Pressure-sensitive nutrient consumption via dynamic normal stress in rotational bioreactors

Pressure-sensitive biological response is simulated in "rotating-cup" bioreactors with unidirectional modulations in compressive stress at the cylindrical wall that stimulate bone-tissue growth. Anchorage-dependent mammalian cells (i) adhere to a protein coating, (ii) receive nutrients and oxygen from an aqueous medium via radial diffusion toward the active surface, and (iii) respond to physiological modulations in centrifual-force-induced fluid pressure at the cell/aqueous-medium interface. This process is modeled by the classic diffusion equation (i.e., Fick's second law), with a time-dependent reaction/diffusion boundary condition at the wall. Non-reversing angular velocity modulations resemble pulsations at physiological frequencies. Computer simulations of nutrient consumption profiles suggest that rotational bioreactor designs should consider the effects of normal stress when the pressure-sensitive Damköhler number (i.e., ratio of the pressure-dependent zeroth-order rate of nutrient consumption relative to the rate of nutrient diffusion toward active cells adhered to the cylindrical wall), evaluated under steady rotation, is greater than approximately 10-20% of the stress-free Damköhler number (i.e., beta(0,1st-order)=0.025) for simple 1st-order stress-free kinetics, and approximately 1% of the stress-free Damköhler number (i.e., beta(0,2nd-order)=0.40) for complex 2nd-order stress-free nutrient consumption. When the peak-to-peak amplitude of angular velocity modulations of the cylindrical wall is the same as or larger than the angular velocity for steady rotation, the effect of non-reversing centrifugal-force-induced dynamic normal stress in rotational bioreactors, superimposed on steady rotation, can be significant when one is below the critical value of the pressure-sensitive Damköhler number that has been identified under steady rotation.