A multiphase model of tumor and tissue growth including cell adhesion and plastic reorganization

Mathematical Models and Methods in Applied Sciences

Volumn 21, Issue 9, 2011, Pages 1901-1932

  Preziosi, Luigi ^a   Vitale, Guido ^a  

^a POLITECNICO DI TORINO   (Italy)

Author keywords

adhesion; cell motion; Multiphase modeling

Indexed keywords

ADHESION PHENOMENA; BOND FORMATION; BOND RUPTURE; CELL MOTION; CELLULAR COMPONENTS; CELLULAR CONSTITUENTS; DEFORMATION GRADIENTS; DETACHMENT FORCES; HIGH STRESS; INTERACTION FORCES; MACROSCOPIC LEVELS; MESENCHYMAL CELLS; MIXTURE THEORY; MULTIPHASE MODEL; MULTIPHASE MODELING; NATURAL CONFIGURATIONS; PDE MODEL; RELATIVE VELOCITY; SINGLE ADHESION; SUB-CELLULAR; TISSUE GROWTH;

CELL ADHESION; CELLS; CHEMICAL BONDS; DEFORMATION; DYNAMICS; TISSUE;

ADHESION;

EID: 80053174489     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218202511005593     Document Type: Article

References (67)

1. D. Ambrosi and F. Mollica, On the mechanics of a growing tumor, Int. J. Engrg. Sci. 40 (2002) 1297-1316. (Pubitemid 34715668)
2. D. Ambrosi and F. Mollica, The role of stress in the growth of a multicell spheroid, J. Math. Biol. 48 (2004) 477-499. (Pubitemid 40882739)
3. D. Ambrosi and L. Preziosi, On the closure of mass balance models for tumor growth, Math. Models Methods Appl. Sci. 12 (2002) 737-754.
4. D. Ambrosi and L. Preziosi, Cell adhesion mechanisms and stress relaxation in the mechanics of tumours, Biomech. Model. Mechanobiol. 8 (2009) 397-413.
5. D. Ambrosi, L. Preziosi and G. Vitale, The insight of mixture theory for growth and remodeling, Z. Angew. Math. Phys. 61 (2010) 177-191.
6. R. P. Araujo and D. L. S. McElwain, A linearélastic model of anisotropic tumour growth, Eur. J. Appl. Math. 15 (2004) 365-384. (Pubitemid 39315772)
7. R. P. Araujo and D. L. S. McElwain, A history of the study of solid tumour growth: The contribution of mathematical modeling, Bull. Math. Biol. 66 (2004) 1039-1091. (Pubitemid 39033599)
8. R. P. Araujo and D. L. S. McElwain, A mixture theory for the genesis of residual stresses in growing tissues, I: A general formulation, SIAM J. Appl. Math. 65 (2005) 1261-1284. (Pubitemid 41343745)
9. R. P. Araujo and D. L. S. McElwain, 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. 65 (2005) 1285-1299.
10. N. J. Armstrong, K. J. Painter and J. A. Sherratt, A continuum approach to modelling cell-cell adhesion, J. Theor. Biol. 243 (2006) 98-113. (Pubitemid 44465967)
11. N. J. Armstrong, K. J. Painter and J. A. Sherratt, Adding adhesion to the cell cycle model for somite formation, Bull. Math. Biol. 71 (2009) 1-24.
12. S. Baek, K. R. Rajagopal and J. D. Humphrey, A theoretical model of enlarging intracranial fusiform aneurysms, J. Biomech. Engrg. 128 (2006) 142-149.
13. I. V. Basov and V. V. Shelukhin, Generalized solutions to the equations of compressible Bingham flows, Z. Angew. Math. Mech. 79 (1999) 185-192.
14. W. Baumgartner, P. Hinterdorfer, W. Ness, A. Raab, D. Vestweber and H. D. D. Schindler, Cadherin interaction probed by atomic force microscopy, Proc. Natl. Acad. Sci. USA 97 (2000) 4005-4010. (Pubitemid 30226077)
15. N. Bellomo, Modeling Complex Living Systems - Kinetic Theory and Stochastic Game Approach (Birkhäuser, 2008).
16. N. Bellomo, N. K. Li and P. K. Maini, On the foundations of cancer modelling: Selected topics, speculations and perspectives, Math. Models Methods Appl. Sci. 18 (2008) 593-646. (Pubitemid 351730142)
17. R. M. Bowen, Theory of mixtures, in Continuum Physics, ed. A. C. Eringen (Academic Press, New York, 1976).
18. R. M. Bowen, Incompressible porous media models by the use of the theory of mixtures, Int. J. Engrg. Sci. 18 (1980) 1129-1148.
19. R. M. Bowen, Compressible porous media models by the use of the theory of mixtures, Int. J. Engrg. Sci. 20 (1982) 697-735.
20. H. Byrne and L. Preziosi, Modeling solid tumor growth using the theory of mixtures, Math. Med. Biol. 20 (2004) 341-360.
21. E. Canetta, A. Duperray, A. Leyrat and C. Verdier, Measuring cell viscoelastic properties using a force-spectrometer: Influence of the protein-cytoplasm interactions, Biorheology 42 (2005) 298-303.
22. M. Chaplain, L. Graziano and L. Preziosi, Mathematical modelling of the loss of tissue compression responsiveness and its role in solid tumour development, Math. Med. Biol. 23 (2005) 197-229. (Pubitemid 44592715)
23. V. Cristini, X. Li, J. Lowengrub and S. M. Wise, Nonlinear simulations of solid tumor growth using a mixture model: Invasion and branching, J. Math. Biol. 58 (2009) 723-763.
24. A. DiCarlo and S. Quiligotti, Growth and balance, Mech. Res. Commun. 29 (2002) 449-456. (Pubitemid 35401688)
25. G. Forgacs, R. Foty, Y. Shafrir and M. Steinberg, Viscoelastic properties of living embryonic tissues: A quantitative study, Biophys. J. 74 (1998) 2227-2234. (Pubitemid 28225220)
26. R. A. Foty, G. Forgacs, S. Pfleger and M. Steinberg, Surface tensions of embryonic tissues predict their mutual envelopment behavior, Development 122 (1996) 1611-1620. (Pubitemid 26159647)
27. S. Franks, H. Byrne, J. King, J. Underwood and C. Lewis, Modelling the early growth of ductal carcinoma in situ of the breast, J. Math. Biol. 47 (2003) 424-452. (Pubitemid 38261106)
28. S. Franks, H. Byrne, H. Mudhar, J. Underwood and C. Lewis, Mathematical modelling of comedo ductal carcinoma in situ of the breast, Math. Med. Biol. 20 (2003) 277-308. (Pubitemid 37526838)
29. S. Franks and J. King, Interactions between a uniformly proliferating tumor and its surrounding uniform material properties, Math. Med. Biol. 20 (2003) 47-89.
30. L. Graziano and L. Preziosi, Mechanics in tumour growth, in Modeling of Biological Materials, eds. K. Rajagopal, F. Mollica and L. Preziosi (Birkhäuser, 2007), pp. 267-328.
31. T. Hillen, K. Painter and C. Schmeiser, Global existence for chemotaxis with finite sampling radius, Discrete Contin. Dyn. Syst. 7 (2007) 125-144.
32. J. Humphrey and K. Rajagopal, A constrained mixture model for growth and remodeling of soft tissues, Math. Models Methods Appl. Sci. 22 (2002) 407-430.
33. J. Humphrey and K. Rajagopal, A constrained mixture model for arterial adaptations to a sustained step change in blood flow, Biomech. Model. Mechanobiol. 2 (2003) 109-126.
34. M. Iannelli, M. Martcheva and F. A. Milner, Gender-structured population modeling - Mathematical methods, numerics, and simulations, SIAM Frontiers Appl. Math. (2005).
35. A. Iordan, A. Duperray and C. Verdier, Fractal approach to the rheology of concentrated cell suspensions, Phys. Rev. E 77 (2008) 011911.
36. A. F. Jones, H. M. Byrne, J. S. Gibson and J. W. Dold, A mathematical model of the stress induced during solid tumour growth, J. Math. Biol. 40 (2000) 473-499.
37. J. Jou and A. M. Diehl, Epithelial-mesenchymal transitions and hepatocarcinogenesis, J. Clin. Invest. 120 (2010) 1031-1034.
38. S. M. Klisch and A. Hoger, Volumetric growth of thermoelastic materials and mixtures, Math. Mech. Solids 8 (2003) 377-402.
39. J. S. Lowengrub, H. B. Frieboes, F. Jin, Y. L. Chuang, X. Li, P. Macklin, S. M. Wise and V. Cristini, Nonlinear modelling of cancer: Bridging the gap between cells and tumours, Nonlinearity 23 (2010) R1-R91.
40. J. Lowengrub, S. M. Wise, H. B. Frieboes and V. Cristini, Three-dimensional multispecies nonlinear tumor growth, I: Model and numerical method, J. Theor. Biol. 253 (2008) 524-543.
41. P. Macklin and J. Lowengrub, Nonlinear simulation of the effect of the microenvironment on tumor growth, J. Theor. Biol. 245 (2007) 677-704. (Pubitemid 46454401)
42. W. A. Malik, S. C. Prasad, K. R. Rajagopal and L. Preziosi, On the modeling of the viscoelastic response of embryonic tissues, Math. Mech. Solids 13 (2008) 81-91. (Pubitemid 350303169)
43. L. E. Malvern, Introduction of the Mechanics of a Continuous Medium (Prentice-Hall, 1969).
44. M. Novothny, J. Brabek, K. Pankova and D. Rosel, The molecular mechanisms of transition between mesenchymal and amoeboid invasiveness in tumor cells, Cell. Mol. Life Sci. 67 (2010) 63-71.
45. J. T. Oden, A. Hawkins and S. Proudhomme, General diffuse-interface theories and an approach to predictive tumor growth modeling, Math. Models Methods Appl. Sci. 20 (2010) 477-517.
46. D. Ölz and C. Schmeiser, How do cells move? Mathematical modelling of cytoskeleton dynamics and cell migration, in Cell Mechanics: From Single Scale-Based Model to Multiscale Modeling, eds. L. Preziosi A. Chauviere and C. Verdier (Chapman and Hall/CRC Press, 2010).
47. D. Ölz, C. Schmeiser and V. Small, Modelling of the actin-cytoskeleton in symmetric lamellipodial fragments, Cell Adhesion Migration 2 (2008) 117-126.
48. P. Panorchan, M. S. Thompson, K. J. Davis, Y. Tseng, K. Konstantopoulos and D. Wirtz, Single-molecule analysis of cadherin-mediated cell-cell adhesion, J. Cell Sci. 119 (2006) 66-74. (Pubitemid 43169299)
49. J. J. Pop and R. M. Bowen, A theory of mixtures with a long range spatial iteraction, Acta Mech. 29 (1978) 21-34.
50. L. Preziosi, D. Ambrosi and C. Verdier, An elasto-visco-plastic model of cell aggregates, J. Theor. Biol. 262 (2010) 35-47.
51. L. Preziosi and A. Farina, On Darcy's law for growing porous media, Int. J. Nonlinear Mech. 37 (2001) 485-491. (Pubitemid 33034186)
52. L. Preziosi and A. Tosin, Multiphase and multiscale trends in cancer modelling, Math. Model. Natl. Phenom. 4 (2009) 1-11.
53. L. Preziosi and A. Tosin, Multiphase modeling of tumor growth and extracellular matrix interaction: Mathematical tools and applications, J. Math. Biol. 58 (2009) 625-656.
54. I. Rao, J. Humphrey and K. Rajagopal, Biological growth and remodeling: A uniaxial example with possible application to tendons and ligaments, Comp. Mod. Engrg. Sci. 4 (2003) 439-495.
55. E. K. Rodriguez, A. Hoger and A. McCulloch, Stress-dependent finite growth in soft elastic tissues, J. Biomechanics 27 (1994) 455-467. (Pubitemid 24102058)
56. C. Schmeiser and D. Ölz, Derivation of a model for symmetric lamellipodia with instantaneous cross-link turnover, Arch. Rational Mech. Anal. 198 (2010) 963-980.
57. M. Scianna, R. Merks, L. Preziosi and E. Medico, Individual cell-based models of cell scatter of aro and mlp-29 cells in response to hepatocyte growth factor, J. Theor. Biol. 260 (2009) 151-160.
58. M. Scianna, L. Munaron and L. Preziosi, A multiscale hybrid approach for vasculogenesis and related potential blocking therapies, submitted to Prog. Biophys. Mol. Biol., DOI: 10.1016/p.biomolbio.2011.01.004.
59. M. Sun, J. Graham, B. Hegedus, F. Marga, Y. Zhang, G. Forgacs and M. Grandbois, Multiple membrane tethers probed by atomic force microscopy, Biophys. J. 89 (2005) 4320-4329. (Pubitemid 41725650)
60. L. A. Taber and J. D. Humphrey, Stress modulated growth, residual stress and vascular heterogeneity, ASME J. Biomech. Engrg. 123 (2001) 528-535. (Pubitemid 34016544)
61. P. Tracqui, Biophysical models of tumour growth, Rep. Prog. Phys. 72 (2009) 056701.
62. D. Valdembri, P. T. Caswell, K. I. Anderson, J. P. Schwartz, E. Astanina, F. Caccavari, J. C. Norman, M. J. Humphries, F. Bussolino and G. Serini, Neuropilin-1/gipc1 signaling regulates a5b1 integrin traffic and function in endothelial cells, PLoS Biol. 7 (2009), DOI:10.1371/journal.pbio.1000025.
63. C. Verdier, J. Etienen, A. Duperray and L. Preziosi, Review: Rheological properties of biological materials, C. R. Acad. Sci. Phys. 10 (2009) 790-811.
64. K. Wilmanski, Lagrangean model of a two phases porous material, J. Non-Equilib. Thermodyn. 20 (1995) 50-77.
65. B. Winters, S. Shepard and R. Foty, Biophysical measurement of brain tumor cohesion, Int. J. Cancer 114 (2005) 371-379. (Pubitemid 40279956)
66. S. M. Wise, J. Lowengrub, H. B. Frieboes, F. Jin, Y. L. Chuang and V. Cristini, Threedimensional multispecies nonlinear tumor growth, II: Tumor invasion and angiogenesis, J. Theor. Biol. 264 (2010) 1254-1278.
67. L. Yuan, M. J. Fairchild, A. D. Perkins and G. Tanentzapf, Analysis of integrin turnover in fly myotendinous junctions, J. Cell Sci. 123 (2010) 939-946.