Skip to main content

Left Ventricle Composite Material Model for Stress-Strain Analysis

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2673))

Abstract

Mechanical properties of the myocardium have been investigated intensively in the last four decades. Due to the nonlinearity and history dependence of the myocardial deformation, many complex strain energy functions have been used to describe the stress-strain relationship of myocardium. These functions are good at fitting in-vitro experimental data from myocardial stretch testing. However it is difficult to model in-vivo myocardium by using the strain energy functions. In a previous paper [24], we have implemented transversely anisotropic material model to estimate in-vivo strain-stress analysis in the myocardium. In this work, the fiber orientation is updated at each time step from the end of diastole to the end of systole, and the stiffness matrix is recalculated using the current fiber orientation. We also extended our model to include residual ventricular stresses and time dependent blood pressure in the left ventricle cavity.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. L. Glass, P. Hunter, A. McCulloch. Theory of Heart: Biomechanics, Biophysics, and Nonlinear Dynamics of Cardiac Function. Springer-Verlag, 1991.

    Google Scholar 

  2. J.B. Caulfield, T.K. Borg. The collagen networks of the heart. Lab. Invest., 40:364–371, 1979.

    Google Scholar 

  3. D. D. Streeter Jr., W. T. Hanna. Engineering mechanics for successive states in canine left ventricular myocardium: I. Cavity and wall geometry. Circulation Research, 33:639–655, 1973.

    Google Scholar 

  4. I.J. LeGrice, B.H. Smaill, L.Z. Chai, S.G. Edgar, J.B. Gavin, P.J. Hunter. Laminar structure of the heart: ventricular myocyte arrangement and connective tissue architecture in the dog. Am. J. Physiol. 269(2 Pt 2): H571–82, 1995.

    Google Scholar 

  5. I.J. LeGrice, P.J. Hunter, B.H. Smaill. Laminar structure of the heart: a mathematical model. Am. J. Physiol. Heart Circ. Physiol. 272(5 Pt 2):H2466–76, 1997.

    Google Scholar 

  6. J. G. Pinto, Y. C. Fung. Mechanical properties of the heart muscle in the passive state. Journal of Biomechanics, 6:597–616,1973.

    Article  Google Scholar 

  7. Y. C. Pao, G. K. Nagendra, R. Padiyar, E. L. Ritman. Derivation of myocardial fiber stiffness equation on theory of laminated composite. Journal of Biomechanical Engineering, 102:252–257, 1980.

    Google Scholar 

  8. L. L. Demer, F.C.P. Yin. Passive biaxial properties of isolated canine myocardium. Journal of Physiology, 339:615–630, 1983.

    Google Scholar 

  9. F.C.P. Yin, R. K. Strumpf, P.H. Chew, S.L. Zeger. Quantification of the mechanical properties of non-contracting myocardium. Journal of Biomechanics, 20:577–589, 1987.

    Article  Google Scholar 

  10. J.D. Humphrey, F.C.P. Yin. Biomechanical experiments on excised myocardium: Theoretical considerations. Journal of Biomechanics, 22:377–383, 1989.

    Article  Google Scholar 

  11. J.D. Humphery, F.C.P. Yin. On constitutive relations and finite deformations of passive cardiac tissue: I. A pseudostrain-energy function. Journal of Biomechanical Engineering, 109:298–304, 1987.

    Article  Google Scholar 

  12. L. Axel, L. Dougherty. Heart wall motion: Improved method of spatial modulation of magnetization for MR imaging. Radiology, 272:349–50, 1989.

    Google Scholar 

  13. D. N. Metaxas. Physics-based deformable models: applications to computer vision, graphics, and medical imaging. Kluwer Academic Publishers, Cambridge, 1996.

    Google Scholar 

  14. I. Haber, D. N. Metaxas, L. Axel. Three-dimensional motion reconstruction and analysis of the right ventricle using tagged MRI. Medical Image Analysis, 4, 2000.

    Google Scholar 

  15. I. Haber. Three dimensional motion reconstruction and analysis of the right ventricle from planar tagged MRI. Ph.D. Dissertation, University of Pennsylvania, Philadelphia, PA, 2000.

    Google Scholar 

  16. K. Bathe. Finite element procedures in engineering analysis. Prentice Hall, 1982.

    Google Scholar 

  17. F.J. Vetter, A.D. McCulloch. Three-dimensional analysis of regional cardiac function: a model of rabbit ventricular anatomy. Progress in Biophysics & Molecular Biology, 69:157–183, 1998.

    Article  Google Scholar 

  18. A.K. Kaw. Mechanics of Composite Materials. CRC press, 1997.

    Google Scholar 

  19. M. W. Hyer. Stress Analysis of Fiber-Reinforced Composite Materials. McGraw-Hill, 1998.

    Google Scholar 

  20. A.A. Amini, Y. Chen, R. W. Curwen, V. Manu, J. Sun. Coupled B-Snake grides and constrained thin-plate splines for analysis of 2D tissue deformations from tagged MRI. IEEE Transaction on Medical Imaging 17(3),344–356, 1998.

    Article  Google Scholar 

  21. F.C. Hoppensteadt, C.S. Peskin. Modeling and Simulation in Medicine and the Life Sciences. Springer, 2002.

    Google Scholar 

  22. T. P. Usyk, R. Mazhari, A. D. McCulloch. Effect of laminar orthotropic myofiber architecture on regional stress and strain in the canine left ventricle. Journal of Elasticity, 61, 2000.

    Google Scholar 

  23. P. J. Bickel, K. A. Doksum. Mathematical statistics: basic ideas and selected topics, Vol. I. Prentice Hall, 2001.

    Google Scholar 

  24. Z. Hu, D.N. Metaxas, L. Axel. In-vivo strain and stress estimation of the left ventricle from MRI images. Medical Image Computing and Computer-Assisted Intervention (MICCAI’02), 2002.

    Google Scholar 

  25. Y.C. Fung. Biodynamics: Circulation. Springer-Verlag, New York, 1984.

    Google Scholar 

  26. J.H. Omens. Left Ventricular Strain in the No-load State due to the Existence of Residual Stress. PhD thesis, University of California, La Jolla, CA, 1988.

    Google Scholar 

  27. J.H. Omens, Y.C. Fung. Residual strain in rat left ventricle. Circ. Res., 66:37–45,1990.

    Google Scholar 

  28. K. Costa, K. May-Newman, D. Farr, W.G. O’dell, A.D. McCulloch, J.H. Omens. Threedimensional residual strain in midanterior canine left ventricle. Am. J. Physiol. 273:H1968–76,1997.

    Google Scholar 

  29. X. Papademetris, E.T. Onat, A.J. Sinusas, D.P. Dione, R.T. Constable, J.S. Duncan. the Active Elastic Model. Information Processing in Medical Imaging, 2001.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Hu, Z., Metaxas, D., Axel, L. (2003). Left Ventricle Composite Material Model for Stress-Strain Analysis. In: Ayache, N., Delingette, H. (eds) Surgery Simulation and Soft Tissue Modeling. IS4TM 2003. Lecture Notes in Computer Science, vol 2673. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45015-7_21

Download citation

  • DOI: https://doi.org/10.1007/3-540-45015-7_21

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40439-2

  • Online ISBN: 978-3-540-45015-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics