A Preliminary Study of 2D Leaflet Motions in the Left Ventricle using Arbitrary Lagrangian – Eulerian (ALE) Approach

Abstract

Current flow pattern simulation in the left ventricle requires method to tackle the interaction between the moving blood flow and the deforming valves structures. Capturing essence of these mechanics are feasible with the use of mathematical formulations derived from the differential domains. The degree of complexity stemming from these equations often requires high computing resources. For this reason, the equations are first modeled on two-dimensional (2D) geometries to optimize the degree of freedom and limit the computing power. Enhancement of the prototype into 3D is usually done later to produce better graphical presentation. In this research, the dynamic movement of the heart valves and the blood flow pattern in the left ventricle is studied using advanced numerical-computational technique known as the Arbitrary Lagrangian-Eulerian (ALE). The ALE uses two sets of reference frames; the Eulerian reference frame to tracks the flowing blood and the Lagrangian reference frame to handle the deforming leaflets. An arbitrary grid is used as base for the reference frames to compute simulations of the fluid-structure interaction A working prototype of the ALE model depicting the leaflet motions in 2D is developed and results pertaining to the velocity pattern prior to periodicity mechanics of the leaflets are presented in a time-step fashion.