The Modeling of the Heart and the Aortic Arch applying Differential Geometrical Method and Simulation of Blood Flow

Abstract

The aorta is the largest artery in the body. It consists of the ascending aorta that leaves the left ventricle, the aortic arch where it curves about 180°, and the descending aorta. Three prominent branches to the head and upper limbs leave the aortic arch. In addition to this complex configuration, it was recently pointed out that the centerline of the aortic arch does not lie in a plane, and has a three dimensional (3D) distortion. This distortion induces very strong deviation of the 3D structure of the blood flow from that usually assumed to occur in flows in simple curved pipes (Caro et al. 1996). This 3D flow structure is thought to be responsible for some serious aortic diseases, including aortic aneurysms. It has been reported that the flow in a real human aorta is not the well-known twin vortex-type symmetrical secondary flow that is well established theoretically and experimentally for a simple curved pipe. Kilner et al. (1993) observed a single helical and retrograde secondary flow pattern by Magnetic Resonance Imaging (MRI).