To cite this version:Laurence A. Belfiore, M. Nazmul Karim. Tubular bioreactor models that include onsager-curie scalar cross-phenomena to describe stress-dependent rates of cell proliferation. Biophysical Chemistry, Elsevier, 2008, 135 (1-3) This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPT
AbstractThe theory of heterogeneous catalysis in chemical reactors is employed to simulate laminar flow through tubes at large mass transfer Peclet numbers in which anchorage-dependent cells (i) adhere to a protein coating on the inner surface at r = R wall , (ii) receive nutrients and oxygen from an aqueous medium via transverse diffusion toward the active wall, and (iii) proliferate in the presence of viscous shear at the cell/aqueous-medium interface. This process is modeled as convective diffusion in cylindrical coordinates with chemical reaction at the boundary, where chemical reaction describes the rate of nutrient consumption. The formalism of irreversible thermodynamics is employed to describe an unusual coupling between viscous shear, or velocity gradients at the cell/aqueousmedium interface, and rates of nutrient consumption. Linear transport laws in chemically reactive systems that obey Curie's theorem predict the existence of cross-phenomena between fluxes (i.e., scalar reaction rates) and driving forces (i.e., second-rank velocity gradient tensor) whose tensorial ranks differ by an even integer---in this case, two. This methodology for stress-dependent chemical reactions yields an additional zeroth-order contribution, via the magnitude of the velocity gradient tensor, to heterogeneous kinetic rate expressions because nutrient consumption and cell proliferation are stress-sensitive. Computer simulations of nutrient consumption suggest that bioreactor designs should consider stress-sensitive reactions when the shear-rate-based Damköhler number (i.e., defined for the first time in this study as the stress-dependent zeroth-order rate of nutrient consumption relative to the rate of nutrient diffusion toward active cells adhered to the tube wall) is greater than 10-20% of the stress-free Damköhler number. Models of bioreactor performance are presented for simple 1 st -order, simple 2 nd -order, and complex chemical kinetic rate expressions, where the latter considers adsorption/desorption equilibria via the Fowler-Guggenheim modification of the Langmuir isotherm for cell-protein docking on active sites, accompanied by cell-cell attraction. Stress sensitivity is magnified in physically realistic cell-based tubular bioreactors with complex stress-free kinet...