Model of oxygen transport limitations in hollow fiber bioreactors

Abstract

Axial and radial oxygen depletion are believed to be critical scale-limiting factors in the design of cell culture hollow fiber bioreactors. A mathematical analysis of oxygen depletion has been performed in order to develop effectiveness factor plots to aid in the scaling of hollow fiber bioreactors with cells immobilized in the shell-side. Considerations of the lumen mass transport resistances and the axial gradients were added to previous analyses of this immobilization geometry. An order of magnitude analysis was used to evaluate the impact of the shell-side convective fluxes on the oxygen transport. A modified Thiele modulus and a lumen and membrane resistance factor have been derived from the model. Use of these terms in the effectiveness factor plots results in a considerable simplification of the presentation and use of the model. Design criteria such as fiber dimensions and spacing, reactor lengths, and recycle flow rates can be selected using these plots. Model predictions of the oxygen limitations were compared to experimental measurements of the axial cell distributions in a severely oxygen limited hollow fiber bioreactor. Despite considerable uncertainty in our parameters and nonidealities in hollow fiber geometry, the cell distribution correlated well with the modeling results.

Mass Transfer through Catalytic Membrane Reactor

“…The structure, the thickness of this mass transport layer can be very different, thus, the mass transport parameters, namely diffusion coefficient, convective velocity, the bio-reaction rate constant, their dependency on the concentration and/or space coordinate is characteristic of the porous layer and of the nature of the biocatalysts. Several investigators modeled the mass transport through this biocatalyst layer, through enzyme membrane layer or cell culture membrane layer (Schonberg & Belfort, 1990, Kelsey et al, 1990, Piret & Cooney, 1991, Ferreira et al, 2001) Recently Nagy (2009aNagy ( , 2009b) studied the mass transfer rate into a biocatalytic membrane layer with constant mass transport parameters. He defined the mass transfer rates for both side of the membrane surface.…”

“…When there is no change of volume of the fluid phase because the low convective permeation rate or the case of dilute fluid phase, the mass balance equation given by eq. 126 should be taken into account during the mass transport calculation (Piret & Cooney, 1991).…”

“…Membrane layer is especially useful for immobilizing whole cells (bacteria, yeast, mammalian and plant cells) (Brotherton and Chau, 1990;Sheldon and Small, 2005), bioactive molecules such as enzymes (Rios et al, 2007;Charcosset, 2006;Frazeres and Cabral, 2001) to produce wide variety of chemicals and substances. The main advantages of the membrane, especially the hollow fiber, bioreactor are the large specific surface area (internal and external surface of the membrane) for cell adhesion or enzyme immobilization; the ability to grow cells to high density; the possibility for simultaneous reaction and separation; relatively short diffusion path in the membrane layer; the presence of convective velocity through the membrane if it is necessary in order to avoid the nutrient limitation (Belfort, 1989;Piret and Cooney, 1991;Sardonini and DiBiasio, 1992). This work analyzes the mass transport through biocatalytic membrane layer, either live cells or enzymes, inoculated into the shell and immobilized within the membrane matrix or in a thin layer at the membrane matrix matrix-shell interface.…”

“…The introduction of convective transport is crucial in overcoming diffusive mass transport limitation of nutrients (Nakajima and Cardoso, 1989) especially of the sparingly soluble oxygen. Several investigators modeled the mass transport through this biocatalyst layer, through enzyme membrane layer (Ferreira et al, 2001;Long et al, 2003;Belfort, 1989;Hossain and Do, 1989;Calabro et al, 2002;Waterland et al, 1975; www.intechopen.com Salzman et al, 1999;Carvalho et al, 2000) or cell culture membrane layer (Melo and Oliveira, 2001;Chau, 1990, 1996;Piret and Cooney, 1991;Sardonini and Dibiasio, 1992;Lu et al, 2001;Schonberg and Belfort, 1987). These studies analyze both the mass transport through the membrane and the bulk phase concentration change.…”

Membrane supported scaffold architectures for tissue engineering

“…Moreover, nutrient and oxygen gradients will be present in the outer regions of the tissue, which could result in non-uniform cell differentiation and integration [80]. An engineering solution to supply oxygen and essential nutrients to the growing tissue may be to use hollow fiber membrane bioreactor; so that the hollow fiber membrane embedded in-between reduces the diffusion distance while mimicking the blood capillary system [99][100][101][102]. Evidence of endothelial cells growing on porous polymeric (PES) hollow fiber membranes has been reported [103], illustrating the possibility to connect hollow fiber to host vascular system to enhance capillary in-growth in-vivo.…”