title: Interstitial growth and remodeling of biological tissues: tissue composition as state variables.
abstract: Growth and remodeling of biological tissues involves mass exchanges between soluble building blocks in the tissue's interstitial fluid and the various constituents of cells and the extracellular matrix. As the content of these various constituents evolves with growth, associated material properties, such as the elastic modulus of the extracellular matrix, may similarly evolve. Therefore, growth theories may be formulated by accounting for the evolution of tissue composition over time in response to various biological and mechanical triggers. This approach has been the foundation of classical bone remodeling theories that successfully describe Wolff's law by establishing a dependence between Young's modulus and bone apparent density and by formulating a constitutive relation between bone mass supply and the state of strain. The goal of this study is to demonstrate that adding tissue composition as state variables in the constitutive relations governing the stress-strain response and the mass supply represents a very general and straightforward method to model interstitial growth and remodeling in a wide variety of biological tissues. The foundation for this approach is rooted in the framework of mixture theory, which models the tissue as a mixture of multiple solid and fluid constituents. A further generalization is to allow each solid constituent in a constrained solid mixture to have its own reference (stress-free) configuration. Several illustrations are provided, ranging from bone remodeling to cartilage tissue engineering and cervical remodeling during pregnancy.
authors.affiliation: Department of Mechanical Engineering, Columbia University. Electronic address: kmm2233@columbia.edu.
authors.forename: Kristin
authors.initials: K
authors.lastname: Myers
authors.forename: Gerard A
authors.initials: GA
authors.lastname: Ateshian
mesh_terms: D000818:Animals; D002584:Cervix Uteri / Q000166:cytology / Q000502:physiology; D004548:Elasticity; D045604:Extracellular Fluid / Q000378:metabolism*; D005260:Female; D006801:Humans; D008954:Models, Biological; D009928:Organ Specificity; D011247:Pregnancy; D013314:Stress, Mechanical
keywords: Growth mechanics; Mixture theory; Tissue engineering; Tissue remodeling
references.citation: Am J Obstet Gynecol. 1983 Nov 15;147(6):662-6
references.pmid: 6638110
references.citation: J Biomech. 1992 Dec;25(12):1425-41
references.pmid: 1491020
references.citation: J Biomech Eng. 2012 Jan;134(1):011005
references.pmid: 22482660
references.citation: Science. 1976 Dec 10;194(4270):1174-6
references.pmid: 996549
references.citation: J Biomech Eng. 2009 Jun;131(6):061003
references.pmid: 19449957
references.citation: Endocrinology. 2012 Jul;153(7):3493-503
references.pmid: 22529214
references.citation: J Cell Biol. 1997 Feb 10;136(3):729-43
references.pmid: 9024701
references.citation: Eur J Obstet Gynecol Reprod Biol. 2009 May;144 Suppl 1:S82-9
references.pmid: 19303693
references.citation: Tohoku J Exp Med. 1980 Jul;131(3):289-99
references.pmid: 7414609
references.citation: J Math Biol. 1996;34(8):889-914
references.pmid: 8858855
references.citation: J Orthop Res. 1993 Jul;11(4):500-13
references.pmid: 8340823
references.citation: Am J Physiol Heart Circ Physiol. 2008 Mar;294(3):H1197-205
references.pmid: 18156194
references.citation: Tissue Eng. 2006 Dec;12(12):3487-96
references.pmid: 17518685
references.citation: Arch Biochem Biophys. 1998 Mar 15;351(2):207-19
references.pmid: 9515057
references.citation: Tissue Eng Part A. 2009 Aug;15(8):2065-72
references.pmid: 19196151
references.citation: J Biomech Eng. 2003 Oct;125(5):602-14
references.pmid: 14618919
references.citation: J Mech Phys Solids. 2011 Apr 1;59(4):863-883
references.pmid: 21532929
references.citation: J Biomech. 1988;21(2):155-68
references.pmid: 3350829
references.citation: Biotechnol Bioeng. 1999 Apr 20;63(2):197-205
references.pmid: 10099596
references.citation: J Biomech Eng. 1998 Jun;120(3):355-61
references.pmid: 10412403
references.citation: Anat Rec A Discov Mol Cell Evol Biol. 2006 Jan;288(1):84-90
references.pmid: 16345078
references.citation: Annu Rev Biomed Eng. 2012;14:97-111
references.pmid: 22809138
references.citation: J Biomech. 1994 Nov;27(11):1389-94
references.pmid: 7798290
references.citation: J Bone Joint Surg Am. 1977 Oct;59(7):954-62
references.pmid: 561786
references.citation: J Biomech. 2003 Dec;36(12):1853-64
references.pmid: 14614939
references.citation: J Biomech. 2011 Jun 3;44(9):1654-9
references.pmid: 21481875
references.citation: Biotechnol Prog. 2005 Jul-Aug;21(4):1252-61
references.pmid: 16080709
references.citation: Am J Physiol. 1996 May;270(5 Pt 2):H1736-43
references.pmid: 8928881
references.citation: Biomech Model Mechanobiol. 2009 Jun;8(3):167-81
references.pmid: 18470548
references.citation: Prog Biophys Biophys Chem. 1956;6:57-84
references.pmid: 13420188
references.citation: J Biomech Eng. 2000 Jun;122(3):252-60
references.pmid: 10923293
references.citation: J Theor Biol. 1982 Feb 7;94(3):555-77
references.pmid: 7078218
references.citation: Br J Obstet Gynaecol. 1989 Oct;96(10):1198-202
references.pmid: 2590655
references.citation: Clin Obstet Gynecol. 1983 Mar;26(1):7-13
references.pmid: 6839572
references.citation: J Biomech. 1987;20(1):7-17
references.pmid: 3558431
references.citation: J Biomech Eng. 2011 Jan;133(1):011010
references.pmid: 21186900
references.citation: J Biomech. 1987;20(11-12):1135-50
references.pmid: 3429459
references.citation: J Biomech. 2010 Jan 5;43(1):166-75
references.pmid: 19818962
references.citation: J Biomech Eng. 2001 Dec;123(6):528-35
references.pmid: 11783722
references.citation: Endocrinology. 2011 Mar;152(3):1036-46
references.pmid: 21209014
references.citation: Ann Biomed Eng. 1983;11(3-4):263-95
references.pmid: 6670786
references.citation: Tissue Eng Part A. 2008 Nov;14(11):1821-34
references.pmid: 18611145
references.citation: Biotechnol Bioeng. 2010 Mar 1;105(4):842-53
references.pmid: 19845002
references.citation: Osteoarthritis Cartilage. 2009 May;17(5):677-85
references.pmid: 19022685
references.citation: J Biomech. 2006;39(8):1489-97
references.pmid: 15990101
references.citation: Mech Res Commun. 2012 Jun 1;42:1-14
references.pmid: 22919118
references.citation: Biomech Model Mechanobiol. 2010 Dec;9(6):689-702
references.pmid: 20238138
references.citation: J Biomech. 1993 Apr-May;26(4-5):369-82
references.pmid: 8478342
references.citation: Reproduction. 2012 Apr;143(4):429-38
references.pmid: 22344465
references.citation: J Biomech. 1994 Apr;27(4):455-67
references.pmid: 8188726
references.citation: Clin Obstet Gynecol. 1995 Jun;38(2):267-79
references.pmid: 7554594
references.citation: Obstet Gynecol. 1993 Jan;81(1):88-92
references.pmid: 8416467
references.citation: Ann Biomed Eng. 2004 Jan;32(1):35-49
references.pmid: 14964720
references.citation: Am J Obstet Gynecol. 1974 Nov 1;120(5):641-51
references.pmid: 4278606
references.citation: J Biomech. 1988;21(2):131-9
references.pmid: 3350827
references.citation: J Biomech Eng. 2009 Oct;131(10):101001
references.pmid: 19831471
references.citation: J Biomech Eng. 1986 May;108(2):189-92
references.pmid: 3079517
references.citation: J Biomed Opt. 2010 Mar-Apr;15(2):026020
references.pmid: 20459265
references.citation: Am J Obstet Gynecol. 1947 Apr;53(4):541-60
references.pmid: 20291226
references.citation: J Math Biol. 1997 Sep;35(8):869-907
references.pmid: 9314193
references.citation: NMR Biomed. 2010 Oct;23(8):907-12
references.pmid: 20878968
references.citation: Semin Reprod Med. 2007 Jan;25(1):69-79
references.pmid: 17205425
references.citation: Biol Reprod. 2011 May;84(5):1053-62
references.pmid: 21248285
references.citation: J Biomech Eng. 1991 Aug;113(3):245-58
references.pmid: 1921350
references.citation: Coll Relat Res. 1988 Mar;8(2):103-12
references.pmid: 3378391
references.citation: J Biomech Eng. 2003 Apr;125(2):169-79
references.pmid: 12751278
references.citation: Mech Mater. 2012 Jan;44:47-57
references.pmid: 22184481
references.citation: Biomech Model Mechanobiol. 2007 Nov;6(6):423-45
references.pmid: 17206407
references.citation: Am J Obstet Gynecol. 1960 Nov;80:939-45
references.pmid: 13719582
references.citation: Mech Res Commun. 2012 Jun 1;42:118-125
references.pmid: 22904576
references.citation: Biomech Model Mechanobiol. 2010 Aug;9(4):403-19
references.pmid: 20039091
references.citation: Trends Endocrinol Metab. 2010 Jun;21(6):353-61
references.pmid: 20172738
references.citation: Tissue Eng Part A. 2010 May;16(5):1781-90
references.pmid: 20028219
references.citation: Am J Physiol Heart Circ Physiol. 2007 Oct;293(4):H2328-34
references.pmid: 17573459
references.citation: Osteoarthritis Cartilage. 2007 Sep;15(9):1025-33
references.pmid: 17498976
references.citation: J Mech Med Biol. 2009;9(2):243-257
references.pmid: 20209075
references.citation: J Biomech. 2012 Mar 15;45(5):780-9
references.pmid: 22236524