Abstract
One goal of cardiac research is to perform numerical simulations to describe/reproduce the mechanoelectrical function of the human myocardium in health and disease. Such simulations are based on a complex combination of mathematical models describing the passive mechanical behavior of the myocardium and its electrophysiology, i.e., the activation of cardiac muscle cells. The problem in developing adequate constitutive models is the shortage of experimental data suitable for detailed parameter estimation in specific functional forms. A combination of shear and biaxial extension tests with different loading protocols on different specimen orientations is necessary to capture adequately the direction-dependent (orthotropic) response of the myocardium. In most experimental animal studies, where planar biaxial extension tests on the myocardium have been conducted, the generated shear stresses were neither considered nor discussed. Hence, in this study a method is presented which allows the quantification of shear deformations and related stresses. It demonstrates an approach for experimenters as to how the generation of these shear stresses can be minimized during mechanical testing. Experimental results on 14 passive human myocardial specimens, obtained from nine human hearts, show the efficiency of this newly developed method. Moreover, the influence of the clamping technique of the specimen, i.e., the load transmission between the testing device and the tissue, on the stress response is determined by testing an isotropic material (Latex). We identified that the force transmission between the testing device and the specimen by means of hooks and cords does not influence the performed experiments. We further showed that in-plane shear stresses definitely exist in biaxially tested human ventricular myocardium, but can be reduced to a minimum by preparing the specimens in an appropriate manner. Moreover, we showed whether shear stresses can be neglected when performing planar biaxial extension tests on fiber-reinforced materials. The used method appears to be robust to quantify normal and shear deformations and corresponding stresses in biaxially tested human myocardium. This method can be applied for the mechanical characterization of any fiber-reinforced material using planar biaxial extension tests.
Similar content being viewed by others
References
Chew, P. H., F. C. Yin, and S. L. Zeger. Biaxial stress-strain properties of canine pericardium. J. Mol. Cell Cardiol. 18:567–578, 1986.
Demer, L. L., and F. C. P. Yin. Passive biaxial mechanical properties of isolated canine myocardium. J. Physiol. Lond. 1983;339:615–630.
Dokos, S., B. H. Smaill, A. A. Young, and I. J. LeGrice. Shear properties of passive ventricular myocardium. Am. J. Physiol. 283:H2650–H2659, 2002.
Eilaghi, A., J. G. Flanagan, G. W. Brodland, and C. R. Ethier. Strain uniformity in biaxial specimens is highly sensitive to attachment details. J. Biomech. Eng. 131:0910031–0910037, 2009.
Eriksson, T. S. E., A. J. Prassl, G. Plank, and G. A. Holzapfel. Influence of myocardial fiber/sheet orientations on left ventricular mechanical contraction. Math. Mech. Solids 18:592–606, 2013.
Eriksson, T. S. E., A. J. Prassl, G. Plank, and G. A. Holzapfel. Modeling the dispersion in electro-mechanically coupled myocardium. Int. J. Numer. Methods Biomed. Eng. 29:1267–1284, 2013.
Frank, J. S., and G. A. Langer. The myocardial interstitium: its structure and its role in ionic exchange. J. Cell Biol. 60:586–601, 1974.
Freed, A. D., D. R. Einstein, and M. S. Sacks. Hypoelastic soft tissues: part II: in-plane biaxial experiments. Acta Mech. 2010;213:205–222.
Fung, Y. C. Biomechanics. Mechanical Properties of Living Tissues, 2nd ed. New York: Springer-Verlag, 1993.
Ghaemi, H., K. Behdinan, and A. D. Spence. In vitro technique in estimation of passive mechanical properties of bovine heart part I. Experimental techniques and data. Med. Eng. Phys. 31:76–82, 2009.
Gutierrez, C., and D. G. Blanchard. Diastolic heart failure: challenges of diagnosis and treatment. Am. Family Phys. 69:2609–2616, 2004.
Holzapfel, G. A. Nonlinear Solid Mechanics. A Continuum Approach for Engineering. Chichester: John Wiley & Sons, 2000.
Holzapfel, G. A., and R. W. Ogden. On planar biaxial tests for anisotropic nonlinearly elastic solids. A continuum mechanical framework. Math. Mech. Solids 14:474–489, 2009.
Holzapfel, G. A., R. W. editors. Biomechanical Modelling at the Molecular, Cellular and Tissue Levels. Wien-New York: Springer-Verlag, 2009.
Holzapfel, G. A., and R. W. Ogden. Constitutive modelling of passive myocardium: a structurally based framework for material characterization. Philos. Trans. R. Soc. A. 367:3445–3475, 2009.
Humphrey, J. D. Cardiovascular Solid Mechanics. Cells, Tissues, and Organs. New York: Springer-Verlag, 2002.
Humphrey, J. D., D. L. Vawter, and R. P. Vito. Quantification of strains in biaxially tested soft tissues. J. Biomech. 20:59–65, 1987.
Humphrey, J. D., and F. C. P. Yin. On constitutive relations and finite deformations of passive cardiac tissue—Part I: a pseudo-strain energy function. J. Biomech. Eng. 109:298–304, 1987.
Humphrey, J. D., and F. C. Yin. Biomechanical experiments on excised myocardium: theoretical considerations. J. Biomech. 22:377–383, 1989.
Humphrey, J. D., and F. C. P. Yin. Constitutive relations and finite deformations of passive cardiac tissue: II. Stress analysis in the left ventricle. Circ. Res. 65:805–817, 1989.
Humphrey, J. D., R. K. Strumpf, and F. C. P. Yin. Biaxial mechanical behavior of excised ventricular epicardium. Am. J. Physiol. Heart Circ. Physiol. 259:H101–H108, 1990
Humphrey, J. D., R. K. Strumpf, and F. C. P. Yin. Determination of constitutive relation for passive myocardium: I. A new functional form. J. Biomech. Eng. 112:333–339, 1990.
