Evaluation of a post-processing approach for multiscale analysis of biphasic mechanics of chondrocytes

REFERENCES

• AbusaraZ, SeerattanR, LeumannA, ThompsonR, HerzogW. 2011. A novel method for determining articular cartilage chondrocyte mechanics in vivo. J Biomech. 44:930–934.
   PubMed Web of Science ®Google Scholar
• AlexopoulosLG, SettonLA, GuilakF. 2005. The biomechanical role of the chondrocyte pericellular matrix in articular cartilage. Acta Biomater. 1:317–325.
   PubMed Web of Science ®Google Scholar
• AltmanDG, BlandJM. 1983. Measurement in medicine: the analysis of method comparison studies. Statistician. 32:307–317.
   Google Scholar
• AteshianGA, EllisBJ, WeissJA. 2007. Equivalence between short-time biphasic and incompressible elastic material responses. J Biomech Eng. 129:405–412.
   PubMed Web of Science ®Google Scholar
• AteshianGA, RajanV, ChahineNO, CanalCE, HungCT. 2009. Modeling the matrix of articular cartilage using a continuous fiber angular distribution predicts many observed phenomena. J Biomech Eng. 131:061003.
   PubMed Web of Science ®Google Scholar
• BellBJ, NaumanE, Voytik-HarbinSL. 2012. Multiscale strain analysis of tissue equivalents using a custom-designed biaxial testing device. Biophys J.102:1303–1312.
   PubMed Web of Science ®Google Scholar
• CaoL, GuilakF, SettonLA. 2011. Three-dimensional finite element modeling of pericellular matrix and cell mechanics in the nucleus pulposus of the intervertebral disk based on in situ morphology. Biomech Model Mechanobiol. 10:1–10.
   PubMed Web of Science ®Google Scholar
• ChenJ, IriantoJ, InamdarS, PravincumarP, LeeDA, BaderDL, KnightMM. 2012. Cell mechanics, structure, and function are regulated by the stiffness of the three-dimensional microenvironment. Biophys J.103:1188–1197.
   PubMed Web of Science ®Google Scholar
• FisherRA. 1921. On the ‘probable error’ of a coefficient of correlation deduced from a small sample. Metron. 1:1–32.
   Google Scholar
• GeersMGD, KouznetsovaVG, BrekelmansWAM. 2010. Multi-scale computational homogenization: trends and challenges. J Comput Appl Math. 234:2175–2182.
   Web of Science ®Google Scholar
• GitmanIM, AskesH, SluysLJ. 2007. Representative volume: existence and size determination. Eng Fract Mech. 74:2518–2534.
   Web of Science ®Google Scholar
• GoldsmithAA, HayesA, CliftSE. 1996. Application of finite elements to the stress analysis of articular cartilage. Med Eng Phys. 18:89–98.
   PubMed Web of Science ®Google Scholar
• GrodzinskyAJ, LevenstonME, JinM, FrankEH. 2000. Cartilage tissue remodeling in response to mechanical forces. Annu Rev Biomed Eng. 2:691–713.
   PubMed Web of Science ®Google Scholar
• GuilakF, MowVC. 2000. The mechanical environment of the chondrocyte: a biphasic finite element model of cell–matrix interactions in articular cartilage. J Biomech. 33:1663–1673.
   PubMed Web of Science ®Google Scholar
• HalloranJP, SiboleS, Van DonkelaarCC, Van TurnhoutMC, OomensCWJ, WeissJA, GuilakF, ErdemirA. 2012. Multiscale mechanics of articular cartilage: potentials and challenges of coupling musculoskeletal, joint, and microscale computational models. Ann Biomed Eng. 40:2456–2474.
   PubMed Web of Science ®Google Scholar
• HolmesMH, MowVC. 1990. The nonlinear characteristics of soft gels and hydrated connective tissues in ultrafiltration. J Biomech. 23:1145–1156.
   PubMed Web of Science ®Google Scholar
• HunzikerEB, QuinnTM, HäuselmannH-J. 2002. Quantitative structural organization of normal adult human articular cartilage. Osteoarthr Cartil.10:564–572.
   PubMed Web of Science ®Google Scholar
• IhakaR, GentlemanR. 1996. R: a language for data analysis and graphics. J Comput Graph Stat. 5:299–314.
   Google Scholar
• JulkunenP, WilsonW, JurvelinJS, KorhonenRK. 2009. Composition of the pericellular matrix modulates the deformation behaviour of chondrocytes in articular cartilage under static loading. Med Biol Eng Comput. 47:1281–1290.
