Skip to main content
SpringerLink
Log in

A modified mathematical model of the anatomy of the cardiac left ventricle

  • Complex Systems Biophysics
  • Published:
Biophysics Aims and scope Submit manuscript

Abstract

A modification of the mathematical model of the shape and fiber direction field of the left cardiac ventricle is presented. The model was developed based on the idea of nested spiral surfaces. The ventricle is composed of surfaces that model myocardial layers. Each layer is filled with curves corresponding to myocardial fibers. The tangents to these curves form the myofiber direction field. A modified spherical coordinate system is linked with the model left ventricle, where the ventricular boundaries are coordinate surfaces. The model is based on echocardiographic, computed-tomography, or magnetic-resonance-imaging data. For this purpose, four-chamber and two-chamber echocardiography views or sections along the long axis of the left ventricle from these tomographic data in several positions are approximated with a model profile. To construct a 3D model, we then interpolate model parameters by periodic cubic splines and the vector field of the tangents to the model fibers is calculated. For verification of the model, we used diffusion-tensor magneticresonance-imaging data of the human heart.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

LV:

left ventricle

DT-MRI:

diffusion-tensor magnetic resonance imaging

References

  1. E. J. Crampin, M. Halstead, P. J. Hunter, et al., Exp. Physiol. 89 (1), 1 (2004).

    Article  Google Scholar 

  2. P. Kohl and D. Noble, Molec. Systems Biol. 5 (1), 292, (2009).

    Google Scholar 

  3. R. L. Winslow, N. Trayanova, D. Geman, and M. I. Miller, Sci. Transl. Med. 4 (158), 158rv11 (2012).

    Google Scholar 

  4. P. J. Hunter, W. W. Li, A. D. McCulloch, and D. Noble, Computer, No. 11, 48 (2006).

    Article  Google Scholar 

  5. S. Goktepe and E. Kuhl, Comput. Mechanics 45 (2–3), 227 (2010).

    Article  ADS  MathSciNet  Google Scholar 

  6. S. F. Pravdin, H. Dierckx, L. B. Katsnelson, et al., PLOS ONE 9 (5), e93617 (2014).

    Article  ADS  Google Scholar 

  7. V. Gurev, T. Lee, J. Constantino, et al., Biomechanics and Modeling in Mechanobiology 10 (3), 295 (2011).

    Article  Google Scholar 

  8. P. A. Helm, H. J. Tseng, L. Younes, et al., Magn. Reson. Med. 54 (4), 850 (2005).

    Article  Google Scholar 

  9. V. Y. Wang, Modelling In Vivo Cardiac Mechanics Using MRI and FEM (Univ. of Auckland Press, Auckland, New Zealand, 2012).

    Google Scholar 

  10. J. Aguado-Sierra, A. Krishnamurthy, C. Villongco, et al., Progr. Biophys. Mol. Boil. 107 (1), 147 (2011).

    Article  Google Scholar 

  11. P. Helm, M. F. Beg, M. I. Miller, and R. L. Winslow, Ann. N. Y. Acad. Sci. 1047, 296 (2005).

    Article  ADS  Google Scholar 

  12. Y. Zhang, X. Liang, J. Ma, et al., Med. Image Anal. 16 (6), 1130 (2012).

    Article  Google Scholar 

  13. J. D. Bayer, R. C. Blake, G. Plank, and N. A. Trayanova, Ann. Biomed. Eng. 40 (10), 2243 (2012).

    Article  Google Scholar 

  14. R. Beyar and S. Sideman, Circ. Res. 55 (3), 358 (1984).

    Article  Google Scholar 

  15. M. J. Bishop, G. Plank, R. A. B. Burton, et al., Am. J. Physiol. Heart Circ. Physiol. 298 (2), H699 (2010).

    Article  Google Scholar 

  16. R. Hren, A Realistic Model of the Human Ventricular Myocardium: Application to the Study of Ectopic Activation (Halifax, Canada, 1996).

    Google Scholar 

  17. G. Seemann, Modeling of Electrophysiology and Tension Development in the Human Heart (Universitatsverlag, Karlsruhe, 2005).

    Google Scholar 

  18. S. F. Pravdin, V. I. Berdyshev, A. V. Panfilov, et al., Biomed. Eng. Online 54 (12), 21 (2013).

    Google Scholar 

  19. S. Pravdin, Russ. J. Biomech. 17 (4), 75–94 (2013).

    Google Scholar 

  20. D. D. Streeter, in Handbook of Physiology (Am. Physiol. Soc., Bethesda, MD, 1979), Vol. 1, Part 2, pp. 61–112.

    Google Scholar 

  21. H. Feigenbaum, Echocardiography, 5th ed. (Williams & Wilkins, Baltimore, MD, 1994; Vidar, Moscow, 1999).

    Google Scholar 

  22. DT-MRI Dataset of a Human Heart. http://gforge.icm.jhu.edu/gf/project/dtmri_data_sets/docman/?subdir=93.

  23. C. Geuzaine and J. F. Remacle, Int. J. Numeric. Methods Eng. 79 (11), 1309 (2009).

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Ural Federal University named after the first President of Russia B.N. Yeltsin, ul. Mira 19, Yekaterinburg, 620002, Russia

    A. A. Koshelev, A. E. Bazhutina, S. F. Pravdin, K. S. Ushenin, L. B. Katsnelson & O. E. Solovyova

  2. Krasovskii Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, ul. Sof’i Kovalevskoi 16, Yekaterinburg, 620990, Russia

    A. A. Koshelev, S. F. Pravdin, K. S. Ushenin, L. B. Katsnelson & O. E. Solovyova

  3. Institute of Immunology and Physiology, Ural Branch, Russian Academy of Sciences, ul. Pervomaiskaya 106, Yekaterinburg, 620041, Russia

    K. S. Ushenin & O. E. Solovyova

Authors
  1. A. A. Koshelev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. E. Bazhutina
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. F. Pravdin
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. K. S. Ushenin
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. L. B. Katsnelson
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. O. E. Solovyova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. A. Koshelev.

Additional information

Original Russian Text © A.A. Koshelev, A.E. Bazhutina, S.F. Pravdin, K.S. Ushenin, L.B. Katsnelson, O.E. Solovyova, 2016, published in Biofizika, 2016, Vol. 61, No. 5, pp. 986–995.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Koshelev, A.A., Bazhutina, A.E., Pravdin, S.F. et al. A modified mathematical model of the anatomy of the cardiac left ventricle. BIOPHYSICS 61, 785–792 (2016). https://doi.org/10.1134/S0006350916050134

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0006350916050134

Keywords

Search

Navigation