Lagrangian-averaged vorticity deviation of spiraling blood flow in the heart during isovolumic contraction and ejection phases

The formation of vortex rings in the left ventricular (LV) blood flow is a mechanism for optimized blood transport from the mitral valve inlet to aortic valve outlet, and the vorticity is an important measure of a well-functioning LV. However, due to lack of quantitative methods, the process of defining the boundary of a vortex in the LV and identifying the dominant vortex components has not been studied previously. The Lagrangian-averaged vorticity deviation (LAVD) can enable us to compute the trajectory integral of the normed difference of the vorticity from its spatial mean. Therefore, in this work, we have employed LAVD to identify the Lagrangian vortices and Eulerian vortices for measuring the vortex volume and vorticity in the LV blood flow. We found that during the LV ejection period, the positive (counterclockwise) and negative (clockwise) vorticity of patients are consistently stronger than those of the healthy groups, and the counterclockwise vortex volume of healthy groups (0.84+0.26 ml) is greater than that of patients (0.55+0.28 ml) during the pre-ejection period. Then, during the middle ejection phase, the counterclockwise vortex ring volume of patients (1.89+0.36 ml) exceeds that of healthy groups (1.38+0.43 ml). Finally, during the end-ejection period, the counterclockwise vortex ring volume of healthy subjects (0.61+0.17 ml) is the same as that of patients (0.60+0.19 ml). The results presented in this paper can provide new insights into the blood flow patterns within the LV. It can accurately indicate the role of vortices and vorticity values in intra-LV flow, and portray how cardiomyopathy (and its distorted contractile mechanism) can affect intra-LV flow patterns and mitigate adequate LV outflow.