2D Arbitrary Lagrangian-Eulerian (ALE) Model of Blood Flow in the Left Ventricle (LV) of the Heart

Current flow pattern simulation in the left ventricle (LV) requires method to tackle the interaction between the moving blood (fluid) and the deforming valves (structure). This fluid-structure interaction is the mechanism behind continuous cardiac activities. Capturing essence of these mechanics often involves solving complex mathematical equations which demands high computing resources. Limiting computing power has resulted in the need to optimize the degree of freedom (DOF) stemming from three-dimensional (3D) geometries. Many heart simulation projects aims to develop a 3D model for the reason that in three dimensional, the true motion of the heart muscle is better depicted. Unfortunately, higher DOF in 3D leads to difficulties in the equations modeling. For this reason, the complex equations, which in most cases derived from the differential domains; the partial differential equations (PDEs) and ordinary differential equations (ODEs), are usually modeled first on two-dimensional (2D) geometries. The focus of these prototypes is to ensure the equation modeling essentially captures the core of the fluid-structure interaction in the heart and enhancement of the prototype into 3D is usually done later to produce better graphical simulation.

In this research, the dynamic movement of heart valves and the blood flow pattern in the LV is studied using advanced numerical-computational technique. This approach is known as the Arbitrary Lagrangian-Eulerian (ALE) and is introduced by means of a mesh movement method in a finite element environment. The ALE uses two sets of reference systems; the Eulerian reference system to track the moving blood and the Lagrangian reference system to handle the deforming valves. A working prototype of the ALE model in 2D is developed and results pertaining to the velocity pattern prior to periodicity mechanics of the valves in the LV are presented graphically in a time-step fashion.