Search Advanced

AIMS Materials Science

2017, Volume 4, Issue 3: 680-705. doi: 10.3934/matersci.2017.3.680
Previous Article Next Article
Review Topical Sections

Theoretical methods and models for mechanical properties of soft biomaterials

  • 1.
    Graduate School of Science and Engineering, Yamagata University, Japan
  • 2.
    Graduate School of Medical Science, Yamagata University, Japan
  • 3.
    Integrative Bioscience and Biomedical Engineering, Graduate School of Waseda University, Japan
  • Received: 24 March 2017 Accepted: 31 May 2017 Published: 05 June 2017

  • We review the most commonly used theoretical methods and models for the mechanical properties of soft biomaterials, which include phenomenological hyperelastic and viscoelastic models, structural biphasic and network models, and the structural alteration theory. We emphasize basic concepts and recent developments. In consideration of the current progress and needs of mechanobiology, we introduce methods and models for tackling micromechanical problems and their applications to cell biology. Finally, the challenges and perspectives in this field are discussed.

    Citation: Zhonggang Feng, Tadashi Kosawada, Takao Nakamura, Daisuke Sato, Tatsuo Kitajima, Mitsuo Umezu. Theoretical methods and models for mechanical properties of soft biomaterials[J]. AIMS Materials Science, 2017, 4(3): 680-705. doi: 10.3934/matersci.2017.3.680

    Related Papers:

  • We review the most commonly used theoretical methods and models for the mechanical properties of soft biomaterials, which include phenomenological hyperelastic and viscoelastic models, structural biphasic and network models, and the structural alteration theory. We emphasize basic concepts and recent developments. In consideration of the current progress and needs of mechanobiology, we introduce methods and models for tackling micromechanical problems and their applications to cell biology. Finally, the challenges and perspectives in this field are discussed.


    加载中
    [1] Jabbari E, Leijten J, Xu Q, et al. (2016) The matrix reloaded: the evolution of regenerative hydrogels. Mater Today 19: 190–196. doi: 10.1016/j.mattod.2015.10.005
    [2] Green J, Elisseeff J (2016) Mimicking biological functionality with polymers for biomedical applications. Nature 540: 386–394. doi: 10.1038/nature21005
    [3] Brandl F, Sommer F, Goepferich A (2007) Rational design of hydrogels for tissue engineering: Impact of physical factors on cell behavior. Biomaterials 28: 134–146. doi: 10.1016/j.biomaterials.2006.09.017
    [4] Hu Y, You J, Aizenberg J (2016) Micropatterned hydrogel surface with high-aspect-ratio features for cell guidance and tissue growth. ACS Appl Mater Interfaces 8: 21939–21945. doi: 10.1021/acsami.5b12268
    [5] Liu X, Tang T, Tham E, et al. (2017) Stretchable living materials and devices with hydrogel–elastomer hybrids hosting programmed cells. Proc Natl Acad Sci USA 114: 2200–2205. doi: 10.1073/pnas.1618307114
    [6] Engler AJ, Sen S, Sweeney HL, et al. (2006) Matrix elasticity directs stem cell lineage specification. Cell 126: 677–689. doi: 10.1016/j.cell.2006.06.044
    [7] Bordeleau F, Mason B, Lollis E, et al. (2017) Matrix stiffening promotes a tumor vasculature phenotype. Proc Natl Acad Sci USA 114: 492–497. doi: 10.1073/pnas.1613855114
    [8] Chaudhuri O, Gu L, Klumpers D, et al. (2016) Hydrogels with tunable stress relaxation regulate stem cell fate and activity. Nat Mater 15: 326–334.
    [9] Chaudhuri O, Gu L, Darnell M, et al. (2015) Substrate stress relaxation regulates cell spreading. Nat Commun 6: 6364. doi: 10.1038/ncomms7364
    [10] Lin D, Horkay F (2008) Nanomechanics of polymer gels and biological tissues: A critical review of analytical approaches in the Hertzian regime and beyond. Soft Matter 4: 669–682. doi: 10.1039/b714637j
    [11] Andreu I, Luque T, Sancho A, et al. (2014) Heterogeneous micromechanical properties of the extracellular matrix in healthy and infarcted hearts. Acta Biomater 10: 3235–3242. doi: 10.1016/j.actbio.2014.03.034
    [12] Gimenez A, Uriarte J, Vieyra J, et al. (2017) Elastic properties of hydrogels and decellularized tissue sections used in mechanobiology studies probed by atomic force microscopy. Microsc Res Techniq 80: 85–96. doi: 10.1002/jemt.22740
    [13] Chen D, Wen Q, Janmey P, et al. (2010) Rheology of soft materials. Annu Rev Conden Ma P 1: 301–322. doi: 10.1146/annurev-conmatphys-070909-104120
    [14] Voigtmann T (2014) Nonlinear glassy rheology. Curr Opin Colloid In 19: 549–560. doi: 10.1016/j.cocis.2014.11.001
    [15] Freutel M, Schmidt H, Dürselen L, et al. (2014) Finite element modeling of soft tissues: material models, tissue interaction and challenges. Clin Biomech 29: 363–372. doi: 10.1016/j.clinbiomech.2014.01.006
    [16] Bhatia SK (2012) Engineering biomaterials for regenerative medicine: novel technologies for clinical applications, Springer Science Business Media, LLC.
    [17] Wiles K, Fishman J, De Coppi P, et al. (2016) The host immune response to tissue-engineered organs: current problems and future directions. Tissue Eng B-Rev 22: 208–219.
    [18] Seal BL, Otero TC, Panitch A (2001) Polymeric biomaterials for tissue and organ regeneration. Mat Sci Eng R 34: 147–230. doi: 10.1016/S0927-796X(01)00035-3
    [19] Green AE, Adkins JE (1960) Large elastic deformations, New York: Oxford University Press.
    [20] Ogden RW (1984) Non-linear elastic deformations, Dover Publications, Inc.
    [21] Fung YC (1993) Biomechanics: mechanical properties of living tissues, 2nd edition, Springer-Verlag New York, Inc.
    [22] Bechir H, Chevalier L, Chaouche M, et al. (2006) Hyperelastic constitutive model for rubber-like materials based on the first Seth strain measures invariant. Eur J Mech A-Solid 25: 110–124. doi: 10.1016/j.euromechsol.2005.03.005
    [23] Chagnon G, Rebouah M, Favier D (2015) Hyperelastic energy densities for soft biological tissues: a review. J Elasticity 120: 129–160.
