RUPTURE RISK PREDICTION OF INTRACRANIAL ANEURYSMS USING OPEN SOURCE CFD SOFTWARE

Computational Fluid Dynamics (CFD) is an important tool for simulating blood flow in intracranial aneurysms. The objective of this study is to help classify intracranial aneurysms based on data obtained from CFD simulations, so that the best treatment can be selected. We randomly selected 3 ruptured and 5 unruptured intracranial aneurysms with good quality CT angiogram (CTA). The open-source VMTK R © (Vascular Modeling Toolkit) software was used to create surface models and CFD meshes. The open-source OpenFOAM R © CFD solver was used to perform the CFD simulations and ParaView R © was used for post-processing. Typical parameters associated with aneurysm rupture, such as wall shear stress (WSS), oscillatory shear index (OSI) and WSS gradient, were evaluated to determine if they may help predict aneurysm rupture probability. We have encountered regions where the WSS remained low during the entire cardiac cycle combined with high values of OSI and regions where the WSS remained high combined high WSS gradient. We associate these regions with high risk of rupture. This allowed us to predict, with a relatively high degree of certitude, the probability of rupture of a given aneurysm. INTRODUCTION Aneurysms are arterial lesions defined as thinned and dilated regions of the arterial wall. These abnormalities can arise in different areas of the human vascular system, more commonly found in the abdominal aorta and the arteries of the brain. Cases of intracranial aneurysms usually occur in the arterial bifurcations of the called circle of Willis (Figure 1). These aneurysms represent a high risk and can lead to neurological cerebral death with present mortality rates between 40 and 50 [e.g., Hop et al., 1997]. It is estimated also that 2-3% of the world population have intracranial aneurysms [e.g., Qureshi et al., 2007]. It is reported that 85% of cases of subarachnoid hemorrhage are caused by rupture of these aneurysms [e.g., van Gijn et al., 2007]. Hop et al. [1997] concluded that fatal cases of subarachnoid hemorrhage occurred from 32 to 67% of patients and about one third of those who survived showed permanent sequels. Figure 1. Schematic figure of the circle of Willis in the human brain (MCA: middle cerebral artery, ICA: internal carotid artery). [Torii et al., 2008] Currently, there are no reliable experimental techniques for quantifying blood flow patterns in intracranial aneurysms. Measurements of hemodynamic parameters in live patients are becoming more achievable, but are still very difficult to perform. In general, experimental studies on intracranial aneurysms were performed using idealized geometries or induced aneurysms in animals [e.g., Gonzalez et al., 1992; Nakatani et al., 1991; Satoh et al., 2003]. Computational Fluid Dynamics (CFD) techniques have been widely used to simulate flow problems in intracranial aneurysms [e.g., Steinman et al., 2003; Bazilevs et al., 2009; Lu et al., 2011]. With the development of mapping techniques of the brain arteries (such as: Computational Tomography Angiography CTA) numerical simulations with real geometries of aneurysms started to be performed, thereby increasing the reliability of the results. Recent studies agree that effects of blood flow within the vessels (hemodynamic) are crucial in the development of aneurysms [e.g., Penn et al., 2011]. Some of the hemodynamic parameters usually included in these studies are: the wall shear stress (WSS), the wall tension, the hydrostatic pressure and the transmural pressure. Among these parameters, the WSS seems to be the most important one [e.g., Shojima et al., 2004; Sforza et al., 2009]. Also, Cebral and Cerrolaza [2003] studied the influence of the area and direction of the jet colliding in the aneurysm entrance and vortex formation inside the dome on the rupture of aneurysms. The parameters leading to the formation, growth and rupture of intracranial aneurysms are still poorly understood. The purpose of this work is to test some cases of intracranial aneurysms using CFD to verify the influence of hemodynamic parameters in the rupture of aneurysms. The final objective of this type of work is to create a tool to be used in medical intervention decisions. To broaden the appeal and access to other researchers of the simulation methodology, we chose to use only open source software for creating surface contours from CTA, for meshing, for the CFD simulation and for post-processing. This will allow the community to make use of the tools we developed without being burdened by commercial software issues. COMPUTATIONAL METHOD AND MATHEMATICAL MODELING Problems found in Solid and Fluid Mechanics are governed by a set of partial differential equations, obtained from basic Physics conservation principles. Given the complex nature of the governing mathematical equations it is impossible to obtain analytical solution to these equations. The problem is further complicated by the geometries involved. Thus, numerical techniques such as Finite Volume Method and Finite Element Method are required to solve them. Computer packages are designed to numerically solve the governing equations using one of the above methods. In this work, we propose to use the OpenFOAM R © (Open Field Operation and Manipulation) software to solve the numerical problem. This package is primarily a set of libraries written in C++ language that provides solvers to handle Continuum Mechanics problems. The equations governing the blood flow through arteries are the conservation of mass and the linear momentum equation, Eqs. (1) and (2), for laminar flow and considering the blood as a Newtonian fluid with constant properties, namely: density 1,000kg/m3 and kinematic viscosity 3.3x10−6m2/s.