Quantification of the blood mixing in the left ventricle using Finite Time Lyapunov Exponents

Thrombus formation is one of the major complications in myocardial infarction. One of the causes is known to be the regional hemostasis, i.e. the presence of zones where the intraventricular flow is characterised by low stretching of the fluid elements and low mixing. Though Finite Time Lyapunov Exponents (FTLE) have been used both in vivo and in vitro to identify the overall features of cardiovascular flows by means of the Lagrangian Coherent Structures (LCS), they have been introduced in fluid dynamics as descriptors of mixing. Therefore, we investigate the alteration of the intraventricular mixing in an infarcted left ventricle by means of FTLE, looking for the signature of regional hemostasis. The study is carried out on 3D numerical simulations: a ventricle dyskinetic and dilated because of an ischemic pathology is compared to a healthy one and to another with a deviated inlet velocity profile, simulating the presence of a Mechanical Prosthetic Valve in anatomical position. The LCS analysis highlighted the key vortical structures of the flow and their evolution, revealing how they are affected by changes of the ventricle geometry and mobility. Afterwards, the FTLE statistics showed a similar behaviour in the healthy and deviated inlet cases, where hemostasis was not observed, although flow patterns were very different to each other. Conversely, the infarcted ventricle exhibited significantly different values of FTLE statistics, indicating a much lower mixing that is related to the presence of a stagnating region close to the apex. Such differences suggest that FTLE can be considered a potentially useful tool for the characterisation of the mixing properties of the intraventricular flow and, in particular, for the identification of regional hemostasis. Therefore, further investigations are needed to test the sensitivity and specificity of FTLE statistics to the severity of the pathology.