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Computational Modeling in Tissue Engineering pp 85–105Cite as

Computational Modeling of Mass Transport and Its Relation to Cell Behavior in Tissue Engineering Constructs

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Part of the book series: Studies in Mechanobiology, Tissue Engineering and Biomaterials ((SMTEB,volume 10))

Abstract

Effective recapitulation of extracellular matrix properties into a Tissue Engineering strategy is strongly involved with the need for a proper transport environment. Consumption and production of soluble medium components gives rise to gradients which influence cell behavior in various ways. Understanding how transport related phenomena can shape these gradients is targeted in this chapter by the combined use of experiments and mathematical modeling. An overview of different models is given that describe solute transport and its relation to specific cell behavior. From the simulation results important information can be extracted which help to unravel mechanisms that drive solute transport. Finally we describe the genuine efforts that have been taken to translate this information into real tissue engineering setups (e.g., optimization of culture conditions and controlled-release of growth factors).

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References

  1. Acosta, M.A., Ymele-Leki, P., Kostov, Y.V., Leach, J.B.: Fluorescent microparticles for sensing cell microenvironment oxygen levels within 3D scaffolds. Biomaterials 30(17), 3068–3074 (2009). doi:10.1016/j.biomaterials.2009.02.021

    Article  Google Scholar 

  2. Alberts, B., Johnson, A., Lewis, J., Raff, M., Roberts, K., Walter, P.: Molecular Biology of the Cell, 4th edn. Garland Science, New York (2007)

    Google Scholar 

  3. Ando, R., Mizuno, H., Miyawaki, A.: Regulated fast nucleocytoplasmic shuttling observed by reversible protein highlighting. Science 306(5700), 1370–1373 (2004). doi:10.1126/science.1102506. 306/5700/1370[pii]

    Article  Google Scholar 

  4. Arany, Z., Foo, S.Y., Ma, Y.H., Ruas, J.L., Bommi-Reddy, A., Girnun, G., Cooper, M., Laznik, D., Chinsomboon, J., Rangwala, S.M., Baek, K.H., Rosenzweig, A., Spiegelman, B.M.: HIF-independent regulation of VEGF and angiogenesis by the transcriptional coactivator PGC-1 alpha. Nature 451(7181), 1008–U1008 (2008). doi:10.1038/Nature06613

    Article  Google Scholar 

  5. Armstrong, C.G., Lai, W.M., Mow, V.C.: An analysis of the unconfined compression of articular-cartilage. J. Biomech. Eng. Trans. ASME 106(2), 165–173 (1984)

    Article  Google Scholar 

  6. Beard, D.A., Qian, H.: Chemical Biophysics: Quantitative Analysis of Cellular Systems. Cambridge Texts in Biomedical Engineering. Cambridge University Press, New York (2008)

    Book  Google Scholar 

  7. Bibby, S.R.S., Jones, D.A., Ripley, R.M., Urban, J.P.G.: Metabolism of the intervertebral disc: effects of low levels of oxygen, glucose, and pH on rates of energy metabolism of bovine nucleus pulposus cells. Spine 30(5), 487–496 (2005)

    Article  Google Scholar 

  8. Bishop, J.R., Schuksz, M., Esko, J.D.: Heparan sulphate proteoglycans fine-tune mammalian physiology. Nature 446(7139), 1030–1037 (2007). doi:10.1038/Nature05817

    Article  Google Scholar 

  9. Blum, J.J., Lawler, G., Reed, M., Shin, I.: Effect of cytoskeletal geometry on intracellular diffusion. Biophys. J. 56(5), 995–1005 (1989). doi:10.1016/S0006-3495(89)82744-4. S0006-3495(89)82744-4[pii]

    Article  Google Scholar 

  10. Brown, D.A., MacLellan, W.R., Laks, H., Dunn, J.C., Wu, B.M., Beygui, R.E.: Analysis of oxygen transport in a diffusion-limited model of engineered heart tissue. Biotechnol. Bioeng. 97(4), 962–975 (2007). doi:10.1002/bit.21295

    Article  Google Scholar 

  11. Brown, E.B., Wu, E.S., Zipfel, W., Webb, W.W.: Measurement of molecular diffusion in solution by multiphoton fluorescence photobleaching recovery. Biophys. J. 77(5), 2837–2849 (1999)

    Article  Google Scholar 

  12. Brown, G.C.: Control of respiration and Atp synthesis in mammalian mitochondria and cells. Biochem. J. 284, 1–13 (1992)

    Google Scholar 

  13. Bursac, P.M., Freed, L.E., Biron, R.J., Vunjak-Novakovic, G.: Mass transfer studies of tissue engineered cartilage. Tissue Eng. 2(2), 141–150 (1996). doi:10.1089/ten.1996.2.141

    Article  Google Scholar 

  14. 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)

    Article  Google Scholar 

  15. Cassell, O.C., Morrison, W.A., Messina, A., Penington, A.J., Thompson, E.W., Stevens, G.W., Perera, J.M., Kleinman, H.K., Hurley, J.V., Romeo, R., Knight, K.R.: The influence of extracellular matrix on the generation of vascularized, engineered, transplantable tissue. Ann. N. Y. Acad. Sci. 944, 429–442 (2001)

