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Mathematical Biosciences and Engineering (MBE)
 

Monte carlo simulation of heterotypic cell aggregation in nonlinear shear flow

Pages: 683 - 696, Volume 3, Issue 4, October 2006      doi:10.3934/mbe.2006.3.683

 
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Jiakou Wang - Department of Mathematics, Penn State University, University Park, PA 16802, United States (email)
Margaret J. Slattery - Department of Bioengineering, Penn State University, University Park, PA 16802, United States (email)
Meghan Henty Hoskins - Department of Bioengineering, Penn State University, University Park, PA 16802, United States (email)
Shile Liang - Department of Bioengineering, Penn State University, University Park, PA 16802, United States (email)
Cheng Dong - Department of Bioengineering, Penn State University, University Park, PA 16802, United States (email)
Qiang Du - Department of Mathematics, Pennsylvania State University, University Park, PA 16802, United States (email)

Abstract: In this paper, we develop a population balance model for cell aggregation and adhesion process in a nonuniform shear flow. Some Monte Carlo simulation results based on the model are presented for the heterotypic cell-cell collision and adhesion to a substrate under dynamic shear forces. In particular, we focus on leukocyte (PMN)-melanoma cell emboli formation and subsequent tethering to the vascular endothelium (EC) as a result of cell-cell aggregation. The simulation results are compared with the results of experimental measurement. Discussions are made on how we could further improve the accuracy of the population balance type modelling.

Keywords:  cell aggregation, nonlinear shear flow, tumor metastasis, Smolu-chowski equation, population balance model, numerical simulation, parallel plate flow chamber experiments.
Mathematics Subject Classification:  92C35,92C10,92-08.

Received: May 2006;      Accepted: June 2006;      Published: August 2006.