On the correlation between Eulerian and Lagrangian Hemostasis Indices in the Left Atrium

Eulerian indices derived from wall-shear stress (WSS) and kinetic energy (KE) are often used to study hemostasis in the cardiac chambers. The calculation of these indices is convenient as it does not require integrating over multiple heartbeats. The averaged WSS, oscillatory shear index, relative residence time (RRT), and endothelial cell activation potential are among the most common. Also, KE below a certain threshold is used to indicate blood stasis. Most of these indices were conceptualized for tube-shaped vessels where low, oscillatory WSS and KE reveal disturbed-flow regions of recirculation and stasis. However, flow in the left atrium (LA) is highly 3D, and the correlation between Lagrangian and Eulerian indices has not yet been analyzed, let alone established. Here, we examine the correlation between Eulerian and Lagrangian indices in the LA, focusing on the left atrial appendage (LAA), where clots form preferentially. Our results show a low to moderate correlation between Eulerian indices and their Lagrangian counterparts (e.g., RRT and actual residence time), suggesting that care must be exercised when interpreting Eulerian indices in the LA and the LAA.