Multiscale numerical analyses of arterial tissue with embedded elements in the finite strain regime

Misael Dalbosco1,2, Thiago A. Carniel3, Eduardo A. Fancello2,4, Gerhard A. Holzapfel1,5
1Institute of Biomechanics, Graz University of Technology, Stremayrgasse 16-II, Graz 8010, Austria
2GRANTE, Department of Mechanical Engineering, Federal University of Santa Catarina (UFSC), Florianópolis, SC, Brazil
3ACEA – Area of Exact and Environmental Sciences, Community University of Chapecó Region, Chapecó, SC, Brazil
4LEBm, University Hospital, Federal University of Santa Catarina (UFSC), Florianópolis, SC, Brazil
5Norwegian University of Science and Technology (NTNU), Department of Structural Engineering, Trondheim 7491, Norway

Tài liệu tham khảo

Lanir, 1983, Constitutive equations for fibrous connective tissues, J. Biomech., 16, 1, 10.1016/0021-9290(83)90041-6 Young, 2013, 464 Gartner, 2017, 672 Holzapfel, 2015, Modelling non-symmetric collagen fibre dispersion in arterial walls, J. R. Soc. Interface, 12, 10.1098/rsif.2015.0188 Niestrawska, 2016, Microstructure and mechanics of healthy and aneurysmatic abdominal aortas: experimental analysis and modelling, J. R. Soc. Interface, 13, 10.1098/rsif.2016.0620 Holzapfel, 2018, Biomechanical relevance of the microstructure in artery walls with a focus on passive and active components, Am. J. Physiol.-Heart Circ. Physiol., 315, H540, 10.1152/ajpheart.00117.2018 Holzapfel, 2000, 470 Holzapfel, 2019, On fibre dispersion modelling of soft biological tissues: a review, Proc. R. Soc. A, 475, 10.1098/rspa.2018.0736 Chen, 1997, Geometric control of cell life and death, Science, 276, 1425, 10.1126/science.276.5317.1425 Humphrey, 2012, Mechanics, mechanobiology, and modeling of human abdominal aorta and aneurysms, J. Biomech., 45, 805, 10.1016/j.jbiomech.2011.11.021 Humphrey, 2014, Mechanotransduction and extracellular matrix homeostasis, Nature Rev. Mol. Cell Biol., 15, 802, 10.1038/nrm3896 Baker, 2015, Cell-mediated fibre recruitment drives extracellular matrix mechanosensing in engineered fibrillar microenvironments, Nature Mater., 14, 1262, 10.1038/nmat4444 Niestrawska, 2019, The role of tissue remodeling in mechanics and pathogenesis of abdominal aortic aneurysms, Acta Biomater., 88, 149, 10.1016/j.actbio.2019.01.070 Stylianopoulos, 2007, Multiscale, structure-based modeling for the elastic mechanical behavior of arterial walls, J. Biomech. Eng., 129, 611, 10.1115/1.2746387 Speirs, 2008, An approach to the mechanical constitutive modelling of arterial tissue based on homogenization and optimization, J. Biomech., 41, 2673, 10.1016/j.jbiomech.2008.06.020 DeBotton, 2013, Analytical and numerical analyses of the micromechanics of soft fibrous connective tissues, Biomech. Model. Mechanobiol., 12, 151, 10.1007/s10237-012-0388-5 Shah, 2014, Prefailure and failure mechanics of the porcine ascending thoracic aorta: experiments and a multiscale model, J. Biomech. Eng., 136, 1, 10.1115/1.4026443 Thunes, 2016, A structural finite element model for lamellar unit of aortic media indicates heterogeneous stress field after collagen recruitment, J. Biomech., 49, 1562, 10.1016/j.jbiomech.2016.03.034 Witzenburg, 2017, Failure of the porcine ascending aorta: multidirectional experiments and a unifying microstructural model, J. Biomech. Eng., 139, 1, 10.1115/1.4035264 Thunes, 2018, Structural modeling reveals microstructure-strength relationship for human ascending thoracic aorta, J. Biomech., 71, 84, 10.1016/j.jbiomech.2018.01.037 Rocha, 2018, Multi-scale modelling of arterial tissue: Linking networks of fibres to continua, Comput. Methods Appl. Mech. Engrg., 341, 740, 10.1016/j.cma.2018.06.031 Carniel, 2019, On multiscale boundary conditions in the