    Article  Google Scholar 

  16. Chen, R.R., Silva, E.A., Yuen, W.W., Brock, A.A., Fischbach, C., Lin, A.S., Guldberg, R.E., Mooney, D.J.: Integrated approach to designing growth factor delivery systems. FASEB J. 21(14), 3896–3903 (2007). doi:10.1096/fj.06-7873com

    Article  Google Scholar 

  17. Chen, Y., Whetstone, H.C., Lin, A.C., Nadesan, P., Wei, Q.X., Poon, R., Alman, B.A.: Beta-catenin signaling plays a disparate role in different phases of fracture repair: implications for therapy to improve bone healing. PLoS Med 4(7), 1216–1229 (2007). doi:10.1371/journal.pmed.0040249. ARTN e249

    Article  Google Scholar 

  18. Clague, D.S., Phillips, R.J.: Hindered diffusion of spherical macromolecules through dilute fibrous media. Phys. Fluids 8(7), 1720–1731 (1996)

    Article  MATH  Google Scholar 

  19. Contois, D.E.: Kinetics of bacterial growth: relationship between population density and specific growth rate of continuous cultures. J. Gen. Microbiol. 21, 40–50 (1959)

    Article  Google Scholar 

  20. Crabtree, H.G.: Observations on the carbohydrate metabolism of tumours. Biochem. J. 23(3), 536–545 (1929)

    Google Scholar 

  21. Crampin, E.J., Hackborn, W.W., Maini, P.K.: Pattern formation in reaction-diffusion models with nonuniform domain growth. Bull. Math. Biol. 64(4), 747–769 (2002). doi:10.1006/bulm.2002.0295

    Article  Google Scholar 

  22. Croll, T.I., Gentz, S., Mueller, K., Davidson, M., O’Connor, A.J., Stevens, G.W., Cooper-White, J.J.: Modelling oxygen diffusion and cell growth in a porous, vascularising scaffold for soft tissue engineering applications. Chem. Eng. Sci. 60(17), 4924–4934 (2005). doi:10.1016/j.cea.2005.03.051

    Article  Google Scholar 

  23. Dallon, J.C.: Multiscale modeling of cellular systems in biology. Curr. Opin. Colloid Interface Sci. 15(1–2), 24–31 (2010). doi:10.1016/j.cocis.2009.05.007

    Article  Google Scholar 

  24. Dehmelt, L., Bastiaens, P.I.H.: Spatial organization of intracellular communication: insights from imaging. Nat. Rev. Mol. Cell Biol. 11(6), 440–452 (2010). doi:10.1038/Nrm2903

    Article  Google Scholar 

  25. Demol, J., Lambrechts, D., Geris, L., Schrooten, J., Van Oosterwyck, H.: Towards a quantitative understanding of oxygen tension and cell density evolution in fibrin hydrogels. Biomaterials 32(1), 107–118 (2011). doi:10.1016/j.biomaterials.2010.08.093

    Article  Google Scholar 

  26. Dor, Y., Porat, R., Keshet, E.: Vascular endothelial growth factor and vascular adjustments to perturbations in oxygen homeostasis. Am. J. Physiol. Cell Physiol. 280(6), C1367–C1374 (2001)

    Google Scholar 

  27. Durlofsky, L., Brady, J.F.: Analysis of the Brinkman equation as a model for flow in porous-media. Phys. Fluids 30(11), 3329–3341 (1987)

    Article  MATH  Google Scholar 

  28. Efrat, S., Linde, S., Kofod, H., Spector, D., Delannoy, M., Grant, S., Hanahan, D., Baekkeskov, S.: Beta-cell lines derived from transgenic mice expressing a hybrid insulin gene-oncogene. Proc. Natl. Acad. Sci. U. S. A. 85(23), 9037–9041 (1988)

    Article  Google Scholar 

  29. Elisseeff, J., McIntosh, W., Fu, K., Blunk, T., Langer, R.: Controlled-release of IGF-I and TGF-beta 1 in a photopolymerizing hydrogel for cartilage tissue engineering. J. Orthop. Res. 19(6), 1098–1104 (2001)

    Article  Google Scholar 

  30. Engler, A.J., Sen, S., Sweeney, H.L., Discher, D.E.: Matrix elasticity directs stem cell lineage specification. Cell 126(4), 677–689 (2006). doi:10.1016/j.cell.2006.06.044. S0092-8674(06)00961-5[pii]

    Article  Google Scholar 

  31. Esko, J.D., Selleck, S.B.: Order out of chaos: assembly of ligand binding sites in heparan sulfate. Annu. Rev. Biochem. 71, 435–471 (2002). doi:10.1146/annurev.biochem.71.110601.13545

    Article  Google Scholar 

  32. Evans, R.C., Quinn, T.M.: Dynamic compression augments interstitial transport of a glucose-like solute in articular cartilage. Biophys. J. 91(4), 1541–1547 (2006). doi:10.1529/biophysj.105.080366

    Article  Google Scholar 

  33. Evans, R.C., Quinn, T.M.: Solute convection in dynamically compressed cartilage. J. Biomech. 39(6), 1048–1055 (2006). doi:10.1016/j.jbiomech.2005.02.017. S0021-9290(05)00127-2[pii]

    Article  Google Scholar 

  34. Fassnacht, D., Portner, R.: Experimental and theoretical considerations on oxygen supply for animal cell growth in fixed-bed reactors. J. Biotechnol. 72(3), 169–184 (1999). S0168165699001297[pii]

    Article  Google Scholar 

  35. Fleury, M.E., Boardman, K.C., Swartz, M.A.: Autologous morphogen gradients by subtle interstitial flow and matrix interactions. Biophys. J. 91(1), 113–121 (2006). doi:10.1529/biophysj.105.080192

    Article  Google Scholar 

  36. Galban, C.J., Locke, B.R.: Analysis of cell growth kinetics and substrate diffusion in a polymer scaffold. Biotechnol. Bioeng. 65(2), 121–132 (1999)

    Article  Google Scholar 

  37. Garzon-Alvarado, D.A., Garcia-Aznar, J.M., Doblare, M.: A reaction-diffusion model for long bones growth. Biomech. Model. Mechan. 8(5), 381–395 (2009). doi:10.1007/s10237-008-0144-z

    Article  Google Scholar 

  38. Gefen, A., Cornelissen, L.H., Gawlitta, D., Bader, D.L., Oomens, C.W.: The free diffusion of macromolecules in tissue-engineered skeletal muscle subjected to large compression strains. J. Biomech. 41(4), 845–853 (2008). doi:10.1016/j.jbiomech.2007.10.023. S0021-9290(07)00471-X[pii]

    Article  Google Scholar 

  39. Gerber, H.P., Vu, T.H., Ryan, A.M., Kowalski, J., Werb, Z., Ferrara, N.: VEGF couples hypertrophic cartilage remodeling, ossification and angiogenesis during endochondral bone formation. Nat. Med. 5(6), 623–628 (1999)

    Article  Google Scholar 

  40. Geris, L., Gerisch, A., Maes, C., Carmeliet, G., Weiner, R., Vander Sloten, J., Van Oosterwyck, H.: Mathematical modeling of fracture healing in mice: comparison between experimental data and numerical simulation results. Med. Biol. Eng. Comput. 44(4), 280–289 (2006). doi:10.1007/s11517-006-0040-6

    Article  Google Scholar 

  41. Geris, L., Schugart, R., Van Oosterwyck, H.: In silico design of treatment strategies in wound healing and bone fracture healing. Philos. Trans. A Math. Phys. Eng. Sci. 368(1920), 2683–2706 (2010). doi:10.1098/rsta.2010.0056. 368/1920/2683[pii]

    Article  Google Scholar 

  42. Griffith, L.G., Swartz, M.A.: Capturing complex 3D tissue physiology in vitro. Nat. Rev. Mol. Cell Biol. 7(3), 211–224 (2006). doi:10.1038/Nrm1858

    Article  Google Scholar 

  43. Grimshaw, M.J., Mason, R.M.: Bovine articular chondrocyte function in vitro depends upon oxygen tension. Osteoarthr. Cartil. 8(5), 386–392 (2000). doi:10.1053/joca.1999.0314. S1063-4584(99)90314-X[pii]

    Article  Google Scholar 

  44. Gross, J.D., Constantinidis, I., Sambanis, A.: Modeling of encapsulated cell systems. J. Theor. Biol. 244(3), 500–510 (2007). doi:10.1016/j.jtbi.2006.08.012. S0022-5193(06)00365-1[pii]

    Article  MathSciNet  Google Scholar 

  45. Guaccio, A., Borselli, C., Oliviero, O., Netti, P.A.: Oxygen consumption of chondrocytes in agarose and collagen gels: a comparative analysis. Biomaterials 29(10), 1484–1493 (2008). doi:10.1016/j.biomaterials.2007.12.020

    Article  Google Scholar 

  46. Gurdon, J.B., Bourillot, P.Y.: Morphogen gradient interpretation. Nature 413(6858), 797–803 (2001)

    Article  Google Scholar 

  47. Gurskaya, N.G., Verkhusha, V.V., Shcheglov, A.S., Staroverov, D.B., Chepurnykh, T.V., Fradkov, A.F., Lukyanov, S., Lukyanov, K.A.: Engineering of a monomeric green-to-red photoactivatable fluorescent protein induced by blue light. Nat. Biotechnol. 24(4), 461–465 (2006). doi:10.1038/Nbt1191

    Article  Google Scholar 

  48. Hacker, U., Nybakken, K., Perrimon, N.: Heparan sulphate proteoglycans: the sweet side of development. Nat. Rev. Mol. Cell Biol. 6(7), 530–541 (2005). 10.1038/nrm1681]nrm1681[pii]

    Article  Google Scholar 

  49. Happel, J.: Viscous flow relative to arrays of cylinders. AIChE J. 5(2), 174–177 (1959)

    Article  Google Scholar 

  50. Helm, C.L.E., Fleury, M.E., Zisch, A.H., Boschetti, F., Swartz, M.A.: Synergy between interstitial flow and VEGF directs capillary morphogenesis in vitro through a gradient amplification mechanism. Proc. Natl. Acad. Sci. U. S. A. 102(44), 15779–15784 (2005). doi:10.1073/pnas.0503681102

    Article  Google Scholar 

  51. Heywood, H.K., Bader, D.L., Lee, D.A.: Rate of oxygen consumption by isolated articular chondrocytes is sensitive to medium glucose concentration. J. Cell. Physiol. 206(2), 402–410 (2006). doi:10.1002/Jcp.20491

    Article  Google Scholar 

  52. Heywood, H.K., Knight, M.M., Lee, D.A.: Both superficial and deep zone articular chondrocyte subpopulations exhibit the crabtree effect but have different basal oxygen consumption rates. J. Cell. Physiol. 223(3), 630–639 (2010). doi:10.1002/Jcp.22061

    Google Scholar 

  53. Higdon, J.J.L., Ford, G.D.: Permeability of three-dimensional models of fibrous porous media. J. Fluid Mech. 308, 341–361 (1996)

    Article  MATH  Google Scholar 

  54. Hilton, M.J., Gutierrez, L., Martinez, D.A., Wells, D.E.: EXT1 regulates chondrocyte proliferation and differentiation during endochondral bone development. Bone 36(3), 379–386 (2005). doi:10.1016/j.bone.2004.09.025

    Article  Google Scholar 

  55. Hrabe, J., Hrabetova, S., Segeth, K.: A model of effective diffusion and tortuosity in the extracellular space of the brain. Biophys. J. 87(3), 1606–1617 (2004). doi:10.1529/biophysj.103.039495

    Article  Google Scholar 

  56. Hunziker, E.B., Driesang, I.M.: Functional barrier principle for growth-factor-based articular cartilage repair. Osteoarthr. Cartil. 11(5), 320–327 (2003). S1063458403000311[pii]

    Article  Google Scholar 

  57. Johansson, L., Lofroth, J.E.: Diffusion and interaction in gels and solutions. 4. Hard-sphere Brownian dynamics simulations. J. Chem. Phys. 98(9), 7471–7479 (1993)

    Article  Google Scholar 

  58. Karsenty, G., Wagner, E.F.: Reaching a genetic and molecular understanding of skeletal development. Dev. Cell 2(4), 389–406 (2002)

    Article  Google Scholar 

  59. Kholodenko, B.N.: Cell-signalling dynamics in time and space. Nat. Rev. Mol. Cell Biol. 7(3), 165–176 (2006). doi:10.1038/Nrm1838

    Article  Google Scholar 

  60. Kirkpatrick, C.J., Fuchs, S., Unger, R.E.: Co-culture systems for vascularization—learning from nature. Adv. Drug Deliv. Rev. 63(4–5), 291–299 (2011). doi:10.1016/j.addr.2011.01.009

    Article  Google Scholar 

  61. Kleinman, H.K., Philp, D., Hoffman, M.P.: Role of the extracellular matrix in morphogenesis. Curr. Opin. Biotechnol. 14(5), 526–532 (2003). S0958166903001186[pii]

    Article  Google Scholar 

  62. Kosto, K.B., Deen, W.M.: Diffusivities of macromolecules in composite hydrogels. AIChE J. 50(11), 2648–2658 (2004). doi:10.1002/Aic.10216

    Article  Google Scholar 

  63. Koziel, L., Kunath, M., Kelly, O.G., Vortkamp, A.: Ext1-dependent heparan sulfate regulates the range of Ihh signaling during endochondral ossification. Dev. Cell 6(6), 801–813 (2004)

    Article  Google Scholar 

  64. Kronenberg, H.M.: Developmental regulation of the growth plate. Nature 423(6937), 332–336 (2003). doi:10.1038/Nature01657

    Article  Google Scholar 

  65. Lanske, B., Karaplis, A.C., Lee, K., Luz, A., Vortkamp, A., Pirro, A., Karperien, M., Defize, L.H.K., Ho, C., Mulligan, R.C., AbouSamra, A.B., Juppner, H., Segre, G.V., Kronenberg, H.M.: PTH/PTHrP receptor in early development and Indian hedgehog-regulated bone growth. Science 273(5275), 663–666 (1996)

    Article  Google Scholar 

  66. Leddy, H.A., Guilak, F.: Site-specific effects of compression on macromolecular diffusion in articular cartilage. Biophys. J. 95(10), 4890–4895 (2008). doi:10.1529/biophysj.108.137752

    Article  Google Scholar 

  67. Lee, R.B., Urban, J.P.: Evidence for a negative Pasteur effect in articular cartilage. Biochem. J. 321(Pt 1), 95–102 (1997)

    Google Scholar 

  68. Lee, R.B., Urban, J.P.: Functional replacement of oxygen by other oxidants in articular cartilage. Arthritis Rheum. 46(12), 3190–3200 (2002). doi:10.1002/art.10686

    Article  Google Scholar 

  69. Levick, J.R.: Flow through interstitium and other fibrous matrices. Q. J. Exp. Physiol. CMS 72(4), 409–438 (1987)

    Google Scholar 

  70. Lewis, M.C., MacArthur, B.D., Malda, J., Pettet, G., Please, C.P.: Heterogeneous proliferation within engineered cartilaginous tissue: the role of oxygen tension. Biotechnol. Bioeng. 91(5), 607–615 (2005). doi:10.1002/Bit.20508

    Article  Google Scholar 

  71. Lutolf, M.P., Hubbell, J.A.: Synthetic biomaterials as instructive extracellular microenvironments for morphogenesis in tissue engineering. Nat. Biotechnol. 23(1), 47–55 (2005). doi:10.1038/Nbt1055

    Article  Google Scholar 

  72. Lutolf, M.R., Weber, F.E., Schmoekel, H.G., Schense, J.C., Kohler, T., Muller, R., Hubbell, J.A.: Repair of bone defects using synthetic mimetics of collagenous extracellular matrices. Nat. Biotechnol. 21(5), 513–518 (2003). doi:10.1038/Nbt818

    Article  Google Scholar 

  73. Mackie, J.S., Meares, P.: The diffusion of electrolytes in a cation-exchange resin membrane. 1. Theoretical. Proc. R. Soc. Lond. Ser. A 232(1191), 498–509 (1955a)

    Google Scholar 

  74. Mackie, J.S., Meares, P.: The diffusion of electrolytes in a cation-exchange resin membrane. 2. Experimental. Proc. R. Soc. Lond. Ser. A 232(1191), 510–518 (1955b)

    Google Scholar 

  75. Madzvamuse, A.: Time-stepping schemes for moving grid finite elements applied to reaction-diffusion systems on fixed and growing domains. J. Comput. Phys. 214(1), 239–263 (2006). doi:10.1016/j.jcp.2005.09.012

    Article  MathSciNet  MATH  Google Scholar 

  76. Maes, C., Carmeliet, G.: Vascular and nonvascular roles of VEGF in bone development. In: Ruhrberg, C. (ed.) VEGF in Development, pp. 79–90. Springer, New York (2008)

    Chapter  Google Scholar 

  77. Mahoney, M.J., Krewson, C., Miller, J., Saltzman, W.M.: Impact of cell type and density on nerve growth factor distribution and bioactivity in 3-dimensional collagen gel cultures. Tissue Eng. 12(7), 1915–1927 (2006)

    Article  Google Scholar 

  78. Maini, P.K.: Using mathematical models to help understand biological pattern formation. C. R. Biol. 327(3), 225–234 (2004). doi:10.1016/j.crvi.2003.05.006

    Article  MathSciNet  Google Scholar 

  79. Makarenkova, H.P., Hoffman, M.P., Beenken, A., Eliseenkova, A.V., Meech, R., Tsau, C., Patel, V.N., Lang, R.A., Mohammadi, M.: Differential interactions of FGFs with heparan sulfate control gradient formation and branching morphogenesis. Sci. Signal 2(88), ra55 (2009). doi:2/88/ra55[pii]10.1126/scisignal.2000304

    Google Scholar 

  80. Malda, J., Rouwkema, J., Martens, D.E., le Comte, E.P., Kooy, F.K., Tramper, J., van Blitterswijk, C.A., Riesle, J.: Oxygen gradients in tissue-engineered PEGT/PBT cartilaginous constructs: measurement and modeling. Biotechnol. Bioeng. 86(1), 9–18 (2004). doi:10.1002/Bit.20038

    Article  Google Scholar 

  81. Marcus, R.E.: The effect of low oxygen concentration on growth, glycolysis, and sulfate incorporation by articular chondrocytes in monolayer culture. Arthritis Rheum. 16(5), 646–656 (1973)

    Article  Google Scholar 

  82. Martin, I., Wendt, D., Heberer, M.: The role of bioreactors in tissue engineering. Trends Biotechnol. 22(2), 80–86 (2004). doi:10.1016/j.tibtech.2003.12.001

    Article  Google Scholar 

  83. Mauck, R.L., Hung, C.T., Ateshian, G.A.: Modeling of neutral solute transport in a dynamically loaded porous permeable gel: Implications for articular cartilage biosynthesis and tissue engineering (vol. 125, 602, 2003). J. Biomech. Eng. Trans. ASME 126(3), 392–392 (2004)

    Google Scholar 

  84. Mcelwain, D.L.S., Ponzo, P.J.: Model for growth of a solid tumor with nonuniform oxygen-consumption. Math. Biosci. 35(3–4), 267–279 (1977)

    Article  MATH  Google Scholar 

  85. Mizuno, S., Allemann, F., Glowacki, J.: Effects of medium perfusion on matrix production by bovine chondrocytes in three-dimensional collagen sponges. J. Biomed. Mater. Res. 56(3), 368–375 (2001). doi:10.1002/1097-4636(20010905). 56:3<368:AID-JBM1105>3.0.CO;2-V[pii]

    Article  Google Scholar 

  86. Mizutani, C.M., Nie, Q., Wan, F.Y.M., Zhang, Y.T., Vilmos, P., Sousa-Neves, R., Bier, E., Marsh, J.L., Lander, A.D.: Formation of the BMP activity gradient in the Drosophila embryo. Dev. Cell 8(6), 915–924 (2005). doi:10.1016/j.devcel.2005.04.009

    Article  Google Scholar 

  87. Moseley, J.B., Mayeux, A., Paoletti, A., Nurse, P.: A spatial gradient coordinates cell size and mitotic entry in fission yeast. Nature 459(7248), 857–U858 (2009). doi:10.1038/Nature08074

    Article  Google Scholar 

  88. Moser, H.: Structure and dynamics of bacterial populations maintained in the chemostat. Cold Spring Harb. Symp. Quant. Biol. 22, 121–137 (1957)

    Article  Google Scholar 

  89. Mow, V.C., Kuei, S.C., Lai, W.M., Armstrong, C.G.: Biphasic creep and stress relaxation of articular cartilage in compression? Theory and experiments. J. Biomech. Eng. 102(1), 73–84 (1980)

    Article  Google Scholar 

  90. Murry, C.E., Keller, G.: Differentiation of embryonic stem cells to clinically relevant populations: lessons from embryonic development. Cell 132(4), 661–680 (2008). doi:10.1016/j.cell.2008.02.008

    Article  Google Scholar 

  91. Ng, C.P., Swartz, M.A.: Fibroblast alignment under interstitial fluid flow using a novel 3-D tissue culture model. Am. J. Physiol. Heart Circ. Physiol. 284(5), H1771–H1777 (2003). doi:10.1152/ajpheart.01008.2002

    Google Scholar 

  92. Nimer, E., Schneiderman, R., Maroudas, A.: Diffusion and partition of solutes in cartilage under static load. Biophys. Chem. 106(2), 125–146 (2003). doi:10.1016/S0301-4622(03)00157-1

    Article  Google Scholar 

  93. Obradovic, B., Carrier, R.L., Vunjak-Novakovic, G., Freed, L.E.: Gas exchange is essential for bioreactor cultivation of tissue engineered cartilage. Biotechnol. Bioeng. 63(2), 197–205 (1999). doi:10.1002/(SICI)1097-0290(19990420). 63:2<197:AID-BIT8>3.0.CO;2-2[pii]

    Article  Google Scholar 

  94. Obradovic, B., Meldon, J.H., Freed, L.E., Vunjak-Novakovic, G.: Glycosaminoglycan deposition in engineered cartilage: experiments and mathematical model. AIChE J. 46(9), 1860–1871 (2000)

    Article  Google Scholar 

  95. Ogston, A.G., Preston, B.N., Wells, J.D., Ogston, A.G., Preston, B.N., Snowden, J.M., Wells, J.D.: Transport of compact particles through solutions of chain-polymers. Proc. R. Soc. Lond. A Mat. 333(1594), 297–316 (1973)

    Article  Google Scholar 

  96. Otte, P.: Basic cell metabolism of articular cartilage. Manometric studies. Z. Rheumatol. 50(5), 304–312 (1991)

    Google Scholar 

  97. Page-McCaw, A., Ewald, A.J., Werb, Z.: Matrix metalloproteinases and the regulation of tissue remodelling. Nat. Rev. Mol. Cell Biol. 8(3), 221–233 (2007). doi:10.1038/nrm2125. nrm2125 [pii]

    Article  Google Scholar 

  98. Papas, K.K., Long Jr, R.C., Constantinidis, I., Sambanis, A.: Effects of oxygen on metabolic and secretory activities of beta TC3 cells. Biochim. Biophys. Acta 1291(2), 163–166 (1996). 0304-4165(96)00062-1[pii]

    Article  Google Scholar 

  99. Patterson, G.H., Lippincott-Schwartz, J.: A photoactivatable GFP for selective photolabeling of proteins and cells. Science 297(5588), 1873–1877 (2002)

    Article  Google Scholar 

  100. Patterson, J., Martino, M.M., Hubbell, J.A.: Biomimetic materials in tissue engineering. Mater. Today 13(1–2), 14–22 (2010)

    Article  Google Scholar 

  101. Phelps, E.A., Landazuri, N., Thule, P.M., Taylor, W.R., Garcia, A.J.: Bioartificial matrices for therapeutic vascularization. Proc. Natl. Acad. Sci. U. S. A. 107(8), 3323–3328 (2010). doi:10.1073/pnas.0905447107

    Article  Google Scholar 

  102. Phillips, J.E., Burns, K.L., Le Doux, J.M., Guldberg, R.E., Garcia, A.J.: Engineering graded tissue interfaces. Proc. Natl. Acad. Sci. U. S. A. 105(34), 12170–12175 (2008). doi:10.1073/pnas.0801988105. 0801988105 [pii]

    Article  Google Scholar 

  103. Phillips, R.J., Deen, W.M., Brady, J.F.: Hindered transport of spherical macromolecules in fibrous membranes and gels. AIChE J. 35(11), 1761–1769 (1989)

    Article  Google Scholar 

  104. Picioreanu, C., van Loosdrecht, M.C., Heijnen, J.J.: A new combined differential-discrete cellular automaton approach for biofilm modeling: application for growth in gel beads. Biotechnol. Bioeng. 57(6), 718–731 (1998). doi:10.1002/(SICI)1097-0290(19980320)57:6<718:AID-BIT9>. 3.0.CO;2-O [pii]

    Article  Google Scholar 

  105. Place, E.S., Evans, N.D., Stevens, M.M.: Complexity in biomaterials for tissue engineering. Nat. Mater. 8(6), 457–470 (2009). doi:10.1038/Nmat2441

    Article  Google Scholar 

  106. Pugh, C.W., Ratcliffe, P.J.: Regulation of angiogenesis by hypoxia: role of the HIF system. Na.t Med. 9(6), 677–684 (2003). doi:10.1038/nm0603-677nm0603-677 [pii]

    Google Scholar 

  107. Qutub, A.A., Mac Gabhann, F., Karagiannis, E.D., Vempati, P., Popel, A.S.: Multiscale models of angiogenesis. IEEE Eng. Med. Biol. Mag. 28(2), 14–31 (2009). doi:10.1109/MEMB.2009.931791

    Article  Google Scholar 

  108. Rajpurohit, R., Koch, C.J., Tao, Z., Teixeira, C.M., Shapiro, I.M.: Adaptation of chondrocytes to low oxygen tension: relationship between hypoxia and cellular metabolism. J. Cell. Physiol. 168(2), 424–432 (1996). doi:10.1002/(SICI)1097-4652(199608). 168:2<424:AID-JCP21>3.0.CO;2-1[pii]10.1002/(SICI)1097-4652(199608)168:2<424:AID-JCP21>3.0.CO;2-1

    Article  Google Scholar 

  109. Rolfe, D.F., Brown, G.C.: Cellular energy utilization and molecular origin of standard metabolic rate in mammals. Physiol. Rev. 77(3), 731–758 (1997)

    Google Scholar 

  110. Sengers, B.G., Heywood, H.K., Lee, D.A., Oomens, C.W.J., Bader, D.L.: Nutrient utilization by bovine articular chondrocytes: A combined experimental and theoretical approach. J. Biomech. Eng. Trans. ASME 127(5), 758–766 (2005). doi:10.1115/1.1993664

    Article  Google Scholar 

  111. Sengers, B.G., van Donkelaar, C.C., Oomens, C.W.J., Baaijens, F.P.T.: Computational study of culture conditions and nutrient supply in cartilage tissue engineering. Biotechnol. Prog. 21(4), 1252–1261 (2005). doi:10.1021/Bp0500157

    Article  Google Scholar 

  112. Singh, A.B., Harris, R.C.: Autocrine, paracrine and juxtacrine signaling by EGFR ligands. Cell. Signal. 17(10), 1183–1193 (2005). doi:10.1016/j.cellsig.2005.03.026

    Article  Google Scholar 

  113. Soukane, D.M., Shirazi-Adl, A., Urban, J.P.G.: Computation of coupled diffusion of oxygen, glucose and lactic acid in an intervertebral disc. J. Biomech. 40(12), 2645–2654 (2007). doi:10.1016/j.jbiomech.2007.01.003

    Article  Google Scholar 

  114. Southern, J., Pitt-Francis, J., Whiteley, J., Stokeley, D., Kobashi, H., Nobes, R., Kadooka, Y., Gavaghan, D.: Multi-scale computational modelling in biology and physiology. Prog. Biophys. Mol. Biol. 96(1–3), 60–89 (2008). doi:10.1016/j.pbiomolbio.2007.07.019. S0079-6107(07)00067-3 [pii]

    Article  Google Scholar 

  115. Sternlicht, M.D., Werb, Z.: How matrix metalloproteinases regulate cell behavior. Annu. Rev. Cell Dev. Biol. 17, 463–516 (2001)

    Article  Google Scholar 

  116. Stevens, M.M., Marini, R.P., Schaefer, D., Aronson, J., Langer, R., Shastri, V.P.: In vivo engineering of organs: the bone bioreactor. Proc. Natl. Acad. Sci. U. S. A. 102(32), 11450–11455 (2005). doi:10.1073/pnas.0504705102. 0504705102 [pii]

    Article  Google Scholar 

  117. Stylianopoulos, T., Barocas, V.H.: Volume-averaging theory for the study of the mechanics of collagen networks. Comput. Method Appl. Mech. Eng. 196(31–32), 2981–2990 (2007). doi:10.1016/j.cma.2006.06.019

    Article  MathSciNet  MATH  Google Scholar 

  118. Stylianopoulos, T., Diop-Frimpong, B., Munn, L.L., Jain, R.K.: Diffusion anisotropy in collagen gels and tumors: the Effect of fiber network orientation. Biophys. J. 99(10), 3119–3128 (2010). doi:10.1016/j.bpj.2010.08.065

    Article  Google Scholar 

  119. Sumi, T., Tsuneyoshi, N., Nakatsuji, N., Suemori, H.: Defining early lineage specification of human embryonic stem cells by the orchestrated balance of canonical Wnt/beta-catenin. Activin/Nodal BMP signal. Dev. 135(17), 2969–2979 (2008). doi:10.1242/Dev.021121

    Google Scholar 

  120. Swartz, M.A., Fleury, M.E.: Interstitial flow and its effects in soft tissues. Annu. Rev. Biomed. Eng. 9, 229–256 (2007). doi:10.1146/annure/bioeng.9.060906.151850

    Article  Google Scholar 

  121. Teleman, A.A., Strigini, M., Cohen, S.M.: Shaping morphogen gradients. Cell 105(5), 559–562 (2001). S0092-8674(01)00377-4 [pii]

    Article  Google Scholar 

  122. Tschumperlin, D.J., Dai, G.H., Maly, I.V., Kikuchi, T., Laiho, L.H., McVittie, A.K., Haley, K.J., Lilly, C.M., So, P.T.C., Lauffenburger, D.A., Kamm, R.D., Drazen, J.M.: Mechanotransduction through growth-factor shedding into the extracellular space. Nature 429(6987), 83–86 (2004)

    Article  Google Scholar 

  123. Tsuji, K., Bandyopadhyay, A., Harfe, B.D., Cox, K., Kakar, S., Gerstenfeld, L., Einhorn, T., Tabin, C.J., Rosen, V.: BMP2 activity, although dispensable for bone formation, is required for the initiation of fracture healing. Nat. Genet. 38(12), 1424–1429 (2006). doi:10.1038/Ng1916

    Article  Google Scholar 

  124. van der Eerden, B.C.J., Karperien, M., Wit, J.M.: Systemic and local regulation of the growth plate. Endocr. Rev. 24(6), 782–801 (2003). doi:10.1210/Er.2002-0033

    Article  Google Scholar 

  125. van Donkelaar, C.C., Huiskes, R.: The PTHrP-Ihh feedback loop in the embryonic growth plate allows PTHrP to control hypertrophy and Ihh to regulate proliferation. Biomech. Model. Mechanbiol. 6(1–2), 55–62 (2007). doi:10.1007/s10237-006-0035-0

    Article  Google Scholar 

  126. Vortkamp, A., Lee, K., Lanske, B., Segre, G.V., Kronenberg, H.M., Tabin, C.J.: Regulation of rate of cartilage differentiation by Indian hedgehog and PTH-related protein. Science 273(5275), 613–622 (1996)

    Article  Google Scholar 

  127. Williams, R.M., Zipfel, W.R., Tinsley, M.L., Farnum, C.E.: Solute transport in growth plate cartilage: in vitro and in vivo. Biophys. J. 93(3), 1039–1050 (2007). doi:10.1529/biophysj.106.097675

    Article  Google Scholar 

  128. Wood, B.D., Quintard, M., Whitaker, S.: Calculation of effective diffusivities for biofilms and tissues. Biotechnol. Bioeng. 77(5), 495–516 (2002). 10.1002/bit.10075 [pii]

    Article  Google Scholar 

  129. Wood, B.D., Whitaker, S.: Diffusion and reaction in biofilms. Chem. Eng. Sci. 53(3), 397–425 (1998)

    Article  Google Scholar 

  130. Zhou, S., Cui, Z., Urban, J.P.G.: Nutrient gradients in engineered cartilage: metabolic kinetics measurement and mass transfer modeling. Biotechnol. Bioeng. 101(2), 408–421 (2008). doi:10.1002/Bit.21887

    Article  Google Scholar 

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  1. Department of Metallurgy and Materials Engineering, KU Leuven, Kasteelpark Arenberg 44-box 2450, 3001, Leuven, Belgium

    Dennis Lambrechts & Jan Schrooten

  2. Prometheus, Division of Skeletal Tissue Engineering Leuven, KU Leuven, Herestraat 49-box 813, 3000, Leuven, Belgium

    Dennis Lambrechts, Jan Schrooten & Hans Van Oosterwyck

  3. TiGenix NV, Haasrode Researchpark 1724, Romeinse straat 12 box 2, 3001, Leuven, Belgium

    Tom Van de Putte

  4. Biomechanics Section, KU Leuven, Celestijnenlaan 300C-box 2419, 3001, Leuven, Belgium

    Hans Van Oosterwyck

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    Liesbet Geris

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Lambrechts, D., Schrooten, J., Van de Putte, T., Van Oosterwyck, H. (2012). Computational Modeling of Mass Transport and Its Relation to Cell Behavior in Tissue Engineering Constructs. In: Geris, L. (eds) Computational Modeling in Tissue Engineering. Studies in Mechanobiology, Tissue Engineering and Biomaterials, vol 10. Springer, Berlin, Heidelberg. https://doi.org/10.1007/8415_2012_139

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