The present focus of heart flow studies is largely based on flow within the left ventricle and how this flow changes when subject to disease. However, despite recent advancements, a simple tractable model of even healthy left ventricular flow has not been produced and made available. Reduced-order modeling techniques, such as proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD), offer an effective means of expressing the large datasets obtained from experiments or numerical simulations using low-dimensional models. While POD and DMD are often used to identify coherent structures in fluid dynamics, their use as a modeling tool has not found much merit in the cardiovascular flow community. In this work, we use POD and DMD to construct reduced-order models for a healthy left ventricular flow as well as for that under the influence of a particular disease shown to exhibit rich and unique intraventricular fluid dynamics, namely, aortic regurgitation (a leaking aortic valve). The performance of the two methods in reconstructing the intraventricular flows and derived quantities is evaluated, and the selected reduced-order models are made available.

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.

This experimental in vitro work investigates material transport properties in a model left ventricle in the case of aortic regurgitation, a valvular disease characterized by a leaking aortic valve and consequently double-jet filling within the elastic left ventricular geometry. This study suggests that material transport phenomena are strongly determined by the motion of the counterrotating vortices driven by the regurgitant aortic and mitral jets. The overall particle residence time appears to be significantly longer with moderate aortic regurgitation, attributed to the dynamics resulting from the timing between the onset of the two jets. Increasing regurgitation severity is shown to be associated with higher frequencies in the time-frequency spectra of the velocity signals at various points in the flow, suggesting nonlaminar mixing past moderate regurgitation. Additionally, a large part of the regurgitant inflow is retained for at least one cardiac cycle. Such an increase in particle residence time accompanied by the occurrence and persistence of a number of attracting Lagrangian coherent structures presents favorable conditions and locations for activated platelets to agglomerate within the left ventricle, potentially posing an additional risk factor for patients with aortic regurgitation.