computational homogenization of an RVE of tendon fascicles, J. Mech. Behav. Biomed. Mater., 91, 131, 10.1016/j.jmbbm.2018.12.003 Carniel, 2019, A variational homogenization approach applied to the multiscale analysis of the viscoelastic behavior of tendon fascicles, Contin. Mech. Thermodyn., 31, 607, 10.1007/s00161-018-0714-y Carniel, 2019, A numerical insight on the pericellular matrix and elastin fibers in the multiscale mechanics of tendon fascicles, Eur. J. Mech. A Solids, 76, 146, 10.1016/j.euromechsol.2019.04.001 Ben-Or Frank, 2019, Micromechanically-motivated analysis of fibrous tissue, J. Mech. Behav. Biomed. Mater., 96, 69, 10.1016/j.jmbbm.2019.04.007 McIntosh, 2009, Impact of bone geometry on effective properties of bone scaffolds, Acta Biomater., 5, 680, 10.1016/j.actbio.2008.09.010 Yuan, 2011, A new model to simulate the elastic properties of mineralized collagen fibril, Biomech. Model. Mechanobiol., 10, 147, 10.1007/s10237-010-0223-9 Vaughan, 2012, A three-scale finite element investigation into the effects of tissue mineralisation and lamellar organisation in human cortical and trabecular bone, J. Mech. Behav. Biomed. Mater., 12, 50, 10.1016/j.jmbbm.2012.03.003 Holzapfel, 2000, A new constitutive framework for arterial wall mechanics and a comparative study of material models, J. Elasticity, 61, 1, 10.1023/A:1010835316564 Maiti, 2020, Computational modeling of the strength of the ascending thoracic aortic media tissue under physiologic biaxial loading conditions, J. Biomech., 108, 10.1016/j.jbiomech.2020.109884 de Souza Neto, 2010, Variational foundations of large strain multiscale solid constitutive models: kinematical formulation, 341 Goudarzi, 2019, Discrete inclusion models for reinforced composites: comparative performance analysis and modeling challenges, Comput. Methods Appl. Mech. Engrg., 355, 535, 10.1016/j.cma.2019.06.026 Blanco, 2016, Variational foundations and generalized unified theory of RVE-based multiscale models, Arch. Comput. Methods Eng., 23, 191, 10.1007/s11831-014-9137-5 de Souza Neto, 2015, An RVE-based multiscale theory of solids with micro-scale inertia and body force effects, Mech. Mater., 80, 136, 10.1016/j.mechmat.2014.10.007 Phillips, 1976, Finite element non-linear linear analysis of concrete structures, Proc. Inst. Civ. Eng., 61, 59 Elwi, 1991, Finite element model for curved embedded reinforcement, J. Eng. Mech., 117, 714, 10.1061/(ASCE)0733-9399(1991)117:3(714.2) Garimella, 2019, Embedded finite elements for modeling axonal injury, Ann. Biomed. Eng., 47, 1889, 10.1007/s10439-018-02166-0 Hartl, 2002 Hill, 1963, Elastic properties of reinforced solids: Some theoretical principles, J. Mech. Phys. Solids, 11, 357, 10.1016/0022-5096(63)90036-X Hill, 1965, Continuum micro-mechanics of elastoplastic polycrystals, J. Mech. Phys. Solids, 13, 89, 10.1016/0022-5096(65)90023-2 Hill, 1965, A self-consistent mechanics of composite materials, J. Mech. Phys. Solids, 13, 213, 10.1016/0022-5096(65)90010-4 Hill, 1972, On constitutive macro-variables for heterogeneous solids at finite strain, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 326, 131 Mandel, 1972, Plasticité classique et viscoplasticité Carniel, 2018, A multiscale numerical approach for the finite strains analysis of materials reinforced with helical fibers, Mech. Mater., 126, 75, 10.1016/j.mechmat.2018.07.014 Miehe, 2003, Computational micro-to-macro transitions for discretized micro-structures of heterogeneous materials at finite strains based on the minimization of averaged incremental energy, Comput. Methods Appl. Mech. Engrg., 192, 559, 10.1016/S0045-7825(02)00564-9 Saeb, 2016, Aspects of computational homogenization at finite deformations: a unifying review from Reuss’ to