    [24] Madireddy S, Sista B, Vemaganti K (2016) Bayesian calibration of hyperelastic constitutive models of soft tissue. J Mech Behav Biomed 59: 108–127. doi: 10.1016/j.jmbbm.2015.10.025
    [25] Jhun C, Evans MC, Barocas VH, et al. (2009) Planar biaxial mechanical behavior of bioartificial tissues possessing prescribed fiber alignment. J Biomech Eng 131: 081006. doi: 10.1115/1.3148194
    [26] Sander EA, Stylianopoulos T, Tranquillo RT, et al. (2009) Image-based multiscale modeling predicts tissue-level and network-level fiber reorganization in stretched cell-compacted collagen gels. Proc Natl Acad Sci USA 106: 17675–17680. doi: 10.1073/pnas.0903716106
    [27] Lanir Y (1980) A microstructural model for the rheology of mammalian tendon. J Biomech Eng 102: 332–339.
    [28] Lanir Y (1983) Constitutive equations for fibrous connective tissues. J Biomech 16: 1–12. doi: 10.1016/0021-9290(83)90041-6
    [29] Rajagopal KR, Wineman AS (1992) A constitutive equation for nonlinear solids which undergo deformation induced microstructural changes. Int J Plasticity 8: 385–395. doi: 10.1016/0749-6419(92)90056-I
    [30] Ogden RW, Roxburgh DG (1999) A pseudo-elastic model for the Mullins effect in filled rubber. Proceedings A 455: 2861–2877.
    [31] Lu T, Wang J, Yang R, et al. (2016) A constitutive model for soft materials incorporating viscoelasticity and Mullins effect. J Appl Mech 84: 021010. doi: 10.1115/1.4035180
    [32] Horgan CO, Murphy JG (2011) Simple shearing of soft biological tissues. Proceedings A 467: 760–777.
    [33] Ben Amar M, Wu M, Trejo M, et al. (2015) Morpho-elasticity of inflammatory fibrosis: the case of capsular contracture. J R Soc Interface 12: 20150343. doi: 10.1098/rsif.2015.0343
    [34] Saxena T, Gilbert JL, Hasenwinkel JM (2009) A versatile mesoindentation system to evaluate the micromechanical properties of soft, hydrated substrates on a cellular scale. J Biomed Mater Res A 90: 1206–1217.
    [35] White CC, Vanlandingham MR, Drzal PL, et al. (2005) Viscoelastic characterization of polymers using instrumented indentation. II. dynamic testing. J Polym Sci Pol Phys 43: 1812–1824.
    [36] Tirella A, Mattei G, Ahluwalia A (2014) Strain rate viscoelastic analysis of soft and highly hydrated biomaterials. J Biomed Mater Res A 102: 3352–3360. doi: 10.1002/jbm.a.34914
    [37] Feng Z, Yamato M, Akutsu T, et al. (2003) Investigation on the mechanical properties of contracted collagen gels as a scaffold for tissue engineering. Artif Organs 27: 84–91. doi: 10.1046/j.1525-1594.2003.07187.x
    [38] Feng Z, Seya D, Kitajima T (2010) Viscoelastic characteristics of contracted collagen gels populated with rat fibroblasts or cardiomyocytes. J Artif Organs 13: 139–144. doi: 10.1007/s10047-010-0508-x
    [39] Toyjanova J, Hannen E, Bar-Kochba E, et al. (2014) 3D Viscoelastic traction force microscopy. Soft Matter 10: 8095–8106. doi: 10.1039/C4SM01271B
    [40] Zacharatos A, Kontou E (2015) Nonlinear viscoelastic modeling of soft polymers. J Appl Polym Sci 132: 42141.
    [41] Chen J, Hu H, Li S, et al. (2016) Quantitative relation between the relaxation time and the strain rate for polymeric solids under quasi-static conditions. J Appl Polym Sci 133: 44114.
    [42] Kikuchi M, Feng Z, Kosawada T, et al. (2016) Stress relaxation and stress-strain characteristics of porcine amniotic membrane. Bio-Med Mater Eng 27: 603–611.
    [43] Fujita K, Tuchida Y, Seki H, et al. (2015) Characterizing and modulating the mechanical properties of hydrogels from ventricular extracellular matrix. Proceeding of 10th Asian Control Conference (ASCC 2015), 718–722.
    [44] Taira Y, Shiraishi Y, Inoue Y, et al. (2016) Spatially distributed modeling of esophageal function by nonlinear characteristic analyses. Proceeding of Japanese Biomedical Engineering Symposium, 1P-3-1.
    [45] Scott-Blair GW (1947) The role of psychophysics in rheology. J Colloid Sci 2: 21–32. doi: 10.1016/0095-8522(47)90007-X
    [46] Schiessel H, Metzler R, Blumen A, et al. (1995) Genneralized viscoelastic models: their fractional equations with solutions. J Phys A-Math Gen 28: 6567–6584. doi: 10.1088/0305-4470/28/23/012
