Stress-sensitive nutrient consumption via steady and non-reversing dynamic shear in continuous-flow rotational bioreactors

Stress-sensitive biological response is simulated in a modified parallel-disk viscometer that implements steady and unidirectional dynamic shear under physiological conditions. Anchorage-dependent mammalian cells adhere to a protein coating on the surface of the rotating plate, receiving nutrients and oxygen from an aqueous medium that flows radially and tangentially, accompanied by transverse diffusion in the z-direction toward the active surface. This process is modeled as radial convection and axial diffusion with angular symmetry in cylindrical coordinates. The reaction/diffusion boundary condition on the surface of the rotating plate includes position-dependent stress-sensitive nutrient consumption via the zr- and zTheta-elements of the velocity gradient tensor at the cell/aqueous-medium interface. Linear transport laws in chemically reactive systems that obey Curie's theorem predict the existence of cross-phenomena between scalar reaction rates and the magnitude of the second-rank velocity gradient tensor, selecting only those elements of nabla v experienced by anchorage-dependent cells that are bound to protein-active sites. Stress sensitivity via the formalism of irreversible thermodynamics introduces a zeroth-order contribution to heterogeneous reaction rates that must be quenched when nutrients, oxygen, chemically anchored cells, or vacant active protein sites are not present on the surface of the rotating plate. Computer simulations of nutrient consumption profiles via simple nth-order kinetics (i.e., n=1,2) suggest that rotational bioreactor designs should consider stress-sensitivity when the shear-rate-based Damköhler number (i.e., ratio of the stress-dependent zeroth-order rate of nutrient consumption relative to the rate of nutrient diffusion toward active cells adhered to the rotating plate) is greater than approximately 25% of the stress-free Damköhler number. Rotational bioreactor simulations are presented for simple 1st-order, simple 2nd-order, and complex stress-free kinetics, where the latter includes a 4th-order rate expression that considers adsorption/desorption equilibria via the Fowler-Guggenheim modification of the Langmuir isotherm for receptor-mediated cell-protein binding, accompanied by the formation of receptor complexes. Dimensionless parameters are identified to obtain equivalent stress-free nutrient consumption in the exit streams of 2-dimensional creeping-flow rotational bioreactors and 1-dimensional laminar-flow tubular bioreactors. Modulated rotation of the active plate at physiological frequencies mimics pulsatile cardiovascular flow and demonstrates that these rotational bioreactors must operate above the critical stress-sensitive Damköhler number, identified under steady shear conditions, before dynamic shear has a distinguishable effect on bioreactor performance.