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Computational Modeling of Healthy Myocardium in Diastole

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Abstract

In order to better understand the mechanics of the heart and its disorders, engineers increasingly make use of the finite element method (FEM) to investigate healthy and diseased cardiac tissue. However, FEM is only as good as the underlying constitutive model, which remains a major challenge to the biomechanics community. In this study, a recently developed structurally based constitutive model was implemented to model healthy left ventricular myocardium during passive diastolic filling. This model takes into account the orthotropic response of the heart under loading. In-vivo strains were measured from magnetic resonance images (MRI) of porcine hearts, along with synchronous catheterization pressure data, and used for parameter identification of the passive constitutive model. Optimization was performed by minimizing the difference between MRI measured and FE predicted strains and cavity volumes. A similar approach was followed for the parameter identification of a widely used phenomenological constitutive law, which is based on a transversely isotropic material response. Results indicate that the parameter identification with the structurally based constitutive law is more sensitive to the assigned fiber architecture and the fit between the measured and predicted strains is improved with more realistic sheet angles. In addition, the structurally based model is capable of generating a more physiological end-diastolic pressure–volume relationship in the ventricle.

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References

  1. Augenstein, K. F., B. R. Cowan, I. J. LeGrice, and A. A. Young (2006) Estimation of cardiac hyperelastic material properties from MRI tissue tagging and diffusion tensor imaging. In: Medical Image Computing and Computer-Assisted Intervention–MICCAI 2006. Berlin: Springer, pp. 628–635.

  2. Baillargeon, B., N. Rebelo, D. D. Fox, R. L. Taylor, and E. Kuhl. The living heart project: a robust and integrative simulator for human heart function. Eur. J. Mech. A. Solids 48:38–47, 2014.

    Article  PubMed  PubMed Central  Google Scholar 

  3. Costa, K. D., J. W. Holmes, and A. D. McCulloch. Modelling cardiac mechanical properties in three dimensions. Philos Trans. R. Soc A. 359(1783):1233–1250, 2001.

    Article  Google Scholar 

  4. Dokos, S., B. H. Smaill, A. A. Young, and I. J. LeGrice. Shear properties of passive ventricular myocardium. Am. J. Physiol. Heart Circ. Physiol. 283(6):H2650–H2659, 2002.

    Article  CAS  PubMed  Google Scholar 

  5. Gao, H., D. Carrick, C. Berry, and X. Luo. Parameter estimation of the Holzapfel–Ogden law for healthy myocardium. J. Eng. Math. 2014. doi:10.1007/s10665-014-9740-3.

    Google Scholar 

  6. Gasser, T. C., R. W. Ogden, and G. A. Holzapfel. Hyperelastic modelling of arterial layers with distributed collagen fibre orientations. J. R. Soc. Interface 3(6):15–35, 2006.

    Article  PubMed  PubMed Central  Google Scholar 

  7. Gilbert, S. H., A. P. Benson, P. Li, and A. V. Holden. Regional localisation of left ventricular sheet structure: integration with current models of cardiac fibre, sheet and band structure. Eur. J. Cardiothorac. Surg. 32(2):231–249, 2007.

    Article  PubMed  Google Scholar 

  8. Göktepe, S., S. N. S. Acharya, J. Wong, and E. Kuhl. Computational modeling of passive myocardium. Int. J. Numer. Methods Biomed. Eng. 27(1):1–12, 2011.

    Article  Google Scholar 

  9. Grimm, A., K. Katele, H.-L. Lin, and J. Fletcher. Fiber bundle direction in the mammalian heart. Basic Res. Cardiol. 71(4):381–388, 1976.

    Article  CAS  PubMed  Google Scholar 

  10. Guccione, J., A. McCulloch, and L. Waldman. Passive material properties of intact ventricular myocardium determined from a cylindrical model. J. Biomech. Eng. 113(1):42–55, 1991.

    Article  CAS  PubMed  Google Scholar 

  11. Holzapfel, G. A. Nonlinear Solid Mechanics. Chichester: Wiley, 2000.

    Google Scholar 

  12. Holzapfel, G. A., and R. W. Ogden. Constitutive modelling of passive myocardium: a structurally based framework for material characterization. Philos. Trans. A Math. Phys. Eng. Sci. 367(1902):3445–3475, 2009.

    Article  PubMed  Google Scholar 

  13. Humphrey, J., R. Strumpf, and F. Yin. Determination of a constitutive relation for passive myocardium: I. A new functional form. J. Biomech. Eng. 112(3):333–339, 1990.

