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.

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