Novel processing of Doppler-echocardiography data was used to study blood transport in the left ventricle (LV) of 6 patients with dilated cardiomyopathy and 6 healthy volunteers. Bi-directional velocity field maps in the apical long axis of the LV were reconstructed from color-Doppler echocardiography. Resulting velocity field data were used to perform trajectory-based computation of Lagrangian coherent structures (LCS). LCS were shown to reveal the boundaries of blood injected and ejected from the heart over multiple beats. This enabled qualitative and quantitive assessments of blood transport patterns and residence times in the LV. Quantitative assessments of stasis in the LV are reported, as well as characterization of LV vortex formations from E-wave and A-wave filling.

Platelet activation is a precursor for blood clotting, which plays leading roles in many vascular complications and causes of death. Platelets can be activated by chemical or mechanical stimuli. Mechanically, platelet activation has been shown to be a function of elevated shear stress and exposure time. These contributions can be combined by considering the cumulative stress or strain on a platelet as it is transported. Here we develop a framework for computing a hemodynamic-based activation potential that is derived from a Lagrangian integral of strain rate magnitude. We demonstrate that such a measure is generally maximized along, and near to, distinguished material surfaces in the flow. The connections between activation potential and these structures are illustrated through stenotic flow computations. We uncover two distinct structures that may explain observed thrombus formation at the apex and downstream of stenoses. More broadly, these findings suggest fundamental relationships may exist between potential fluid mechanic pathways for mechanical platelet activation and the mechanisms governing their transport.

It has become increasingly clear that the dynamics of the left ventricle (LV) plays a major role in dictating overall cardiac health. Phase-contrast magnetic resonance imaging (PCMRI) and Doppler-ultrasound echocardiography can measure flow characteristics inside the human left ventricle in vivo, including diagnostic data useful for evaluating pathological conditions such as cardiomyopathies. Studying these flow patterns is a potential avenue for heart failure diagnosis. Traditional studies based on Eulerian measures computed from instantaneous velocity data, e.g. streamlines, vorticity, Q-criterion, etc., can be insufficient or unreliable to fully understand unsteady blood flow behavior. We used the Finite-Time Lyapunov Exponent (FTLE) approach to compute Lagrangian coherent structures (LCS) to gain insight into how blood is transported inside the LV. LCS can be thought of as special moving boundaries in the flow that partition regions with different dynamics, and whose coordinated motion organizes transport and mixing.

As platelets are transported they are continuously stretched, compressed and sheared by local gradients in the flow. Exposure to elevated gradients can cause platelets to actively react with conformational, chemical and enzymatic responses, i.e. becoming activated. Once switched to the activated state, platelets perform multifaceted roles to orchestrate clotting. Mechanically-induced platelet activation under pathological conditions has been studied since the late 1970s. This work builds on [1], which introduced a trajectory-based level of activation parameter for platelets, and [2] describing coherent structures in cardiovascular flow. We introduce a new direction-independent Lagrangian measure. This measure is introduced as an activation potential in two senses. First, it provides a measure of mechanical strain, which has been shown to have the potential to activate platelets. Second, it is plotted at the initial location of the platelets. This latter condition is subtle, but it enables us to uncover an interesting observation that locations of highest activation potential tend to occur along structures that have important implications to the transport topology.

No abstract