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Quantification of Shear Deformations and Corresponding Stresses in the Biaxially Tested Human Myocardium

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.

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References

  1. 1.

    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.

    CAS  Article  PubMed  Google Scholar 

  2. 2.

    Demer, L. L., and F. C. P. Yin. Passive biaxial mechanical properties of isolated canine myocardium. J. Physiol. Lond. 1983;339:615–630.

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  3. 3.

    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.

    CAS  Google Scholar 

  4. 4.

    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.

    Article  Google Scholar 

  5. 5.

    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.

    Article  Google Scholar 

  6. 6.

    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.

    Article  Google Scholar 

  7. 7.

    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.

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  8. 8.

    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.

    Article  PubMed  PubMed Central  Google Scholar 

  9. 9.

    Fung, Y. C. Biomechanics. Mechanical Properties of Living Tissues, 2nd ed. New York: Springer-Verlag, 1993.

  10. 10.

    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.

    Article  PubMed  Google Scholar 

  11. 11.

    Gutierrez, C., and D. G. Blanchard. Diastolic heart failure: challenges of diagnosis and treatment. Am. Family Phys. 69:2609–2616, 2004.

    Google Scholar 

  12. 12.

    Holzapfel, G. A. Nonlinear Solid Mechanics. A Continuum Approach for Engineering. Chichester: John Wiley & Sons, 2000.

  13. 13.

    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.

    Article  Google Scholar 

  14. 14.

    Holzapfel, G. A., R. W. editors. Biomechanical Modelling at the Molecular, Cellular and Tissue Levels. Wien-New York: Springer-Verlag, 2009.

    Google Scholar 

  15. 15.

    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.

    Article  Google Scholar 

  16. 16.

    Humphrey, J. D. Cardiovascular Solid Mechanics. Cells, Tissues, and Organs. New York: Springer-Verlag, 2002.

  17. 17.

    Humphrey, J. D., D. L. Vawter, and R. P. Vito. Quantification of strains in biaxially tested soft tissues. J. Biomech. 20:59–65, 1987.

    CAS  Article  PubMed  Google Scholar 

  18. 18.

    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.

    CAS  Article  PubMed  Google Scholar 

  19. 19.

    Humphrey, J. D., and F. C. Yin. Biomechanical experiments on excised myocardium: theoretical considerations. J. Biomech. 22:377–383, 1989.

    CAS  Article  PubMed  Google Scholar 

  20. 20.

    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.

    CAS  Article  PubMed  Google Scholar 

  21. 21.

    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

    CAS  Google Scholar 

  22. 22.

    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.

    CAS  Article  PubMed  Google Scholar 

  23. 23.

    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.

    CAS  Article  PubMed  Google Scholar 

  24. 24.

    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.

    CAS  Article  PubMed  Google Scholar 

  25. 25.

    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.

    CAS  Google Scholar 

  26. 26.

    Ogden, R. W. Non-linear Elastic Deformations. New York: Dover, 1997.

    Google Scholar 

  27. 27.

    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.

    Article  Google Scholar 

  28. 28.

    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.

  29. 29.

    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.

    Article  PubMed  Google Scholar 

  30. 30.

    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.

    CAS  Google Scholar 

  31. 31.

    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.

    CAS  Article  Google Scholar 

  32. 32.

    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.

    CAS  Article  PubMed  Google Scholar 

  33. 33.

    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.

    CAS  Article  PubMed  Google Scholar 

  34. 34.

    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.

    CAS  Article  PubMed  Google Scholar 

  35. 35.

    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).

  36. 36.

    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.

  37. 37.

    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.

    Article  PubMed  Google Scholar 

  38. 38.

    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.

    Article  PubMed  Google Scholar 

  39. 39.

    Truesdell, C., and W. Noll. In: The Non-linear Field Theories of Mechanics, 3rd edn, edited by S. S. Antman. Berlin: Springer-Verlag; 2004.

  40. 40.

    Yin, F. C. P. Ventricular wall stress. Circ. Res. 49:829–842, 1981.

    CAS  Article  PubMed  Google Scholar 

  41. 41.

    Yin, F. C. P., C. Chan, and R. Judd. Compressibility of perfused passive myocardium. Am. J. Physiol. Heart Circ. Physiol. 8:1864–1870, 1996.

    Google Scholar 

  42. 42.

    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.

    CAS  Article  PubMed  Google Scholar 

  43. 43.

    Zienkiewicz, O. C., and R. L. Taylor. The Finite Element Method. The Basis, vol. 1, 5th ed. Oxford: Butterworth Heinemann, 2000.

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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.

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Correspondence to Gerhard Sommer.

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Associate Editor Estefanía Peña oversaw the review of this article.

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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

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Keywords

  • Biaxial extension test
  • Shear deformation
  • Shear stress
  • Passive human left ventricular myocardium
  • Mechanical property