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 Sciences2Ural Federal University, Yekaterinburg, Russia

Workshop MMMBM, October 29-31, 2014

Heterogeneity – an attribute of normal myocardium

Anatomy of the heart wall

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Functional heterogeneity of myocardium

HETEROGENEITY – an ATTRIBUTE of NORMAL MYOCARDIUM

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Temporal gradients of activation

A sequence of activation of ventricular regions from the endocardium to the epicardium, and from the apex to the base.

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

Wan X, Bryant S et al., 2003

Experimental data on isolated cells

Laurita K, et al., 2003

ENDO, EPI and MID- myocytes of LV wall differ in their electrophysiological and mechanical properties

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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 ischemiaSubepicardial ischemia

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Experimental data on isolated cells

Qi X. et al., 2000

Experimental data on isolated tissue

Lukas A. et al., 1993

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Left figure from Bers D. Cardiac excitation–contraction coupling,2002

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/

Solovyova O. et al. Inter J Bifurcation & Chaos. 2003

Ekaterinburg - Oxford modelRheological scheme of

cardiomyocyte

CE – contractile element

(sarcomere)

PE, SE – parallel and series elastic

elements

XSE – external series elastic element

VS – parallel viscous element

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Electrical block of the model

Solovyova O. et al. Inter J Bifurcation & Chaos. 2003

Membrane potential

Noble D. 1998

Vm – membrane potential Cm – membrane capacity

ii – ionic current

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Ionic currents:

gx – channel conductivityEx – reversal potential[X]o и [X]i –extracellular and intracellular ion concentration

Noble D. 1998

Electrical block of the model

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Mechanical block of the model

Sulman et al., Bulletin of mathematical biology. 2008

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

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Rheological scheme of cardiomyocyte

CE – contractile element

(sarcomere)

PE, SE – parallel and series elastic

elements

XSE – external series elastic element

VS – parallel viscous element

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Cooperative Mechanisms

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 concentration of strongly bound XBr (N) about each Ca-TnC complex (aoff depends 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

Nk-N)-(1(A,...)k dt

dN

A)

K

A(1

1)

A

N(a-CaA)-(1a

dt

dA

offon

moffon

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Heterogeneity in ENDO and EPI model parameters and modeled cell activity

Vasilyeva A., Solovyova О. CinC. 2012.

Vasilyeva A., Solovyova О. Biophysics. 2012.

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Weiss et al., 1991

t,min [ATP],mM [K+]0,mM

0 6.8 4.05 6.1 5.6

10 4.8 7.815 3.4 9.4

Simulation of cell responses to the acute ischemia

Input model parameters of time-dependent changes in [ATP]i and in [K+]o during 5, 10, and 15 minutes of the acute ischemia.

Experimental data

Model parameters

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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.

Equations are adapted from Rudy et al., 1997

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

Simulation of cell responses to the acute ischemiaModeling ATP-sensitive potassium current IK(ATP)

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Experimental data from Furukawa et al., 1991

ENDO EPI

k0.5, µM 23.6 97.6

h 2.09 1.59

Simulation of cell responses to the acute ischemia

Model parameters

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

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

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Continuous model of cardiac muscle fiber

Vikulova N. et al. Russ J Numer Anal Math Modelling. 2014. 18

Continuous model of cardiac muscle fiber

l1(x,t) – sarcomere deformation

l (x,t) – cell deformation

Global parameters Local parameters

ˆ( )( )

l t xl x t

x

Micro- and macro mechanics coupling

- deviation of XSE from slack length

ˆ( )l x t - deviation of cell x from ref. position

)(tlex

Isometric mode of contraction:ˆ( ) ( )F exl x t l t const

3 3(exp( ) 1)x x xPE VS CE ex exF F F F l

Isotonic mode of contraction:𝐹𝑥 = 𝐹𝑒𝑥 = 𝐹ത.

Local deformation of the fiber at point x in the macrospace is equal to the relative deformation of cell x in the microspace. 19

1 point = 1 cell (microlevel)

Boundary conditions Left border: Right border:

( )0FV x t

x

Initial conditions

( 0) restV x V

0,0 xI stim s] 25[0.06;0.06t3

,0

whennAI

x

stim

V(0,t) = VODE(t).

),()(

1

)),(1(

),()),(1(

3

'2

2

txixCtxl

x

Vtxltxl

x

V

Dt

Vion

m

x

Continuous model of cardiac muscle fiberMicro- and macro electrical coupling

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Effects of ischemia in 1D tissue model

Control Ischemia 15 min

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Conclusions:1. 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.

2. 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.

3. 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.

4. 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.

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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).

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