Relationship Between Cardiac Electrical and Mechanical Activation Markers by Coupling Bidomain and Deformation Models

  • Piero Colli-Franzone
  • Luca F. PavarinoEmail author
  • Simone Scacchi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9126)


The aim of this study is to simulate the electromechanical behavior of a cardiac wedge following an endo- or epicardial stimulation, and to study different markers of mechanical contraction times. We investigate how tissue anisotropy affects the performance of the mechanical markers and we evaluate their delay distributions with respect to the electrical activation time. The main results of this study show that: the electrical and mechanical activation sequences are very well correlated; the electromechanical delay displays heterogeneous distributions even if the electrical and mechanical cellular properties are assumed homogeneous; the electromechanical delay is larger in the regions where depolarization proceeds along fiber than across fiber.


Cardiac electromechanical markers Cardiac excitation and contraction Orthotropic bidomain model 3D parallel simulations 


  1. 1.
    Adeniran, I., Hancox, J.C., Zhang, H.: Effect of cardiac ventricular mechanical contraction on the characteristics of the ECG: a simulation study. J. Biomed. Sci. Eng. 6, 47–60 (2013)CrossRefGoogle Scholar
  2. 2.
    Ambrosi, D., et al.: Electromechanical coupling in cardiac dynamics: the active strain approach. SIAM J. Appl. Math. 71, 605–621 (2011)zbMATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    Ashikaga, H., et al.: Transmural dispersion of myofiber mechanics. J. Am. Coll. Cardiol. 49, 909–916 (2007)CrossRefGoogle Scholar
  4. 4.
    Augustijn, C.H., et al.: Mapping the sequence of contraction of the canine left ventricle. Pflug. Arch. 419, 529–533 (1991)CrossRefGoogle Scholar
  5. 5.
    Badke, F.R., Boinay, P., Covell, J.W.: Effects of ventricular pacing on regional left ventricular performance in the dog. Am. J. Physiol. 238, H858–H867 (1980)Google Scholar
  6. 6.
    Balay, S., et al.: PETSc users manual. Technical report, ANL-95/11 - Revision 3.3, Argonne National Laboratory (2012)Google Scholar
  7. 7.
    Bovendeerd, P.H.M., Kroon, W., Delhaas, T.: Determinants of left ventricular shear strain. Am. J. Physiol. HCP 297, H1058–H1068 (2009)CrossRefGoogle Scholar
  8. 8.
    Carapella, V., et al.: Quantitative study of the effect of tissue microstructure on contraction in a computational model of rat left ventricle. PLoS One 9, e92792 (2014)CrossRefGoogle Scholar
  9. 9.
    Colli Franzone, P., Pavarino, L.F., Scacchi, S.: Mathematical Cardiac Electrophysiology. MSA, vol. 13. Springer, New York (2014)zbMATHGoogle Scholar
  10. 10.
    Colli Franzone, P., Pavarino, L.F., Scacchi, S.: Parallel multilevel solvers for the cardiac electro-mechanical coupling. Appl. Numer. Math. (To appear) (2014)Google Scholar
  11. 11.
    P. Colli Franzone, L. F. Pavarino, and S. Scacchi, A numerical simulation study of the influence of mechanical feedbacks on the bioelectrical activity in a cardiac electro-mechanical model, Math. Mod. Meth. Appl. Sci. (2015) (Submitted)Google Scholar
  12. 12.
    Constantino, J., Hu, Y., Trayanova, N.A.: A computational approach to understanding the cardiac electromechanical activation sequence in the normal and failing heart, with translation to the clinical practice of CRT. Progr. Biophys. Mol. Biol. 110, 372–379 (2012)CrossRefGoogle Scholar
  13. 13.
    de Oliveira, B.L., et al.: Effects of deformation on transmural dispersion of repolarization using in silico models of human left ventricular wedge. Int. J. Numer. Meth. Biomed. Eng. 29, 1323–1337 (2013)CrossRefGoogle Scholar
  14. 14.
    Eriksson, T.S.E., et al.: Influence of myocardial fiber/sheet orientations on left ventricular mechanical contraction. Math. Mech. Solids 18, 592–606 (2013)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Fritz, T., et al.: Simulation of the contraction of the ventricles in a human heart model including atria and pericardium. Biomech. Mod. Mechanobiol. 13(3), 627–641 (2014)CrossRefGoogle Scholar
  16. 16.
    Gurev, V., et al.: Distribution of electromechanical delay in the heart: insights from a three-dimensional electromechanical model. Biophys. J. 99, 745–754 (2010)CrossRefGoogle Scholar
  17. 17.
    Kerckhoffs, R.C.P., et al.: Homogeneity of cardiac contraction despite physiological asyncrony of depolarization: a model study. Ann. Biomed. Eng. 31, 536–547 (2003)CrossRefGoogle Scholar
  18. 18.
    Kerckhoffs, R.C.P., et al.: Timing of depolarization and contraction in the paced canine left ventricle: model and experiment. J. Cardiovasc. Electrophysiol. 14, S188–S195 (2003)CrossRefGoogle Scholar
  19. 19.
    Kerckhoffs, R.C.P., et al.: Intra- and interventricular asynchrony of electromechanics in the ventricularly paced heart. J. Eng. Math. 47, 201–216 (2003)zbMATHMathSciNetCrossRefGoogle Scholar
  20. 20.
    Kerckhoffs, R.C.P., et al.: Electromechanics of paced left ventricle simulated by straightforward mathematical model: comparison with experiments. Am. J. Physiol. HCP 289, H1889–H1897 (2005)CrossRefGoogle Scholar
  21. 21.
    Land, S., et al.: An analysis of deformation-dependent electromechanical coupling in the mouse heart. J. Physiol. 590, 4553–4569 (2012)CrossRefGoogle Scholar
  22. 22.
    Niederer, S.A., Smith, N.P.: A mathematical model of the slow force response to stretch in rat ventricular myocites. Biophys. J. 92, 4030–4044 (2007)CrossRefGoogle Scholar
  23. 23.
    Pavarino, L.F., Scacchi, S.: Multilevel additive Schwarz preconditioners for the Bidomain reaction-diffusion system. SIAM J. Sci. Comput. 31, 420–443 (2008)zbMATHMathSciNetCrossRefGoogle Scholar
  24. 24.
    Pluijmert, M., et al.: Effects of activation pattern and active stress development on myocardial shear in a model with adaptive myofiber reorientation. Am. J. Physiol. HCP 306, H538–H546 (2014)CrossRefGoogle Scholar
  25. 25.
    Prinzen, F.W., et al.: The time sequence of electrical and mechanical activation during spontaneous beating and ectopic stimulation. Eur. Heart. J. 13, 535–543 (1992)Google Scholar
  26. 26.
    Rossi, S., et al.: Thermodynamically consistent orthotropic activation model capturing ventricular systolic wall thickening in cardiac electromechanics. Eur. J. Mech. A-Solids 48, 129–142 (2014)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Sainte-Marie, J., et al.: Modeling and estimation of cardiac electromechanical activity. Comput. Struct. 84, 1743–1759 (2006)MathSciNetCrossRefGoogle Scholar
  28. 28.
    ten Tusscher, K.H.W.J., et al.: A model for human ventricular tissue. Am. J. Phys. HCP 286, H1573–H1589 (2004)Google Scholar
  29. 29.
    Usyk, T.P., McCulloch, A.D.: Relationship between regional shortening and asynchronous electrical activation in a three-dimensional model of ventricular electromechanics. J. Cardiovasc. Electrophysiol. 14, S196–S202 (2003)CrossRefGoogle Scholar
  30. 30.
    Wall, S.T., et al.: Electromechanical feedback with reduced cellular connectivity alters electrical activity in an infarct injures left ventricle: a finite element model study. Am J. Physiol. HCP 302, H206–H214 (2012)CrossRefGoogle Scholar
  31. 31.
    Weise, L.D., Nash, M.P., Panfilov, A.V.: A discrete model to study reaction-diffusion-mechanics systems. PLos One 6(7), e21934 (2011)CrossRefGoogle Scholar
  32. 32.
    Wyman, B., et al.: Mapping propagation of mechanical activation in the paced heart with MRI tagging. Am. J. Physiol. HCP 45, H881–H891 (1999)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Piero Colli-Franzone
    • 1
  • Luca F. Pavarino
    • 2
    Email author
  • Simone Scacchi
    • 2
  1. 1.Dipartimento di Matematica, Istituto di Matematica Applicata e Tecnologie InformaticheUniversità di Pavia and IMATI-CNRPaviaItaly
  2. 2.Dipartimento di MatematicaUniversità di MilanoMilanoItaly

Personalised recommendations