Humphrey, J. D., R. K. Strumpf, and F. C. P. Yin. Determination of constitutive relation for passive myocardium: II. Parameter estimation. J. Biomech. Eng. 112:340–346, 1990.
Langdon, S. E., R. Chernecky, C. A. Pereira, and D. A. J. M. Lee. Biaxial mechanical/structural effects of equibiaxial strain during crosslinking of bovine pericardial xenograft materials. Biomaterials 20:137–153, 1999.
Nielsen, P. M. F., I. J. LeGrice, B. H. Smaill, and P. J. Hunter. Mathematical model of geometry and fibrous structure of the heart. Am. J. Physiol. Cell. Physiol. 260:H1365–H1378, 1991.
Ogden, R. W. Non-linear Elastic Deformations. New York: Dover, 1997.
Rohmer, D., A. Sitek, and G. T. Gullberg. Reconstruction and visualization of fiber and laminar structure in the normal human heart from ex vivo diffusion tensor magnetic resonance imaging (DTMRI) data. Investig. Radiol. 42:777–789, 2007.
Sands, G. B., B. H. Smaill, and I. J. LeGrice. Virtual sectioning of cardiac tissue relative to fiber orientation. In: Proceedings of the 30th Annual International Conference of the IEEE Engineering in Medicine and Biology Society EMBS 2008, 2008, pp. 226–229.
Sands, G. B., D. A. Gerneke, D. A. Hooks, C. R. Green, B. H. Smaill, and I. J. LeGrice. Automated imaging of extended tissue volumes using confocal microscopy. Microsc. Res. Tech. 67:227–239, 2005.
Scollan, D. F., A. Holmes, R. Winslow, and J. Forder. Histological validation of myocardial microstructure obtained from diffusion tensor magnetic resonance imaging. Am. J. Physiol. Heart. Circ. Physiol. 275(6):H2308–H2318, 1998.
Sharpe, W. N. Jr., J. Pulskamp, D. G. Gianola, C. Eberl, R. G. Polcawich, and R. J. Thompson. Strain measurement of silicon dioxide microspecimens by digital image processing. Exp. Mech. 47:649–658, 2007.
Sommer, G., P. Regitnig, L. Költringer, and G. A. Holzapfel. Biaxial mechanical properties of intact and layer-dissected human carotid arteries at physiological and supra-physiological loadings. Am. J. Physiol. Heart Circ. Physiol. 298:H898–H912, 2010.
Sommer, G., M. Eder, L. Kovacs, H. Pathak, L. Bonitz, C. Mueller, et al. Multiaxial mechanical properties and constitutive modeling of human adipose tissue: a basis for preoperative simulations in plastic and reconstructive surgery. Acta Biomater. 9:9036–9048, 2013.
Sommer, G., A. Schriefl, G. Zeindlinger, A. Katzensteiner, H. Ainödhofer, A. Saxena, et al. Multiaxial mechanical response and constitutive modeling of esophageal tissues: impact on esophageal tissue engineering. Acta Biomater. 9:9379–9091, 2013.
Sommer, G., A. J. Schriefl, M. Andrä, M. Sacherer, C. Viertler, H. Wolinski, et al. Biomechanical properties and microstructure of human ventricular myocardium. Acta Biomater. (submitted).
Sommer, G., M. Schwarz, M. Kutschera, R. Kresnik, P. Regitnig, A. J. Schriefl, et al. Biomechanical properties of the human ventricular myocardium. Biomedizinische Technik. 58(Suppl. 1), 2013.
Streeter, D. D., and W. T. Hanna. Engineering mechanics for successive states in canine left ventricular myocardium. I. Cavity and wall geometry. Circ. Res. 33:639–655, 1973.
Toursel, T., L. Stevens, H. Granzier, and Y. Mounier. Passive tension of rat skeletal soleus muscle fibers: effects of unloading conditions. J. Appl. Physiol. 92:1465–1472, 2002.
Truesdell, C., and W. Noll. In: The Non-linear Field Theories of Mechanics, 3rd edn, edited by S. S. Antman. Berlin: Springer-Verlag; 2004.
Yin, F. C. P. Ventricular wall stress. Circ. Res. 49:829–842, 1981.
Yin, F. C. P., C. Chan, and R. Judd. Compressibility of perfused passive myocardium. Am. J. Physiol. Heart Circ. Physiol. 8:1864–1870, 1996.
Young, A. A., I. J. Legrice, M. A. Young, and B. H. Smaill. Extended confocal microscopy of myocardial laminae and collagen network. J. Microsc. 192:139–150, 1998.
Zienkiewicz, O. C., and R. L. Taylor. The Finite Element Method. The Basis, vol. 1, 5th ed. Oxford: Butterworth Heinemann, 2000.
Acknowledgments
The authors are grateful to A. Abbasi for her substantial contributions to the experiments, and to F. Heinzel from Medical University of Graz, Department of Cardiology, for many discussions on this subject matter. We thank also Daniel Han for his editorial support during preparing this manuscript. This project was supported by the Austrian Science Fund (FWF) with Grant number P 23830-N13. The authors gratefully acknowledge this support.
Author information
Authors and Affiliations
Corresponding author
Additional information
Associate Editor Estefanía Peña oversaw the review of this article.
Rights and permissions
About this article
Cite this article
Sommer, G., Haspinger, D.C., Andrä, M. et al. Quantification of Shear Deformations and Corresponding Stresses in the Biaxially Tested Human Myocardium. Ann Biomed Eng 43, 2334–2348 (2015). https://doi.org/10.1007/s10439-015-1281-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10439-015-1281-z