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An inflation–extension test with human vena cava inferior was performed with the aim to fit a material model. The vein was modeled as a thick–walled tube loaded by internal pressure and axial force. The material was assumed to be an incompressible hyperelastic fiber reinforced continuum. Fibers are supposed to be arranged in two families of anti–symmetric helices. Considered anisotropy corresponds to local orthotropy. Used strain energy density function was based on a concept of limiting strain extensibility. The pressurization was comprised by four pre–cycles under physiological venous loading (0 – 4kPa) and four cycles under nonphysiological loading (0 – 21kPa). Each overloading cycle was performed with different value of axial weight. Overloading data were used in regression analysis to fit material model. Considered model did not fit experimental data so good. Especially predictions of axial force failed. It was hypothesized that due to nonphysiological values of loading pressure and different values of axial weight the material was not preconditioned enough and some damage occurred inside the wall. A limiting fiber extensibility parameter Jm was assumed to be in relation to supposed damage. Each of overloading cycles was fitted separately with different values of Jm. Other parameters were held the same. This approach turned out to be successful. Variable value of Jm can describe changes in the axial force – axial stretch response and satisfy pressure – radius dependence simultaneously., {"references":["J. V. Psaila, and J. Melhuish, \"Viscoelastic properties and collagen\ncontent of the long saphenous vein in normal and varicose veins,\" B. J.\nSurg., vol. 76, no. 1, pp. 37-40, January 1989.","T. Azuma, and M. Hasegawa, \"Distensibility of the vein: From the\narchitectural point of view\", Biorheology, vol. 10, pp. 469-479, 1973.","V. Milesi, A. Rebolledo, F. A. Paredes, et al., \"Mechanical properties of\nhuman saphenosu veins from normotensive and hypertensive patients,\"\nAnn. Thorac. Surg., vol. 66, no. 2, pp. 455-461, August 1998.","R. L. Wesly, R. N. Vaishnav, J. C. Fuchs, D. J. Patel, and J. C.\nGreenfield, Jr., \"Static linear and nonlinear elastic properties of normal\nand arterialized venous tissue in dog and man,\" Circ. Research, vol. 37,\nno. 4, pp. 509-520, 1975.","H. W. Weizsacker, \"Passive elastic properties of the rat abdominal vena\ncava,\" Pfluger Archs., vol. 412, no. 1-2, pp. 147-154, July 1988.","R. Rezakhaniha, and N. Stergiopulos, \"A structural model of the venous\nwall considering elastin anisotropy,\" J. Biomech. Eng. - Trans. ASME,\nvol. 130, no. 3, article no. 031017, Jun 2008.","C. O. Horgan, and G. Saccomandi, \"A description of arterial wall\nmechanics using limiting chain extensibility constitutive models,\"\nBiomechan. Model. Mechanobiol., vol. 1, no. 4, pp. 251-266, Aprile\n2003.","C. O. Horgan, and G. Saccomandi, \"A new constitutive theory for fiber-\nreinforced incompressible nonlinear elastic solids,\" J. Mech. Phys.\nSolids, vol. 53, no. 9, pp. 1985-2015, September 2005.","A. N. Gent, \"New constitutive relation for rubber,\" Rub. Chem.\nTechnol., vol. 69, no. 1, pp. 59-61, Mach-April 1996.\n[10] G. A. Holzapfel, Nonlinear solid mechanics - A continuum approach for\nengineering. Chichester: John Wiley & Sons, 2000, ch. 6.\n[11] L. Horny, R. Zitny, and H. Chlup, \"Strain energy function for arterial\nwalls based on limiting fiber extensibility,\" Proceedings of 4th European\nCongress for Medical and Biomedical Engineering 2008, 23-27 Nov\n2008 Antwerp, Belgium, IFBME (Accepted for publication)."]}

