A homogenized constrained mixture (and mechanical analog) model for growth and remodeling of soft tissue

Albero AB, Ehret AE, Böl M (2014) A new approach to the simulation of microbial biofilms by a theory of fluid-like pressure-restricted finite growth. Comput Methods Appl Mech Eng 272:271–289

Ambrosi D, Ateshian GA, Arruda EM, Cowin SC, Dumais J, Goriely A, Holzapfel GA, Humphrey JD, Kemkemer R, Kuhl E, Olberding JE, Taber LA, Garikipati K (2011) Perspectives on biological growth and remodeling. J Mech Phys Solids 59(4):863–883

Ateshian GA, Humphrey JD (2012) Continuum models of biological growth and remodeling: past successes and future opportunities. Annu Rev Biomed Eng 14:97–111

Bai Y, Lee PF, Humphrey JD, Yeh AT (2014) Sequential multimodal microscopic imaging and biaxial mechanical testing of living multicomponent tissue constructs. Ann Biomed Eng 42(9):1791–1805

Brown RA, Prajapati R, McGrouther DA, Yannas IV, Eastwood M (1998) Tensional homeostasis in dermal fibroblasts: mechanical responses to mechanical loading in three-dimensional substrates. J Cell Physiol 175(3):323–332

Cyron C, Wall W (2012) Numerical method for the simulation of the Brownian dynamics of rod-like microstructures with three-dimensional nonlinear beam elements. Int J Numer Methods Eng 90(8):955–987

Cyron CJ, Humphrey JD (2014) Vascular homeostasis and the concept of mechanobiological stability. Int J Eng Sci 85:203–223

Cyron CJ, Humphrey JD (2016) Growth and remodeling of load-bearing soft tissues. Meccanica (submitted)

Cyron CJ, Wall WA (2009) Finite-element approach to Brownian dynamics of polymers. Phys Rev E 80(6):066704

Cyron CJ, Wilson JS, Humphrey JD (2014) Mechanobiological stability: a new paradigm to understand the enlargement of aneurysms? J R Soc Interface 11(100):20140680

Dafalias YF (1998) Plastic spin: necessity or redundancy? Int J Plast 14(9):909–931

Ezra DG, Ellis JS, Beaconsfield M, Collin R, Bailly M (2010) Changes in fibroblast mechanostat set point and mechanosensitivity: an adaptive response to mechanical stress in floppy eyelid syndrome. Invest Ophthalmol Vis Sci 51(8):3853–3863

Figueroa CA, Baek S, Taylor CA, Humphrey JD (2009) A computational framework for fluid-solid-growth modeling in cardiovascular simulations. Comput Methods Appl Mech Eng 198(45–46):3583–3602

Hannon P, Knapp K (2006) Forensic biomechanics. Lawyers & Judges Publishing Company, Tucson

Himpel G, Kuhl E, Menzel A, Steinmann P (2005) Computational modelling of isotropic multiplicative growth. Comput Model Eng Sci 8:119–134

Holzapfel G (2000) Nonlinear solid mechanics: a continuum approach for engineering. Wiley, New York

Howard J (2001) Mechanics of motor proteins and the cytoskeleton. Sinauer Associates Publishers, Sunderland

Humphrey JD, Dufresne ER, Schwartz MA (2014) Mechanotransduction and extracellular matrix homeostasis. Nat Rev Mol Cell Biol 15(12):802–812

Humphrey JD, Rajagopal KR (2002) A constrained mixture model for growth and remodeling of soft tissues. Math Models Methods Appl Sci 12(03):407–430

Kroon M, Holzapfel GA (2009) A theoretical model for fibroblast-controlled growth of saccular cerebral aneurysms. J Theor Biol 257(1):73–83

Mark JE, Erman B, Roland M (2013) The science and technology of rubber. Elsevier Science, Amsterdam

Menzel A, Kuhl E (2012) Frontiers in growth and remodeling. Mech Res Commun 42:1–14

Mofrad MRK, Kamm RD (2006) Cytoskeletal mechanics: models and measurements in cell mechanics. Cambridge University Press, Cambridge

Onck P, Koeman T, Van Dillen T, Van der Giessen E (2005) Alternative explanation of stiffening in cross-linked semiflexible networks. Phys Rev Lett 95(17):178102

Rajagopal K, Srinivasa A (1998) Mechanics of the inelastic behavior of materials—part 1, theoretical underpinnings. Int J Plast 14(10):945–967

Rajagopal KR, Wineman AS (1992) A constitutive equation for nonlinear solids which undergo deformation induced microstructural changes. Int J Plast 8(4):385–395

Reese S, Govindjee S (1998) A theory of finite viscoelasticity and numerical aspects. Int J Solids Struct 35(26):3455–3482

Rodriguez EK, Hoger A, McCulloch AD (1994) Stress-dependent finite growth in soft elastic tissues. J Biomech 27(4):455–467

Simo JC, Hughes TJR (2000) Computational inelasticity. Springer, New York

Simon DD, Humphrey JD (2014) Learning from tissue equivalents: biomechanics and mechanobiology. Bio-inspired materials for biomedical engineering. Wiley, New York 281–308

Simon DD, Murtada SI, Humphrey JD (2014) Computational model of matrix remodeling and entrenchment in the free-floating fibroblast-populated collagen lattice. Int J Numer Methods in Biomed Eng 30(12):1506–1529

Stein AM, Vader DA, Weitz DA, Sander LM (2011) The micromechanics of three-dimensional collagen-I gels. Complexity 16(4):22–28

Valentin A, Cardamone L, Baek S, Humphrey JD (2009) Complementary vasoactivity and matrix remodelling in arterial adaptations to altered flow and pressure. J R Soc Interface 6(32):293–306

Valentín A, Holzapfel GA (2012) Constrained mixture models as tools for testing competing hypotheses in arterial biomechanics: a brief survey. Mech Res Commun 42:126–133

Vandiver R, Goriely A (2009) Morpho-elastodynamics: the long-time dynamics of elastic growth. J Biol Dyn 3(2–3):180–195

Watton PN, Selimovic A, Raberger NB, Huang P, Holzapfel GA, Ventikos Y (2011) Modelling evolution and the evolving mechanical environment of saccular cerebral aneurysms. Biomech Model Mechanobiol 10(1):109–132

Wilson JS, Baek S, Humphrey JD (2013) Parametric study of effects of collagen turnover on the natural history of abdominal aortic aneurysms. Proc R Soc A 469(2150):20120556