Mass transport in morphogenetic processes: A second gradient theory for volumetric growth and material remodeling

Journal of the Mechanics and Physics of Solids

Volumn 60, Issue 3, 2012, Pages 432-450

  Ciarletta, P ^a   Ambrosi, D ^b   Maugin, G A ^a  

^a SORBONNE UNIVERSITÉ   (France)

^b POLITECNICO DI MILANO   (Italy)

Author keywords

Mass transport; Mechanobiology; Morphogenesis; Remodeling; Volumetric growth

Indexed keywords

BALANCE EQUATIONS; BIOCHEMICAL SPECIES; CONFIGURATIONAL FORCE; CONSTITUTIVE RELATIONS; CONTINUUM MODEL; COVARIANT; DRIVING FORCES; ESHELBY; EVOLUTION LAW; FIRST-ORDER; GRADIENT THEORY; GROWTH FACTOR; GROWTH REGULATION; HYPERELASTIC THEORY; HYPERSTRESS; INELASTIC MATERIALS; INHOMOGENEITIES; INTERNAL STRESS; MASS DIFFUSION; MATERIAL DERIVATIVE; MECHANO-BIOLOGY; MORPHOGENESIS; MORPHOGENETIC PROCESS; MORPHOGENS; PATHOLOGICAL CONDITIONS; REGENERATIVE MEDICINE; REGULATION MECHANISMS; REMODELING; SECOND ORDERS; THERMO-MECHANICAL; VOLUMETRIC GROWTH;

BIOLOGY; BIOMECHANICS; CONTINUUM MECHANICS; LAWS AND LEGISLATION; MASS TRANSFER; MATERIALS; SCAFFOLDS (BIOLOGY); TISSUE;

GROWTH (MATERIALS);

EID: 84855805257     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmps.2011.11.011     Document Type: Article

References (66)

1. A. Aman, and T. Piotrowski Cell migration during morphogenesis Dev. Biol. 341 2010 20 33
2. D. Ambrosi, and F. Mollica On the mechanics of a growing tumor Int. J. Eng. Sci. 40 2002 1297 1316 (Pubitemid 34715668)
3. D. Ambrosi, and F. Guana Stress modulated growth Math. Mech. Solids 12 2007 319 343
4. D. Ambrosi, L. Preziosi, and G. Vitale The insight of mixtures theory for growth and remodeling Z. Angew. Math. Phys. 61 2010 177 191
5. D. Ambrosi, G.A. Athesian, E.M. Arruda, S.C. Cowin, J. Dumais, A. Goriely, G.A. Holzapfel, J.D. Humphrey, R. Kemkemer, E. Kuhi, J.E. Olberding, L.A. Taber, and K. Garikipati Perspectives on growth and remodeling J. Mech. Phys. Solids 59 2011 863 883
6. G.A. Ateshian On the theory of reactive mixtures for modeling biological growth Biomech. Model Mechanobiol. 6 2009 423 445 (Pubitemid 47551864)
7. Bard, J., 1990. Morphogenesis. Developmental and Cell Biology Series, vol. 23, 1st ed. Cambridge University Press, Cambridge, UK.
8. M. Ben Amar, and P. Ciarletta Swelling instability of surface-attached gels as a model of soft tissue growth under geometrical constraints J. Mech. Phys. Solids 58 7 2010 935 954
9. I.B. Bischofs, and U.S. Schwarz Cell organization in soft media due to active mechanosensing Proc. Natl. Acad. Sci. USA 100 16 2003 9274 9279 (Pubitemid 37033919)
10. H. Byrne, and M.A.J. Chaplain Growth of nonnecrotic tumors in the presence and absence of inhibitors Math. Biosci. 130 1995 151 181
11. J.J. Casciari, S.V. Sotirchos, and R.M. Sutherland Variations in tumor cell growth rates and metabolism with oxygen concentration, glucose concentration, and extracellular pH J. Cell. Physiol. 151 2005 386 394
12. C.S. Chen, M. Mrksich, S. Huang, G.M. Whitesides, and D.E. Ingber Geometric control of cell life and death Science 276 1997 1425 1428 (Pubitemid 27235413)
13. M. Ciarletta, M. Ben Amar, and M. Labouesse Continuum model of epithelial morphogenesis during C. elegans embryonic elongation Philos. Trans. R. Soc. A 367 2009 3379 3400
14. P. Ciarletta, M. Foret, and M. Ben Amar The radial growth phase of malignant melanoma: multiphase modeling, numerical simulations and linear stability analysis J. R. Soc. Interface 8 2011 345 368
15. B.D. Coleman, and W. Noll The thermodynamics of elastic materials with heat conduction and viscosity Arch. Ration. Mech. Anal. 13 1963 167 178
16. S.C. Cowin Tissue growth and remodeling Annu. Rev. Biomed. Eng. 6 2004 1 31
17. C.S. Cowin, and H.D. Hegedus Bone remodeling I: theory of adaptive elasticity J. Elasticity 6 1976 313 326
18. F. dellIsola, and P. Seppecher Edge contact forces and quasi-balanced power Meccanica 32 1997 33 52 (Pubitemid 127506344)
19. F. dellIsola, G. Sciarra, and S. Vidoli Generalized Hookes law for isotropic second gradient materials Proc. R. Soc. A 465 2009 2177 2196
20. J. Dervaux, and M. Ben Amar Morphogenesis of growing soft tissues Phys. Rev. Lett. 6 2008 068101
21. J. Dervaux, P. Ciarletta, and M. Ben Amar Morphogenesis of thin hyperelastic plates: a constitutive theory of biological growth in the Fopplvon Karman limit J. Mech. Phys. Solids 57 3 2009 458 471
22. M. Destrade, J.G. Murphy, and R.W. Ogden On deforming a sector of a cylindrical tube into an intact tube: existence, unicity and stability Int. J. Eng. Sci 48 2010 1212 1224
23. A. Di Carlo, and S. Quiligotti On growth and balance Mech. Res. Commun. 29 2007 449 456
24. M. Elzanowski, and M. Epstein On the symmetry group of second-grade materials Int. J. Nonlinear Mech. 27 1992 635 638
25. M. Epstein Toward a complete second-order evolution law Math. Mech. Solids 4 1999 251 266
26. M. Epstein, and G.A. Maugin Thermomechanics of volumetric growth in uniform bodies Int. J. Plasticity 16 2000 951 978
27. M. Epstein, and M. Elzanowski Material Inhomogeneities and their Evolution first ed. 2007 Springer-Verlag Berlin, Heidelberg
28. S. Forest, J.M. Cardona, and R. Sievert Thermoelasticity of second-grade media G.A. Maugin, R. Drouot, F. Sidoroff, Continuum Thermomechanics: The Art and Science of Modeling Material Behavior 2002 Kluwer Academic Publishers 163 176
29. S.J. Franks, H.M. Byrne, J.R. King, J.C. Underwood, and C.E. Lewis Modeling the early growth of ductal carcinoma in situ J. Math. Biol. 47 2003 424 452 (Pubitemid 38261106)
30. S.J. Franks, H.M. Byrne, J.C. Underwood, and C.E. Lewis Biological inferences from a mathematical model of comedo ductal carcinoma in situ of the breast J. Theor. Biol. 232 2005 523 543 (Pubitemid 39575095)
31. J.F. Ganghoffer Mechanical modeling of growth considering domain variation. Part II: volumetric and surface growth involving Eshelby tensors J. Mech. Phys. Solids 58 2010 1434 1459
32. K. Garikipati, E.M. Arruda, K. Grosh, H. Narayanana, and S. Calve A continuum treatment of growth in biological tissue: the coupling of mass transport and mechanics J. Mech. Phys. Solids 52 2004 1595 1625
33. R. Garrett, and C.M. Grisham Biochemistry 2005 Thompson Brooks Belmont, CA
34. P. Germain La méthode des puissances virtuelles en mécanique des milieux continus J. Méc. 12 2 1973 235 274
35. G. Helmlinger, P.A. Netti, H.C. Lichtenbeld, R.J. Melder, and R.K. Jain Solid stress inhibits the growth of multicellular tumor spheroids Nat. Biotechnol. 15 1997 778 783 (Pubitemid 27329482)
36. N. Kirchner, and P. Steinmann On the material setting of gradient hyperelasticity Math. Mech. Solids 12 2007 559 580 (Pubitemid 47487887)
37. W. Hong, X. Zhao, J. Zhuo, and Z. Suo A theory of coupled diffusion and large deformation in polymeric gels J. Mech. Phys. Solids 56 2008 1779 1793
38. J.D. Humphrey, and E. Wilson A potential role of smooth muscle tone in early hypertension: a theoretical study J. Biomech. 36 2003 1595 1601 (Pubitemid 37163758)
39. A. Jacinto, A. Martinez-Arias, and P. Martin Mechanisms of epithelial fusion and repair Nature Cell. Biol. 5 2001 E117 E123 (Pubitemid 32422076)
40. S. Kondo, and T. Miura Reactiondiffusion model as a framework for understanding biological pattern formation Science 329 2010 1616 1620
41. M. Lazar, and G.A. Maugin Nonsingular stress and strain fields of dislocations and disclination in first gradient elasticity Int. J. Eng. Sci. 43 2005 1157 1184 (Pubitemid 41285286)
42. T. Lecuit, and P.F. Lenne Cell surface mechanics and the control of cell shape, tissue patterns and morphogenesis Nat. Rev. Mol. Cell. Biol. 8 2007 633 644 (Pubitemid 47108184)
43. T. Lecuit, and L. Le Goff Orchestrating size and shape during morphogenesis Nature 450 2007 189 192 (Pubitemid 350100541)
44. M. de Leon, and M. Epstein On the integrability of second-order G-structures with application to continuous theories of dislocations Rep. Math. Phys. 33 1993 419 436
45. H.A. Levine, S. Pamuk, B.D. Sleeman, and N. Nilsen-Hamilton Mathematical modeling of capillary formation and development in tumor angiogenesis: penetration into the stroma Bull. Math. Biol. 63 2001 801 863 (Pubitemid 32834844)
46. G.A. Maugin Eshelby stress in plasticity and fracture Int. J. Plasticity 10 1994 393 408
47. G.A. Maugin Pseudo-plasticity and pseudo-inhomogeneity effects in materials mechanics J. Elasticity 71 2003 81 103
48. G.A. Maugin On inhomogeneity, growth, ageing and the dynamics of the materials J. Mech. Mater. Struct. 4 2009 731 741
49. G.A. Maugin Configurational Forces: Thermomechanics, Physics, Mathematics and Numerics first ed. 2011 CRC Press, Taylor and Francis Boca Raton, FL
50. G.A. Maugin, and C. Trimarco Pseudo-momentum and material forces in nonlinear elasticity: variational formulations and application to brittle fracture Acta Mech. 94 1992 1 28
51. R.D. Mindlin Second gradient of strain and surface tension in linear elasticity Int. J. Solids Struct. 1 1965 417 438
52. H. Narayanan, S.N. Verner, K.L. Mills, R. Kemkemer, and K. Garikipati In silico estimates of the free energy rates in growing tumor spheroids J. Phys. Condens. Matter 22 2010 194122
53. C.M. Nelson, R.P. Jean, J.L. Tan, W.F. Liu, N.J. Sniadecki, A.A. Spector, and C.S. Chen Emergent patterns of growth controlled by multicellular form and mechanics Proc. Natl. Acad. Sci. USA 102 33 2005 11594 11599 (Pubitemid 41170771)
54. R.W. Ogden Nonlinear elasticity, anisotropy and residual stresses in soft tissue CISM Lecture Series 2003 Springer Wien 65 108
55. R.J. Okamoto, J.E. Wagenseil, W. DeLong, S.J. Peterson, N.T. Kouchoukos, and T.M. Sundt Mechanical properties of dilated human ascending aorta Ann. Biomed. Eng. 30 2002 624 635 (Pubitemid 34783430)
56. E.K. Rodriguez, A. Hoger, and A.D. McCulloch Stress-dependent finite growth in soft elastic tissues J. Biomech. 27 1994 455 467 (Pubitemid 24102058)
57. M. Rumpler, A. Woesz, J.W. Dunlop, J.T. van Dongen, and P. Fratzl The effect of geometry on three-dimensional tissue growth J. R. Soc. Interface 5 2008 1173 1180
58. B.I. Shraiman Mechanical feedback as a possible regulator of tissue growth Proc. Natl. Acad. Sci. USA 102 9 2005 3318 3323 (Pubitemid 40328043)
59. R. Skalak, G. Dasgupta, M. Moss, E. Otten, P. Dullemeijer, and H. Vilmann Analytical description of growth J. Theor. Biol. 94 1982 555 577 (Pubitemid 12154339)
60. S. Suresh Biomechanics and biophysics of cancer cells Acta Biomater. 3 2007 413 438 (Pubitemid 46865787)
61. B. Svendsen On the modeling of anisotropic elastic and inelastic material behavior at large deformation Int. J. Solids Struct. 38 2001 9579 9599 (Pubitemid 34021243)
62. B. Svendsen, P. Neff, and A. Menzel On constitutive and configurational aspects of models for gradient continua with microstructure Z. Angew. Math. Mech. 89 8 2009 687 697
63. L.A. Taber Biomechanics of growth, remodeling, and morphogenesis Appl. Mech. Rev. 48 1995 487 545
64. L.A. Taber Towards a unified theory for morphomechanics Philos. Trans. R. Soc. A 367 2009 3555 3583
65. L. Wolpert Positional information and the spatial pattern of cellular differentiation J. Theor. Biol. 25 1969 1 47
66. S.R. Yu, M. Burkhardt, M. Nowak, J. Ries, Z. Petrasek, S. Scholpp, P. Schwille, and M. Brand Fgf8 morphogen gradient forms by a sourcesink mechanism with freely diffusing molecules Nature 461 2009 533 537