Coronary artery bypass grafts (CABG) are widely studied with respect to hemodynamic conditions which play important role in presence of a restenosis. However, papers which concern with constitutive modeling of CABG are lacking in the literature. The purpose of this study is to find a constitutive model for CABG tissue. A sample of the CABG obtained within an autopsy underwent an inflation–extension test. Displacements were recoredered by CCD cameras and subsequently evaluated by digital image correlation. Pressure – radius and axial force – elongation data were used to fit material model. The tissue was modeled as onelayered composite reinforced by two families of helical fibers. The material is assumed to be locally orthotropic, nonlinear, incompressible and hyperelastic. Material parameters are estimated for two strain energy functions (SEF). The first is classical exponential. The second SEF is logarithmic which allows interpretation by means of limiting (finite) strain extensibility. Presented material parameters are estimated by optimization based on radial and axial equilibrium equation in a thick-walled tube. Both material models fit experimental data successfully. The exponential model fits significantly better relationship between axial force and axial strain than logarithmic one., {"references":["R. L. Leask, J. Butany, K. W. Johnston, C. R. Ethier, M. Ojha, \"Human\nsaphenous vein coronary artery bypass graft morphology, geometry and\nhemodynamics,\" Ann. Biomed. Eng., vol. 33, no. 3, pp. 301-309, March\n2005.","R. Tran-Son-Tay, et al., \"An experiment-based model of vein graft\nremodeling induced by shear stress,\" Ann. Biomed. Eng., vol. 36, no. 7,\npp. 1083-1091, July 2008.","C. M. Fernandez, et al., \"Impact of shear stress on early vein graft\nremodeling: A biomechanical analysis,\" Ann. Biomed. Eng., vol. 32, no.\n11, pp. 1484-1493, November 2004.","F. Cacho, M. Doblaré and G. A. Holzapfel, ÔÇ×A procedure to simulate\ncoronary artery bypass graft surgery,\" Med. Bio. Eng. Cmput., vol. 45,\npp. 819-827, August 2007.","C. Herbst, K. Splitthof, \"Q-400 Basics of 3D digital image\ncorrelation,\" [online]. Available on\nhttp://www.dantecdynamics.com/Default.aspx?ID=855.","D. Zhang, C. D. Eggleton and D. D. Arola, \"Evaluationg the mechanical\nbehavior of arterial tissue using digital image correlation,\" Exp. Mech.,\nvol. 42, no. 4, pp. 409 - 416, December 2002.","G. A. Holzapfel, T. C. Gasser, and R. W. Ogden, \"A new constitutive\nframework for arterial wall mechanics and a comparative study of\nmaterial models,\" J. Elast., vol. 61, no. 1-3, pp. 1-48, July 2000.","J. Stalhand, \"Determination of human arterial wall parameters from\nclinical data,\" Biomechan. Model. Mechanobiol., (Accepted for\npublication).","G. A. Holzapfel, G. Sommer, C. T. Gasser and P. Regitnig,\n\"Determination of layer-specific mechanical properties of human\ncoronary arteries with nonatherosclerotic intimal thickening and related\nconstitutive modeling,\" Am. J. Physiol. Heart Circ. Physiol., vol. 289,\nno. 5, pp. H2048-H2058, November 2005.\n[10] C. O. Horgan, and G. Saccomandi, \"A description of arterial wall\nmechanics using limiting chain extensibility constitutive models,\"\nBiomechan. Model. Mechanobiol., vol. 1, no. 4, pp. 251-266, Aprile\n2003.\n[11] C. O. Horgan, and G. Saccomandi, \"A new constitutive theory for fiber-\nreinforced incompressible nonlinear elastic solids,\" J. Mech. Phys.\nSolids, vol. 53, no. 9, pp. 1985-2015, September 2005.\n[12] A. N. Gent, \"New constitutive relation for rubber,\" Rub. Chem.\nTechnol., vol. 69, no. 1, pp. 59-61, Mach-April 1996.\n[13] L. Horny, R. Zitny, and H. Chlup, \"Strain energy function for arterial\nwalls based on limiting fiber extensibility,\" Proceedings of 4th European\nCongress for Medical and Biomedical Engineering 2008, 23-27 Nov\n2008 Antwerp, Belgium, IFBME (Accepted for publication).\n[14] G. A. Holzapfel, Nonlinear solid mechanics - A continuum approach for\nengineering. Chichester: John Wiley & Sons, 2000, ch. 6."]}