Non-Linear or Quasi-Linear Viscoelastic Property of Blood for Hemodynamic Simulations

Abstract

Hemodynamic simulations with the complex rheology of blood is still a challenge. They can be used to obtain an auxiliary clinical tool, as close as possible to reality, with great potential for the development of preventive measures, diagnosis and treatment of cardiovascular diseases. A wide range of models defining the rheological behavior of blood, ranging from the Newtonian to the purely shearthinning non-Newtonian models have been used by many authors. However, in vessels, such as carotid or coronary arteries, the validity of such simplified models for blood is not completely clear, mainly in stenotic or aneurysm cases - regions of high velocity gradients. It iswell-known, from literature, that blood has complex rheology, behaving as a viscoelastic non-Newtonian fluid due to the storage and release of elastic energy from red blood cells aggregates. Therefore, authors of the present work implemented the viscoelastic property of blood, in UDFs of Ansys® software, in order to simulate the most accurate hemodynamics. Afterwards, the velocity contours, in the middle plane of a 3D idealized coronary artery, were obtained considering the purely shear-thinning model, Carreau model, and two viscoelastic non-Newtonian models. Using the Generalized Oldroyd-B, a quasi-linear model, the viscoelastic effects are not highlighted. Comparing results taking into account the multi-mode Giesekus, a non-linear model, and Carreau model, differences are significant and equal to 0.20 m/s under a maximum velocity of 1.40 m/s (14.3%). Using the multi-mode Giesekus model, the viscoelastic effects are pronounced in addition to the shear-thinning, mainly in regions with high velocity gradients as the stenotic region.