Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

Mechano-electric effect and a heart assist device in the synergistic model of cardiac function

1 Fluid and Complex Systems Research Centre, Coventry University, Coventry, CV1 5FB, UK
2 School of Mathematics and Statistics, University of Sheffield, Sheffield, S3 7RH, UK
3 Royal Brompton & Harefield NHS Foundation Trust, Royal Brompton Hospital, Sydney Street, Chelsea, London SW3 6NP, UK

Special Issues: Fluctuations in biosystems

The breakdown of cardiac self-organization leads to heart diseases and failure, the number one cause of death worldwide. Within the traditional time-varying elastance model, cardiac self-organization and breakdown cannot be addressed due to its inability to incorporate the dynamics of various feedback mechanisms consistently. To face this challenge, we recently proposed a paradigm shift from the time-varying elastance concept to a synergistic model of cardiac function by integrating mechanical, electric and chemical activity on micro-scale sarcomere and macro-scale heart. In this paper, by using our synergistic model, we investigate the mechano-electric feedback (MEF) which is the effect of mechanical activities on electric activity—one of the important feedback loops in cardiac function. We show that the (dysfunction of) MEF leads to various forms of heart arrhythmias, for instance, causing the electric activity and left-ventricular volume and pressure to oscillate too fast, too slowly, or erratically through periodic doubling bifurcations or ectopic excitations of incommensurable frequencies. This can result in a pathological condition, reminiscent of dilated cardiomyopathy, where a heart cannot contract or relax properly, with an ineffective cardiac pumping and abnormal electric activities. This pathological condition is then shown to be improved by a heart assist device (an axial rotary pump) since the latter tends to increase the stroke volume and aortic pressure while inhibiting the progression (bifurcation) to such a pathological condition. These results highlight a nontrivial effect of a mechanical pump on the electric activity of the heart.
  Article Metrics

Keywords haemodynamics; cardiac cycle; axial rotary pump; mechano-electric effect; arrhythmias; feedback; lumped-parameter model; biological complexity; self-organization; nonlinear dynamics

Citation: Eun-jin Kim, Massimo Capoccia. Mechano-electric effect and a heart assist device in the synergistic model of cardiac function. Mathematical Biosciences and Engineering, 2020, 17(5): 5212-5233. doi: 10.3934/mbe.2020282


