Extracting Lagrangian coherent structures in cardiovascular flows using Lagrangian descriptors

Abstract

In cardiovascular flows, Lagrangian coherent structures have been used to explore the skeleton of blood transport. Revealing these transport barriers is instrumental to quantify the mixing and stagnation of blood as well as to highlight locations of elevated strain rate on blood elements. Nevertheless, the clinical use of Lagrangian coherent structures in cardiovascular flows is rarely reported due largely to its non-intuitive nature and computational expense. Here, we explore a recently developed approach called "Lagrangian descriptors,"which quantifies the finite time Euclidean arc length of Lagrangian trajectories released from a grid of initial positions. Moreover, the finite time arc lengths of a set of trajectories capture signatures of Lagrangian coherent structures computed from the same initial condition. Remarkably, the Lagrangian descriptors approach has the most rapid computational performance among all its Lagrangian counterparts. In this work, we explore the application of Lagrangian descriptors for the first time in cardiovascular flows. For this purpose, we consider two in vitro flow models studied previously by our group: flow in an abdominal aortic aneurysm and that in a healthy left ventricle. In particular, we will demonstrate the ability of the Lagrangian descriptors approach to reveal Lagrangian coherent structures computed via the classical geometrical approach, though at a significantly reduced computational cost.