Multiphase modelling of tumour growth and extracellular matrix interaction: mathematical tools and applications (original) (raw)

• Ambrosi D, Guana F (2007) Stress modulated growth. Math Mech Solids 12(3): 319–342
  Article MATH MathSciNet Google Scholar
• Ambrosi D, Mollica F (2002) On the mechanics of a growing tumor. Int J Eng Sci 40(12): 1297–1316
  Article MathSciNet Google Scholar
• Ambrosi D, Mollica F (2004) The role of stress in the growth of a multicell spheroid. J Math Biol 48(5): 477–499
  Article MATH MathSciNet Google Scholar
• Ambrosi D, Preziosi L (2008) Cell adhesion mechanisms and elasto-viscoplastic mechanics of tumours. Biomech Model Mechanobiol (to appear)
• Ambrosi D, Preziosi L (2002) On the closure of mass balance models for tumor growth. Math Models Methods Appl Sci 12(5): 737–754
  Article MATH MathSciNet Google Scholar
• Araujo RP, McElwain DLS (2004) A history of the study of solid tumour growth: the contribution of mathematical modelling. Bull Math Biol 66(5): 1039–1091
  Article MathSciNet Google Scholar
• Araujo RP, McElwain DLS (2004) A linear-elastic model of anisotropic tumour growth. Eur J Appl Math 15(3): 365–384
  Article MATH MathSciNet Google Scholar
• Araujo RP, McElwain DLS (2005) A mixture theory for the genesis of residual stresses in growing tissues. I. A general formulation. SIAM J Appl Math 65(4): 1261–1284 (electronic)
  Article MATH MathSciNet Google Scholar
• Araujo RP, McElwain DLS (2005) A mixture theory for the genesis of residual stresses in growing tissues. II. Solutions to the biphasic equations for a multicell spheroid. SIAM J Appl Math 66(2): 447–467 (electronic)
  Article MATH MathSciNet Google Scholar
• Astanin S, Preziosi L (2007) Multiphase models of tumour growth. In: Bellomo N, Chaplain M, DeAngelis E (eds) Selected topics on cancer modelling: genesis—evolution—immune competition—therapy. Birkhäuser, Basel
  Google Scholar
• Baumgartner W, Hinterdorfer P, Ness W, Raab A, Vestweber D, Schindler H, Drenckhahn D (2000) Cadherin interaction probed by atomic force microscopy. Proc Nat Acad Sci USA 97: 4005–4010
  Article Google Scholar
• Behravesh E, Timmer MD, Lemoine JJ, Liebschner MA, Mikos AG (2002) Evaluation of the in vitro degradation of macroporous hydrogels using gravimetry, confined compression testing, and microcomputed tomography. Biomacromolecules 3: 1263–1270
  Article Google Scholar
• Bertuzzi A, Fasano A, Gandolfi A (2004/2005) A free boundary problem with unilateral constraints describing the evolution of a tumor cord under the influence of cell killing agents. SIAM J Math Anal 36(3): 882–915 (electronic)
  Article MathSciNet Google Scholar
• Bertuzzi A, Fasano A, Gandolfi A (2005) A mathematical model for tumor cords incorporating the flow of interstitial fluid. Math Models Methods Appl Sci 15(11): 1735–1777
  Article MATH MathSciNet Google Scholar
• Breward CJW, Byrne HM, Lewis CE (2001) Modelling the interactions between tumour cells and a blood vessel in a microenvironment within a vascular tumour. Eur J Appl Math 12(5): 529–556
  Article MATH MathSciNet Google Scholar
• Breward CJW, Byrne HM, Lewis CE (2002) The role of cell–cell interactions in a two-phase model for avascular tumour growth. J Math Biol 45(2): 125–152
  Article MATH MathSciNet Google Scholar
• Breward CJW, Byrne HM, Lewis CE (2003) A multiphase model describing vascular tumour growth. Bull Math Biol 65: 609–640
  Article Google Scholar
• Byrne HM, King JR, McElwain DLS, Preziosi L (2003) A two-phase model of solid tumour growth. Appl Math Lett 16(4): 567–573
  Article MATH MathSciNet Google Scholar
• Byrne HM, Preziosi L (2004) Modeling solid tumor growth using the theory of mixtures. Math Med Biol 20: 341–366
  Article Google Scholar
• Canetta E, Leyrat A, Verdier C, Duperray A (2005) Measuring cell viscoelastic properties using a force-spectrometer: influence of the protein–cytoplasm interactions. Biorheology 42(5): 321–333
  Google Scholar
• Chaplain M, Graziano L, Preziosi L (2006) Mathematical modelling of the loss of tissue compression responsiveness and its role in solid tumour development. Math Med Biol 23: 197–229
  Article MATH Google Scholar
• De Masi A, Luckhaus S, Presutti E (2007) Two scales hydrodynamic limit for a model of malignant tumour cells. Ann IHP Prob Stat 43(3): 257–279
  MATH Google Scholar
• DiMilla PA, Kenneth B, Lauffenburger DA (1991) Mathematical model for the effects of adhesion and mechanics on cell migration speed. Biophys J 60(1): 15–37
  Article Google Scholar
• DiMilla PA, Stone JA, Quinn JA, Albelda SA, Lauffenburger DA (1993) Maximal migration of human smooth muscle cells fibronectin and type iv collagen occurs at an intermediate attachment strength. J Cell Biol 122: 729–737
  Article Google Scholar
• Forgacs G, Foty RA, Shafrir Y, Steinberg MS (1998) Viscoelastic properties of living embryonic tissues: a quantitative study. Biophys J 74: 2227–2234
  Article Google Scholar
• Franks SJ, Byrne HM, King JR, Underwood JCE, Lewis CE (2003) Modelling the early growth of ductal carcinoma in situ of the breast. J Math Biol 47(5): 424–452
  Article MATH MathSciNet Google Scholar
• Franks SJ, Byrne HM, Mudhar HS, Underwood JCE, Lewis CE (2003) Mathematical modelling of comedo ductal carcinoma in situ of the breast. Math Med Biol 20: 277–308
  Article MATH Google Scholar
• Franks SJ, King JR (2003) Interactions between a uniformly proliferating tumor and its surrounding. Uniform material properties. Math Med Biol 20: 47–89
  Article MATH Google Scholar
• Fung YC (1993) Biomechanics: mechanical Properties of living tissues. Springer, Heidelberg
  Google Scholar
• Graziano L, Preziosi L (2007) Mechanics in tumour growth. In: Mollica F, Preziosi L, Rajagopal KR (eds) Modeling of biological materials. Birkhäuser, Basel, pp 267–328
  Google Scholar
• Greenspan HP (1976) On the growth and stability of cell-cultures and solid tumours. J Theor Biol 56: 229–242
  Article MathSciNet Google Scholar
• Gu WY, Yao H, Huang CY, Cheung HS (2003) New insight into deformation-dependent hydraulic permeability of gels and cartilage, and dynamic behavior of agarose gels in confined compression. J Biomech 36: 593–598
  Article Google Scholar
• Humphrey JD, Rajagopal KR (2002) A constrained mixture model for growth and remodeling of soft tissues. Math Mod Meth Appl Sci 12: 407–430
  Article MATH MathSciNet Google Scholar
• Humphrey JD, Rajagopal KR (2003) A constrained mixture model for arterial adaptations to a sustained step-change in blood flow. Biomech Model Mechanobiol 2: 109–126
  Article Google Scholar
• Iordan A, Duperray A, Verdier C (2008) A fractal approach to the rheology of concentrated cell suspensions. Phys Rev E 77: 011911
  Article Google Scholar
• Iredale JP (2007) Models of liver fibrosis: exploring the dynamic nature of inflammationa and repair in a solid organ. J Clin Invest 117(3): 539–548
  Article Google Scholar
• Johnson PRA (2001) Two scales hydrodynamic limit for a model of malignant tumour cells. Clin Exp Pharm Physiol 28: 233–236
  Article Google Scholar
• Lanza V, Ambrosi D, Preziosi L (2006) Exogenous control of vascular network formation in vitro: a mathematical model. Netw Heterog Media 1(4): 621–637 (electronic)
  MATH MathSciNet Google Scholar
• Liotta LA, Kohn EC (2007) The microenvironment of the tumor–host interface. Nature 411: 375–379
  Article Google Scholar
• Newby AC, Zaltsman AB (2000) Molecular mechanisms in intimal hyperplasia. J Pathol 190: 300–309
  Article Google Scholar
• Oxlund H, Andreassen TT (1980) The roles of hyaluronic acid, collagen and elastin in the mechanical properties of connective tissues. J Anat 131(4): 611–620
  Google Scholar
• Pujuguet PP, Hammann A, Moutet M, Samuel JL, Martin F, Martin M (1996) Expression of fibronectin eda+ and edb+ isoforms by human and experimental colorectal cancer. Am J Patho 148: 579–592
  Google Scholar
• Palecek SP, Loftus JC, Ginsberg MH, Lauffenburger DA, Horwitz AF (1997) Integrin-ligand binding properties govern cell migration speed through cell-substratum adhesiveness. Nature 385: 537–540
  Article Google Scholar
• Preziosi L (ed) (2003) Cancer modelling and simulation. Chapman & Hall/CRC Mathematical Biology and Medicine Series, Boca Raton/FL
• Preziosi L, Farina A (2001) On Darcy’s law for growing porous media. Int J Nonlinear Mech 37: 485–491
  Article Google Scholar
• Rao IJ, Humphrey JD, Rajagopal KR (2003) Biological growth and remodeling: a uniaxial example with possible application to tendons and ligaments. CMES 4: 439–455
  MATH Google Scholar
• Sun M, Graham JS, Hegedus B, Marga F, Zhang Y, Forgacs G, Grandbois M (2005) Multiple membrane tethers probed by atomic force microscopy. Biophys J 89: 4320–4329
  Article Google Scholar
• Tosin A (2008) Multiphase modeling and qualitative analysis of the growth of tumor cords. Netw Heterog Media 3: 43–83
  MATH MathSciNet Google Scholar
• Truskey GA, Yuan F, Katz DF (2004) Transport phenomena in biological systems. Prentice Hall, Englewood Cliffs
  Google Scholar
• Winters BS, Shepard SR, Foty RA (2005) Biophysical measurement of brain tumor cohesion. Int J Cancer 114: 371–379
  Article Google Scholar