    [47] Jaishankar A, McKinley GH (2012) Power-law rheology in the bulk and at the interface: quasi-properties and fractional constitutive equations. Proceedings A 20120284.
    [48] De Sousa JS, Santos JAC, Barros EB, et al. (2017) Analytical model of atomic-force-microscopy force curves in viscoelastic materials exhibiting power law relaxation. J Appl Phys 121: 034901. doi: 10.1063/1.4974043
    [49] Biot MA (1941) General theory of three-dimensional consolidation. J Appl Phys 12: 155–164. doi: 10.1063/1.1712886
    [50] Bowen RM (1976) Theory of mixtures, In: Eringen AC, Continuum Physics, New York: Academic Press, 1–127.
    [51] Green AE, Naghdi PM (1970) The flow of fluid through an elastic solid. Acta Mech 9: 329–340. doi: 10.1007/BF01179830
    [52] Mow VC, Kuei SC, Lai WM, et al. (1980) Biphasic creep and stress relaxation of articular cartilage in compression: theory and experiments. J Biomech Eng 102: 73–84. doi: 10.1115/1.3138202
    [53] Ehlers W, Acartürk A, Karajan N (2010) Advances in modelling saturated soft biological tissues and chemically active gels. Arch Appl Mech 80: 467–478. doi: 10.1007/s00419-009-0386-y
    [54] Gao X, Gu W (2014) A new constitutive model for hydration-dependent mechanical properties in biological soft tissues and hydrogels. J Biomech 47: 3196–3200. doi: 10.1016/j.jbiomech.2014.06.012
    [55] Bonilla MR, Lopez-Sanchez P, Gidley MJ, et al. (2016) Micromechanical model of biphasic biomaterials with internal adhesion: Application to nanocellulose hydrogel composites. Acta Biomater 29: 149–160. doi: 10.1016/j.actbio.2015.10.032
    [56] Olberding JE, Suh JF (2006) A dual optimization method for the material parameter identification of a biphasic poroviscoelastic hydrogel: Potential application to hypercompliant soft tissues. J Biomech 39: 2468–2475. doi: 10.1016/j.jbiomech.2005.07.019
    [57] Castro APG, Laity P, Shariatzadeh M, et al. (2016) Combined numerical and experimental biomechanical characterization of soft collagen hydrogel substrate. J Mater Sci-Mater M 27: 79. doi: 10.1007/s10856-016-5688-3
    [58] Gentile G, Greco F, Larobina D (2013) Stress-relaxation behavior of a physical gel: Evidence of co-occurrence of structural relaxation and water diffusion in ionic alginate gels. Eur Polym J 49: 3929–3936. doi: 10.1016/j.eurpolymj.2013.08.023
    [59] Galli M, Comley K, Shean T, et al. (2009) Viscoelastic and poroelastic mechanical characterization of hydrated gels. J Mater Res 24: 973–979. doi: 10.1557/jmr.2009.0129
    [60] Bush BG, Shapiro JM, DelRio FW, et al. (2015) Mechanical measurements of heterogeneity and length scale effects in PEG-based hydrogels. Soft Matter 11: 7191–7200. doi: 10.1039/C5SM01210D
    [61] Oyen ML (2015) Nanoindentation of hydrated materials and tissues. Curr Opin Solid St M 19: 317–323. doi: 10.1016/j.cossms.2015.03.001
    [62] Wang Q, Mohan AC, Oyen ML, et al. (2014) Separating viscoelasticity and poroelasticity of gels with different length and time scales. Acta Mech Sin 30: 20–27. doi: 10.1007/s10409-014-0015-z
    [63] Guth E, James HM, Mark H (1946) The kinetic theory of rubber elasticity. In: Mark H, Whitby GS, Scientific progress in the field of rubber and synthetic elastomers, New York: Interscience Publishers, 253–299.
    [64] Treloar L (1975) The physics of rubber elasticity, Oxford: Oxford University Press.
    [65] Flory PJ (1989) Statistical mechanics of chain molecules, New York: Hanser Publishers.
    [66] Doi M, Edwards SF (1986) The theory of polymer dynamics, Oxford: Clarendon Press.
    [67] Arruda EM, Boyce MC (1993) A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials. J Mech Phys Solids 41: 389–412. doi: 10.1016/0022-5096(93)90013-6
    [68] Broedersz CP, Mao X, Lubensky TC, et al. (2011) Criticality and isostaticity in fibre networks. Nat Phys 7: 983–988. doi: 10.1038/nphys2127
    [69] Head DA, Levine AJ, MacKintosh FC (2003) Deformation of cross-linked semiflexible polymer networks. Phys Rev Lett 91: 108102. doi: 10.1103/PhysRevLett.91.108102
