1. Effect of mechanical factors on rhythm disturbances in mathematical model of cardiac fiber 30/10/2014 1 Alexander Kursanov, L.B. Katsnelson, N.A. Vikulova, O.E. Solovyova, V.S. Markhasin Institute of Immunology and Physiology of the UB RAS Ural Federal University 6th Russian Workshop on Mathematical Models and Numerical Methods in Biomathematics

2. Continuous model of cardiac muscle 30/10/2014 2 Model of ventricular cardiomyocyte «Ekb-Oxford» Katsnelson L.B., et al., Russ J Numer Anal Math Modelling. 2014

3. EC coupling in cardiomyocytes 30/10/2014 3 Bers D. Nature (2002) Rheological scheme of cardiomyocyte model «Ekaterinburg- Oxford». CE – contractile element (sarcomere); PE, SE -- parallel and series elastic elements; XSE – external series elastic element; VS – parallel viscous element Mechanical block Electrical block

4. Experimental validation of cellular modeling predictions 30/10/2014 4 N (normal NKP)SC (sub-critical NKP inhibition and Ca 2+ SR overload) P (pathological NKP inhibition and Ca 2+ SR overload) K m,Na <37 mM K m,Na <153% * 37 mM≤K m,Na <40 mM 153% * ≤K m,Na <165% * K m,Na ≥40 mM K m,Na ≥165% * Sulman et al., Bull Math Biol, 2008 Na + -Ca 2+ exchanger Reduced Na + -K + pump Gradual increase in [Na + ] i Accumulation of Ca 2+ in cytosol Na + -Ca 2+ exchanger Spontaneous Ca 2+ release to cytosol between stimuli SpontaneousAPSpontaneouscontraction Accumulation of Ca 2+ in SR Ca 2+ overload of SR terminal cisterns

5. Experimental validation of cellular modeling predictions 30/10/2014 5 According to the model predictions the following mechanical factors appear to facilitate arrhythmia emergence: 1)a decrease in the mechanical load in afterloaded contractions; 2)a decrease in the initial length of sarcomeres in isometric twitches. 0,9 Lmax0,88 Lmax0,85 Lmax 0,82 Lmax

6. Continuous model of cardiac muscle 30/10/2014 6

7. Micro- and macroelectrical links 30/10/2014 7 Boundary conditions Left border: Right border: Initial conditions

8. Links between micro- and macromechanics 30/10/2014 8 Global parameter Local parameters

9. 30/10/2014 9

10. Model of tissue in study of cardiac pathology 30/10/2014 10 NP 20 mm 10%

11. Model of tissue in study of cardiac pathology 30/10/2014 11 NP 20 mm 10%

12. Model of tissue in study of cardiac pathology 30/10/2014 12 NP 20 mm 10%

13. Model of tissue in study of cardiac pathology 30/10/2014 13

14. Model of tissue in study of cardiac pathology 30/10/2014 14 SC 20 mm

15. Model of tissue in study of cardiac pathology 30/10/2014 15 NSC 20 mm 10%

16. Model of tissue in study of cardiac pathology 30/10/2014 16 NSC 20 mm 10% 1,2 Hrz

17. Model of tissue in study of cardiac pathology 30/10/2014 17 N SC 20 mm 10% 1,2 Hrz

18. Model of tissue in study of cardiac pathology 30/10/2014 18 NSC 20 mm 10% 1,2 Hrz

19. Model of tissue in study of cardiac pathology 30/10/2014 19

20. 30/10/2014 20 The results obtained in the model suggest that ectopic activity may emerge in a sub-critical myocardial region, e.g. comprising cardiomyocytes with moderately depressed sodium-potassium pump, due to its mechanical interactions in the myocardial tissue. Moreover, such ectopic zone may expand by capturing normal regions in myocardium via the electro-mechanical coupling between cardiomyocytes.

21. 30/10/2014 21 THANK YOU for ATTENTION!