Computational Fluid Dynamics Simulations of Blood Flow Through an Injured Arteriole1

Blood may be modeled as a continuous fluid with relatively high accuracy in large vessels (diameter over 1 mm). However, as blood flows through smaller vessels, e.g., arterioles and capillaries, the components of blood begin to affect the flow more significantly. When modeling blood flow in arterioles, a multiphase approach best describes the interactions of blood. The focus of this research is to analyze the velocity profiles of blood plasma and red blood cells (RBCs) as they flow through arterioles with an incision in the arteriole wall using computational fluid dynamics (CFD).CFD modeling of blood flow through vessels has gained interest in recent years. In this case, CFD is an effective approach to analyze arterioles due to their microscopic size. Another advantage of CFD is that it allows modifications to the vessel or to the flow itself quite readily.For most blood flow simulations, blood can be represented as a continuous fluid, but in vessels on the scale of arterioles the interactions between individual blood cells and the plasma ought to be accounted for in its own right. This study used a two-phase flow (RBCs and blood plasma) to simulate blood flow through an injured arteriole. Multiphase flows have been used readily to model blood with some studies also representing white blood cells and platelets [1]. When considering vascular device analysis, it is often useful to understand the forces and interactions that individual cells or groups of cells are experiencing. The individual cells must be modeled as separate components of the blood in order to study these interactions computationally. The overall goals of this study are to develop a representative model of two-phase blood flow and to better understand hemodynamics in an injured arteriole.This study implemented star-ccm+ version 9.04 by CD-Adapco to calculate the fluid analysis on a simplified arteriole. CFD uses the second-order differential Navier–Stokes equations to simulate the fluid dynamics and flow mechanics throughout a system. The 3D model for the arteriole geometry was created using SolidWorks 2015, a commercially available parametric computer-aided design software. The arteriole was represented as a horizontal cylinder with a rectangular cross section laceration made at the center of the vessel. The diameter of the arteriole was set to 0.05 mm. The total length of the arteriole was 1.00 mm. The injury to the arteriole was represented by a rectangular cut at the center of the length of the arteriole. The laceration was modeled to be 0.10 mm long and 0.02 mm deep. The laceration geometry was modeled to represent an injury inflicted by a razor (as the length of the laceration is within the range of thicknesses of razor blades). The geometry remained constant for all the simulations and is displayed in Fig. 1.The blood flow was simulated as a two-phase flow consisting of liquid blood plasma and dispersed solid RBCs. Blood plasma was modeled as a Eulerian fluid with a density of 1025 kg/m3 and a dynamic viscosity of 0.0015 Pa·s [2]. This flow was modeled as implicit unsteady and laminar. RBCs were modeled as solid spheres with a diameter of 7.5 × 10−6 m and a mass density of 1098 kg/m3 [3]. These spheres were modeled to rebound from any impact with the endothelium. Blood was allowed to leave through the cut based on predefined flow splits including 30%, 50%, and 70% of flow exiting the vessel through the cut. These flow splits simulate a varying severity of injury to the vessel, while allowing the geometry to remain constant.Simulating an injury to a blood vessel introduces several challenges. In an actual blood vessel, the severity of the injury would depend on the geometry of the injury. A more severe injury to the vessel would result in more flow exiting the vessel through the cut. In a CFD analysis, changing the geometry makes it a challenge to compare results between each simulation. Instead, for this study, the geometry was constant and the amount of blood exiting the vessel through the laceration was controlled using a flow-split outlet model.In order to analyze hemodynamics in this study, three parameters were used. The first parameter was the velocity of the RBCs relative to the blood plasma. This relative velocity is a suitable indicator of the magnitude of the interaction between RBCs and the surrounding blood plasma. The second parameter used was the time average wall shear stress (TAWSS). High values of TAWSS can lead to endothelial damage [4](1)TAWSS=1T∫0T|τw|dtwhere T is the number of time steps, and τw is the wall shear stress.The second parameter, relative residence time (RRT), is useful because of its correlation to clotting. Higher values of RRT have been shown to correlate with higher rates of clotting [5]. For this reason, RRT was used to determine likelihood of clot formation in each of the simulations(2)RRT=1(1−2*OSI)*TAWSSwhereOSI=12[1−|∫0ττwdt|∫0ττwdt]The average RBC velocity was compared to the corresponding average blood plasma velocity for each simulation. The compared velocities for the 30% leak are displayed in Table 1. As expected, the blood plasma velocities are greater than the RBC velocities. The greatest relative velocity was found in the 50% simulation.In Figs. 2 and 3, TAWSS and RRT plots are displayed in order of increasing cut severity. The top vessel in each figure is the 30% leak simulation, and the bottom vessel in each figure is the 70% leak simulation.The TAWSS increased as more flow was allowed to exit through the injured portion of the vessel. As the injury becomes more severe, the likelihood that the flow will cause damage to healthy endothelial tissue increases. These results can be visualized in Fig. 2.The RRT decreased as more blood was allowed to exit through the injured geometry. In the 30% simulation, 25.4% of the endothelial surface area experienced an RRT over 0.03 m2/N. This value can be compared to the 10.0% of surface area above 0.03 m2/N experienced in the 70% simulation. The plots representing this data are shown in Fig. 3.This study shows how RBCs interact with the surrounding blood plasma and how these interactions change with respect to severity of an injury in the immediate region. It has been shown that the RBCs experience the greatest relative velocity in the 50% flow-split. The 30% flow-split experiences the least relative velocity.This study also created a model that relates RRT and TAWSS with the severity of an injury. It was found that RRT tends to decrease as the severity of an injury increases. This information shows that less severe injuries or leaks from a vessel are more likely to clot near the injured region. More severe flows are less likely to clot in the immediate region. TAWSS was determined to increase as injury severity increases. As severity of blood vessel injuries increases, the likelihood of endothelial damage due to blood flow mechanics increases. Less severe leaks are less likely to cause damage to endothelial tissue. The results of this study are to be confirmed using microchannels for fluid blood flow.Many medical devices used in the cardiovascular system such as endovascular stent grafts or drug-delivery balloons affect the blood physiology in ways that are not always self-evident. Blood cells that interact with foreign objects in the vascular system may become damaged or affected in ways that significantly affect the health of the patient. Devices or materials that are implanted in the body can damage blood cells. These occurrences can be analyzed using many of the techniques used in this study to improve the design of cardiovascular devices.