Red blood cell and platelet diffusivity and margination in the presence of cross-stream gradients in blood flows (original) (raw)

Large scale simulation of red blood cell aggregation in shear flows

Journal of Biomechanics, 2013

Aggregation of highly deformable red blood cells (RBCs) significantly affects the blood flow in the human circulatory system. To investigate the effect of deformation and aggregation of RBCs in blood flow, a mathematical model has been established by coupling the interaction between the fluid and the deformable solids. The model includes a three-dimensional finite volume method solver for incompressible viscous flows, the combined finite-discrete element method for computing the deformation of the RBCs, a JKR model-Johnson, Kendall and Roberts (1964-1971) (Johnson et al., 1971) to take account of the adhesion forces between different RBCs and an iterative direct-forcing immersed boundary method to couple the fluid-solid interactions. The flow of 49,512 RBCs at 45% concentration under the influence of aggregating forces was examined, improving the existing knowledge on simulating flow and structural characteristics of blood at a large scale: previous studies on the particular issue were restricted to simulating the flow of 13,000 aggregative ellipsoidal particles at a 10% concentration. The results are in excellent agreement with experimental studies. More specifically, both the experimental and the simulation results show uniform RBC distributions under high shear rates (60-100/s) whereas large aggregation structures were observed under a lower shear rate of 10/s. The statistical analysis of the simulation data also shows that the shear rate has significant influence on both the flow velocity profiles and the frequency distribution of the RBC orientation angles.

Numerical Modelling of Cell Distribution in Blood Flow

Mathematical Modelling of Natural Phenomena, 2014

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.

Numerical simulation of blood flows with non-uniform distribution of erythrocytes and platelets

Russian Journal of Numerical Analysis and Mathematical Modelling, 2000

Blood cell interactions present an important mechanism in many processes occurring in blood. Due to different blood cell properties, cells of different types behave differently in the flow. One of observed behaviours is segregation of erythrocytes, which group near the flow axis, and platelets, which migrate towards the blood vessel wall. In this work, a three dimensional model based on Dissipative Particle Dynamics method is used to study the interaction of erythrocytes and platelets in a flow inside a cylindrical channel. The erythrocytes are modelled as elastic highly deformable membranes, while platelets are modelled as elastic spherical membranes which tend to preserve their spherical shape. As the result of modelling, the separation of erythrocytes and platelets in a cylindrical vessel flow is shown for vessels of different diameters. Erythrocyte and platelet distribution profiles in vessel cross-section are in good agreement with existing experimental results. The described 3-D model can be used for further modelling of blood flow-related problems.

Numerical simulation of lateral migration of red blood cells in Poiseuille flows

International Journal for Numerical Methods in Fluids, 2012

A spring model is applied to simulate the skeleton structure of the red blood cell (RBC) membrane and to study the RBC rheology in two-dimensional Poiseuille flows using an immersed boundary method. The lateral migration properties of the cells in Poiseuille flows have been investigated. The simulation results show that the rate of migration toward the center of the channel depends on the swelling ratio and the deformability of the cells. We have also combined the above methodology with a fictitious domain method to study the motion of RBCs in a two-dimensional micro-channel with a constriction with an application to blood plasma separation. 2012; 68:1 -140 393 8 L. SHI, T.-W. PAN AND R. GLOWINSKI

Computational model of whole blood exhibiting lateral platelet motion induced by red blood cells

International Journal for Numerical Methods in Biomedical Engineering, 2010

An Immersed Boundary method is developed in which the fluid's motion is calculated using the lattice Boltzmann method. The method is applied to explore the experimentally-observed lateral redistribution of platelets and platelet-sized particles in concentrated suspensions of red blood cells undergoing channel flow. Simulations capture red-blood-cell-induced lateral platelet motion and the consequent development of a platelet concentration profile that includes an enhanced concentration within a few microns of the channel walls. In the simulations, the near-wall enhanced concentration develops within approximately 400 msec starting from a random distribution of red blood cells and a uniform distribution of platelet-sized particles.

