Numerical Modelling of Cell Distribution in Blood Flow

Abstract

Properties of blood cells and their interaction determine their distribution in flow. It is observed experimentally that erythrocytes migrate to the flow axis, platelets to the vessel wall, and leucocytes roll along the vessel wall. In this work, a three-dimensional model based on Dissipative Particle Dynamics method and a new hybrid (discrete-continuous) model for blood cells is used to study the interaction of erythrocytes with platelets and leucocytes in flow. Erythrocytes are modelled as elastic highly deformable membranes, while platelets and leucocytes as elastic membranes with their shape close to a sphere. Separation of erythrocytes and platelets in flow is shown for different values of hematocrit. Erythrocyte and platelet distributions are in a good qualitative agreement with the existing experimental results. Migration of leucocyte to the vessel wall and its rolling along the wall is observed.

Methods of Blood Flow Modelling

“…Figure 3 shows the scheme of the numerical experiment and comparison with experiments for the three models. Nonlinear surface element model (Model III) gives the best agreement with the experiment [15]. Other two models give approximately linear dependence of the diameters on force, and differ from the experimental dependence.…”

“…Erythrocytes are concentrated more to the axis of the flow (Fähraeus -Lindqvist effect) and push platelets and leucocytes to the vessel walls. Examples of numerical simulations of blood flow with erythrocytes and platelets are shown in Figure 4 for different values of hematocrit [15]. The diameter of cylinder is 27 µm, its length is 100 µm (only a part of it is shown).…”

“…The experiment provides the values of transversal and longitudinal diameters of a cell under two stretching loads [127]. In order to determine parameters of our erythrocyte model, this experiment can be reproduced in numerical simulations [15,47,63]. Consider a RBC with the initial biconcave shape.…”

“…It is applied to the vertices of triangles in the direction normal to the surface. Another erythrocyte model that combines the continuous description of an elastic body for surface elements and a spring model for the angle between these elements is suggested in [15]. The membrane is represented as a two-dimensional surface that consists of elastic triangular elements.…”

“…It is practically incompressible and resistant to the change of surface area and planar shear deformation. It can be modelled as a two-dimensional network of particles [15,62,63,63,64,97,138,139]. They are connected by springs modelled by Hooke's law to form an irregular polyhedron with triangular faces.…”