Skip to main content

Connection Forms for Beating the Heart

LV Mechanics Challenge (Methods)

  • Conference paper
  • First Online:
Book cover Statistical Atlases and Computational Models of the Heart - Imaging and Modelling Challenges (STACOM 2014)

Abstract

We combine recent work on modeling cardiac mechanics using a finite volume method with the insight that heart wall myofiber orientations exhibit a particular volumetric geometry. In our finite volume mechanical simulation we use Maurer-Cartan one-forms to add a geometrical consistency term to control the rate at which myofiber orientation changes in the direction perpendicular to the heart wall. This allows us to estimate material properties related to both the passive and active parameters in our model. We have obtained preliminary results on the 4 canine datasets of the 2014 mechanics challenge using the FEBio software suite. In ongoing work we are validating and improving the model using rat heart (ex-vivo DTI and in-vivo tagging) MRI datasets, from which we have estimated strain tensors.

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

Access this chapter

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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Wang, V.Y., Lam, H., Ennis, D.B., Cowan, B.R., Young, A.A., Nash, M.P.: Modelling passive diastolic mechanics with quantitative mri of cardiac structure and function. Medical Image Analysis 13(5), 773–784 (2009)

    Article  Google Scholar 

  2. Holzapfel, G.A., Ogden, R.W.: Biomechanical Modelling at the Molecular, Cellular, and Tissue Levels, vol. 508. Springer (2009)

    Google Scholar 

  3. Rossi, S., Ruiz-Baier, R., Pavarino, L.F., Quarteroni, A.: Orthotropic active strain models for the numerical simulation of cardiac biomechanics. International Journal for Numerical Methods in Biomedical Engineering 28(6–7), 761–788 (2012)

    Article  MathSciNet  Google Scholar 

  4. Savadjiev, P., Strijkers, G.J., Bakermans, A.J., Piuze, E., Zucker, S.W., Siddiqi, K.: Heart wall myofibers are arranged in minimal surfaces to optimize organ function. Proc. Natl. Acad. Sci. USA 109(24), 9248–9253 (2012)

    Article  Google Scholar 

  5. Wang, H., Gao, H., Luo, X., Berry, C., Griffith, B., Ogden, R., Wang, T.: Structure-based finite strain modelling of the human left ventricle in diastole. International Journal for Numerical Methods in Biomedical Engineering 29(1), 83–103 (2013)

    Article  MathSciNet  Google Scholar 

  6. Irving, G., Schroeder, C., Fedkiw, R.: Volume conserving finite element simulations of deformable models. ACM Transactions on Graphics (TOG) 26, 13 (2007)

    Article  Google Scholar 

  7. Sifakis, E., Barbic, J.: Fem simulation of 3d deformable solids: a practitioner’s guide to theory, discretization and model reduction. In: ACM SIGGRAPH 2012 Courses, p. 20. ACM (2012)

    Google Scholar 

  8. Niederer, S., Hunter, P., Smith, N.: A quantitative analysis of cardiac myocyte relaxation: a simulation study. Biophysical Journal 90(5), 1697–1722 (2006)

    Article  Google Scholar 

  9. Piuze, E., Sporring, J., Siddiqi, K.: Moving frames for heart fiber geometry. In: Gee, J.C., Joshi, S., Pohl, K.M., Wells, W.M., Zöllei, L. (eds.) IPMI 2013. LNCS, vol. 7917, pp. 524–535. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  10. Streeter, D., Bassett, D.: An engineering analysis of myocardial fiber orientation in pig’s left ventricle in systole. The Anatomical Record 155(4), 503–511 (2005)

    Article  Google Scholar 

  11. Bruurmijn, L.C.M., Kause, H.B., Filatova, O.G., Duits, R., Fuster, A., Florack, L.M.J., van Assen, H.C.: Myocardial deformation from local frequency estimation in tagging mri. In: Ourselin, S., Rueckert, D., Smith, N. (eds.) FIMH 2013. LNCS, vol. 7945, pp. 284–291. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  12. Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. Johns Hopkins University Press, Baltimore (1996)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Kaleem Siddiqi .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Mensch, A. et al. (2015). Connection Forms for Beating the Heart. In: Camara, O., Mansi, T., Pop, M., Rhode, K., Sermesant, M., Young, A. (eds) Statistical Atlases and Computational Models of the Heart - Imaging and Modelling Challenges. STACOM 2014. Lecture Notes in Computer Science(), vol 8896. Springer, Cham. https://doi.org/10.1007/978-3-319-14678-2_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-14678-2_9

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-14677-5

  • Online ISBN: 978-3-319-14678-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics