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References
Adam, J.A. (1986) A simplified mathematical model of tumour growth.Math. Biosc. 81, 229–244.
Alarcon, T., H. Byrne, and P. Maini (2003) A cellular automaton model for tumour growth in inhomogeneous environment.J. Theor. Biol. 225(15.2), 257– 274.
Anderson, A.R.A., B.D.S. Sleeman, I.M. Young, and B.S. Griffiths (1997) Nematode movement along a chemical gradient in a structurally heterogeneous environment: II Theory.Fundam. Appl. Nematol. 20, 165–172.
Anderson, A.R.A., and M.A.J. Chaplain (1998) Continuous and discrete mathematical models of tumor-induced angiogenesis.Bull. Math. Biol. 60, 857–899.
Ausprunk, D.H., and J. Folkman (1977) Migration and proliferation of endothelial cells in preformed and newly formed blood vessels during tumour angiogenesis.Microvasc. Res.14, 53–65.
Baish, J.W., Y. Gazit, D.A. Berk, M. Nozue, L.T. Baxter, and R.K. Jain (1996) Role of tumor vascular architecture in nutrient and drug delivery: an invasion percolation-based network model.Microvasc. Res. 51, 327–346.
Baish, J.W., P.A. Netti, and R.K. Jain (1997) Transmural coupling of fluid flow in microcirculatory network and interstitium in tumours.Microvasc. Res. 53, 128–141.
Bray, D. (1992)Cell Movements, Garland Publishing, New York.
Benjamin, L.E., I. Hemo, and E. Keshet (1998) A plasticity window for blood vessel remodelling is defined by pericyte coverage of the preformed endothelial network and is regulated by PDGF-B and VEGF.Development 125, 1591–1598.
Breward, C.J.W., H.M. Byrne, and C.E. Lewis (2003) A multiphase model describing vascular tumour growth.Bull. Math. Biol. 65, 609–640.
Chaplain, M.A.J., and G. Lolas (2005) Mathematical modelling of cancer cell invasion of tissue: the role of the urokinase plasminogen activation system.Math. Modell. Methods. Appl. Sci. 15, 1685–1734.
Chatzis, I., and F.A.L. Dullien (1977) Modelling pore structure by 2D and 3D networks with application to sandstone.J. Can. Pet. Technol. 16, 97.
Ciofalo, M., M.W. Collins, and T.R. Hennessy (1999) Microhydrodynamics phenomena in the circulation, in Nanoscale Fluid Dynamics in Physiological Processes, A Review Study. WIT Press, Southampton, UK, 219–236.
Davis, G.E., K.A. Pintar Allen, R. Salazar, and S.A. Maxwell (2000) Matrix metalloproteinase-1 and –9 activation by plasmin regulates a novel endothelial cell-mediated mechanism of collagen gel contraction and capillary tube regression in three-dimensional collagen matrices.J. Cell Sci. 114, 917–930.
El-Kareh, A.W., and T.W. Secomb (1997) Theoretical models for drug delivery to solid tumours.Crit. Rev. Biomed. Eng.25(6), 503–571.
Folkman, J., and M. Klagsbrun (1987) Angiogenic factors.Science 235, 442– 447.
Franks, S.J., H.M. Byrne, J.R. King, J.C.E. Underwood, and C.E. Lewis (2005) Biological inferences from a mathematical model of comedo ductal carcinoma in situ of the breast.J. Theor. Biol. 232(15.4), 523–543.
Fung, Y.C. (1993)Biomechanics. Springer-Verlag, New York.
Gatenby, R.A., and E.T. Gawlinski (2003) The glycolytic phenotype in carcinogenesis and tumour invasion. Insights through mathematical modelling.Cancer Res.63, 3847–3854.
Gimbrone, M.A., R.S. Cotran, S.B. Leapman, and J. Folkman (1974) Tumor growth and neovascularization: an experimental model using the rabbit cornea.J. Natl. Cancer Inst.52, 413–427.
Glass, L. (1973) Instability and mitotic patterns in tissue growth.J. Dyn. Syst. Meas. Control. 95, 324–327.
Gödde, R., and H. Kurz (2001) Structural and biophysical simulation of angiogenesis and vascular remodeling,Developmental Dynamics 220, 387–401.
Gottlieb, M.E. (1990) Modelling blood vessels: a deterministic method with fractal structure based on physiological rules.Proc 12 th Int Conf of IEEE EMBS, 1386–1387, IEEE Press, New York.
Greenspan, H.P. (1972) Models for the growth of a solid tumour by diffusion.Stud. Appl. Math. 52, 317–340.
Greenspan, H.P. (1976). On the growth and stability of cell cultures and solid tumours.J. Theor. Biol. 56, 229–242.
Gruionu, G., J.B. Hoyling, A.R. Pries, and T.W. Secomb (2005) Structural remodelling of mouse gracilis artery after chronic alteration in blood supply.Am. J. Physiol. Heart. Circ. Physiol. 288, 2047–2054.
Hidalgo, M., and S.G. Eckkhardt (2001) Development of matrix metalloproteinase inhibitors in cancer therapy.J. Natl. Cancer Inst. 93, 178–193.
Honda, H., and K. Yoshizato (1997) Formation of the branching pattern of blood vessels in the wall of the avian yolk sac studied by a computer simulation.Develop. Growth Differ.39, 581–589.
Jackson, T.L. (2002) Vascular tumour growth and treatment: consequences of polyclonality, competition and dynamic vascular support.J. Math. Biol. 44, 201–226.
Kamiya, A., R. Bukhari, and T. Togawa (1984) Adaptive regulation of wall shear stress optimizing vascular tree function.Bull. Math. Biol. 46, 127–137.
Krenz, G.S., and C.A. Dawson (2002) Vessel distensibility and flow distribution in vascular trees.J. Math. Biol. 44, 360–374.
Lankelma, J., R.F. Luque, H. Dekker, W. Shinkel, and H.M. Pinedao (2000) A mathematical model of drug transport in human breast cancer.Microvasc. Res. 59, 149–161.
Serve, A.W., and K. Hellmann (1972) Metastases and normalization of tumor blood-vessels by icrf 159—new type of drug action.Br. Med. J. 1, 597– 601.
Levine, H.A., S. Pamuk, B.D. Sleeman, and M. Nielsen-Hamilton (2001) Mathematical modeling of the capillary formation and development in tumor angiogenesis: penetration into the stroma,Bull. Math. Biol. 63(15.5), 801–863.
35. Lolas, G. (2003) Mathematical modelling of the urokinase plasminogen activator system and its role in cancer invasion of tissue. PhD Thesis, University of Dundee.
McDougall, S.R., and K. Sorbie (1997) The application of network modelling techniques to multiphase flow in porous media.Petroleum Geosci.3, 161–169.
McDougall, S.R., A.R.A. Anderson, M.A.J. Chaplain, and J.A. Sherratt (2002) Mathematical modelling of flow through vascular networks: implications for tumour-induced angiogenesis and chemotherapy strategies.Bull. Math. Biol.64(15.4), 673–702.
McDougall, S.R., A.R.A. Anderson, and M.A.J. Chaplain (2006) Mathematical modelling of dynamic adaptive tumour-induced angiogenesis: clinical implications and therapeutic targeting strategies.J. Theor. Biol. 241, 564–589.
McElwain, D.L.S., and G.J. Pettet (1993) Cell migration in multicell spheroids: swimming against the tide.Bull. Math. Biol. 55, 655–674.
Madri, J.A., and B.M. Pratt (1986) Endothelial cell-matrix interactions: in vitro models of angiogenesis.J. Histochem. Cytochem. 34, 85–91.
Mohanty, K.K., and S.J. Salter (1982) Multiphase flow in porous media: II Pore-level modelling. SPE 11018 presented at the 57th Annual Conference of the SPE, New Orleans, Louisiana.
Mollica, F., R.K. Jain, and P.A. Netti (2003) A model for temporal heterogeneities of tumour blood flow.Microvasc. Res.65, 56–60.
Morikawa, S., P. Baluk, T. Kaidoh, et al. (2002) Abnormalities in pericytes on blood vessels and endothelial sprouts in tumors.Am. J. Pathol. 160, 985–1000.
Muthukkaruppan, V.R., L. Kubai, and R. Auerbach (1982) Tumor-induced neovascularization in the mouse eye.J. Natl. Cancer Inst.69, 699–705.
Nekka, F., S. Kyriacos, C. Kerrigan, and L. Cartilier (1996) A model for growing vascular structures.Bull. Math. Biol. 58(15.3), 409–424.
Netti, P.A., S. Roberge, Y. Boucher, L.T. Baxter, and R.K. Jain (1996) Effect of transvascular fluid exchange on pressure-flow relationship in tumours: a proposed mechanism for tumour blood flow heterogeneity.Microvasc. Res.52, 27–46.
Othmer, H., and A. Stevens (1997) Aggregation, blowup and collapse. The ABCs of taxis and reinforced random walks.SIAM. J. Appl. Math. 57, 1044–1081.
Paweletz, N., and M. Knierim (1989) Tumor-related angiogenesis.Crit. Rev. Oncol. Hematol. 9, 197–242.
Piri, M., and M.J. Blunt (2005a) Three-dimensional mixed-wet random porescale network modeling of two- and three-phase flow in porous media. I. Model description.Phys. Rev. E. 71, 026301.
Piri, M., and M.J. Blunt (2005b) Three-dimensional mixed-wet random porescale network modeling of two- and three-phase flow in porous media. II. Results.Phys. Rev. E. 71, 026302.
Plank, M.J., and B.D.S. Sleeman (2004) Lattice and non-lattice models of tumour angiogenesis.Bull. Math. Biol. 66(6), 1785–1819.
Please, C.P., G.J. Pettet, and D.L.S. McElwain (1998) A new approach to modelling the formation of necrotic regions in tumours.Appl. Math. Lett. 11, 89–94.
Popel, A.S., and P.C. Johnson (2005) Microcirculation and haemorheology.Ann. Rev. Fluid Mech. 37, 43–69.
Preziosi, L., and A. Farina (2002) On Darcy’s law for growing porous media.Int. J. Non-linear Mechanics.37, 485–491.
Pries, A.R., T.W. Secomb, P. Gaehtgens, and J.F. Gross (1990) Blood flow in microvascular networks. Experiments and simulation.Circulation Res., 67, 826–834.
Pries, A.R., T.W. Secomb, and P. Gaehtgens (1996) Biophysical aspects of blood flow in the microvasculature.Cardiovasc. Res., 32, 654–667.
Pries, A.R., T.W. Secomb, and P. Gaehtgens (1998) Structural adaptation and stability of microvascular networks: theory and simulation.Am. J. Physiol. 275 (Heart Circ. Physiol. 44), H349–H360.
Pries, A.R., B. Reglin, and T.W. Secomb (2001a) Structural adaptation of microvascular networks: functional roles of adaptive responses.Am. J. Physiol. Heart Circ. Physiol. 281, H1015–H1025.
Pries, A.R., B. Reglin, and T.W. Secomb (2001b) Structural adaptation of vascular networks: role of the pressure response.Hypertension 38, 1476–1479.
Pries, A.R., B. Reglin, and T.W. Secomb (2005) Remodelling of blood vessels: response of diameter and wall thickness to haemodynamic and metabolic stimuli.Hypertension 46, 725–731.
Pries, A.R., and T.W. Secomb (2005) Control of blood vessel structure: insights from theoretical models.Am. J. Physiol. Heart Circ. Physiol. 288, 1010–1015.