  • 1. H. Haken, Information and Self-Organization: A Macroscopic Approach to Complex Systems, Springer Series in Synergetics, Heidelberg: Springer-Verlag, Berlin, 2006.
  • 2. T. Wright, J. Twaddle, C. Humphries, S. Hayes, E. Kim, Variability and degradation of selforganization in self-sustained oscillators, Math. Biosci., 273 (2016), 57-69.
  • 3. K. Ascrof, Available from: https://sheffield.academia.edu/KieranAscroft (accessed on 23 August 2019).
  • 4. Z. Knudsen, A. Holden, J. Brindley, Qualitative modeling of mechano-electrical feedback in a ventricular cell, Bull. Math. Biol., 6 (1997), 115-181.
  • 5. G. Tse, S. T. Wong, V. Tse, Y. T. Lee, H. Y. Lin, J. M. Yeo, Cardiac dynamics: Alternans and arrhythmogenesis, J. Arrhythm, 32 (2016), 411-417.
  • 6. M. R. Franz, Mechano-electrical feedback in ventricular myocardium, Cardiovascular Res., 32 (1996), 15-24.
  • 7. M. J. Lab, D. G. Allen, C. H. Orchard, The effects of shortening on myoplasmic calcium concentration and action potential in mammalian ventricular muscle, Circ. Res., 55 (1984), 825- 829.
  • 8. A. Kamkin, I. Kiseleva, K. D. Wagner, H. Scholz, Mechano-Electric Feedback in the Heart: Evidence from Intracellular Microelectrode Recordings on Multicellular Preparations and Single Cells from Healthy and Diseased Tissue, in Mechanosensitivity in Cells and Tissues (eds. A. Kamkin and I. Kiseleva), Moscow: Academia, 2005.
  • 9. P. Kohl, P. Hunter, D. Noble, Stretch-induced changes in heart rate and rhythm: clinical observations, experiments and mathematical models, in Biophysics and Molecular Biology, 71 (1999), 91-138.
  • 10. A. Collet, J. Bragard, P. C. Dauby, Temperature, geometry, and bifurcations in the numerical modeling of the cardiac mechano-electric feedback, Chaos, 27 (2017), 093924.
  • 11. S. Galice, D. M. Bers, D. Sato, Stretch-activated current can promote or suppress cardiac alternans depending on voltage-calcium interaction, Biophys. J., 110 (2016), 2671-2677.
  • 12. O. Bikou, C. Kho, K. Ishikawa, Atrial stretch and arrhythmia after myocardial infarction, Aging, 11 (2019), 11-12.
  • 13. P. Kohl, A. D. Nesbitt, P. J. Cooper, M. Lei, Sudden cardiac death by commotio cordis: role of mechano-electric feedback, Cardiovasc. Res., 50 (2001), 280-289.
  • 14. C. Madias, M. B. J. J. Weinstock, N. R. Estes, M. S. Link, Commotio cordis-sudden cardiac death with chest wall impact, J. Cardiovasc. Electrophysiol., 18 (2007), 115-122.
  • 15. W. Li, P. Kohl, N. Trayanova, Induction of ventricular arrhythmias following mechanical impact: a simulation study in 3d, J. Mol. Histol., 35 (2004), 679-686.
  • 16. W. Li, P. Kohl, N. Trayanova, Myocardial ischemia lowers precordial thump ef!cacy: an inquiry into mechanisms using three-dimensional simulations, Heart Rhythm, 3 (2006), 179-186.
  • 17. M. J. Lab, Transient depolarization and action potential alterations following mechanical changes in isolated myocardium, Cardiovasc. Res., 14 (1980), 624-637.
  • 18. M. R. Franz, D. Burkho, D. T. Yue, K. Sagawa, Mechanically induced action potential changes and arrhythmia in isolated and in situ canine hearts, Cardiovasc. Res., 23 (1989), 213-223.
  • 19. H. Hu, F. Sachs, Stretch-induced ion channels in the heart, J. Mol. Cell. Cardiol., 29 (1997), 1511-1523.
  • 20. E. G. Tolkacheva, D. G. Schaeffer, D. J. Gauthier, C. C. Mitchell, Analysis of the Fenton-Karma model through an approximation by a one-dimensional map, Chaos, 12 (2002), 1034-1042.
  • 21. M. Radszuweit, E. Alvarez-Lacalle, M. Bar, B. Echebarria, Cardiac contraction induces discordant alternans and localized block, Phys. Rev. E, 91 (2015), 022703.
  • 22. A. Hazim, Y. Belhamadia, S. Dubljevicet, Effects of mechano-electrical feedback on the onset of alternans: A computational study, Chaos, 29 (2019), 063126.
  • 23. F. Fenton, A. Karma, Vortex dynamics in three-dimensional continuous myocardium with fiber rotation: Filament instability and fibrillation, Chaos, 8 (1998), 20-47.
  • 24. F. Yapari, D. Deshpande, Y. Belhamadia, S. Dubljevic, Control of cardiac alternans by mechanical and electrical feedback, Phys. Rev. E, 90 (2014), 012706.
  • 25. L. D. Weise, A. V. Panfilov, Discrete Mechanical Modeling of Mechanoelectrical Feedback in Cardiac Tissue: Novel Mechanisms of Spiral Wave Initiation, in Modeling the Heart and the Circulatory System, Springer, Cham, 14 (2015), 29-50.
