet, the effect is not pronounced. The simulation models gives insight of the pressure drop observed due to blockage. This blockage due to low sensitivity of stress tests goes undetected at early stages. It provides clinicians a modeling tool to gain a better understanding of the blockage deposition and analyses to be used for optimal medical management. Another potential application of the model is in vivo diagnosis of coronary artery disease. The understanding can help detect heart diseases at a very early stage and avoid by-pass surgery. Furthermore, this approach can also be utilized for solving patient-specific realistic geometries. The model developed in this workprovides an excellent foundation for future arterial blood flow and CAD models with potentially lifesaving applications. The results from this work suggest a wide range of future research projects with different set of assumptions. Among others, new models can be developed for diagnosing different kind of diseases in various organs. REFERENCES [1] P. Chuchard, et. al, 211 Numerical simulation of blood flow through the system of coronary arteries with diseased left anterior descending, International Journal of Mathematics and Computers in Simulation, 5, 334. [2] M. Siebert, P. Fodor, 29 Newtonian and Non-Newtonian Blood Flow over a Backward-Facing Step-A Case Study, COMSOL Users conference, Boston. [3] D. Espino, et. al, 26 Simulation of blood flow through the mitral valve of the heart: A fluid structure interaction model, COMSOL Users conference, Birminham. [4] Howe G. L., Multiphysics simulation of a coronary artery, Thesis, The Faculty of California Polytechnic State University, 213. [5] J. Blazek, Computational fluid dynamics: Principles and applications, Elsevier,ISBN ,

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