A multiphase model for three-dimensional tumor growth

New Journal of Physics

Volumn 15, Issue , 2013, Pages

  Sciume G ^a,b   Shelton, S ^c   Gray, W G ^c   Miller, C T ^c   Hussain, F ^d,e   Ferrari, M ^e,f   Decuzzi, P ^e   Schrefler, B A ^a,e  

^a UNIVERSITY OF PADOVA   (Italy)

^b Grande Voie des Vignes   (France)

^c University of North Carolina at Chapel Hill   (United States)

^d UNIVERSITY OF HOUSTON   (United States)

^e HOUSTON METHODIST RESEARCH INSTITUTE   (United States)

^f WEILL CORNELL MEDICAL COLLEGE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CELL DENSITY RATIOS; CULTURE MEDIUM; EXTRACELLULAR MATRICES; GOVERNING EQUATIONS; HEALTHY TISSUES; INTERSTITIAL FLUIDS; MALIGNANT CELLS; MALIGNANT MASS; MATHEMATICAL FORMULATION; MECHANICAL STRAIN; MICROVESSELS; MULTI-PHASE MEDIUM; MULTICELLULAR TUMOR SPHEROIDS; MULTIPHASE MODEL; MULTIPHASE POROUS MEDIA; NECROTIC CELLS; NUTRIENT CONCENTRATIONS; THERAPEUTIC STRATEGY; THERMODYNAMICALLY CONSTRAINED AVERAGING THEORIES; THREE DIMENSIONAL GEOMETRY; TIME DEPENDENT BEHAVIOR; TIME-DEPENDENT; TUMOR CELLS; TUMOR CORDS; TUMOR GROWTH; TUMOR MASS; TUMOR SIZE;

CELL ADHESION; CELL CULTURE; CELLS; DIGITAL STORAGE; ENZYME INHIBITION; FINITE ELEMENT METHOD; NUTRIENTS; POROUS MATERIALS; THREE DIMENSIONAL; TRANSPORT PROPERTIES;

TUMORS;

EID: 84873377603     PISSN: 13672630     EISSN: None     Source Type: Journal    
DOI: 10.1088/1367-2630/15/1/015005     Document Type: Article

References (52)

1. Ambrosi D, Preziosi L and Vitale G 2012 The interplay between stress and growth in solid tumors Mech. Res. Comm. 42 87-91
2. Anderson A R 2005 A hybrid mathematical model of solid tumour invasion: the importance of cell adhesion Math. Med. Biol. 22 163-86 (Pubitemid 41511340)
3. Astanin S and Preziosi L 2009 Mathematical modelling of the Warburg effect in tumour cords J. Theor. Biol. 258 578-90
4. Baumgartner W, Hinterdorfer P, Ness W, Raab A, Vestweber D, Schindler H and Drenckhahn D 2000 Cadherin interaction probed by atomic force microscopy Proc. Natl Acad. Sci. USA 97 4005-10 (Pubitemid 30226077)
5. Bearer E L, Lowengrub J S, Frieboes H B, Chuang Y L, Jin F, Wise S M, Ferrari M, Agus D B and Cristini V 2009 Multiparameter computational modeling of tumor invasion Cancer Res. 69 4493-501
6. Bidan C M, Kommareddy K P, Rumpler M, Kollmannsberger P, Bréchet Y J M, Fratzl P and Dunlop J W C 2012 How linear tension converts to curvature: geometric control of bone tissue growth PLoS One 7 e36336
7. Brooks R H and Corey A T 1964 Hydraulic properties of porous media Hydrology Paper 3 Colorado State University, Fort Collins, CO
8. Brooks R H and Corey A T 1966 Properties of porous media affecting fluid flow J. Irrig. Drainage Div. (Proc. Am. Soc. Civil Eng.) 92 61-88
9. Byrne H M and Chaplain M A J 1996 Modelling the role of cell-cell adhesion in the growth and development of carcinomas Math. Comput. Modelling 24 1-17 (Pubitemid 27118822)
10. Byrne H M, King J R and McElwain D L S 2003 A two-phase model of solid tumor growth Appl. Math. Lett. 16 567-73
11. Casciari J J, Sotirchos S V and Sutherland R M 1992 Mathematical modelling of and growth microenvironment in EMT6/Ro multicellular tumor spheroids Cell Prolif. 25 1-22
12. Chaplain M A 2000 Mathematical modelling of angiogenesis J. Neurooncol. 50 37-51 (Pubitemid 32166289)
13. Chignola R, Foroni R, Franceschi A, Pasti M, Candiani C, Anselmi C, Fracasso G, Tridente G and Colombatti M 1995 Heterogeneous response of individual multicellular tumour spheroids to immunotoxins and ricin toxin Br. J. Cancer 72 607-14
14. Chignola R, Schenetti A, Andrighetto G, Chiesa E, Foroni R, Sartoris S, Tridente G and Liberati D 2000 Forecasting the growth of multicell tumour spheroids: implications for the dynamic growth of solid tumours Cell Prolif. 33 219-29
15. Corey A T, Rathjens C H, Henderson J H and Wyllie M R J 1956 Three-phase relative permeability J. Pet. Technol. 375 63-5
16. Cristini V, Li X, Lowengrub J S and Wise S M 2009 Nonlinear simulation of solid tumor growth using a mixture model: invasion and branching J. Math. Biol. 58 723-63
17. Deisboeck T S, Wang Z, Macklin P and Cristini V 2011 Multiscale cancer modelling Annu. Rev. Biomed. Eng. 13 127-55
18. Dunlop J W, Gamsjäger E, Bidan C, Kommareddy K P, Kollmansberger P, Rumpler M, Fischer F D and Fratzl P 2011 The modeling of tissue growth in confined geometries, effect of surface tension Proc. CMM-2011 (Warsaw) Computer Methods in Mechanics
19. Gawin D, Pesavento F and Schrefler B A 2006 Hygro-thermo-chemo-mechanical modelling of concrete at early ages and beyond. Part I: Hydration and hygro-thermal phenomena Int. J. Numer. Methods Eng. 67 299-331 (Pubitemid 44082401)
20. Gomez H, Calo V M, Bazilevs Y and Hughes T R J 2008 Isogeometric analysis of the Cahn-Hilliard phase field model Comput. Methods Appl. Mech. Eng. 197 4333-52
21. Gray W G, Leijnse A, Kolar R L and Blain C A 1993 Mathematical Tools for Changing Spatial Scales in the Analysis of Physical Systems (Boca Raton, FL: CRC Press) p 232
22. Gray W G and Miller C T 2005 Thermodynamically constrained averaging theory approach for modeling flow and transport phenomena in porous medium systems: 1. Motivation and overview Adv. Water Resources 28 161-80 (Pubitemid 40102392)
23. Gray W G and Miller C T 2009 Thermodynamically constrained averaging theory approach for modeling flow and transport phenomena in porous medium systems: 5. Single-fluid-phase transport Adv. Water Resources 32 681-711
24. Gray W G, Miller C T and Schrefler B A 2012 Averaging theory for description of environmental problems: what have we learned Adv. Water Resources doi:10.1016/j.advwatres.2011.12005
25. Gray W G and Schrefler B A 2007 Analysis of the solid stress tensor in multiphase porous media Int. J. Numer. Anal. Methods Geomech. 31 541-581 (Pubitemid 46502012)
26. Hawkins-Daarud A, van der Zee K G and Oden J T 2012 Numerical simulation of a thermodynamically consistent four-species tumor growth model Int. J. Numer. Methods Biomed. Eng. 28 3-24
27. Jackson A S, Miller C T and Gray W G 2009 Thermodynamically constrained averaging theory approach for modelling flow and transport phenomena in porous medium systems: 6. Two-fluid-phase flow Adv. Water Resources 32 779-95
28. Jain R K and Stylianopoulos T 2010 Delivering nanomedicine to solid tumors Nature Rev. Clin. Oncol. 7 653-64
29. Jain R K 1999 Transport of molecules, particles, and cells in solid tumors Annu. Rev. Biomed. Eng. 1 241-63 (Pubitemid 129740012)
30. Jou D, Casas-Vazquez J and Lebon G 2001 Extended Irreversible Thermodynamics (Berlin: Springer)
31. Lowengrub J S, Frieboes H B, Jin F, Chuang Y-L, Li X, Macklin P, Wise S M and Cristini V 2010 Nonlinear modeling of cancer: bridging the gap between cells and tumors Nonlinearity 23 R1-R91
32. Lewis R W and Schrefler B A 1998 The Finite Element Method in the Static and Dynamic Deformation and Consolidation of Porous Media (Chichester: Wiley)
33. Maugin G A 1999 The Thermomechanics of Nonlinear Irreversible Behaviors: An Introduction (Singapore: World Scientific)
34. Mueller-Klieser W, Freyer J P and Sutherland R M 1986 Influence of glucose and oxygen supply conditions on the oxygenation of multicellular spheroids Br. J. Cancer 53 345-53 (Pubitemid 16133104)
35. Murthy V, Valliappan S and Khalili-Naghadeh N 1989 Time step constraints in finite element analysis of the Poisson type equation Comput. Struct. 31 269-73
36. Oden J T, Hawkins A and Prudhomme S 2010 General diffusive-interface theories and an approach to predictive tumor growth modeling Math. Models Methods Appl. Sci. 20 477-517
37. Perfahl H et al 2011 Multiscale modelling of vascular tumor growth in 3D: the roles of domain size and boundary conditions PLoS One 6 e14790
38. Preziosi L and Tosin A 2009 Multiphase modelling of tumour growth and extracellular matrix interaction: mathematical tools and applications J. Math. Biol. 58 625-56
39. Preziosi L and Vitale G 2011a Mechanical aspects of tumour growth: multiphase modelling, adhesion evolving natural configurations New Trends in the Physics and Mechanics of Biological Systems (Lecture Notes of the Les Houches Summer School vol 92) ed M Ben Amar, A Goriely, M M Müller and L F Cugliandolo (Oxford: Oxford University Press) pp 177-228
40. Preziosi L and Vitale G 2011b A multiphase model of tumour and tissue growth including cell adhesion and plastic re-organisation Math. Models Methods Appl. Sci. 21 1901-32
41. Rank E, Katz C and Werner H 1983 On the importance of the discrete maximum principle in transient analysis using finite element methods Int. J. Num. Methods Eng. 19 1771-82 (Pubitemid 14508883)
42. Roose T, Netti P A, Munn L L, Bucher Y and Jain R K 2003 Solid stress generated by spheroid growth estimated using a linear poroelasticity model Microvascular Res. 66 204-12 (Pubitemid 37373595)
43. Roose T, Chapman S J and Maini P K 2007 Mathematical models of avascular tumor growth SIAM Rev. 49 179-208 (Pubitemid 46888016)
44. Sarntinoranont M, Rooney F and Ferrari M 2003 Interstitial stress and fluid pressure within a growing tumor Ann. Biomed. Eng. 31 327-35
45. Schrefler B A 2002 Mechanics and thermodynamics of saturated-unsaturated porous materials and quantitative solutions Appl. Mech. Rev. (ASME) 55 351-88 (Pubitemid 40205893)
46. Turska E, Wisniewski K and Schrefler B A 1994 Error propagation of staggered solution procedures for transient problems Comput. Methods Appl. Mech. Eng. 144 177-88
47. van Genuchten M T 1980 A closed-form equation for predicting the hydraulic conductivity of unsaturated soils Soil. Sci. Soc. Am. J. 44 892-8
48. 1990 Geoderma 46 1-297 (special issue)
49. Wise S M, Lowengrub J S, Frieboes H B and Cristini V 2008 Three-dimensional multispecies nonlinear tumor growth: I. Model and numerical method J. Theor. Biol. 253 524-43
50. Yuhas J M, Li A P, Martinez A O and Ladman A J 1977 A simplified method for production and growth of multicellular tumor spheroids Cancer Res. 37 3639-43 (Pubitemid 8198426)
51. Zavarise G, Wrigger P and Schrefler B A 1995 On augmented Lagrangian algorithms for thermomechanical contact problems with friction Int. J. Numer. Methods Eng. 38 2929-49
52. Zienkiewicz O C and Taylor R L 2000 The Finite Element Method vol 2 (Heinemann: Butterworth)