  • 26. A. Hazim, Y. Belhamadia, S. Dubljevicet, Control of cardiac alternans based on electromechanical model for cardiac tissue, Comput. Biol. Med., 63 (2015), 108117.
  • 27. C. Franzone, L. F. Pavarino, S. Scacchiet, Effects of mechanical feedback on the stability of cardiac scroll waves: A bidomain electro-mechanical simulation study, Chaos, 27 (2017), 093905.
  • 28. A. Hazim, Y. Belhamadia, S. Dubljevic, Mechanical perturbation control of cardiac alternans, Phys. Rev. E, 97 (2018), 052407.
  • 29. A. Amar, S. Zlochiver, O. Barnea, Mechano-electric feedback effects in a three-dimensional (3D) model of the contracting cardiac ventricle, PLoSONE, 13 (2018), e0191238.
  • 30. R. R. Alievand, A. V. Panfilov, A simple two-variable model of cardiac excitation, Chaos, Solitons Fractals, 7 (1996), 293-301.
  • 31. A. Bueno-Orovio, E. M. Cherry, H. Flavio, F. H. Fenton, Minimal model for human ventricular action potentials in tissue, J. Theo. Biology, 253 (2008), 544-560.
  • 32. V. Timmermann, L. A. Dejgaard, K. H. Haugaa, A. G. Edwards, J. Sundnes, A. D. McCulloch, et al., An integrative appraisal of mechano-electric feedback mechanisms in the heart, Prog. Biophys. Mol. Biol., 130 (2017), 404-417.
  • 33. M. Varela, A. Roy, J. Lee, A survey of pathways for mechano-electric coupling in the Atria, preprint, arXiv:2005.08121.
  • 34. Z. Qu, G. Hu, A. Garfinkel, J. N. Weiss, Nonlinear and stochastic dynamics in the heart, Phys. Rep., 543 (2014), 61-162.
  • 35. A. P. Newton, E. Kim, On the self-organizing process of large scale shear flows, Phys. Plasmas, 20 (2013), 092306.
  • 36. H. Suga, K. Sagawa, A. A. Shoukas, Load independence of the instantaneous pressure-volume ratio of the canine left ventricle and effects of epinephrine and heart rate on the ratio, Circ. Res., 32 (1973), 314-322.
  • 37. K. Sagawa, The ventricular pressure-volume diagram revisited, Circ. Res., 43 (1978), 677-687.
  • 38. M. A. Simaan, Rotary heart assist devices, in Springer Handbook of Automation, Springer, (2009), 1409-1421.
  • 39. M. A. Simaan, A. Ferreira, S. Chen, J. F. Antaki, D. G. Galati, A dynamical state space representation and performance analysis of feedback-controlled rotary left ventricular assist device IEEE Trans, Control Syst. Tech., 17 (2019), 15-28.
  • 40. T. E. Claessens, D. Georgakopoulos, M. Afanasyeva, S. J. Vermeersch, H. D. Millar, N. Stergiopulos, et al., Nonlinear isochrones in murine left ventricular pressure-volume loops: how well does the time-varying elastance concept hold?, Am. J. Physiol. Heart Circ. Physiol., 290 (2006), H1474-H1483.
  • 41. S. Vandenberghe, P. Segers, P. Steendijk, B. Meyns, R. A. E. Dion, J. F. Antaki, et al., Modelling ventricular function during cardiac assist: Does time-varying elastance work?, Am. Soc. Artif. Intern. Organs J., 52 (2006), 4-8.
  • 42. E. Kim, M. Capoccia, Synergistic model of cardiac function with a heart assist device, Bioengineering, 7 (2019), 1-16.
  • 43. M. Capoccia, Development and characterization of the arterial windkessel and its role during left ventricular assist device assistance, Artif. Organs, 39 (2015), E138.
  • 44. M. Capoccia, S. Marconi, S. A. Singh, D. M. Pisanelli, C. De Lazzari, Simulation as a preoperative planning approach in advanced heart failure patients: A retrospective clinical analysis, Bio. Med. Eng. OnLine, 7 (2018), 52.
  • 45. G. Ferrari, A. Di Molfetta, K. Zieliński, L. Fresiello, Circulatory modelling as a clinical decision support and an educational tool, Biomed. Data J., 1 (2015), 45-50.
  • 46. J. Bestel, F. Clément, M. Sorine, A biomechanical model of muscle contraction, in Medical Image Computing and Computer-Assisted Intervention MICCAI 2001, Springer, Berlin, Heidelberg, (2001), 1159-1161.
  • 47. J. Bestel, Modèle différentiel de la contraction musculaire contrôlée: Application au système cardio-vasculaire, Ph.D thesis, Universit Paris 9, 2000.
  • 48. Available from: https://www.cellml.org/ (accessed on 8 July 2020).
  • 49. Available from: https://www.scholarpedia.org/article/Models of cardiac cell (accessed on 8 July 2020).
  • 50. E. Ott, Chaos in Dynamical Systems, Cambridge University Press, 1993.


Reader Comments

your name: *   your email: *  

© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved