On modelling large deformations of heterogeneous biological tissues using a mixed finite element formulation

References

• Babarenda GamageTP, RajagopalV, EhrgottM, NashMP, NielsenPMF. 2011. Identification of mechanical properties of heterogeneous soft bodies using gravity loading. Int J Numer Methods Biomed Eng. 27(4):391–407.
   Google Scholar
• Babarenda GamageTP, RajagopalV, NielsenPMF, NashMP. 2011. Patient-specific modeling of breast biomechanics with applications to breast cancer detection and treatment. In: Studies in mechanobiology, tissue engineering and biomaterials. Heidelberg and New York (NY): Springer. p. 379–412.
   Google Scholar
• BarbarinoGG, JabareenM, MazzaE. 2011. Experimental and numerical study on the mechanical behavior of the superficial layers of the face. Skin Res Technol.17(4):434–444.
   PubMed Web of Science ®Google Scholar
• BarbarinoGG, JabareenM, TrzewikJ, NkengneA, StamatasG, MazzaE. 2009. Development and validation of a three-dimensional finite element model of the face. J Biomech Eng.131(4):041006.
   PubMed Web of Science ®Google Scholar
• BatheKJ. 2001. The inf–sup condition and its evaluation for mixed finite element methods. Comput Struct.79(2):243–252.
   Web of Science ®Google Scholar
• BradleyCP, PullanAJ, HunterPJ. 1997. Geometric modeling of the human torso using cubic hermite elements. Ann Biomed Eng.25(1):96–111.
   PubMed Web of Science ®Google Scholar
• ChenQ, ManducaA, AnK-N. 2008. Characterization of skeletal muscle elasticity using magnetic resonance elastography. In: FatimM, Al-JumailyA, editors. Biomedical applications of vibration and acoustics in imaging and characterizations. New York (NY): ASME Press. p. 143–159.
   Google Scholar
• ChenG, SchmutzB, EpariD, RathnayakaK, IbrahimS, SchuetzMA, PearcyMJ. 2010. A new approach for assigning bone material properties from CT images into finite element models. J Biomech.43(5):1011–1015.
   PubMed Web of Science ®Google Scholar
• CheungJTM, ZhangM. 2008. Parametric design of pressure-relieving foot orthosis using statistics-based finite element method. Med Eng Phys.30(3):269–277.
   PubMed Web of Science ®Google Scholar
• CriscioneJC, HumphreyJD, DouglasAS, HunterWC. 2000. An invariant basis for natural strain which yeilds orthogonal stress response terms in isotropic hyperelasticity. J Mech Phys Solids.48(12):2445–2465.
   Web of Science ®Google Scholar
• FloryPJ. 1961. Thermodynamic relations for high elastic materials. Trans Faraday Soc.57:829–838.
   Google Scholar
• FlynnC, TabernerA, NielsenP. 2011. Modeling the mechanical response of in vivo human skin under a rich set of deformations. Ann Biomed Eng.39(7):1935–1946.
   PubMed Web of Science ®Google Scholar
• FungYC. 1993. Biomechanics: mechanical properties of living tissues. 2nd ed. New York (NY): Springer-Verlag.
   Google Scholar
• GuptaKB, RatcliffeMB, FallertMA, BogenDK, Jr. 1994. Changes in passive mechanical stiffness of myocardial tissue with aneurysm formation. Circulation. 89(5):2315–2326.
   PubMed Web of Science ®Google Scholar
• HendriksFM, BrokkenD, OomensCWJ, BaderDL, BaaijensFPT. 2006. The relative contributions of different skin layers to the mechanical behavior of human skin in vivo using suction experiments. Med Eng Phys.28(3):259–266.
   PubMed Web of Science ®Google Scholar
• HendriksFM, BrokkenD, van EemerenJT, OomensCW, BaaijensFP, HorstenJB. 2003. A numerical-experimental method to characterize the non-linear mechanical behaviour of human skin. Skin Res Technol.9(3):274–283.
   PubMed Web of Science ®Google Scholar
• LiG, SuggsJ, GillT. 2002. The effect of anterior cruciate ligament injury on knee joint function under a simulated muscle load: a three-dimensional computational simulation. Ann Biomed Eng.30(5):713–720.
   PubMed Web of Science ®Google Scholar
• LimKH, ChewCM, ChenPC, JeyapalinaS, HoHN, RappelJK, LimBH. 2008. New extensometer to measure in vivo uniaxial mechanical properties of human skin. J Biomech.41(5):931–936.
   PubMed Web of Science ®Google Scholar
• MendelsonB. 2009. Facelift anatomy, SMAS, retaining ligaments and facial spaces. In: Aston J, Steinbrech DS, Walden JL, editors. Aesthetic plastic surgery. Edinburgh: Saunders. p. 6:1–6:22.
   Google Scholar
• MithraratneK, HungA, SagarM, HunterPJ. 2010. An efficient heterogeneous continuum model to simulate active contraction of facial soft tissue structures. In: 6th World Congress of Biomechanics (WCB 2010); 2010 Aug 1–6, SingaporeBerlin and Heidelberg: Springer. p. 1024–1027.
   Google Scholar
• NazariMA, PerrierP, ChabanasM, PayanY. 2010. Simulation of dynamic orofacial movements using a constitutive law varying with muscle activation. Comput Methods Biomech Biomed Eng.13(4):469–482.
   PubMed Web of Science ®Google Scholar
• OdenJT. 1972. Finite elements of nonlinear continua. New York (NY): McGraw-Hill.
   Google Scholar
• PezzernentiZ, UrsuD, MisraS, OkamuraAM. 2008. Modeling realistic tool–tissue interactions with haptic feedback: a learning-based method. In: Symposium on Haptics Interfaces for Virtual Environment and Teleoperator Systems 2008 (HAPTICS 2008); 2008 Mar 13–14; Reno (NV). Piscataway (NJ): IEEE Computer Society Press. p. 209–215.
   Google Scholar
• PradoLG, MakarenkoI, AndresenC, KrugerM, OpitzCA, LinkeWA. 2005. Isoform diversity of giant proteins in relation to passive and active contractile properties of rabbit skeletal muscles. J Gen Physiol.126(5):461–480.
   PubMed Web of Science ®Google Scholar
• RiggioE, QuattroneP, NavaM. 2000. Anatomical study of the breast superficial fascial system: the inframammary fold unit. Eur J Plast Surg.23(6):310–315.
   Google Scholar
• RivlinRS. 1948. Large elastic deformations of isotropic materials. IV. Further developments of the general theory. Philos Trans R Soc Lond A.241(835):379–397.
   Web of Science ®Google Scholar
• RivlinRS. 1949. Large elastic deformations of isotropic materials. V. The problem of flexure. Proc R Soc Lond A Math Phys Sci.195(1043):463–473.
   Web of Science ®Google Scholar
• RohrleO, DavidsonJB, PullanAJ. 2008. Bridging scales: a three-dimensional electromechanical finite element model of skeletal muscle. SIAM J Sci Comput.30(6):2882–2904.
   Web of Science ®Google Scholar
• SussmanT, BatheKJ. 1987. A finite-element formulation for nonlinear incompressible elastic and inelastic analysis. Comput Struct.26(1–2):357–409.
   Web of Science ®Google Scholar
• TranHV, CharleuxF, RachikM, EhrlacherA, Ho Ba ThoMC. 2007. In vivo characterization of the mechanical properties of human skin derived from MRI and indentation techniques. Comput Methods Biomech Biomed Eng.10(6):401–407.
   PubMedGoogle Scholar
• TsuiCP, TangCY, LeungCP, ChengKW, NgYF, ChowDHK, LiCK. 2004. Active finite element analysis of skeletal muscle–tendon complex during isometric, shortening and lengthening contraction. Biomed Mater Eng.14(3):271–279.
   PubMed Web of Science ®Google Scholar
• WangK, McCarterR, WrightJ, BeverlyJ, Ramirez-MitchellR. 1991. Regulation of skeletal muscle stiffness and elasticity by titin isoforms: a test of the segmental extension model of resting tension. Proc Natl Acad Sci USA.88(16):7101–7105.
   PubMed Web of Science ®Google Scholar
• WhiteleyJP, GavaghanDJ, ChapmanSJ, BradyJM. 2007. Non-linear modelling of breast tissue. Math Med Biol.24(3):327–345.
   PubMed Web of Science ®Google Scholar
• ZannoniC, MantovaniR, VicecontiM. 1998. Material properties assignment to finite element models of bone structures: a new method. Med Eng Phys.20(10):735–740.
   PubMed Web of Science ®Google Scholar
• ZienkiewiczOC, GerstnerRW. 1960. A stress-function approach to interface and mixed boundary-condition problems (boundary conditions and finite-difference techniques). Int J Mech Sci.2(1–2):93–101.
   Google Scholar
• ZienkiewiczOC, TaylorRL, ZhuJZ. 2005. The finite element method: its basis and fundamentals. 6th ed. Amsterdam/London: Elsevier Butterworth-Heinemann.
   Google Scholar