The effects of non-Newtonian viscosity on the deformation of red blood cells in a shear flow

2005

Submitted for the DFD05 Meeting of The American Physical Society The effects of non-Newtonian viscosity on the deformation of red blood cells in a shear flow JULDEH SESAY, FOLUSO LADEINDE, SUNY Stony Brook-The analyses of the effects of non-Newtonian viscosity on the membrane of red blood cells (RBCs) suspended in a shear flow are presented. The specific objective is to investigate the mechanical deformation on the surfaces of an ellipsoidal particle model. The hydrodynamic stresses and other forces on the surface of the particle are used to determine the cell deformation. We extended previous works, which were based on the Newtonian fluid models, to the non-Newtonian case, and focus on imposed shear rate values between 1 and 100 per second. Two viscosity models are investigated, which respectively correspond to a normal person and a patient with cerebrovascular accident (CVA). The results are compared with those obtained assuming a Newtonian model. We observed that the orientation of the cell influences the deformation and the imposed shear rate drives the local shear rate distribution along the particle surface. The integral particle deformation for the non-Newtonian models in the given shear rate regime is higher than that for the Newtonian reference model. Finally, the deformation of the cell surface decreases as the dissipation ratio increases.

A discrete-particle model of blood dynamics in capillary vessels

Journal of Colloid and Interface Science, 2003

We investigate the physical mechanism of aggregation of red blood cells (RBC) in capillary vessels, using a discrete particle model. This model can accurately capture the scales from 0.001µm to 100µm, far below the scales, which can be modeled numerically with classical computational fluid dynamics. We use a discrete-particle model in 3D for modeling the flow of plasma and RBCs in a capillary tube. The two situations involving necking and no necking have been considered. The flexible viscoelastic red blood cells and the walls of the elastic vessel are made up of solid particles held together by elastic harmonic forces. The blood plasma is represented by a system of dissipative fluid particles. We have simulated the flow of cells of different shapes, such as normal and "sickle" cells. The cells coagulate in spite of the absence of adhesive forces in the model. The total number of fluid and solid particles used ranges from 1 to 3 million. We conclude that aggregation of red blood cells in capillary vessels is stimulated by depletion forces and hydrodynamic interactions. The cluster of "sickle" cells formed in the necking of the conduit efficiently decelerates the flow, while normal cells can pass through. These qualitative results from numerical simulations accord well with laboratory findings.

Large deformation of red blood cell ghosts in a simple shear flow

Physics of Fluids, 1998

Red blood cells are known to change shape in response to local flow conditions. Deformability affects red blood cell physiological function and the hydrodynamic properties of blood. The immersed boundary method is used to simulate three-dimensional membrane-fluid flow interactions for cells with the same internal and external fluid viscosities. The method has been validated for small deformations of an initially spherical capsule in simple shear flow for both neo-Hookean and the Evans-Skalak membrane models. Initially oblate spheroidal capsules are simulated and it is shown that the red blood cell membrane exhibits asymptotic behavior as the ratio of the dilation modulus to the extensional modulus is increased and a good approximation of local area conservation is obtained. Tank treading behavior is observed and its period calculated.

Computation of Blood Flows Accounting for Red-Blood Cell Aggregation/Fragmentation

Proceeding of Seventh International Symposium on Turbulence and Shear Flow Phenomena

This article presents flows computed in non-trivial geometries while accounting for the contribution of the red cells to the Cauchy stress using the haemorheological model of Owens (2006), Owens and Fang (2006). In this model the local shear viscosity is determined in terms of both the local shear rate and the average rouleau size, with the latter being the solution of an advection-reaction equation. The model describes the viscoelastic, shear-thinning and hysteretic behaviour of flowing blood, and includes non-local effects in the determination of the blood viscosity and stresses. We present numerical results for a two dimensional aneurytic channel under both steady and pulsatile flow conditions. We compare the flows for two sets of physiologically relevant Reynolds and Deborah numbers. A 3-D flow in a section of a patientspecific carotid artery is also presented.