    [70] Broedersz CP, MacKintosh FC (2014) Modeling semiflexible polymer networks. Rev Mod Phys 86: 995–1036. doi: 10.1103/RevModPhys.86.995
    [71] Marko JF, Siggia ED (1995) Stretching DNA. Macromolecules 28: 8759–8770. doi: 10.1021/ma00130a008
    [72] Wilhelm J, Frey E (1996) Radial distribution of semiflexible polymers. Phys Rev Lett 77: 2581–2584. doi: 10.1103/PhysRevLett.77.2581
    [73] MacKintosh FC, Kas J, Janmey PA (1995) Elasticity of semiflexible biopolymer networks. Phys Rev Lett 75: 4425–4428. doi: 10.1103/PhysRevLett.75.4425
    [74] Storm C, Pastore JJ, MacKintosh FC, et al. (2005) Nonlinear elasticity in biological gels. Nature 435: 191–194. doi: 10.1038/nature03521
    [75] Odijk T (1995) Stiff chains and filaments under tension. Macromolecules 28: 7016–7018. doi: 10.1021/ma00124a044
    [76] Gardel ML, Shin JH, MacKintosh FC, et al. (2004) Elastic behavior of cross-linked and bundled actin networks. Science 304: 1301–1305. doi: 10.1126/science.1095087
    [77] Yao NY, Broedersz CP, Lin Y, et al. (2010) Elasticity in ionically cross-linked neurofilament networks. Biophys J 98: 2147–2153. doi: 10.1016/j.bpj.2010.01.062
    [78] Kroy K (2006) Elasticity, dynamics and relaxation in biopolymer networks. Curr Opin Colloid In 11: 56–64. doi: 10.1016/j.cocis.2005.10.001
    [79] Wells HC, Sizeland KH, Kayed HR, et al. (2015). Poisson's ratio of collagen fibrils measured by small angle X-ray scattering of strained bovine pericardium. J Appl Phys 117: 044701.
    [80] Arevalo RC, Kumar P, Urbach JS, et al. (2015) Stress heterogeneities in sheared type-I collagen networks revealed by boundary stress microscopy. PloS One 10: e0118021. doi: 10.1371/journal.pone.0118021
    [81] Yang Z, Hemar Y, Hilliou L, et al. (2016) Nonlinear behavior of gelatin networks reveals a hierarchical structure. Biomacromolecules 17: 590–600. doi: 10.1021/acs.biomac.5b01538
    [82] Groot RD (1996) Molecular theory of strain hardening of a polymer gel: application to gelatin. J Chem Phys 104: 9202–9219. doi: 10.1063/1.471611
    [83] Jin T, Stanciulescu I (2016) Numerical simulation of fibrous biomaterials with randomly distributed fiber network structure. Biomech Model Mechan 15: 817–830. doi: 10.1007/s10237-015-0725-6
    [84] Cioroianu AR, Spiesz EM, Storm C (2016) Disorder, pre-stress and non-affinity in polymer 8-chain models. J Mech Phys Solids 89: 110–125. doi: 10.1016/j.jmps.2016.01.014
    [85] Onck PR, Koeman T, van Dillen T, et al. (2005) Alternative explanation of stiffening in cross-linked semiflexible networks. Phys Rev Lett 95: 178102. doi: 10.1103/PhysRevLett.95.178102
    [86] Chandran PL, Barocas VH (2006) Affine versus non-affine fibril kinematics in collagen networks: theoretical studies of network behavior. J Biomech Eng 128: 259–270.
    [87] Feng Z, Ishiguro Y, Fujita K, et al. (2015) A fibril-based structural constitutive theory reveals the dominant role of network characteristics on the mechanical behavior of fibroblast-compacted collagen gels. Biomaterials 67: 365–381. doi: 10.1016/j.biomaterials.2015.07.038
    [88] Tobolsky AV (1960) Properties and structure of polymers, New York: John Wiley and Sons.
    [89] Green MS, Tobolsky AV (1946) A new approach to the theory of relaxing polymeric media. J Chem Phys 14: 80–92. doi: 10.1063/1.1724109
    [90] Simo JC (1987) On a fully three-dimensional finite-strain viscoelastic damage model: formulation and computational aspects. Comput Method Appl M 60: 153–173. doi: 10.1016/0045-7825(87)90107-1
    [91] Septanika EG, Ernst LJ (1998) Application of the network alteration theory for modeling the time-dependent constitutive behaviour of rubbers. Part I. General theory. Mech Mater 30: 253–263.
    [92] Wu X, Levenston ME, Chaikof EL (2006) A constitutive model for protein-based materials. Biomaterials 30: 5315–5325.
    [93] Bergstrom JS, Boyce MC (1998) Constitutive modeling of the large strain time-dependent behavior of elastomers. J Mech Phys Solids 46: 931–954. doi: 10.1016/S0022-5096(97)00075-6
