Multiphase modelling of tumour growth and extracellular matrix interaction: Mathematical tools and applications

Journal of Mathematical Biology

Volumn 58, Issue 4-5, 2009, Pages 625-656

  Preziosi, Luigi ^a   Tosin, Andrea ^a  

^a POLITECNICO DI TORINO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; BIOLOGICAL MODEL; CELL ADHESION; CELL DEATH; CELL PROLIFERATION; CELL SIZE; EXTRACELLULAR MATRIX; FIBROSIS; HUMAN; MATHEMATICAL PHENOMENA; NEOPLASM; PATHOLOGY; PATHOPHYSIOLOGY; PHYSIOLOGY; VASCULARIZATION;

CELL ADHESION; CELL DEATH; CELL PROLIFERATION; CELL SIZE; EXTRACELLULAR MATRIX; FIBROSIS; HUMANS; MATHEMATICAL CONCEPTS; MODELS, BIOLOGICAL; NEOPLASMS;

EID: 58349095136     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s00285-008-0218-7     Document Type: Article

References (50)

1. D Ambrosi F Guana 2007 Stress modulated growth Math Mech Solids 12 3 319 342
2. D Ambrosi F Mollica 2002 On the mechanics of a growing tumor Int J Eng Sci 40 12 1297 1316
3. D Ambrosi F Mollica 2004 The role of stress in the growth of a multicell spheroid J Math Biol 48 5 477 499
4. Ambrosi D, Preziosi L (2008) Cell adhesion mechanisms and elasto-viscoplastic mechanics of tumours. Biomech Model Mechanobiol (to appear)
5. D Ambrosi L Preziosi 2002 On the closure of mass balance models for tumor growth Math Models Methods Appl Sci 12 5 737 754
6. RP Araujo DLS McElwain 2004 A history of the study of solid tumour growth: the contribution of mathematical modelling Bull Math Biol 66 5 1039 1091
7. RP Araujo DLS McElwain 2004 A linear-elastic model of anisotropic tumour growth Eur J Appl Math 15 3 365 384
8. RP Araujo DLS McElwain 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)
9. RP Araujo DLS McElwain 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)
10. 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
11. W Baumgartner P Hinterdorfer W Ness A Raab D Vestweber H Schindler D Drenckhahn 2000 Cadherin interaction probed by atomic force microscopy Proc Nat Acad Sci USA 97 4005 4010
12. E Behravesh MD Timmer JJ Lemoine MA Liebschner AG Mikos 2002 Evaluation of the in vitro degradation of macroporous hydrogels using gravimetry, confined compression testing, and microcomputed tomography Biomacromolecules 3 1263 1270
13. A Bertuzzi A Fasano A Gandolfi 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)
14. A Bertuzzi A Fasano A Gandolfi 2005 A mathematical model for tumor cords incorporating the flow of interstitial fluid Math Models Methods Appl Sci 15 11 1735 1777
15. CJW Breward HM Byrne CE Lewis 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
16. CJW Breward HM Byrne CE Lewis 2002 The role of cell-cell interactions in a two-phase model for avascular tumour growth J Math Biol 45 2 125 152
17. CJW Breward HM Byrne CE Lewis 2003 A multiphase model describing vascular tumour growth Bull Math Biol 65 609 640
18. HM Byrne JR King DLS McElwain L Preziosi 2003 A two-phase model of solid tumour growth Appl Math Lett 16 4 567 573
19. HM Byrne L Preziosi 2004 Modeling solid tumor growth using the theory of mixtures Math Med Biol 20 341 366
20. E Canetta A Leyrat C Verdier A Duperray 2005 Measuring cell viscoelastic properties using a force-spectrometer: influence of the protein-cytoplasm interactions Biorheology 42 5 321 333
21. M Chaplain L Graziano L Preziosi 2006 Mathematical modelling of the loss of tissue compression responsiveness and its role in solid tumour development Math Med Biol 23 197 229
22. A De Masi S Luckhaus E Presutti 2007 Two scales hydrodynamic limit for a model of malignant tumour cells Ann IHP Prob Stat 43 3 257 279
23. PA DiMilla B Kenneth DA Lauffenburger 1991 Mathematical model for the effects of adhesion and mechanics on cell migration speed Biophys J 60 1 15 37
24. PA DiMilla JA Stone JA Quinn SA Albelda DA Lauffenburger 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
25. G Forgacs RA Foty Y Shafrir MS Steinberg 1998 Viscoelastic properties of living embryonic tissues: a quantitative study Biophys J 74 2227 2234
26. SJ Franks HM Byrne JR King JCE Underwood CE Lewis 2003 Modelling the early growth of ductal carcinoma in situ of the breast J Math Biol 47 5 424 452
27. SJ Franks HM Byrne HS Mudhar JCE Underwood CE Lewis 2003 Mathematical modelling of comedo ductal carcinoma in situ of the breast Math Med Biol 20 277 308
28. SJ Franks JR King 2003 Interactions between a uniformly proliferating tumor and its surrounding. Uniform material properties Math Med Biol 20 47 89
29. Fung YC (1993) Biomechanics: mechanical Properties of living tissues. Springer, Heidelberg
30. 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
31. HP Greenspan 1976 On the growth and stability of cell-cultures and solid tumours J Theor Biol 56 229 242
32. WY Gu H Yao CY Huang HS Cheung 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
33. JD Humphrey KR Rajagopal 2002 A constrained mixture model for growth and remodeling of soft tissues Math Mod Meth Appl Sci 12 407 430
34. JD Humphrey KR Rajagopal 2003 A constrained mixture model for arterial adaptations to a sustained step-change in blood flow Biomech Model Mechanobiol 2 109 126
35. A Iordan A Duperray C Verdier 2008 A fractal approach to the rheology of concentrated cell suspensions Phys Rev E 77 011911
36. JP Iredale 2007 Models of liver fibrosis: exploring the dynamic nature of inflammationa and repair in a solid organ J Clin Invest 117 3 539 548
37. PRA Johnson 2001 Two scales hydrodynamic limit for a model of malignant tumour cells Clin Exp Pharm Physiol 28 233 236
38. V Lanza D Ambrosi L Preziosi 2006 Exogenous control of vascular network formation in vitro: a mathematical model Netw Heterog Media 1 4 621 637 (electronic)
39. LA Liotta EC Kohn 2007 The microenvironment of the tumor-host interface Nature 411 375 379
40. AC Newby AB Zaltsman 2000 Molecular mechanisms in intimal hyperplasia J Pathol 190 300 309
41. H Oxlund TT Andreassen 1980 The roles of hyaluronic acid, collagen and elastin in the mechanical properties of connective tissues J Anat 131 4 611 620
42. PP Pujuguet A Hammann M Moutet JL Samuel F Martin M Martin 1996 Expression of fibronectin eda+ and edb+ isoforms by human and experimental colorectal cancer Am J Patho 148 579 592
43. SP Palecek JC Loftus MH Ginsberg DA Lauffenburger AF Horwitz 1997 Integrin-ligand binding properties govern cell migration speed through cell-substratum adhesiveness Nature 385 537 540
44. Preziosi L (ed) (2003) Cancer modelling and simulation. Chapman & Hall/CRC Mathematical Biology and Medicine Series, Boca Raton/FL
45. L Preziosi A Farina 2001 On Darcy's law for growing porous media Int J Nonlinear Mech 37 485 491
46. IJ Rao JD Humphrey KR Rajagopal 2003 Biological growth and remodeling: a uniaxial example with possible application to tendons and ligaments CMES 4 439 455
47. M Sun JS Graham B Hegedus F Marga Y Zhang G Forgacs M Grandbois 2005 Multiple membrane tethers probed by atomic force microscopy Biophys J 89 4320 4329
48. A Tosin 2008 Multiphase modeling and qualitative analysis of the growth of tumor cords Netw Heterog Media 3 43 83
49. Truskey GA, Yuan F, Katz DF (2004) Transport phenomena in biological systems. Prentice Hall, Englewood Cliffs
50. BS Winters SR Shepard RA Foty 2005 Biophysical measurement of brain tumor cohesion Int J Cancer 114 371 379