    Article  CAS  PubMed  Google Scholar 

  14. Humphrey, J., and F. Yin. On constitutive relations and finite deformations of passive cardiac tissue: I. A pseudostrain-energy function. J. Biomech. Eng. 109(4):298–304, 1987.

    Article  CAS  PubMed  Google Scholar 

  15. Hunter, P., M. Nash, and G. Sands. Computational electromechanics of the heart. Comput. Biol. Heart. 12:347–407, 1997.

    Google Scholar 

  16. Hunter, P. J., and B. H. Smaill. The analysis of cardiac function: a continuum approach. Prog. Biophys. Mol. Biol. 52(2):101–164, 1988.

    Article  CAS  PubMed  Google Scholar 

  17. Kerckhoffs, R., P. Bovendeerd, J. Kotte, F. Prinzen, K. Smits, and T. Arts. Homogeneity of cardiac contraction despite physiological asynchrony of depolarization: a model study. Ann. Biomed. Eng. 31(5):536–547, 2003.

    Article  CAS  PubMed  Google Scholar 

  18. Klotz, S., I. Hay, M. L. Dickstein, G.-H. Yi, J. Wang, M. S. Maurer, D. A. Kass, and D. Burkhoff. Single-beat estimation of end-diastolic pressure–volume relationship: a novel method with potential for noninvasive application. Am. J. Physiol. Heart Circ. Physiol. 291(1):H403–H412, 2006.

    Article  CAS  PubMed  Google Scholar 

  19. Krishnamurthy, A., C. T. Villongco, J. Chuang, L. R. Frank, V. Nigam, E. Belezzuoli, P. Stark, D. E. Krummen, S. Narayan, and J. H. Omens. Patient-specific models of cardiac biomechanics. J. Comput. Phys. 244:4–21, 2013.

    Article  PubMed  PubMed Central  Google Scholar 

  20. Lee, W.-N., M. Pernot, M. Couade, E. Messas, P. Bruneval, A. Bel, A. A. Hagege, M. Fink, and M. Tanter. Mapping myocardial fiber orientation using echocardiography-based shear wave imaging. IEEE Trans. Med. Imaging 31(3):554–562, 2012.

    Article  PubMed  Google Scholar 

  21. LeGrice, I. J., B. Smaill, L. Chai, S. Edgar, J. Gavin, and P. J. Hunter. Laminar structure of the heart: ventricular myocyte arrangement and connective tissue architecture in the dog. Am. J. Physiol. Heart Circ. Physiol. 38(2):H571, 1995.

    Google Scholar 

  22. Mojsejenko, D., J. R. McGarvey, S. M. Dorsey, J. H. Gorman, III, J. A. Burdick, J. J. Pilla, R. C. Gorman, and J. F. Wenk. Estimating passive mechanical properties in a myocardial infarction using MRI and finite element simulations. Biomech. Model. Mechanobiol. 14(3):633–647, 2015.

    Article  PubMed  Google Scholar 

  23. Nair, A. U., D. G. Taggart, and F. J. Vetter. Optimizing cardiac material parameters with a genetic algorithm. J. Biomech. 40(7):1646–1650, 2007.

    Article  PubMed  Google Scholar 

  24. Okamoto, R. J., M. J. Moulton, S. J. Peterson, D. Li, M. K. Pasque, and J. M. Guccione. Epicardial suction: a new approach to mechanical testing of the passive ventricular wall. J. Biomech. Eng. 122(5):479–487, 2000.

    Article  CAS  PubMed  Google Scholar 

  25. 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(5):227–239, 2005.

    Article  PubMed  Google Scholar 

  26. Schmid, H., M. Nash, A. Young, and P. Hunter. Myocardial material parameter estimation—a comparative study for simple shear. J. Biomech. Eng. 128(5):742–750, 2006.

    Article  CAS  PubMed  Google Scholar 

  27. Spotnitz, H. M., W. D. Spotnitz, T. S. Cottrell, D. Spiro, and E. H. Sonnenblick. Cellular basis for volume related wall thickness changes in the rat left ventricle. J. Mol. Cell. Cardiol. 6(4):317–331, 1974.

    Article  CAS  PubMed  Google Scholar 

  28. Streeter, D. D., H. M. Spotnitz, D. P. Patel, J. Ross, and E. H. Sonnenblick. Fiber orientation in the canine left ventricle during diastole and systole. Circ. Res. 24(3):339–347, 1969.

    Article  PubMed  Google Scholar 

  29. Sun, K., N. Stander, C.-S. Jhun, Z. Zhang, T. Suzuki, G.-Y. Wang, M. Saeed, A. W. Wallace, E. E. Tseng, and A. J. Baker. A computationally efficient formal optimization of regional myocardial contractility in a sheep with left ventricular aneurysm. J. Biomech. Eng. 131(11):111001, 2009.

    Article  PubMed  PubMed Central  Google Scholar 

  30. Walker, J. C., M. B. Ratcliffe, P. Zhang, A. W. Wallace, B. Fata, E. W. Hsu, D. Saloner, and J. M. Guccione. Mri-based finite-element analysis of left ventricular aneurysm. Am. J. Physiol. Heart Circ. Physiol. 289(2):H692–H700, 2005.

    Article  CAS  PubMed  Google Scholar 

  31. Wang, H. M., H. Gao, X. Y. Luo, C. Berry, B. E. Griffith, R. W. Ogden, and T. J. Wang. Structure-based finite strain modelling of the human left ventricle in diastole. Int. J. Numer. Method Biomed. Eng. 29(1):83–103, 2013.

    Article  PubMed  Google Scholar 

  32. Wang, H., X. Luo, H. Gao, R. Ogden, B. Griffith, C. Berry, and T. Wang. A modified Holzapfel–Ogden law for a residually stressed finite strain model of the human left ventricle in diastole. Biomech. Model. Mechanobiol. 13(1):99–113, 2014.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  33. Wenk, J. F., P. Papadopoulos, and T. I. Zohdi. Numerical modeling of stress in stenotic arteries with microcalcifications: a micromechanical approximation. J. Biomech. Eng. 132(9):091011, 2010.

    Article  PubMed  Google Scholar 

  34. Xi, J., P. Lamata, S. Niederer, S. Land, W. Shi, X. Zhuang, S. Ourselin, S. G. Duckett, A. K. Shetty, and C. A. Rinaldi. The estimation of patient-specific cardiac diastolic functions from clinical measurements. Med. Image Anal. 17(2):133–146, 2013.

    Article  PubMed  Google Scholar 

  35. Xu, C., J. J. Pilla, G. Isaac, J. H. Gorman, 3rd, A. S. Blom, R. C. Gorman, Z. Ling, and L. Dougherty. Deformation analysis of 3D tagged cardiac images using an optical flow method. J. Cardiovasc. Magn. Reson. 12:19, 2010.

    Article  PubMed  PubMed Central  Google Scholar 

  36. Young, A., I. LeGrice, M. Young, and B. Smaill. Extended confocal microscopy of myocardial laminae and collagen network. J. Microsc. 192(2):139–150, 1998.

    Article  CAS  PubMed  Google Scholar 

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Acknowledgments

This study was supported by National Institutes of Health Grants R01 HL063954 (R. Gorman), R01 HL111090 (J. Burdick), R01 HL73021 (J. Gorman), and by a grant from the American Heart Association 14BGIA18850020 (J. Wenk).

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Kentucky, 269 Ralph G. Anderson Building, Lexington, KY, 40506-0503, USA

    Amir Nikou & Jonathan F. Wenk

  2. Gorman Cardiovascular Research Group and Department of Surgery, University of Pennsylvania, Philadelphia, PA, USA

    Jeremy R. McGarvey, Joseph H. Gorman III, James J. Pilla & Robert C. Gorman

  3. Department of Bioengineering, University of Pennsylvania, Philadelphia, PA, USA

    Shauna M. Dorsey & Jason A. Burdick

  4. Department of Radiology, University of Pennsylvania, Philadelphia, PA, USA

    James J. Pilla

  5. Department of Surgery, University of Kentucky, Lexington, KY, USA

    Jonathan F. Wenk

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  1. Amir Nikou
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  2. Shauna M. Dorsey
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Correspondence to Jonathan F. Wenk.

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Associate Editor Andreas Anayiotos oversaw the review of this article.

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Nikou, A., Dorsey, S.M., McGarvey, J.R. et al. Computational Modeling of Healthy Myocardium in Diastole. Ann Biomed Eng 44, 980–992 (2016). https://doi.org/10.1007/s10439-015-1403-7

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  • DOI: https://doi.org/10.1007/s10439-015-1403-7

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