    [94] Bergstrom JS, Boyce MC (2001) Constitutive modeling of the time-dependent and cyclic loading of elastomers and application to soft biological tissues. Mech Mater 33: 523–530. doi: 10.1016/S0167-6636(01)00070-9
    [95] Meng F, Pritchard RH, Terentjev EM (2016) Stress relaxation, dynamics, and plasticity of transient polymer networks. Macromolecules 49: 2843–2852. doi: 10.1021/acs.macromol.5b02667
    [96] Li Y, Tang S, Kröger M, et al. (2016) Molecular simulation guided constitutive modeling on finite strain viscoelasticity of elastomers. J Mech Phys Solids 88: 204–226. doi: 10.1016/j.jmps.2015.12.007
    [97] Li Y, Liu Z, Jia Z, et al. (2017) Modular-based multiscale modeling on viscoelasticity of polymer nanocomposites. Comput Mech 59: 187–201. doi: 10.1007/s00466-016-1346-3
    [98] Wang Q, Gao Z (2016) A constitutive model of nanocomposite hydrogels with nanoparticle crosslinkers. J Mech Phys Solids 94: 127–147. doi: 10.1016/j.jmps.2016.04.011
    [99] Nam S, Hu KH, Butte MJ, et al. (2016) Strain-enhanced stress relaxation impacts nonlinear elasticity in collagen gels. Proc Natl Acad Sci USA 113: 5492–5497.
    [100] Bell GI (1978) Models for the specific adhesion of cells to cells. Science 200: 618–627. doi: 10.1126/science.347575
    [101] Vos BE, Liebrand LC, Vahabi M, et al. (2016) Programming filamentous network mechanics by compression. arXiv:1612.08601.
    [102] Brown RA, Wiseman M, Chuo CB, et al. (2005) Ultrarapid engineering of biomimetic materials and tissues: fabrication of nano- and microstructures by plastic compression. Adv Funct Mater 15: 1762–1770. doi: 10.1002/adfm.200500042
    [103] Ghezzi CE, Rnjak-Kovacina J, Kaplan DL (2015) Corneal tissue engineering: recent advances and future perspectives. Tissue Eng B-Rev 21: 278–287. doi: 10.1089/ten.teb.2014.0397
    [104] Bell E, Ivarsson B, Merrill C (1979) Production of a tissue-like structure by contraction of collagen lattices by human fibroblasts of different proliferative potential in vitro. Proc Natl Acad Sci USA 76: 1274–1278. doi: 10.1073/pnas.76.3.1274
    [105] Brown RA (2013) In the beginning there were soft collagen-cell gels: towards better 3D connective tissue models? Exp Cell Res 319: 2460–2469. doi: 10.1016/j.yexcr.2013.07.001
    [106] Barocas VH, Tranquillo RT (1997) An anisotropic biphasic theory of tissue-equivalent mechanics: the interplay among cell traction, fibrillar network deformation, fibril alignment, and cell contact guidance. J Biomech Eng 119: 137–145. doi: 10.1115/1.2796072
    [107] Zahalak GI, Wagenseil JE, Wakatsuki T, et al. (2009) A cell-based constitutive relation for bio-artificial tissues. Biophys J 79: 2369–2381.
    [108] Feng Z, Wagatsuma Y, Kikuchi M, et al. (2014) The mechanisms of fibroblast-mediated compaction of collagen gels and the mechanical niche around individual fibroblasts. Biomaterials 35: 8078–8091.
    [109] Hall M, Long R, Feng X, et al. (2013) Toward single cell traction microscopy within 3D collagen matrices. Exp Cell Res 319: 2396–2408. doi: 10.1016/j.yexcr.2013.06.009
    [110] Jones C, Cibula M, Feng J, et al. (2015) Micromechanics of cellularized biopolymer networks. Proc Natl Acad Sci USA 112: E5117–E5122. doi: 10.1073/pnas.1509663112
    [111] Zeng X, Li S (2011) Multiscale modeling and simulation of soft adhesion and contact of stem cells. J Mech Behav Biomed 4: 180–189. doi: 10.1016/j.jmbbm.2010.06.002
    [112] Aghvami M, Billiar KL, Sander EA (2016) Fiber network models predict enhanced cell mechanosensing on fibrous gels. J Biomech Eng 138: 101006. doi: 10.1115/1.4034490
    [113] Darling EM, Zauscher S, Block JA, et al. (2007) A thin-layer model for viscoelastic, stress–relaxation testing of cells using atomic force microscopy: do cell properties reflect metastatic potential. Biophys J 92: 1784–1791. doi: 10.1529/biophysj.106.083097
    [114] Darling EM, Topel M, Zauscher S, et al. (2008) Viscoelastic properties of human mesenchymally-derived stem cells and primary osteoblasts, chondrocytes, and adipocytes. J Biomech 41: 454–464. doi: 10.1016/j.jbiomech.2007.06.019
