MICHAEL XENOS, DIMITRIOS KARAKITSOS and DANNY BLUESTEIN

Overview

Ultrasound is the only imaging modality, apart from magnetic resonance imaging (MRI), that provides real-time functional and structural information on the beating heart. However, modeling moving cardiovascular structures is a complex process that requires three- dimensional (3D) reconstruction of two-dimensional (2D) data by fast imaging techniques (e.g., MRI) to thus yield dynamic four-dimensional (4D) views of cardiovascular pulsations. The unique 3D geometry of the cardiovascular system is partially responsible for the diversity of physiologic interactions between blood flow and cardiovascular structures. Recent advances in 3D echocardiography, cardiac computed tomography (CT), and MRI techniques have improved cardiovascular diagnostics considerably. In addition, with the advances achieved in graphics techniques for surface rendering, the potential for attaining useful information from graphics in medical imaging has emerged. Several techniques have been developed, such as the maximum intensity projection, shaded surface display, volumetric rendering, and others. The visualization tool kit (VTK) and the insight tool kit (ITK) are two examples of packages developed for performing image registration and segmentation based on ITK and VTK libraries. These open-source tool kits have an active development community that includes laboratories, institutions, and universities from around the world.^1,2

Notably, with advanced 3D cardiovascular imaging techniques, complex intraventricular and intraaortic blood flow patterns can be partially evaluated. Even sophisticated 4D MRI cannot analyze all the fine details of the miscellaneous phenomena active in a 3D field of cardiovascular flow, which may be important in patients with subtle cardiac dysfunction, or evaluate the interactions between blood flow and vascular structures, which may be captured, for example, by models predicting the evolution of aortic disorders (e.g., predicting rupture of an abdominal aortic aneurysm [AAA]). These considerations have led to the development of numerical simulation models that provide functional imaging approaches to the investigation of blood flow patterns. These models are theoretic, which is a major limitation, and thus do not provide in-vivo data. However, the latter may be integrated into the boundaries used to run numerical simulations. This chapter outlines computational fluid dynamics (CFD) and fluid structure-interaction (FSI) models used in the study of cardiovascular flow phenomena in normal and aneurysmal aortas, respectively.

Computational fluid dynamics model of normal aortic flow

Although 3D imaging techniques are invaluable in the diagnosis of aortic pathology, they do not provide detailed information on intraluminal blood flow patterns and hemodynamically driven wall stress or explain the generation of instability in the 3D aortic flow field with accompanying recirculation zones. Analysis and mapping of intraluminal blood velocity can be performed with CFD models, which use the discretized form of the nonlinear and fully coupled equations of fluid motion (Navier-Stokes equations) on a refined computational grid. CFD works by dividing the area of interest (the aorta in this example) into a large number of cells (the grid). Numerical grid generation is a branch of applied mathematics that is used for running computer-based simulations of fluid flow problems via advanced software packages. The objectives of CFD consist of developing the simulation approach, modeling the geometry and grid generation, providing a numerical solution of flow field mathematic equations, and analyzing the solution.

CFD models were used to describe the fine diversities in normal 3D rotational aortic flow: the aortic vortex.3–5 The aortic geometry (curved-shaped vessel) and preformed asymmetric flow originating from the left ventricle enable the formation of counterrotating helical vortices with associated secondary flow, which are characterized by the dimensionless Dean number. Also, the pulsatility of cardiovascular flow leads to rapid changes in inertia, limited boundary layer development, and the promotion of unstable flow.

Recently, our group used previous CFD models3–5 and patient-derived hemodynamic and transesophageal echocardiography data, which were used as boundaries, to run aortic vortex numerical simulations.6 An example of a simplified CFD model of normal aortic flow that integrates a swirling component of the inlet velocity at the root of the ascending aorta is illustrated in Figure 35-1