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Influence of fluid rheology on blood flow haemodynamics in patient-specific arterial networks of varied complexity - in-silico studies

Tyfa Zbigniew, Reorowicz Piotr, Obidowski Damian, Jóźwik Krzysztof

Acta Mechanica et Automatica

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2024

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Vol. 18, no. 1

8--21

EN

Results obtained with computational fluid dynamics (CFD) rely on assumptions made during a pre-processing stage, including a mathematical description of a fluid rheology. Up to this date there is no clear answer to several aspects, mainly related to the question of whether and under what conditions blood can be simplified to a Newtonian fluid during CFD analyses. Different research groups present contradictory results, leaving the question unanswered. Therefore, the objective of this research was to perform steady-state and pulsatile blood flow simulations using eight different rheological models in geometries of varying complexity. A qualitative comparison of shear- and viscosity-related parameters showed no meaningful discrepancies, but a quantitative analysis revealed significant differences, especially in the magnitudes of wall shear stress (WSS) and its gradient (WSSG). We suggest that for the large arteries blood should be modelled as a non-Newtonian fluid, whereas for the cerebral vasculature the assumption of blood as a simple Newtonian fluid can be treated as a valid simplification.

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Development of multi-phase models of blood flow for medium-sized vessels with stenosis

Kopernik Magdalena, Tokarczyk Paweł

Acta of Bioengineering and Biomechanics

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2019

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Vol. 21, no. 2

63--70

EN

The purpose of the work was to develop two-phase non-Newtonian blood models for medium-sized vessels with stenosis using power law and Herschel–Bulkley models. Methods: The blood flow was simulated in 3D models of blood vessels with 60% stenosis. The Ansys Fluent software was applied to implement the two-phase non-Newtonian blood models. In the present paper, the mixture model was selected to model the two phases of blood: plasma and red blood cells. Results: Simulations were carried out for four blood models: a) single-phase non-Newtonian, b) two-phase non-Newtonian, c) two-phase Herschel–Bulkley with yield stress 0 mPa, and d) two-phase Herschel–Bulkley with yield stress 10 mPa for blood plasma, while flow took place in vessel with stenosis 60%. Presentation of results in this paper shows that stenosis can substantially affect blood flow in the artery, causing variations of velocity and wall shear stress. Thus, the results in the present paper are maximum values of blood velocity and wall shear stress, profiles and distributions of blood velocity and wall shear stress computed for single- and two-phase blood models for medium-sized vessels with stenosis. Conclusions: For the two-phase blood models the influence of initial velocity on blood flow in the stenosis zone is not observed, the velocity profiles are symmetric and parabolic. Contrary, for the single phase non-Newtonian blood model, the velocity profile is flat in the stenosis zone and distribution of velocity is disturbed just behind the stenosis zone. The shapes of wall shear stress profiles for twophase blood models are similar and symmetric in the center of stenosis. The biggest differences in maximum values of velocities and wall shear stress are observed between single phase non-Newtonian power law and Herschel–Bulkley blood models. The comparison of the obtained results with the literature indicates that the two-phase Herschel–Bulkley model is the most suitable for describing flow in medium-sized vessels with stenosis.

3

Modelling of blood thrombosis at microscopicand mesoscopic scales

Kopernik M.

Computer Assisted Methods in Engineering and Science

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2018

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Vol. 25, no. 1

21--45

EN

Blood coagulation at the place of the complete severing of a vessel or puncturing of a vessel sidewall is usually a beneficial reaction, as it protects the body from bleeding and maintains hemostasis, while the formation of a blood clot inside the blood vessel is a pathological phenomenon, which is highly dangerous, and sometimes leads to serious complications. In this paper, two scales of modelling blood thrombosis will be introduced using numerical methods and fluid dynamics. The meso-scale model of the flow is described by Navier-Stokes equations and the blood thrombosis model is based on equations of transport and diffusion. The equations describing levels of concentrations of factors responsible for blood coagulation can be implemented into a solver solving Navier-Stokes equations, what will enable simulation of blood flow and estimation of the risk of thrombus formation related to flow conditions. The proposed micro-scale model is using molecular dynamics to simulate interactions between blood cells and vascular walls. An effective combination of both models is possible thanks to the introduction of the multiple-time stepping algorithm, which enables a full visualization of blood flow, coupling molecular interaction with the fluid mechanics equation. The goal of the paper is to present the latest literature review on the possibilities of blood coagulation modelling in two scales and the main achievements in blood thrombosis research: the key role of transport and experimental background.