In vivo characterization of Lagrangian Coherent Structures Using Lagrangian Descriptors: Application to Left Ventricular flows

Despite the availability of in vivo, instantaneous, and three-dimensional intracardiac flow data, their clinical analysis from a Lagrangian perspective remains limited due to their high computational cost. As an example, identifying Lagrangian coherent structures (LCS) in cardiac flows is not routinely performed in clinical settings despite their ability to identify mixing and stagnation regions along with locations of elevated shear stresses. Here, we explore a recently developed approach, “Lagrangian descriptors”, which quantifies the finite time Euclidean arc-length of Lagrangian trajectories released from a grid of initial positions. Through the evaluated arc-lengths of a set of trajectories, signatures of the LCS (computed from the same initial condition) are captured. Notably, the Lagrangian descriptor approach extracts the LCS within the flow at least five times faster than the common geometrical approach (i.e., using finite-time Lyapunov exponents). In this work, we apply, for the first time, the Lagrangian descriptors approach to in vivo 4D-MRI velocity fields inside left ventricles. The results show the ability of this approach to rapidly reveal the LCS within the left ventricle and how their organization can be altered under healthy and pathological conditions.