   PubMed Web of Science ®Google Scholar
• KouznetsovaVG, GeersMGD, BrekelmansWAM. 2004. Multi-scale second-order computational homogenization of multi-phase materials: a nested finite element solution strategy. Comput Methods Appl Mech Eng. 193:5525–5550.
   Web of Science ®Google Scholar
• LaiWM, HouJS, MowVC. 1991. A triphasic theory for the swelling and deformation behaviors of articular cartilage. J Biomech Eng. 113:245–258.
   PubMed Web of Science ®Google Scholar
• MaasSA, EllisBJ, AteshianGA, WeissJA. 2012. FEBio: finite elements for biomechanics. J Biomech Eng. 134:011005.
   PubMed Web of Science ®Google Scholar
• MononenME, MikkolaMT, JulkunenP, OjalaR, NieminenMT, JurvelinJS, KorhonenRK. 2012. Effect of superficial collagen patterns and fibrillation of femoral articular cartilage on knee joint mechanics – a 3D finite element analysis. J Biomech. 45:579–587.
   PubMed Web of Science ®Google Scholar
• MooEK, HerzogW, HanSK, Abu OsmanNA, Pingguan-MurphyB, FedericoS. 2012. Mechanical behaviour of in situ chondrocytes subjected to different loading rates: a finite element study. Biomech Model Mechanobiol. 11:983–993.
   PubMed Web of Science ®Google Scholar
• MowVC, AteshianGA, SpilkerRL. 1993. Biomechanics of diarthrodial joints: a review of twenty years of progress. J Biomech Eng. 115:460–467.
   PubMed Web of Science ®Google Scholar
• PeetersEAG, BoutenCVC, OomensCWJ, BaderDL, SnoeckxLHEH, BaaijensFPT. 2004. Anisotropic, three-dimensional deformation of single attached cells under compression. Ann Biomed Eng. 32:1443–1452.
   PubMed Web of Science ®Google Scholar
• SchwartzMA. 2010. Integrins and extracellular matrix in mechanotransduction. Cold Spring Harb Perspect Biol. 2:a005066.
   PubMed Web of Science ®Google Scholar
• ShohamN, GefenA. 2012. Deformations, mechanical strains and stresses across the different hierarchical scales in weight-bearing soft tissues. J Tissue Viability. 21:39–46.
   PubMedGoogle Scholar
• Sibole S, Bennetts C, Erdemir A. 2012. A comparison of hexahedral and tetrahedral finite elements for biphasic analysis of cartilage micromechanics. Presented at the ASME Summer Bioengineering Conference, Fajardo, Puerto Rico.
   Google Scholar
• SiboleSC, ErdemirA. 2012. Chondrocyte deformations as a function of tibiofemoral joint loading predicted by a generalized high-throughput pipeline of multi-scale simulations. PLoS ONE. 7:e37538.
   PubMed Web of Science ®Google Scholar
• SoltzMA, AteshianGA. 1998. Experimental verification and theoretical prediction of cartilage interstitial fluid pressurization at an impermeable contact interface in confined compression. J Biomech. 31:927–934.
   PubMed Web of Science ®Google Scholar
• SoulhatJ, BuschmannMD, Shirazi-AdlA. 1999. A fibril-network-reinforced biphasic model of cartilage in unconfined compression. J Biomech Eng. 121:340–347.
   PubMed Web of Science ®Google Scholar
• SpearmanC. 2010. The proof and measurement of association between two things. Int J Epidemiol. 39:1137–1150.
   PubMed Web of Science ®Google Scholar
• UptonML, GilchristCL, GuilakF, SettonLA. 2008. Transfer of macroscale tissue strain to microscale cell regions in the deformed meniscus. Biophys J.95:2116–2124.
   PubMed Web of Science ®Google Scholar
• UptonML, GuilakF, LaursenTA, SettonLA. 2006. Finite element modeling predictions of region-specific cell–matrix mechanics in the meniscus. Biomech Model Mechanobiol. 5:140–149.
   PubMed Web of Science ®Google Scholar
• UrbanJP. 2000. Present perspectives on cartilage and chondrocyte mechanobiology. Biorheology. 37:185–190.
   PubMed Web of Science ®Google Scholar
• WangCC-B, GuoXE, SunD, MowVC, AteshianGA, HungCT. 2002. The functional environment of chondrocytes within cartilage subjected to compressive loading: a theoretical and experimental approach. Biorheology. 39:11–25.
   PubMed Web of Science ®Google Scholar
• YanKC, NairK, SunW. 2010. Three dimensional multi-scale modelling and analysis of cell damage in cell-encapsulated alginate constructs. J Biomech. 43:1031–1038.
   PubMedGoogle Scholar