3D simulation of blood flow in the microcirculation

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Ζαμπέλης, Δημήτριος
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This thesis concerns hemodynamics in the microcirculation. More specifically, it studies the effect of the hematocrit, vessel diameter and shear-rate on the relative apparent viscosity and velocity profile of blood and on the thickness of the cell-free layer in straight microvessels. In this regard, the theoretical framework, upon which the abovementioned dependences are based, consists of all the fundamental hemodynamical phenomena [1], that is, the formation of the cell-free layer, the Fahraeus and Fahraeus-Lindqvist effects and the shear-thinning behavior of blood [2]. To accomplish the above, this research employs the computing framework proposed by Závodszky et al. [1]. On the one hand, the blood cells, here only the red blood cells, are explicitly modeled as deformable membranes, that consist of networks of Lagrangian surface points [3, Ch. 4] and their responses to force fields are dictated by the constitutive model found in [1]. On the other hand, the suspending medium, in this case, the blood plasma, is represented using the lattice Boltzmann method [1], [3, Ch. 4]. Then, the collective blood behavior emerges as a product of the coupling of the aforementioned cellular and liquid components that the immersed boundary algorithm achieves [1], [3, Ch. 4]. Last, it should be noted that all simulations concern blood flows in straight microvessels with circular cross-sections and that the hemodynamical features are always calculated at steady flow conditions. The final results that stem from a systematic parametric study of approximately 70 simulations are presented in three different forms. First, for all three examined hemodynamical features the corresponding data are given in proper diagrams of those features against the shear-rate for various hematocrits or vessel diameters. Second, the microstructural configurations of some representative systems are displayed and third, whenever possible, the algebraic correlations derived from the non-linear fittings on the data are proposed as well. To conclude it should be highlighted that not only all the results are in qualitative agreement with the theoretical remarks mentioned above, but the quantitative comparison also demonstrates that they are in accordance with the few available data points provided in the literature [1], [4].
Blood flow, Microcirculation, Blood viscosity, Velocity profile, Cell-free layer