Effect of mechanical factors on rhythm disturbances in mathematical model of cardiac fiber 30/10/ 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

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

EC coupling in cardiomyocytes 30/10/ 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

Experimental validation of cellular modeling predictions 30/10/ 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

Experimental validation of cellular modeling predictions 30/10/ 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

Continuous model of cardiac muscle 30/10/2014 6

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

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

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

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

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

Model of tissue in study of cardiac pathology 30/10/

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

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

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

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

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

Model of tissue in study of cardiac pathology 30/10/

30/10/ 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.

30/10/ THANK YOU for ATTENTION!