Formal Analysis of Abnormal Excitation in Cardiac Tissue

  • Pei Ye
  • Radu Grosu
  • Scott A. Smolka
  • Emilia Entcheva
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5307)


We present the Piecewise Linear Approximation Model of Ion Channel contribution (PLAMIC) to cardiac excitation. We use the PLAMIC model to conduct formal analysis of cardiac arrhythmic events, namely Early Afterdepolarizations (EADs). The goal is to quantify (for the first time) the contribution of the overall sodium (Na + ), potassium (K + ) and calcium (Ca2 + ) currents to the occurrence of EADs during the plateau phase of the cardiac action potential (AP). Our analysis yields exact mathematical criteria for the separation of the parameter space for normal and EAD-producing APs, which is validated by simulations with classical AP models based on complex systems of nonlinear differential equations. Our approach offers a simple formal technique for the prediction of conditions leading to arrhythmias (EADs) from a limited set of experimental measurements, and can be invaluable for devising new anti-arrhythmic strategies.


Plateau Phase Excitable Cell Cardiac Action Potential Early Repolarization Triangular Function 
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  1. 1.
    Cranefield, P.F., Aronson, R.S.: Cardiac arrhythmias: the role of triggered activity and other mechanisms. Futura Publishing Company (1988)Google Scholar
  2. 2.
    Fozzard, H.: Afterdepolarizations and triggered activity. Basic Res. Cardiol. 87(Suppl. 2), 105–113 (1992)PubMedGoogle Scholar
  3. 3.
    Hiraoka, M., Sunami, A., Zheng, F., Sawanobori, T.: Multiple ionic mechanisms of early afterdepolarizations in isolated ventricular myocytes from guinea-pig hearts. QT Prolongation and Ventricular Arrhythmias, pp. 33–34 (1992)Google Scholar
  4. 4.
    January, C., Moscucci, A.: Cellular mechanism of early afterdepolarizations. QT Prolongation and Ventricular Arrhythmias, pp. 23–32 (1992)Google Scholar
  5. 5.
    Zeng, J., Rudy, Y.: Early afterdepolarizations in cardiac myocytes: mechanism and rate dependence. Biophysical J. 68, 949–964 (1995)CrossRefGoogle Scholar
  6. 6.
    Homma, N., Amran, M., Nagasawa, Y., Hashimoto, K.: Topics on the Na+/Ca2+ exchanger: involvement of Na+/Ca2+ exchange system in cardiac triggered activity. J. Pharmacol. Sci. 102, 17–21 (2006)CrossRefPubMedGoogle Scholar
  7. 7.
    Clusin, W.: Calcium and cardiac arrhythmias: DADs, EADs, and alternans. Crit. Rev. Clin. Lab. Sci. 40, 337–375 (2003)CrossRefPubMedGoogle Scholar
  8. 8.
    Charpentier, F., Drouin, E., Gauthier, C., Marec, H.L.: Early after/depolarizations and triggered activity: mechanisms and autonomic regulation. Fundam. Clin. Pharmacol. 7, 39–49 (1993)CrossRefPubMedGoogle Scholar
  9. 9.
    Luo, C.H., Rudy, Y.: A dymanic model of the cardiac ventricular action potential: I. simulations of ionic currents and concentration changes. Circ. Res. 74, 1071–1096 (1994)CrossRefPubMedGoogle Scholar
  10. 10.
    Hodgkin, A.L., Huxley, A.F.: A quantitative description of membrane currents and its application to conduction and excitation in nerve. J. Physiol. 117, 500–544 (1952)CrossRefPubMedPubMedCentralGoogle Scholar
  11. 11.
    Ye, P., Entcheva, E., Smolka, S., Grosu, R.: A cycle-linear hybrid-automata model for excitable cells. IET Systems Biology 2, 24–32 (2008)CrossRefPubMedGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Pei Ye
    • 1
  • Radu Grosu
    • 1
  • Scott A. Smolka
    • 1
  • Emilia Entcheva
    • 2
  1. 1.Computer Science DepartmentStony Brook UniversityUSA
  2. 2.Biomedical Engineering DepartmentStony Brook UniversityUSA

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