Pries, A.R., and T.W. Secomb (2005) Microvascular blood viscosity in vivo and the endothelial surface layer.Am. J. Physiol. Heart Circ. Physiol. 289, 2657–2664.
Quarteroni, A., M. Tuveri, and A. Veneziani (2000) Computational vascular fluid dynamics: problems, models and methods.Comput. Visual. Sci. 2, 163– 197.
Ribba, B., K. Marron, Z. Agur, T. Alarcon, and P.K. Maini (2005) A mathematical model of Doxorubicin treatment efficacy for non-Hodgkin’s lymphoma.Bull. Math. Biol.67, 79–99.
Salsbury, A.J., K. Burrage, and K. Hellmann (1970) Inhibition of metastatic spread by icrf159—selective deletion of a malignant characteristic.Br. Med. J. 4, 344–346.
Schmid-Schönbein, G.W. (1999) Biomechanics of microcirculatory blood perfusion.Ann. Rev. Biomed. Eng. 1, 73–102.
Schoefl, G.I. (1963) Studies of inflammation III. Growing capillaries: their structure and permeability.Virchows Arch. Path. Anat.337, 97–141.
68. Secomb, T.W. (1995) Mechanics of blood flow in the microcirculation.The Society for Experimental Biology, 305–321.
Sherratt, J.A. and M.A.J. Chaplain (2001) A new mathematical model for avascular tumour growth.J. Math. Biol. 43, 291–312.
Sholley, M.M., G.P. Ferguson, H.R. Seibel, J.L. Montour, and J.D. Wilson (1984) Mechanisms of neovascularization. Vascular sprouting can occur without proliferation of endothelial cells.Lab. Invest.51, 624–634.
Stéphanou, A., S.R. McDougall, A.R.A. Anderson, and M.A.J. Chaplain (2005) Mathematical modelling of flow in 2D and 3D vascular networks: applications to anti-angiogenic and chemotherapeutic drug strategies.Math. Comp. Model.41, 1137–1156.
Stéphanou, A., S.R. McDougall, A.R.A. Anderson, and M.A.J. Chaplain (2006) Mathematical modelling of the influence of blood rheological properties upon adaptive tumour-induced angiogenesis.Math. Comp. Model.44, 96–123.
Sternlicht, M.D., and Z. Werb (2001) How matrix metalloproteinases regulate cell behavior.Annu. Rev. Cell. Dev. Biol. 17, 463–516.
Stokes, C.L., and D.A. Lauffenburger (1991) Analysis of the roles of microvessel endothelial cell random motility and chemotaxis in angiogenesis.J. Theor. Biol.152, 377–403.
Sun, S., M.F. Wheeler, M. Obeyesekere, and P.W. Charles (2005) A deterministic model of growth factor induced angiogenesis.Bull. Math. Biol. 67 (15.2), 313–337.
Thomlinson, R.H., and L.H. Gray (1955) The histological structure of some human lung cancers and the possible implications for radiotherapy.Br. J. Cancer 9, 539–549.
Tong, S., and F. Yuan (2001) Numerical simulations of angiogenesis in the cornea.Microvasc. Res.61, 14–27.
Ward, J.P., and J.R. King (1997) Mathematical modelling of avascular tumour growth.IMA J. Math. Appl. Med. Biol.14, 36–69.
Ward, J.P., and J.R. King (1999) Mathematical modelling of avascular tumour growth. (ii) Modelling growth saturation.IMA J. Math. Appl. Med. Biol. 16, 171–211.
M.A. Moses, S. Huang, and D. Ingber (2000) Adhesion-dependent control of matrix metalloproteinase-2 activation in human capillary endothelial cells.J. Cell Sci. 113, 3979–3987.
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McDougall, S.R. (2008). Dynamically Adaptive Tumour Induced Angiogenesis The Impact of Flow on the Developing Capillary Plexus. In: Selected Topics in Cancer Modeling. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4713-1_15
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