effect of mechanical factors on rhythm disturbances in mathematical model of cardiac fiber...

Effect of mechanical factors on rhythm disturbances in mathematical model of

cardiac fiber

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Alexander Kursanov, L.B. Katsnelson, N.A. Vikulova, O.E. Solovyova,

V.S. Markhasin

Institute of Immunology and Physiology of the UB RASUral Federal University

6th Russian Workshop on Mathematical Models and Numerical Methods in Biomathematics

Continuous model of cardiac muscle

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Model of ventricular

cardiomyocyte «Ekb-Oxford»

Katsnelson L.B., et al., Russ J Numer

Anal Math Modelling. 2014

EC coupling in cardiomyocytes

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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

NlkNllCakdt

dNTnC )()1(),]([ 111

, ][])[,(][])[]([][ 2

TnCTnCoffiTnCtotTnConTnC CaCaNkCaCaCakdt

Cad

Experimental validation of cellular modeling predictions

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N (normal NKP) SC (sub-critical NKP inhibition and Ca2+ SR

overload)

P (pathological NKP inhibition and Ca2+ SR

overload)

Km,Na<37 mMKm,Na<153%*

37 mM≤Km,Na<40 mM153%*≤Km,Na<165%*

Km,Na≥40 mMKm,Na≥165%*

Sulman et al., Bull Math Biol, 2008

NaNa++-Ca-Ca2+2+ exchangerexchanger

Reduced Reduced NaNa++-K-K++ pump pump

Gradual increase Gradual increase in [Nain [Na++]]ii

Accumulation ofAccumulation of CaCa2+2+ in cytosol in cytosol

NaNa++-Ca-Ca2+2+ exchangerexchanger

Spontaneous CaSpontaneous Ca2+2+ release release to cytosol between stimulito cytosol between stimuli

SpontaneousSpontaneousAPAP

SpontaneousSpontaneouscontractioncontraction

Accumulation Accumulation of Caof Ca2+2+ in SRin SR

CaCa2+ 2+ overload of overload of SR terminal cisternsSR terminal cisterns

Experimental validation of cellular modeling predictions

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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 Lmax 0,88 Lmax 0,85 Lmax 0,82 Lmax

Continuous model of cardiac muscle

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Micro- and macroelectrical links

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Boundary conditions

Left border: Right border:

Initial conditions

Links between micro- and macromechanics

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Global parameter

Local parameters

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Model of tissue in study of cardiac pathology

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NP20 mm

10%


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N P20 mm

10%


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NP20 mm

10%


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SC20 mm


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NSC20 mm

10%


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NSC20 mm

10% 1,2 Hrz


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N SC20 mm

10%1,2 Hrz


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NSC20 mm

10% 1,2 Hrz


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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.

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effect of mechanical factors on rhythm disturbances in mathematical model of cardiac fiber...

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