Skip to main content

An Extended Generalized Hill Model for Cardiac Tissue: Comparison with Different Approaches Based on Experimental Data

  • Conference paper
  • First Online:
Functional Imaging and Modeling of the Heart (FIMH 2023)

Abstract

In this work we discuss advantages and drawbacks of active mechanics frameworks often used to represent the material response of cardiac tissue. A formal analysis of the models is followed by the application of these frameworks to represent the experimentally measured active and passive response of cardiac tissue. The active strain model is analyzed first and we show that, for commonly used material energies, this framework is not adequate to represent both active and passive tissue responses simultaneously. The active stress model and the generalized Hill model are discussed next. We incorporate the basic idea from Stålhand et al. (2008) to improve the generalized Hill model. Namely we propose to scale the active energy by a function of cross-bridge formation making the model physiologically more accurate. This modification also allows to relate the new Hill type model to the active stress framework. Finally, we show that this extended Hill model best represents the stress-strain response measured in equibiaxial stretch experiments.

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

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 89.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 119.99
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

Similar content being viewed by others

References

  1. Ambrosi, D., Pezzuto, S.: Active stress vs active strain in mechanobiology: constitutive issues. J. Elast. 107(2), 199–212 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bezanson, J., Edelman, A., Karpinski, S., Shah, V.B.: Julia: a fresh approach to numerical computing. SIAM Rev. 59(1), 65–98 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  3. Cansız, B., Dal, H., Kaliske, M.: Computational cardiology: a modified Hill model to describe the electro-visco-elasticity of the myocardium. CMAME 315, 434–466 (2017)

    MathSciNet  MATH  Google Scholar 

  4. Carlsson, K., Ekre, F.: Tensors.jl — Tensor Computations in Julia. JORS 7(1), 7 (2019)

    Google Scholar 

  5. Danisch, S., Krumbiegel, J.: Makie.jl: flexible high-performance data visualization for Julia. JOSS 6(65), 3349 (2021)

    Article  Google Scholar 

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

    Article  Google Scholar 

  7. Giantesio, G., Musesti, A., Riccobelli, D.: A comparison between active strain and active stress in transversely isotropic hyperelastic materials. J. Elast. 137(1), 63–82 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  8. Göktepe, S., Menzel, A., Kuhl, E.: The generalized Hill model: a kinematic approach towards active muscle contraction. JMPS 72, 20–39 (2014)

    MathSciNet  MATH  Google Scholar 

  9. Holzapfel, G.A., Ogden, R.W.: Constitutive modelling of passive myocardium: a structurally based framework for material characterization. Philos. Trans. Royal Soc. A 367(1902), 3445–3475 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  10. Lin, D.H.S., Yin, F.C.P.: A multiaxial constitutive law for mammalian left ventricular myocardium in steady-state barium contracture or tetanus. J. Biomech. Eng. 120(4), 504–517 (1998)

    Article  Google Scholar 

  11. Marquardt, D.W.: An algorithm for least-squares estimation of nonlinear parameters. J. Soc. Ind. Appl. Math. 11(2), 431–441 (1963)

    Article  MathSciNet  MATH  Google Scholar 

  12. Perotti, L.E., et al.: Estimating cardiomyofiber strain in vivo by solving a computational model. Med. Image Anal. 68, 101932 (2021)

    Article  Google Scholar 

  13. Piersanti, R., et al.: 3D–0D closed-loop model for the simulation of cardiac biventricular electromechanics. CMAME 391, 114607 (2022)

    MathSciNet  MATH  Google Scholar 

  14. Ponnaluri, A., Perotti, L., Ennis, D., Klug, W.: A viscoactive constitutive modeling framework with variational updates for the myocardium. CMAME 314, 85–101 (2017)

    MathSciNet  MATH  Google Scholar 

  15. Rademakers, F.E., et al.: Relation of Regional cross-fiber shortening to wall thickening in the intact heart. Three-dimensional strain analysis by NMR tagging. Circulation 89(3), 1174–1182 (1994)

    Article  Google Scholar 

  16. Rossi, S., Lassila, T., Ruiz-Baier, R., Sequeira, A., Quarteroni, A.: Thermodynamically consistent orthotropic activation model capturing ventricular systolic wall thickening in cardiac electromechanics. Eur. J. Mech. A. Solids 48, 129–142 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  17. Ruiz-Baier, R., et al.: Mathematical modelling of active contraction in isolated cardiomyocytes. Math. Med. Biol. 31(3), 259–283 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  18. Sack, K.L., et al.: Construction and validation of subject-specific biventricular finite-element models of healthy and failing swine hearts from high-resolution DT-MRI. Front. Physiol. 9, 539 (2018)

    Article  Google Scholar 

  19. Stålhand, J., Klarbring, A., Holzapfel, G.A.: Smooth muscle contraction: mechanochemical formulation for homogeneous finite strains. Prog. Biophys. Mol. Biol. 96(1–3), 465–481 (2008)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Dennis Ogiermann .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Ogiermann, D., Balzani, D., Perotti, L.E. (2023). An Extended Generalized Hill Model for Cardiac Tissue: Comparison with Different Approaches Based on Experimental Data. In: Bernard, O., Clarysse, P., Duchateau, N., Ohayon, J., Viallon, M. (eds) Functional Imaging and Modeling of the Heart. FIMH 2023. Lecture Notes in Computer Science, vol 13958. Springer, Cham. https://doi.org/10.1007/978-3-031-35302-4_57

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-35302-4_57

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-35301-7

  • Online ISBN: 978-3-031-35302-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics