×

Mathematical modelling of fibre-enhanced perfusion inside a tissue-engineering bioreactor. (English) Zbl 1400.92205

Summary: We develop a simple mathematical model for forced flow of culture medium through a porous scaffold in a tissue-engineering bioreactor. Porous-walled hollow fibres penetrate the scaffold and act as additional sources of culture medium. The model, based on Darcy’s law, is used to examine the nutrient and shear-stress distributions throughout the scaffold. We consider several configurations of fibres and inlet and outlet pipes. Compared with a numerical solution of the full Navier-Stokes equations within the complex scaffold geometry, the modelling approach is cheap, and does not require knowledge of the detailed microstructure of the particular scaffold being used. The potential of this approach is demonstrated through quantification of the effect the additional flow from the fibres has on the nutrient and shear-stress distribution.

MSC:

92C40 Biochemistry, molecular biology
35Q92 PDEs in connection with biology, chemistry and other natural sciences
76S05 Flows in porous media; filtration; seepage
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] Abousleiman, R.I.; Sikavitsas, V.I., Bioreactors for tissues of the musculoskeletal system, Adv. exp. med. biol., 585, 243-259, (2006)
[2] Bailey, C., Optimisation of fluid distribution inside a porous construct, ()
[3] Bancroft, G.; Sikavitsas, V.; van den Dolder, J.; Sheffield, T.; Ambrose, C.; Jansen, J.; Mikos, A., Fluid flow increases mineralized matrix deposition in 3D perfusion culture of marrow stromal osteoblasts in a dose-dependent manner, Proc. natl. acad. sci. USA, 99, 20, 12600-12605, (2002)
[4] Batchelor, G.K., An introduction to fluid dynamics, (1967), Cambridge University Press Cambridge · Zbl 0152.44402
[5] Bear, J., Dynamics of fluids in porous media, (1988), Dover · Zbl 1191.76002
[6] Boschetti, F.; Raimondo, M.T.; Migliavacca, F.; Dubini, G., Prediction of the micro-fluid dynamic environment imposed to three-dimensional engineered cell systems in bioreactors, J. biomech., 39, 418-425, (2006)
[7] Cartmell, S.H.; Porter, B.D.; Garcia, A.J.; Guldberg, R.E., Effects of medium perfusion rate on cell-seeded three-dimensional bone constructs in vitro, Tissue eng., 9, 6, 1197-1203, (2003)
[8] Cartmell, S.H., Gittings, J.P., Turner, I.G., Chaudhuri, J.B., Ellis, M.J., Waters, S.L., Cummings, L.J., Kuiper, N.J., Michael, V., 2007. Bioreactor design for osteochondral tissue. In: American Society of Bone and Mineral Research, 29th Annual Meeting Abstracts Supplement. J. Bone Miner. Res. 22S1, S162.; Cartmell, S.H., Gittings, J.P., Turner, I.G., Chaudhuri, J.B., Ellis, M.J., Waters, S.L., Cummings, L.J., Kuiper, N.J., Michael, V., 2007. Bioreactor design for osteochondral tissue. In: American Society of Bone and Mineral Research, 29th Annual Meeting Abstracts Supplement. J. Bone Miner. Res. 22S1, S162.
[9] Cimetta, E.; Flaibani, M.; Mella, M.; Serena, E.; Boldrin, L.; De Coppi, P.; Elvassore, N., Enhancement of viability of muscle precursor cells on 3D scaffold in a perfusion bioreactor, Int. J. artif. organs, 30, 5, 415-428, (2007)
[10] Cogan, N.G.; Keener, J.P., The role of the biofilm matrix in structural development, Math. med. biol., 21, 147-166, (2004) · Zbl 1055.92034
[11] Cummings, L.J.; Waters, S.L., Tissue growth in a rotating bioreactor. part II: flow and nutrient transport problems, Math. med. biol., 24, 169-208, (2007) · Zbl 1149.92013
[12] Ellis, M.J.; Chaudhuri, J.B., Poly(lactic-co-glycolic acid) hollow fibre membranes for use as a tissue engineering scaffold, Biotech. bioeng., 96, 1, 177-187, (2007)
[13] Galban, C.J.; Locke, B.R., Analysis of cell growth in a polymer scaffold using a moving boundary approach, Biotech. bioeng., 56, 4, 422-432, (1997)
[14] Galban, C.J.; Locke, B.R., Effects of spatial variations of cells and nutrient and product concentrations coupled with product inhibition on cell growth in a polymer scaffold, Biotech. bioeng., 64, 6, 633-643, (1999)
[15] Gittings, J.P.; Turner, I.G.; Miles, A.W., Calcium phosphate open porous scaffold bioceramics, Key eng. mat., 284-286, 349-354, (2005)
[16] Glowacki, J.; Mizuno, S.; Greenberger, J.S., Perfusion enhances functions of bone marrow stromal cells in three-dimensional culture, Cell transp., 7, 3, 319-326, (1998)
[17] Goldstein, A.; Juarez, T.; Helmke, C.; Gustin, M.; Mikos, A., Effect of convection on osteoblastic cell growth and function in biodegradable polymer foam scaffolds, Biomaterials, 22, 11, 1279-1288, (2001)
[18] Haddock, S.M.; Debes, J.C.; Nauman, E.A.; Fong, K.E.; Arramon, Y.P.; Keaveny, T.M., Structure-function relationships for coralline hydroxyapatite bone substitute, J. biomed. mater. res., 47, 1, 71-78, (1999)
[19] Humphrey, J.D., Continuum biomechanics of soft biological tissues, Proc. R. soc. London A, 459, 1, 3-46, (2003) · Zbl 1116.74385
[20] Invitrogen, 2008. Dulbecco’s Modified Eagle Medium (D-MEM) (1X) #22320022. Media formulations, Invitrogen.; Invitrogen, 2008. Dulbecco’s Modified Eagle Medium (D-MEM) (1X) #22320022. Media formulations, Invitrogen.
[21] Kim, S.S.; Penkala, R.; Abrahimi, P., A perfusion bioreactor for intestinal tissue engineering, J. surg. res., 142, 2, 327-331, (2007)
[22] Knobloch, T.J.; Madhavan, S.; Nam, J.; Agarwal, S.J.; Agarwal, S., Regulation of chondrocytic gene expression by biomechanical signals, Crit. rev. eukaryotic gene exp., 18, 2, 139-150, (2008)
[23] Komarova, S.V.; Ataullakhanov, F.I.; Globus, R.K., Bioenergetics and mitochondrial transmembrane potential during differentiation of cultured osteoblasts, Am. J. physiol. cell physiol., 279, C1220-C1229, (2000)
[24] Koponen, A.; Kataja, M.; Timonen, J., Tortuous flow in porous media, Phys. rev. E, 54, 1, 406-410, (1996)
[25] Lasseux, D.; Ahmadi, A.; Cleis, X.; Garnier, J., A macroscopic model for species transport during in vitro tissue growth obtained by the volume averaging method, Chem. eng. sci., 59, 10, 1949-1964, (2004)
[26] Lemon, G.; King, J.R.; Byrne, H.M.; Jensen, O.E.; Shakesheff, K.M., Mathematical modelling of engineered tissue growth using a multiphase porous flow mixture theory, J. math. biol., 52, 5, 571-594, (2006) · Zbl 1110.92016
[27] Lide, D.R. (Ed.), 2007. CRC Handbook of Chemistry and Physics, 87th ed. CRC.; Lide, D.R. (Ed.), 2007. CRC Handbook of Chemistry and Physics, 87th ed. CRC.
