Large Deformation Characterization of Porcine Thoracic Aortas: Inverse Modeling Fitting of Uniaxial and Biaxial Tests


The elastic behavior of arteries is nonlinear when subjected to large deformations. In order to measure their anisotropic behavior, planar biaxial tests are often used. Typically, hooks are attached along the borders of a square sample of arterial tissue. Cruciform samples clamped with grips can also be used. The current debate on the effect of different biaxial test boundary conditions revolves around the uniformity of the stress distribution in the center of the specimen. Uniaxial tests are also commonly used due to simplicity of data analysis, but their capability to fully describe the in vivo behavior of a tissue remains to be proven. In this study, we demonstrate the use of inverse modeling to fit the material properties by taking into account the non-uniform stress distribution, and discuss the differences between the three types of tests. Square and cruciform samples were dissected from pig aortas and tested equi-biaxially. Rectangular samples were used in uniaxial testing as well. On the square samples, forces were applied on each side of edge sample attached with hooks, and strains were measured in the center using optical tracking of ink dots. On the cruciform and rectangular samples, displacements were applied on grip clamps and forces were measured on the clamps. Each type of experiment was simulated with the finite element method. The parameters of the Mooney-Rivlin constitutive model were adjusted with an optimization algorithm so that the simulation predictions fitted the experimental results. Higher stretch ratios (>1.5) were reached in the cruciform and rectangular samples than in the square samples before failure. Therefore, the nonlinear behavior of the tissue in large deformations was better captured by the cruciform biaxial test and the uniaxial test, than by the square biaxial test. Advantages of cruciform samples over square samples include: 1) higher deformation range; 2) simpler data acquisition and 3) easier attachment of sample. However, the nonuniform stress distribution in cruciform samples requires the use of inverse modeling adjustment of constitutive model parameters.

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Delgadillo, J. , Delorme, S. , Thibault, F. , DiRaddo, R. and Hatzikiriakos, S. (2015) Large Deformation Characterization of Porcine Thoracic Aortas: Inverse Modeling Fitting of Uniaxial and Biaxial Tests. Journal of Biomedical Science and Engineering, 8, 717-732. doi: 10.4236/jbise.2015.810069.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Avanzini, A., Battini, D., Bagozzi, L. and Bisleri, G. (2014) Biomechanical Evaluation of Ascending Aortic Aneurysms. BioMed Research International, 2014, Article ID: 820385.
[2] Khanafer, K., Schlicht, M.S. and Berguer, R. (2013) How Should We Measure and Report Elasticity in Aortic Tissue. European Journal of Vascular and Endovascular Surgery, 45, 332-339.
[3] Sacks, M.S. and Sun, W. (2003) Multiaxial Mechanical Behavior of Biological Materials. Annual Review of Biomedical Engineering, 5, 251-284.
[4] Sokolis, D.P., Kritharis, E.P. and Iliopoulos, D.C. (2012) Effect of Layer Heterogeneity on the Biomechanical Properties of Ascending Thoracic Aortic Aneurysms. Medical and Biological Engineering and Computing, 50, 1227-1237.
[5] Gultova, E., Horny, L., Chlup, H. and Zitny, R. (2011) Effect of Deformation Rate on the Mullins Effect in Arteries. 13th Workshop of Applied Mechanics, CTU in Prague, 5-8.
[6] Duprey, A., Khanafer, K., Schlicht, M., Avril, S., Williams, D. and Berguer, R. (2010) In Vitro Characterisation of Physiological and Maximum Elastic Modulus of Ascending Thoracic Aortic Aneurysms Using Uniaxial Tensile Testing. European Journal of Vascular and Endovascular Surgery, 39, 700-707.
[7] Pham, T., Martin, C., Elefteriades, J. and Sun, W. (2013) Biomechanical Characterization of Ascending Aortic Aneurysm with Concomitant Bicuspid Aortic Valve and Bovine Aortic Arch. Acta Biomaterialia, 9, 7927-7936.
[8] Azadani, A.N., Chitsaz, S., Matthews, P.B., Jaussaud, N., Leung, J. and Tsinman, T. (2012) Comparison of Mechanical Properties of Human Ascending Aorta and Aortic Sinuses. Annals of Thoracic Surgery, 93, 87-94.
[9] Haskett, D., Johnson, G., Zhou, A., Utzinger, U. and Van Geest, J. (2010) Microstructural and Biomechanical Alterations of the Human Aorta as a Function of Age and Location. Biomechanics and Modeling in Mechanobiology, 9, 725-736.
[10] Choudhury, N., Bouchot, O., Rouleau, L., Tremblay, D., Cartier, R. and Butany, J. (2009) Local Mechanical and Structural Properties of Healthy and Diseased Human Ascending Aorta Tissue. Cardiovascular Pathology, 18, 83-91.
[11] Matsumoto, T., Fukui, T., Tanaka, T., Ikuta, N., Ohashi, T. and Kumagai, K. (2009) Biaxial Tensile Properties of Thoracic Aortic Aneurysm Tissues. Journal of Biomechanical Science and Engineering, 4, 518-529.
[12] Zemànek, M., Bursa, J. and Dêtàk, M. (2009) Biaxial Tension Tests with Soft Tissues of Arterial Wall. Journal of Engineering Mechanics, 16, 3-11.
[13] Waldman, S.D. and Lee, J.M. (2005) Effect of Sample Geometry on the Apparent Biaxial Mechanical Behaviour of Planar Connective Tissues. Biomaterials, 26, 7504-7513.
[14] Sacks, M.S. (2000) Biaxial Mechanical Evaluation of Planar Biological Materials. Journal of Elasticity, 61, 199-246.
[15] Hoffman, A.H. and Grigg, P. (1984) A Method for Measuring Strains in Soft Tissue. Journal of Biomechanics, 17, 795-800.
[16] Choudhury, N.Z. (2005) Characterization of Healthy and Diseased Human Ascending Aorta Tissue. Master’s Thesis, McGill University, Montreal.
[17] Lally, C., Reid, A.J. and Pren-dergast, P.J. (2004) Elastic Behavior of Porcine Coronary Artery Tissue under Uniaxial and Equibiaxial Tension. Annals of Biomedical Engineering, 32, 1355-1364.
[18] Okamoto, R.J., Wagenseil, J.E., Delong, W.R., Peterson, S.J., Kouchoukos, N.T. and Sundt III, T.M. (2002) Mechanical Properties of Dilated Human Ascending Aorta. Annals of Biomedical Engineering, 30, 624-635.
[19] Prendergast, P.J., Lally, C., Daly, S., Reid, A.J., Lee, T.C., Quinn, D. and Dolan, F. (2003) Analysis of Prolapse in Cardiovascular Stents: A Constitutive Equation for Vascular Tissue and Finite-Element Modelling. Journal of Biomechanical Engineering, 125, 692-699.
[20] Hjelm, H.E. (1994) Yield Surface for Gray Cast Iron on Biaxial Stress. Journal of Engineering Materials and Technology, 116, 148-154.
[21] Zinov’ev, M.V., Il’ichev, V.Y., Rykov, V.A. and Savva, S.P. (1972) Method of Testing Samples in a Biaxial Stressed State at Low Temperatures. Strength Mater, 4, 637-639.
[22] Sun, W., Sacks, M.S. and Scott, M.J. (2005) Effects of Boundary Conditions on the Estimation of the Planar Biaxial Mechanical Properties of Soft Tissues. Journal of Biomechanical Engineering, 127, 709-715.
[23] Seshaiyer, P. and Humphrey, J.D. (2003) A Sub-Domain Inverse Finite Element Characterization of Hyperelastic Membranes Including Soft Tissues. Journal of Biomechanical Engineering, 125, 363-371.
[24] Fung, Y.C. (1993) Biomechanics: Mechanical Properties of Living Tissues. 2nd Edition, Springer-Verlag, New York, 261-262.
[25] Debergue, P. and Laroche, D. (2001) 3D Finite Elements for the Prediction of Thermoforming Processes. Proceedings of the 4th International ESAFORM Conference on Material Forming, 1, 365-368.
[26] Laroche, D., Kabanemi, K.K., Pecora, L. and DiRaddo, R.W. (1999) Integrated Numerical Modeling of the Blow Molding Process. Polymer Engineering & Science, 39, 1223-1233.
[27] Vande Geest, J.P., Sacks, M.S. and Vorp, D.A. (2006) The Effect of Aneu-rysm on the Biaxial Mechanical Behavior of Human Abdominal Aorta. Journal of Biomechanics, 39, 1324-1334.
[28] Vande Geest, J.P. (2005) Towards an Improved Rupture Potential Index for Abdominal Aortic Aneurysms: Anisotropic Constitutive Modeling and Noninvasive Wall Strength Estimation. PhD Thesis, University of Pittsburgh, Pittsburgh.
[29] Mooney, M.A. (1940) Theory of Large Elastic Deformation. Journal of Applied Physics, 11, 582-592.
[30] Virues-Delgadillo, J.O., Delorme, S., El-Ayoubi, R., DiRaddo, R. and Hatzikiriakos, S.G. (2010) Effect of Freezing on the Biaxial Mechanical Properties of Arterial Samples. Journal of Biomedical Science and Engineering, 3, 645-652.
[31] Virues-Delgadillo, J.O., Delorme, S., Vincent, M., DiRaddo, R. and Hatzikiriakos, S.G. (2010) Effect of Deformation Rate on the Mechanical Properties of Arteries. Journal of Biomedical Science and Engineering, 3, 124-137.
[32] Tezduyar, T.E., Sathe, S., Cragin, T., Nanna, B., Conklin, B.S., Pausewang, J. and Schwaab, M. (2007) Modelling of Fluid-Structure Interactions with the Space-Time Finite Elements: Arterial Fluid Mechanics. International Journal for Numerical Methods in Fluids, 54, 901-922.
[33] Scotti, C.M. and Finol, E.A. (2007) Compliant Biomechanics of Abdominal Aortic Aneurysms: A Fluid-Structure Interaction Study. Computers & Structures, 85, 1097-1113.
[34] Wang, D.H.J., Makaroun, M., Webster, M.W. and Vorp, D.A. (2001) Mechanical Properties and Microstructure of Intraluminal Thrombus from Abdominal Aortic Aneurysm. Journal of Biomechanical Engineering, 123, 536-539.
[35] Raghavan, M.L. and Vorp, D.A. (2000) Toward a Biomechanical Tool to Evaluate Rupture Potential of Abdominal Aortic Aneurysm: Identification of a Finite Strain Constitutive Model and Evaluation of Its Applicability. Journal of Biomechanics, 33, 475-482.
[36] Vanderplaats, G.N. (1999) Numerical Optimization Techniques for Engineering Design. Vanderplaats Research & Development Inc., Colorado Springs.
[37] Waldman, S.D. and Lee, J.M. (2002) Boundary Conditions during Biaxial Testing of Planar Connective Tissues: Part 1: Dynamic Behavior. Journal of Materials Science: Materials in Medicine, 13, 933-938.

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