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Immobilization of suspended mammalian cells: Analysis of hollow fiber and microcapsule bioreactors

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Vertrebrate Cell Culture I

Part of the book series: Advances in Biochemical Engineering/Biotechnology ((ABE,volume 34))

Abstract

Model equations of substrate mass transfer and uptake have been formulated for two bioreactor systems: microcapsules and a hollow fiber reactor. Assumptions include time independence, Fickian diffusion, homogenous cell suspension, and kinetics described by the zero and first order limits of the Monod equation. Glucose and oxygen were the substrates chosen for investigation of the kinetic and diffusion limitations. For microcapsules, the resulting radial concentration profiles indicated the possibility of a necrotic core due to insufficient substrate in those cases where diffusion is low and/or uptake is high. The model equations provide a means of estimating the maximum capsule radius which will allow adequate diffusion of nutrients to all of the contained cells. The simulated concentration gradients developed for a hollow fiber reactor demonstrate that diffusion limitations may exist at the far end of the reactor. Concentration gradients are shown both in the fiber lumens (in the axial direction) as well as in the shell space (in the radial direction). Variation of model parameters provides information on system specifications to avoid these diffusion limitations.

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Abbreviations

A:

radius of membrane fiber (cm)

B:

microcapsule radius or hollow fiber annulus radius (cm)

C0 :

bulk substrate concentration (moles ml−1)

C(r):

concentration as a function of radius (moles ml−1)

C(z):

concentration as a function of axial distance (moles ml−1)

De :

effective diffusivity (cm2 s−1)

I0(x):

modified Bessel fuction of the first kind, order zero

I1(x):

modified Bessel function of the first kind, order one

K0(x):

modified Bessel function of the second kind, order zero

K1(x):

modified Bessel function of the second kind, order one

Km :

Michaelis constant (moles ml−1)

L:

hollow fiber length (cm)

n:

number of hollow fibers

N:

substrate flux (moles cm2 s−1)

r:

radius (cm)

R:

outer radius of microcapsule or hollow fiber module (cm)

R:

uptake of substrate (moles ml−1 s−1)

Vk :

Vm/Km(s−1)

Vm :

maximum reaction rate (moles ml−1 s−1)

Vz :

axial fluid velocity (cm s−1)

z:

axial distance (cm)

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Authors and Affiliations

  1. Department of Chemical Engineering and Environmental Engineering, Rensselaer Polytechnic Institute, 12180-3590, Troy, New York, USA

    Carole Heath & Georges Belfort

Authors
  1. Carole Heath
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  2. Georges Belfort
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© 1987 Springer-Verlag

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Heath, C., Belfort, G. (1987). Immobilization of suspended mammalian cells: Analysis of hollow fiber and microcapsule bioreactors. In: Vertrebrate Cell Culture I. Advances in Biochemical Engineering/Biotechnology, vol 34. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0000671

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  • DOI: https://doi.org/10.1007/BFb0000671

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-17626-8

  • Online ISBN: 978-3-540-47725-9

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