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Transmural heterogeneity of myocardium in norm and pathology

Transmural heterogeneity of myocardium in norm and pathology. Anastasia Vasilyeva 1,2 , Nathalie Vikulova 1 , Olga Solovyova 1,2 , Vladimir S. Markhasin 1,2 1 Institute of Immunology and Physiology, Ural Branch of Russian Academy of Sciences 2 Ural Federal University, Yekaterinburg, Russia.

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Transmural heterogeneity of myocardium in norm and pathology

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  1. Transmural heterogeneity of myocardium in norm and pathology Anastasia Vasilyeva1,2, Nathalie Vikulova1, Olga Solovyova1,2, Vladimir S. Markhasin1,2 1Institute of Immunology and Physiology, Ural Branch of Russian Academy of Sciences 2Ural Federal University, Yekaterinburg, Russia Workshop MMMBM,October29-31, 2014

  2. Anatomy of the heart wall Heterogeneity – an attribute of normal myocardium 2

  3. Functional heterogeneity of myocardium HETEROGENEITY – an ATTRIBUTE of NORMAL MYOCARDIUM Temporal gradients of activation Mechanical gradients These include transmural and apex-base gradients of passive and active mechanical properties, with tension increasing from epicardium to endocardium, and from apex to base A sequence of activation of ventricular regions from the endocardium to the epicardium, and from the apex to the base. 3

  4. Experimental dataon isolated cells Laurita K, et al., 2003 ENDO, EPI and MID- myocytes of LV wall differ in their electrophysiological and mechanical properties Wan X, Bryant S et al., 2003 4

  5. Ischemia Ischemia – is a restriction in blood supply to tissues, causing a shortage of oxygen and glucose needed for cellular metabolism. Ischemic heart disease is the most common cause of death in most Western countries and a major cause of hospital admissions. Subendocardial ischemia Subepicardial ischemia 5

  6. Experimental dataon isolated cells Qi X. et al., 2000 Experimental dataon isolated tissue Lukas A. et al., 1993 6

  7. Ekaterinburg - Oxford model Rheological scheme of cardiomyocyte CE – contractile element (sarcomere) PE, SE – parallel and serieselastic elements XSE – externalseries elastic element VS – parallel viscous element Solovyova O. et al. Inter J Bifurcation & Chaos. 2003 Sulman T. et al. Bulletin of mathematical biology. 2008 The CellML-model representation can be found at the repository at http://models.cellml.org/e/b9/ Left figure from Bers D. Cardiacexcitation–contractioncoupling,2002 7

  8. Electrical block of the model Solovyova O. et al. Inter J Bifurcation & Chaos. 2003 Membrane potential Vm– membrane potential Cm – membrane capacity ii– ionic current Noble D. 1998 8

  9. Electrical block of the model Ionic currents: gx–channel conductivity Ex–reversal potential [X]o и [X]i–extracellular and intracellular ion concentration Noble D. 1998 9

  10. Mechanical block of the model Rheological scheme of cardiomyocyte Sulmanet al., Bulletin of mathematical biology. 2008 CE – contractile element (sarcomere) PE, SE – parallel and serieselastic elements XSE – externalseries elastic element VS – parallel viscous element l1 - deviation of SE from slack length, l2 - deviation of PE from slack length, l3- deviation of XSE from slack length FXSE = FPE+FCE+FVS 10

  11. Type A. Affinity of TnC for Ca2+ increases with [Ca-TnC] (A=[Ca-TnC], aoff depends on A). • Type B.Affinity of TnC for Ca2+ increases with mean concentrationof strongly bound XBr (N) about each Ca-TnC complex (aoffdepends on N/A). • Type C. Fraction of active sites on the thin filament in the overlap zone increases cooperatively due to tropomyosin end-to-end interaction. From A. M. Gordon, M. Regnier, and E. Homsher. Skeletal and Cardiac Muscle Contractile Activation: Tropomyosin “Rocks and Rolls”. News Physiol. Sci. 16:49 –55, 2001 Cooperative Mechanisms 11

  12. Heterogeneity in ENDO and EPI model parameters and modeled cell activity Vasilyeva A., Solovyova О. Biophysics. 2012. Vasilyeva A., Solovyova О. CinC. 2012. 12

  13. Simulation of cell responses to the acute ischemia Experimental data Model parameters Weiss et al., 1991 Input model parameters of time-dependent changes in [ATP]i and in [K+]o during 5, 10, and 15 minutes of the acute ischemia. 13

  14. Simulation of cell responses to the acute ischemia Modeling ATP-sensitive potassium current IK(ATP) gK(ATP) - is the maximum conductance at [ATP]i = 0 mM; PATP- is the open probability of the KATP channel at a given ATP concentration which increases with decreasing [ATP]i; n– model parameter; Vm- membrane potential; EK- K+ reversal potential. k0.5 – is the [ATP]i at which 50% of the KATP channels are open (half-maximal saturation point); h– Hill coefficient characterizing the steepness of relationship Equations are adapted from Rudy et al., 1997 14

  15. Simulation of cell responses to the acute ischemia Model parameters Experimental data from Furukawa et al., 1991 15

  16. Ischemia effects on the electrical activity of single ENDO and EPI cells 16

  17. Ischemia effects on the mechanical activity of single ENDO and EPI cells 17

  18. Continuous model of cardiac muscle fiber Vikulova N. et al. Russ J Numer Anal Math Modelling. 2014. 18

  19. Continuous model of cardiac muscle fiber - deviation of cell x from ref. position Micro- and macro mechanics coupling Isometric mode of contraction: Isotonic mode of contraction: Global parameters Local parameters l1(x,t) – sarcomere deformation l (x,t) – cell deformation - deviation of XSE from slack length Local deformation of the fiber at point x in the macrospace is equal to the relative deformation of cell x in the microspace. 1 point = 1 cell (microlevel) 19

  20. Continuous model of cardiac muscle fiber Micro- and macro electrical coupling Boundary conditions Initial conditions Left border: Right border: V(0,t) = VODE(t). 20

  21. Effects of ischemia in 1D tissue model Control Ischemia 15 min 21

  22. Conclusions: • Modeling results suggest a significant increase in the transmural heterogeneity of the electrical and mechanical activity between EPI and ENDO cells under ischemia, which is consistent with experimental data. • Models suggest that distinguishing ATP-sensitivity of IK(ATP) currents in ENDO and EPI cells may contribute to greater electrical effects of ischemia on EPI cells. Models also predict greater mechanical effects of ischemia on EPI cells as compared to ENDO cells. • In the tissue model, ischemia causes an increase in the electrical heterogeneity between coupled cells and an increase in dispersion of repolarization as substrate for arrhythmia. • Unexpectedly, effects of ischemia on tissue mechanics were less pronounced then that in isolated cells suggesting a compensation mechanism of interaction between the coupled cells. 22

  23. Acknowledgements Institute of Immunology and Physiology: Laboratory of mathematical physiology Ural Federal University This work was supported by The Russian Science Foundation (#14-35-00005). 23

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