A Numerical Study of Pulsatile Flow Through a Hollow Fiber Cartridge:
Growth Factor-Receptor Binding and Dissociation Analysis

February 23, 2009

Changjiang Zhang
Laboratory for High Performance Scientific Computing and Computer Simulation
Department of Computer Science
University of Kentucky
Lexington, KY 40506-0046, USA

Wensheng Shen
Department of Computational Science
SUNY Brockport
BRockport, NY 14420, USA

Kimberly Forsten-Williams
Department of Chemical Engineering
Virginia Polytechnic Institute & State University
Blacksburg, VA 24061, USA

Michael Fannon
Department of Ophthamology and Visual Sciences
University of Kentucky
Lexington, KY 40506, USA

Jun Zhang
Laboratory for High Performance Scientific Computing and Computer Simulation
Department of Computer Science
University of Kentucky
Lexington, KY 40506-0046, USA

Abstract

This paper presents a numerical solution to describe growth factor-receptor binding under flow through hollow fibers of a bioreactor. The multi-physics of fluid flow, the kinetics of fibroblast growth factor (FGF-2) binding to its receptor (FGFR) and heparan sulfate proteoglycan (HSPG) and FGF-2 mass transport is modeled by a set of coupled nonlinear partial differential equations (PDEs) and coupled nonlinear ordinary differential equations (ODEs). A finite volume method is used to discretize the PDEs. The ODEs are solved by a stiff ODE solver CVODE. Overall, second order accuracy in time and space is achieved with the second order implicit Euler scheme. In order to obtain a reasonable accuracy of the binding and dissociation from cells, a uniform mesh is used. To handle pulsatile flow, several assumptions are made including neglecting any entrance effects and an analytical solution for axial velocity within the fibers is obtained. Qualitative and quantitative analysis are presented. Computational results and experimental measurements are compared and observed to agree quite well, indicating that the simulation model and methods could be used as a complementary and even predictable tool for the study of biochemical reactions in a similar flow environment.


Key words: Multigrid, Finite volume, Navier-Stokes equation, Fibroblast growth factor, Mass transport, Biological system.

Mathematics Subject Classification:


Download the PDF file zhang1.pdf.
Technical Report CMIDA-HiPSCCS 014-09, Department of Computer Science, University of Kentucky, Lexington, KY, 2009.

This research work was supported in part by NIH under grant R01-HL086644-01, in part by NSF under grants CCF-0727600 and CCF0527967.