Reactive Interstitial and Reparative Fibrosis as Substrates for Cardiac Ectopic Pacemakers and Reentries

  • Rafael Sachetto Oliveira
  • Bruno Gouvêa de Barros
  • Johnny Moreira Gomes
  • Marcelo Lobosco
  • Sergio Alonso
  • Markus Bär
  • Rodrigo Weber dos Santos
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9656)


Dangerous cardiac arrhythmias have been frequently associated with focal sources of fast pulses, i.e. ectopic pacemakers. However, there is a lack of experimental evidences that could explain how ectopic pacemakers could be formed in cardiac tissue. In recent studies, we have proposed a new theory for the genesis of ectopic pacemakers in pathological cardiac tissues: reentry inside microfibrosis, i.e., a small region where excitable myocytes and non-conductive material coexist. In this work, we continue this investigation by comparing different types of fibrosis, reparative and reactive interstitial fibrosis. We use detailed and modern models of cardiac electrophysiology that account for the micro-structure of cardiac tissue. In addition, for the solution of our models we use, for the first time, a new numerical algorithm based on the Uniformization method. Our simulation results suggest that both types of fibrosis can support reentries, and therefore can generate in-silico ectopic pacemakers. However, the probability of reentries differs quantitatively for the different types of fibrosis. In addition, the new Uniformization method yields 20-fold increase in cardiac tissue simulation speed and, therefore, was an essential technique that allowed the execution of over a thousand of simulations.


Cardiac Tissue Euler Method Continuous Time Markov Chain Uniformization Method Cardiac Electrophysiology 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work was partially funded by Brazilian Science without Borders, CNPq, Capes, Fapemig, UFJF and Finep; Geman DFG project SFB 910; and MINECO Spain under Ramon y Cajal program RYC-2012-11265.


  1. 1.
    Alonso, S., Bär, M.: Reentry near the percolation threshold in a heterogeneous discrete model for cardiac tissue. Phys. Rev. Lett. 110(15), 158101 (2013)CrossRefGoogle Scholar
  2. 2.
    Alonso, S., Sagués, F., Mikhailov, A.S.: Taming winfree turbulence of scroll waves in excitable media. Science 299(5613), 1722–1725 (2003)CrossRefGoogle Scholar
  3. 3.
    Balay, S., Abhyankar, S., Adams, M., Brown, J., Brune, P., Buschelman, K., Eijkhout, V., Gropp, W., Kaushik, D., Knepley, M., et al.: PETSc users manual revision 3.5. Technical report Argonne National Laboratory (ANL) (2014)Google Scholar
  4. 4.
    Bär, M., Eiswirth, M.: Turbulence due to spiral breakup in a continuous excitable medium. Phys. Rev. E 48(3), R1635 (1993)CrossRefGoogle Scholar
  5. 5.
    de Barros, G.B., Oliveira, S.R., Meira, W., Lobosco, M., dos Santos, W.R.: Simulations of complex and microscopic models of cardiac electrophysiology powered by multi-gpu platforms. Computational and Mathematical Methods in Medicine 2012 (2012)Google Scholar
  6. 6.
    de Barros, B.G., dos Santos, R.W., Lobosco, M., Alonso, S.: Simulation of ectopic pacemakers in the heart: multiple ectopic beats generated by reentry inside fibrotic regions. BioMed Research International 2015 (2015)Google Scholar
  7. 7.
    Bondarenko, V., Szigeti, G., Bett, G., Kim, S., Rasmusson, R.: Computer model of action potential of mouse ventricular myocytes. Am. J. Physiol. Heart Circulatory Physiol. 287, H1378–H1403 (2004)CrossRefGoogle Scholar
  8. 8.
    Dos Santos, R.W., Kosch, O., Steinhoff, U., Bauer, S., Trahms, L., Koch, H.: MCG to ECG source differences: measurements and a two-dimensional computer model study. J. Electrocardiol. 37, 123–127 (2004)CrossRefGoogle Scholar
  9. 9.
    Finet, J.E., Rosenbaum, D.S., Donahue, J.K.: Information learned from animal models of atrial fibrillation. Cardiol. Clin. 27(1), 45–54 (2009)CrossRefGoogle Scholar
  10. 10.
    Groop, W., Lusk, E.: User’s guide for mpich, a portable implementation of MPI. Technical report Argonne National Laboratory (1994)Google Scholar
  11. 11.
    Hodgkin, A.L., Huxley, A.F.: A quantitative description of membrane current and its application to conduction in nerve. J. Phisiol. 117, 500–544 (1952)CrossRefGoogle Scholar
  12. 12.
    Hubbard, M.L., Henriquez, C.S.: A microstructural model of reentry arising from focal breakthrough at sites of source-load mismatch in a central region of slow conduction. Am. J. Physiol. Heart Circulatory Physiol. 306(9), H1341–H1352 (2014)CrossRefGoogle Scholar
  13. 13.
    Jensen, A.: Markoff chains as aid in the study of markoff processes. Skandinavisk Aktuarietidskrift 36, 87–91 (1953)MathSciNetMATHGoogle Scholar
  14. 14.
    Laurent, G., Moe, G., Hu, X., Leong-Poi, H., Connelly, K.A., So, P.P.S., Ramadeen, A., Doumanovskaia, L., Konig, A., Trogadis, J., Courtman, D., Strauss, B., Dorian, P.: Experimental studies of atrial fibrillation: a comparison of two pacing models. Am. J. Physiol. Heart Circulatory Physiol. 294(3), H1206–H1215 (2008)CrossRefGoogle Scholar
  15. 15.
    Gomes, M.J., Alvarenga, A., Campos, S.R., Rocha, B., da Silva, C.A., dos Santos, W.R.: Uniformization method for solving cardiac electrophysiology models based on the markov-chain formulation. IEEE Trans. Biomed. Eng. 62(2), 600–608 (2015)CrossRefGoogle Scholar
  16. 16.
    Platonov, P.G., Mitrofanova, L.B., Orshanskaya, V., Ho, S.Y.: Structural abnormalities in atrial walls are associated with presence and persistency of atrial fibrillation but not with age. J. Am. Coll. Cardiol. 58(21), 2225–2232 (2011)CrossRefGoogle Scholar
  17. 17.
    Reibman, A., Trivedi, K.: Numerical transient analysis of markov models. Comput. Oper. Res. 15(1), 19–36 (1988)CrossRefMATHGoogle Scholar
  18. 18.
    Rush, S., Larsen, H.: A practical algorithm for solving dynamic membrane equations. IEEE Trans. Biomed. Eng. 4, 389–392 (1978)CrossRefGoogle Scholar
  19. 19.
    Rush, S., Larsen, H.: A practical algorithm for solving dynamic membrane equations. IEEE Trans. Biomed. Eng. 25(4), 389–392 (1978)CrossRefGoogle Scholar
  20. 20.
    dos Santos, R.W., Campos, F., Neumann, L., Nygren, A., Giles, W., Koch, H.: ATX-II effects on the apparent location of M cells in a computational model of a human left ventricular wedge. J. Cardiovasc. Electrophysiol. 17, S86–S95 (2006)CrossRefGoogle Scholar
  21. 21.
    Silver, M.A., Pick, R., Brilla, C.G., Jalil, J.E., Janicki, J.S., Weber, K.T.: Reactive and reparative fibrillar collagen remodelling in the hypertrophied rat left ventricle: Two experimental models of myocardial fibrosis. Cardiovasc. Res. 24(9), 741–747 (1990)CrossRefGoogle Scholar
  22. 22.
    Sundnes, J.: Computing the Electrical Activity in the Heart. Springer, Heidelberg (2006)MATHGoogle Scholar
  23. 23.
    Sundnes, J., Artebrant, R., Skavhaug, O., Tveito, A.: A second-order algorithm for solving dynamic cell membrane equations. IEEE Trans. Biomed. Eng. 56, 2546–2548 (2009)CrossRefGoogle Scholar
  24. 24.
    Tobon, C., Ruiz-Villa, C.A., Heidenreich, E., Romero, L., Hornero, F., Saiz, J.: A three-dimensional human atrial model with fiber orientation. electrograms and arrhythmic activation patterns relationship. PLoS ONE 8(2), e50883 (2013)CrossRefGoogle Scholar
  25. 25.
    Voigt, N., Dobrev, D.: Cellular and molecular correlates of ectopic activity in patients with atrial fibrillation. Europace 14(suppl 5), v97–v105 (2012)CrossRefGoogle Scholar
  26. 26.
    Weiss, J.N., Karma, A., Shiferaw, Y., Chen, P.S., Garfinkel, A., Qu, Z.: From pulsus to pulseless the saga of cardiac alternans. Circ. Res. 98(10), 1244–1253 (2006)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Rafael Sachetto Oliveira
    • 1
  • Bruno Gouvêa de Barros
    • 2
  • Johnny Moreira Gomes
    • 2
  • Marcelo Lobosco
    • 2
  • Sergio Alonso
    • 3
  • Markus Bär
    • 4
  • Rodrigo Weber dos Santos
    • 2
  1. 1.Departamento de Ciência da ComputaçãoUniversidade Federal de São João del ReiSão João del ReiBrazil
  2. 2.Departamento de Ciência da Computação e Programa em Modelagem ComputacionalUniversidade Federal de Juiz de ForaJuiz de ForaBrazil
  3. 3.Departament de FísicaUniversitat Politècnica de CatalunyaBarcelonaSpain
  4. 4.Physikalisch-Technische BundesanstaltBraunschweig, BerlinGermany

Personalised recommendations