Curtis, A., and Riehle, M., 2001, “Tissue Engineering: The Biophysical Background,” Phys. Med. Biol., 46 , pp. R47–R65.

[CrossRef]Peirce, S., Skalak, T., and Papin, J., 2006, “Multiscale Biosystems Integration: Coupling Intracellular Network Analysis With Tissue-Patterning Simulations,” IBM J. Res. Dev., 50 (6), pp. 601–615.

Cowin, S. C., 2000, “How Is a Tissue Built?,” ASME J. Biomech. Eng., 122 , pp. 553–569.

[CrossRef]Cowin, S., 2004, “Tissue Growth and Remodeling,” Annu. Rev. Biomed. Eng., 6 (1), pp. 77–107.

[CrossRef]Sipe, J., 2002, “Tissue Engineering and Reparative Medicine,” Ann. N.Y. Acad. Sci., 961 , pp. 1–9.

[CrossRef]Powers, M., Rodriguez, R., and Griffith, L., 1997, “Cell-Substratum Adhesion Strength as a Determinant of Hepatocyte Aggregate Morphology,” Biotechnol. Bioeng., 20 (4), pp. 15–26.

Fung, Y., 1991, “What Are Residual Stresses Doing in Our Blood Vessels?,” Ann. Biomed. Eng., 19 , pp. 237–249.

[CrossRef]Ingber, D. E., 2005, “Mechanical Control of Tissue Growth: Function Follows Form,” Proc. Natl. Acad. Sci., 102 (33), pp. 11571–11572.

[CrossRef]Shraiman, B., 2005, “Mechanical Feedback as a Possible Regulator of Tissue Growth,” Proc. Natl. Acad. Sci. U.S.A., 102 (9), pp. 3318–3323.

[CrossRef]Bakker, A., Klein-Nulend, J., and Burger, E., 2004, “Shear Stress Inhibits While Disuse Promotes Osteocyte Apoptosis,” Biochem. Biophys. Res. Commun., 320 , pp. 1163–1168.

[CrossRef]Han, Y., Cowin, S., Schaffler, M., and Weinbaaum, S., 2004, “Mechanotransduction and Strain Amplification in Osteocyte Cell Processes,” Proc. Natl. Acad. Sci. U.S.A., 101 (47), pp. 16689–16694.

[CrossRef]Klein-Nulend, J., Helfrich, M., Sterck, J., Macpherson, H., Joldersma, M., Ralston, S., Semeins, C., and Burger, E., 1998, “Nitric Oxide Response to Shear Stress by Human Bone Cell Cultures Is Endothelial Nitric Oxide Synthase Dependent,” Biochem. Biophys. Res. Commun., 250 , pp. 108–114.

[CrossRef]Klein-Nulend, J., Van Der Plas, A., Semeins, C., Ajubi, N., Frangos, J., Nijweide, P., and Burger, E., 1995, “Sensitivity of Osteocytes to Biomechanical Stress In Vitro,” FASEB J., 9 , pp. 441–445.

Weinbaum, S., Cowin, S., and Zeng, Y., 1994, “A Model for the Excitation of Osteosytes by Mechanical Loading-Induced Bone Fluid Shear Stresses,” J. Biomech., 27 (3), pp. 339–360.

[CrossRef]You, J., Yellowley, C., Donahue, H., Zhang, Y., Chen, Q., and Jacobs, C., 2000, “Substrate Deformation Levels Associated With Routine Physical Activity Are Less Stimulatory to Bone Cells Relative to Loading-Induced Oscillatory Fluid Flow,” ASME J. Biomech. Eng., 122 , pp. 387–393.

[CrossRef]You, L., Cowin, S., Schaffler, M., and Weinbaum, S., 2001, “A Model for Strain Amplification in the Actin Cytoskeleton of Osteocytes Due to Fluid Drag on Pericellular Matrix,” J. Biomech., 34 (11), pp. 1375–1386.

[CrossRef]Martin, I., Wendt, D., and Heberer, M., 2004, “The Role of Bioreactors in Tissue Engineering,” Trends Biotechnol., 22 (2), pp. 80–86.

[CrossRef]Cartmell, S., and El-Haj, A., 2005, “Mechanical Bioreactors for Tissue Engineering,” "*Bioreactors for Tissue Engineering: Principles, Design and Operation*", J.Chaudhuri and M.Al-Rubeai, eds., Springer, Dordrecht, The Netherlands, Chap. 8, pp. 193–208.

Araujo, R., and McElwain, D., 2004, “A History of the Study of Solid Tumour Growth: The Contribution of Mathematical Modelling,” Bull. Math. Biol., 66 (5), pp. 1039–1091.

[CrossRef]Alarcon, T., Byrne, H., Maini, P., and Panovska, J., 2005, “Mathematical Modelling of Angiogenesis and Vascular Adaptation,” "*Studies in Multidisciplinarity*", Elsevier, Amsterdam, Vol. 3 , pp. 369–387.

Chaplain, M., 2000, “Mathematical Modelling of Angiogenesis,” J. Neuro-Oncol., 50 (1–2), pp. 37–51.

[CrossRef]Chaplain, M., McDougall, S., and Anderson, A., 2006, “Mathematical Modeling of Tumor-Induced Angiogenesis,” Annu. Rev. Biomed. Eng., 8 (1), pp. 233–257.

[CrossRef]Ambrosi, D., Bussolino, F., and Preziosi, L., 2005, “A Review of Vasculogenesis Models,” Computational and Mathematical Methods in Medicine, 6 (1), pp. 1–19.

[CrossRef]Sherratt, J., and Dallon, J., 2002, “Theoretical Models of Wound Healing: Past Successes and Future Challenges,” C. R. Biol., 325 (5), pp. 557–564.

[CrossRef]Lemon, G., King, J., Byrne, H., Jensen, O., and Shakesheff, K., 2006, “Multiphase Modelling of Tissue Growth Using the Theory of Mixtures,” J. Math. Biol., 52 (5), pp. 571–594.

[CrossRef]O’Dea, R. D., Waters, S. L., and Byrne, H. M., 2009, “A Multiphase Model for Tissue Construct Growth in a Perfusion Bioreactor,” Journal of Mathematical Medicine and Biology to be published.

[CrossRef]O’Dea, R., Waters, S., and Byrne, H., 2008, “A Two-Fluid Model for Tissue Growth Within a Dynamic Flow Environment,” Eur. J. Appl. Math., 19 (6), pp. 607–634.

[CrossRef]El Haj, A. J., Minter, S. L., Rawlinson, S. C. F., Suswillo, R., and Lanyon, L. E., 1990, “Cellular Responses to Mechanical Loading In Vitro,” J. Bone Miner. Res., 5 (9), pp. 923–932.

[CrossRef]Kaasschieter, E., Frijns, A., and Huyghe, J., 2003, “Mixed Finite Element Modelling of Cartilaginous Tissues,” Math. Comput. Simul., 61 (3–6), pp. 549–560.

[CrossRef]Kelly, D., and Prendergast, P., 2004, “Effect of a Degraded Core on the Mechanical Behaviour of Tissue-Engineered Cartilage Constructs: A Poro-Elastic Finite Element Analysis,” Med. Biol. Eng. Comput., 42 , pp. 9–13.

[CrossRef]Adachi, T., Osako, Y., Tanaka, M., Hojo, M., and Hollister, S., 2006, “Framework for Optimal Design of Porous Scaffold Microstructure by Computational Simulation of Bone Regeneration,” Biomaterials, 27 , pp. 3964–3972.

[CrossRef]Sanz-Herrera, J., García-Aznar, J., and Doblaré, M., 2009, “On Scaffold Designing for Bone Regeneration: A Computational Multiscale Approach,” Acta Biomater., 5 (1), pp. 219–229.

[CrossRef]McGarry, J., Klein-Nulend, J., Mullender, M., and Prendergast, P., 2004, “A Comparison of Strain and Fluid Shear Stress in Stimulating Bone Cell Responses—A Computation and Experimental Study,” FASEB J., 19 (15), pp. 482–484.

Roose, T., Neti, P., Munn, L., Boucher, Y., and Jain, R., 2003, “Solid Stress Generated by Spheroid Growth Estimated Using a Poroelasticity Model,” Microvasc. Res., 66 , pp. 204–212.

[CrossRef]Araujo, R., and McElwain, D., 2005, “A Mixture Theory for the Genesis of Residual Stresses in Growing Tissues I: A General Formulation,” SIAM J. Appl. Math., 65 (4), pp. 1261–1284.

[CrossRef]Byrne, H., and Preziosi, L., 2003, “Modelling Solid Tumour Growth Using the Theory of Mixtures,” Math. Med. Biol., 20 (4), pp. 341–366.

[CrossRef]Chaplain, M., Graziano, L., and Preziosi, L., 2006, “Mathematical Modelling of the Loss of Tissue Compression Responsiveness and Its Role in Solid Tumour Development,” Math. Med. Biol., 23 (3), pp. 197–229.

[CrossRef]Franks, S., and King, J., 2003, “Interactions Between a Uniformly Proliferating Tumour and Its Surroundings: Uniform Material Properties,” Math. Med. Biol., 20 , pp. 47–89.

[CrossRef]Landman, K., and Please, C., 2001, “Tumour Dynamics and Necrosis: Surface Tension and Stability,” IMA J. Math. Appl. Med. Biol., 18 (2), pp. 131–158.

[CrossRef]Bowen, R., 1976, “"*Mixtures and EM Field Theories*",” Continuum Physics , A.C.Eringen, ed., Academic Press, New York, Vol. 3 , pp. 1–127.

Kolev, N., 2002, "*Multiphase Flow Dynamics*", Vol. 1 , Springer-Verlag, Berlin.

Humphrey, J. D., 2003, “Continuum Biomechanics of Soft Biological Tissues,” Proc. R. Soc. London, Ser. A, 459 , pp. 3–46.

[CrossRef]Roelofsen, J., Klein-Nulend, J., and Burger, E., 1995, “Mechanical Stimulation by Intermittent Hydrostatic Compression Promotes Bone-Specific Gene Expression In Vitro,” J. Biomech., 28 (12), pp. 1493–1503.

[CrossRef]Klein-Nulend, J., Roelofsen, J., Sterck, J., Semeins, C., and Burger, E., 1995, “Mechanical Loading Stimulates the Release of Transforming Growth Factor-Beta Activity by Cultured Mouse Calvariae and Periosteal Cells,” J. Cell Physiol., 163 (1), pp. 115–119.

[CrossRef]Acheson, D. J., 1990, "*Elementary Fluid Dynamics*", Clarendon, Oxford.

Osborne, J., 2009, “Numerical and Computational Methods for Simulating Multiphase Models of Tissue Growth,” Ph.D. thesis, University of Oxford, Oxford.

Franks, S., Byrne, H., King, J., Underwood, J., and Lewis, C., 2003, “Modelling the Early Growth of Ductal Carcinoma In Situ of the Breast,” J. Math. Biol., 47 , pp. 424–452.

[CrossRef]King, J., and Franks, S., 2004, “Mathematical Analysis of Some Multi-Dimensional Tissue Growth Models,” Eur. J. Appl. Math., 15 (3), pp. 273–295.

[CrossRef]VonNeumann, J., and Richtmyer, R., 1950, “A Method for the Numerical Calculation of Hydrodynamic Shocks,” J. Appl. Phys., 21 , pp. 232–237.

[CrossRef]Elman, H. C., Silvester, D. J., and Wathen, A. J., 2005, "*Finite Elements and Fast Iterative Solvers With Applications in Incompressible Fluid Dynamics*", 1st ed., Oxford University Press, Oxford.

Lemon, G., and King, J. R., 2007, “Multiphase Modelling of Cell Behaviour on Artificial Scaffolds: Effects of Nutrient Depletion and Spatially Nonuniform Porosity,” Math. Med. Biol., 24 (1), pp. 57–83.

[CrossRef]MacArthur, B., Please, C., Taylor, M., and Oreffo, R., 2004, “Mathematical Modeling of Skeletal Repair,” Biochem. Biophys. Res. Commun., 313 (4), pp. 825–833.

[CrossRef]Wilson, D., King, J., and Byrne, H., 2007, “Modelling Scaffold Occupation by a Growing, Nutrient-Rich Tissue,” Math. Models Meth. Appl. Sci., 17 , pp. 1721–1750.

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