Voigt’s Bound, Appl. Mech. Rev., 68, 10.1115/1.4034024 Holzapfel, 2008, Collagen in arterial walls: biomechanical aspects, 285 Robertson, 2013, Mechanobiology of the arterial wall, 275 Roach, 1957, The reason for the shape of the distensibility curves of arteries, Can. J. Biochem. Physiol., 35, 681, 10.1139/o57-080 Sugita, 2017, Multiphoton microscopy observations of 3D elastin and collagen fiber microstructure changes during pressurization in aortic media, Biomech. Model. Mechanobiol., 16, 763, 10.1007/s10237-016-0851-9 Morin, 2019, Multiscale mechanical behavior of large arteries, 180 Schriefl, 2012, Determination of the layer-specific distributed collagen fibre orientations in human thoracic and abdominal aortas and common iliac arteries, J. R. Soc. Interface, 9, 1275, 10.1098/rsif.2011.0727 Wolinsky, 1967, A lamellar unit of aortic medial structure and function in mammals, Circ. Res., 20, 99, 10.1161/01.RES.20.1.99 Dingemans, 2000, Extracellular matrix of the human aortic media: An ultrastructural histochemical and immunohistochemical study of the adult aortic media, Anat. Rec., 258, 1, 10.1002/(SICI)1097-0185(20000101)258:1<1::AID-AR1>3.0.CO;2-7 O’Connell, 2008, The three-dimensional micro- and nanostructure of the aortic medial lamellar unit measured using 3D confocal and electron microscopy imaging, Matrix Biol., 27, 171, 10.1016/j.matbio.2007.10.008 Humphrey, 2013, Possible mechanical roles of glycosaminoglycans in thoracic aortic dissection and associations with dysregulated transforming growth factor-β, J. Vasc. Res., 50, 1, 10.1159/000342436 Krasny, 2018, Kinematics of collagen fibers in carotid arteries under tension-inflation loading, J. Mech. Behav. Biomed. Mater., 77, 718, 10.1016/j.jmbbm.2017.08.014 Sherifova, 2019, Failure properties and microstructure of healthy and aneurysmatic human thoracic aortas subjected to uniaxial extension with a focus on the media, Acta Biomater., 99, 443, 10.1016/j.actbio.2019.08.038 Holzapfel, 2010, Constitutive modelling of arteries, Proc. R. Soc. A, 466, 1551, 10.1098/rspa.2010.0058 Miyazaki, 1999, Tensile tests of collagen fibers obtained from the rabbit patellar tendon, Biomed. Microdevices, 2, 151, 10.1023/A:1009953805658 Holzapfel, 2020, A damage model for collagen fibres with an application to collagenous soft tissues, Proc. R. Soc. A, 476, 10.1098/rspa.2019.0821 Holzapfel, 2020, An arterial constitutive model accounting for collagen content and cross-linking, J. Mech. Phys. Solids, 136, 10.1016/j.jmps.2019.103682 Lanir, 1979, A structural theory for the homogeneous biaxial stress-strain relationships in flat collagenous tissues, J. Biomech., 12, 423, 10.1016/0021-9290(79)90027-7 Hurschler, 2003, Application of a probabilistic microstructural model to determine reference length and toe-to-linear region transition in fibrous connective tissue, J. Biomech. Eng., 125, 415, 10.1115/1.1579046 Hill, 2012, A theoretical and non-destructive experimental approach for direct inclusion of measured collagen orientation and recruitment into mechanical models of the artery wall, J. Biomech., 45, 762, 10.1016/j.jbiomech.2011.11.016 Weisbecker, 2015, Constitutive modelling of arteries considering fibre recruitment and three-dimensional fibre distribution, J. R. Soc. Interface, 12, 10.1098/rsif.2015.0111 Lanir, 2017, Multi-scale structural modeling of soft tissues mechanics and mechanobiology, J. Elasticity, 129, 7, 10.1007/s10659-016-9607-0 Han, 2018, Mechanobiology in vascular remodeling, Natl. Sci. Rev., 5, 933, 10.1093/nsr/nwx153 Chow, 2014, Arterial extracellular matrix: a mechanobiological study of the contributions and interactions of elastin and collagen, Biophys. J., 106, 2684, 10.1016/j.bpj.2014.05.014 Belytschko, 2000, 667