BIOPHYSICAL THEORY AND MODELING |
Mesoscale Simulation of Blood Flow in Small Vessels
Prosenjit Bagchi 1*
1 Rutgers University
* To whom correspondence should be addressed. E-mail: pbagchi{at}jove.rutgers.edu.
Submitted on August 9, 2006
Revised on September 7, 2006
Accepted on 28 November 2006
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Abstract |
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Computational modeling of blood flow in microvessels with internal diameter 20--500 µm is a major challenge. It is because blood in such vessels behaves as a multiphase suspension of deformable particles. A continuum model of blood is not adequate if the motion of individual red blood cell in the suspension is of interest. At the same time, multiple cells, often a few thousands in number, must also be considered to account for cell-cell hydrodynamic interaction. Moreover, the red blood cells (RBC) are highly deformable. Deformation of the cells must also be considered in the model, as it is a major determinant of many physiologically significant phenomena, such as formation of a cell-free layer, and the Fahraeus-Lindqvist effect. In this paper, we present two dimensional computational simulation of blood flow in vessels of size 20--300 µm at discharge hematocrit of 10--60% taking into consideration the particulate nature of blood and cell deformation. The numerical model is based on the immersed boundary method, and the red blood cells are modeled as liquid capsules. A large RBC population comprising of as many as 2500 cells are simulated. Migration of the cells normal to the wall of the vessel and the formation of the cell-free layer are studied. Results on the trajectory and velocity traces of the RBCs, and their fluctuations are presented. Also presented are the results on the plug flow velocity profile of blood, the apparent viscosity, and the Fahraeus-Lindqvist effect. The numerical results also allow us to investigate the variation of apparent blood viscosity along the cross-section of a vessel. The computational results are compared with the experimental(1-4). To the best of our knowledge, this paper presents the first simulation to simultaneously consider a large ensemble of red blood cells and the cell deformation.
Key Words:
Fahraeus-Lindqvist effect, apparent viscosity of blood, cell-free layer, erythrocyte, hydrodynamics, rheology
