Dispersion-enhanced solute transport in a cell-seeded hollow fibre membrane bioreactor. (English) Zbl 1360.76363
Summary: We present a matched asymptotic analysis of the fluid flow and solute transport in a small aspect ratio hollow fibre membrane bioreactor. A two-dimensional domain is assumed for simplicity, enabling greater understanding of the typical behaviours of the system in a setup which is analytically tractable. The model permits analysis related to Taylor dispersion problems, and allows us to predict the dependence of the mean solute uptake and solute exposure time on key parameters such as the inlet fluid fluxes, porous membrane porosity and cell layer porosity and width, which could be controlled or measured experimentally.
MSC:
| 76Z05 | Physiological flows |
| 92C45 | Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) |
| 76M45 | Asymptotic methods, singular perturbations applied to problems in fluid mechanics |
| 76D08 | Lubrication theory |
| 76S05 | Flows in porous media; filtration; seepage |
References:
| [1] | Stock UA, Vacanti JP (2001) Tissue engineering: current state and prospects. Annu Rev Med 52(1):443-451 · doi:10.1146/annurev.med.52.1.443 |
| [2] | Pörtner R, Nagel-Heyer S, Goepfert C, Adamietz P, Meenen NM (2005) Bioreactor design for tissue engineering. J Biosci Bioeng 100(3):235-245 · doi:10.1263/jbb.100.235 |
| [3] | Martin I, Wendt D, Heberer M (2004) The role of bioreactors in tissue engineering. Trends Biotechnol 22(2):80-86 · doi:10.1016/j.tibtech.2003.12.001 |
| [4] | Martin Y, Vermette P (2005) Bioreactors for tissue mass culture: design, characterization, and recent advances. Biomaterials 26(35):7481-7503 · doi:10.1016/j.biomaterials.2005.05.057 |
| [5] | Pearson NC, Shipley RJ, Waters SL, Oliver JM (2014) Multiphase modelling of the influence of fluid flow and chemical concentration on tissue growth in a hollow fibre membrane bioreactor. Math Med Biol 31(4):393-430 · Zbl 1345.92095 · doi:10.1093/imammb/dqt015 |
| [6] | Pearson NC, Waters SL, Oliver JM, Shipley RJ (2015) Multiphase modelling of the effect of fluid shear stress on cell yield and distribution in a hollow fibre membrane bioreactor. Biomech Model Mechanobiol 14(2):387-402 · doi:10.1007/s10237-014-0611-7 |
| [7] | Lemon G, King JR, Byrne HM, Jensen OE, Shakesheff KM (2006) Mathematical modelling of engineered tissue growth using a multiphase porous flow mixture theory. J Math Biol 52:571-594 · Zbl 1110.92016 · doi:10.1007/s00285-005-0363-1 |
| [8] | O’Dea RD, Waters SL, Byrne HM (2010) A multiphase model for tissue construct growth in a perfusion bioreactor. Math Med Biol 27(2):95-127 · Zbl 1190.92008 · doi:10.1093/imammb/dqp003 |
| [9] | Shipley RJ, Davidson AJ, Chan K, Chaudhuri JB, Waters SL, Ellis MJ (2011) A strategy to determine operating parameters in tissue engineering hollow fiber bioreactors. Biotechnol Bioeng 108(6):1450-1461 · doi:10.1002/bit.23062 |
| [10] | Shipley RJ, Waters SL (2012) Fluid and mass transport modelling to drive the design of cell-packed hollow fibre bioreactors for tissue engineering applications. Math Med Biol 29:329-359 · Zbl 1252.92019 · doi:10.1093/imammb/dqr025 |
| [11] | Aris R (1956) On the dispersion of a solute in a fluid flowing through a tube. Proc R Soc Lond A 235(1200):67-77 · doi:10.1098/rspa.1956.0065 |
| [12] | Taylor G (1953) Dispersion of soluble matter in solvent flowing slowly through a tube. Proc R Soc Lond A 219(1137):186-203 · doi:10.1098/rspa.1953.0139 |
| [13] | Taylor G (1954) Conditions under which dispersion of a solute in a stream of solvent can be used to measure molecular diffusion. Proc R Soc Lond A 225(1163):473-477 · doi:10.1098/rspa.1954.0216 |
| [14] | Griffiths IM, Howell PD, Shipley RJ (2013) Control and optimization of solute transport in a thin porous tube. Phys Fluids 25(3):033101 · Zbl 1315.76038 |
| [15] | Kumar JP, Umavathi JC, Chamkha AJ, Basawaraj A (2012) Solute dispersion between two parallel plates containing porous and fluid layers. J Porous Media 15(11):1031-1047 · doi:10.1615/JPorMedia.v15.i11.40 |
| [16] | Pal D, Veerabhadraiah R, Shivakumar PN, Rudraiah N (1984) Longitudinal dispersion of tracer particles in a channel bounded by porous media using slip condition. Int J Math Math Sci 7(4):755-764 · Zbl 0581.76106 · doi:10.1155/S0161171284000788 |
| [17] | Vikhansky A, Wang W (2011) Taylor dispersion in finite-length capillaries. Chem Eng Sci 66(4):642-649 · doi:10.1016/j.ces.2010.11.019 |
| [18] | Mazumder BS, Mondal KK (2005) On solute transport in oscillatory flow through an annular pipe with a reactive wall and its application to a catheterized artery. Q J Mech Appl Math 58(3):349-365 · Zbl 1112.76097 · doi:10.1093/qjmam/hbi009 |
| [19] | Mondal KK, Mazumder B (2005) On the solute dispersion in a pipe of annular cross-section with absorption boundary. Z Angew Math Mech 85(6):422-430 · Zbl 1071.76053 · doi:10.1002/zamm.200210180 |
| [20] | Van den Broeck C, Dekempeneer E (1983) The effect of boundary absorption on longitudinal dispersion in steady laminar flows. Z Angew Math Phys 34(4):489-501 · Zbl 0539.76105 · doi:10.1007/BF00944710 |
| [21] | Shipley RJ, Waters SL, Ellis MJ (2010) Definition and validation of operating equations for poly(vinyl alcohol)-poly(lactide-co-glycolide) microfiltration membrane-scaffold bioreactors. Biotechnol Bioeng 107(2):382-392 · doi:10.1002/bit.22815 |
| [22] | Meneghello G, Parker DJ, Ainsworth BJ, Perera SP, Chaudhuri JB, Ellis MJ, De Bank PA (2009) Fabrication and characterization of poly(lactic-co-glycolic acid)/polyvinyl alcohol blended hollow fibre membranes for tissue engineering applications. J Membr Sci 344(1-2):55-61 · doi:10.1016/j.memsci.2009.07.034 |
| [23] | Aris R (1959) On the dispersion of a solute by diffusion, convection and exchange between phases. Proc R Soc Lond A 252(1271):538-550 · Zbl 0092.19404 · doi:10.1098/rspa.1959.0171 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