[28] MacArthur, B.D.; Please, C.P.; Taylor, M.; Oreffo, R.O.C., Mathematical modelling of skeletal repair, Biochem. biophys. res. commun., 313, 825-833, (2004)
[29] Martin, I.; Wendt, D.; Heberer, M., The role of bioreactors in tissue engineering, Trends biotechnol., 22, 2, (2004)
[30] Michael, V., Gittings, J.P., Turner, I.G., Chaudhuri, J.B., Ellis, M.J., Waters, S.L., Cummings, L.J., Goodstone, N.J., Cartmell, S.H., 2007. Co-culture bioreactor design for skeletal tissue engineering. In: TERMIS-EU Meeting Abstracts. Tissue Eng. 13(7), 1657-1658.; Michael, V., Gittings, J.P., Turner, I.G., Chaudhuri, J.B., Ellis, M.J., Waters, S.L., Cummings, L.J., Goodstone, N.J., Cartmell, S.H., 2007. Co-culture bioreactor design for skeletal tissue engineering. In: TERMIS-EU Meeting Abstracts. Tissue Eng. 13(7), 1657-1658.
[31] Morgan, S.M.; Tilley, S.; Perera, S.; Ellis, M.J.; Kanczler, J.; Chaudhuri, J.B.; Oreffo, R.O.C., Expansion of human bone marrow stromal cells on poly-(dl-lactide-co-glycolide) (P(DL)LGA) hollow fibres designed for use in skeletal tissue engineering, Biomaterials, 28, 35, 5332-5343, (2007)
[32] Nehring, D.; Adamietz, P.; Meenen, N.M.; Pörtner, R., Perfusion cultures and modelling of oxygen uptake with three-dimensional chondrocyte pellets, Biotechnol. tech., 13, 10, 701-706, (1999)
[33] Ockendon, H.; Ockendon, J.R., Viscous flow, (1995), Cambridge University Press Cambridge · Zbl 0837.76001
[34] O’Dea, R.D.; Waters, S.L.; Byrne, H.M., A two-fluid model for tissue growth within a dynamic flow environment, Eur. J. appl. math., 19, 607-634, (2008) · Zbl 1256.92015
[35] Peterson, L.; Minas, T.; Brittberg, M.; Nilsson, A.; Sjögren-Jansson, E.; Lindahl, A., Two to nine year outcome after autologous chondrocyte transplantation of the knee, Clin. orthop. relat. res., 374, 212-234, (2000)
[36] Porter, B.; Zauel, R.; Stockman, H.; Guldberg, R.; Fyhrie, D., 3D computational modeling of media flow through scaffolds in a perfusion bioreactor, J. biomech., 38, 3, 543-549, (2005)
[37] Ribeiro, A.C.F.; Lobo, V.M.M.; Leaist, D.G.; Natividade, J.J.S.; Veríssimo, L.P.; Barros, M.C.F.; Cabral, A.M.T.D.P.V., Binary diffusion coefficients for aqueous solutions of lactic acid, J. soltn. chem., 34, 1009-1016, (2005)
[38] Rubin, J.; Rubin, C.; Jacobs, C.R., Molecular pathways mediating mechanical signaling in bone, Gene, 367, 1-16, (2006)
[39] Sengers, B.G.; Oomens, C.W.J.; Baaijens, F.P.T., An integrated finite-element approach to mechanics, transport and biosynthesis in tissue engineering, J. biomech. eng., 126, 1, 82-91, (2004)
[40] Tromans, D., Temperature and pressure dependent solubility of oxygen in water: a thermodynamic analysis, Hydrometallurgy, 48, 3, 327-342, (1998)
[41] Waters, S.L.; Cummings, L.J.; Shakesheff, K.M.; Rose, F.R.A.J., Tissue growth in a rotating bioreactor. part I: mechanical stability, Math. med. biol., 23, 311-337, (2006) · Zbl 1117.92020
[42] Yu, B.-M.; Li, J.-H., A geometry model for tortuosity of flow path in porous media, Chin. phys. lett., 21, 8, 1569-1571, (2004)
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.