    [115] Nguyen TD, Oloyede A, Singh S, et al. (2015) Microscale consolidation analysis of relaxation behavior of single living chondrocytes subjected to varying strain-rates. J Mech Behav Biomed 49: 343–354. doi: 10.1016/j.jmbbm.2015.05.003
    [116] Moeendarbary E, Valon L, Fritzsche M, et al. (2013) The cytoplasm of living cells behaves as a poroelastic material. Nat Mater 12: 253–261. doi: 10.1038/nmat3517
    [117] Chen J (2014) Nanobiomechanics of living cells: a review. Interface Focus 4: 20130055. doi: 10.1098/rsfs.2013.0055
    [118] Mattei G, Ahluwalia A (2016) Sample, testing and analysis variables affecting liver mechanical properties: a review. Acta Biomater 45: 60–71 doi: 10.1016/j.actbio.2016.08.055
    [119] Bustamante C, Marko JF, Siggia ED, et al. (1994) Entropic elasticity of λ-phage DNA. Science 265: 1599–1600. doi: 10.1126/science.8079175
    [120] Marszalek PE, Li H, Fernandez JM (2001) Fingerprinting polysaccharides with singlemolecule atomic force microscopy. Nat Biotechnol 19: 258–262. doi: 10.1038/85712
    [121] Van der Rijt JAJ, van der Werf KO, Bennink ML, et al. (2006) Micromechanical testing of individual collagen fibrils. Macromol Biosci 6: 697–702. doi: 10.1002/mabi.200600063
    [122] Buehler MJ, Keten S, Ackbarow T (2008) Theoretical and computational hierarchical nanomechanics of protein materials: Deformation and fracture. Prog Mater Sci 53: 1101–1241. doi: 10.1016/j.pmatsci.2008.06.002
    [123] Sharma A, Licup AJ, Jansen KA, et al. (2016) Strain-controlled criticality governs the nonlinear mechanics of fibre networks. Nat Phys 12: 584–587. doi: 10.1038/nphys3628
    [124] Licup AJ, Munster S, Sharma A, et al. (2015) Stress controls the mechanics of collagen networks. Proc Natl Acad Sci USA 112: 9573–9578. doi: 10.1073/pnas.1504258112
    [125] Wyart M, Liang H, Kabla A, et al. (2008) Elasticity of floppy and stiff random networks. Phys Rev Lett 101: 215501. doi: 10.1103/PhysRevLett.101.215501
    [126] Mao X, Souslov A, Mendoza CI, et al. (2015) Mechanical instability at finite temperature. Nat Commun 6: 5968. doi: 10.1038/ncomms6968
    [127] Roeder BA, Kokini K, Voytik-Harbin SL (2009) Fibril microstructure affects strain transmission within collagen extracellular matrices. J Biomed Eng 131: 031004.
    [128] Lai VK, Lake SP, Frey CR, et al. (2012) Mechanical behavior of collagen-fibrin co-gels reflects transition from series to parallel interactions with increasing collagen content. J Biomed Eng 134: 011004.
    [129] Brown AEX, Litvinov RI, Discher DE, et al. (2009) Multiscale mechanics of fibrin polymer: gel stretching with protein unfolding and loss of water. Science 325: 741–744. doi: 10.1126/science.1172484
    [130] Gupta HS, Seto J, Krauss S, et al. (2010) In situ multi-level analysis of viscoelastic deformation mechanisms in tendon collagen. J Struct Biol 169: 183–191. doi: 10.1016/j.jsb.2009.10.002
    [131] Trappmann B, Gautrot JE, Connelly JT, et al. (2012) Extracellular-matrix tethering regulates stem-cell fate. Nat Mater 11: 642–649. doi: 10.1038/nmat3339
    [132] Chaudhuri O, Koshy ST, Da Cunha CB, et al. (2014) Extracellular matrix stiffness and composition jointly regulate the induction of malignant phenotypes in mammary epithelium. Nat Mater 13: 970–978. doi: 10.1038/nmat4009
    [133] Wen JH, Vincent LG, Fuhrmann A, et al. (2014) Interplay of matrix stiffness and protein tethering in stem cell differentiation. Nat Mater 13: 979–987. doi: 10.1038/nmat4051
    [134] Kumar S (2014) Cellular mechanotransduction: stiffness does matter. Nat Mater 13: 918–920. doi: 10.1038/nmat4094
    [135] Stein AM, Vader DA, Weitz DA, et al. (2011) The micromechanics of three-dimensional collagen-I gels. Complexity 16: 22–28.
  • Reader Comments
  • © 2017 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
AIMS Materials Science
1.4 3.6

Metrics

Article views(7014) PDF downloads(1516) Cited by(4)

Preview PDF
Download XML
Export Citation
Article outline

Figures and Tables

Figures(6)  /  Tables(2)

Other Articles By Authors

Related pages

Tools

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog