Conduction Block in the Human Ischemic Myocardium: Insights from a 1D Electromechanical Model

Figures

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  Figure 4. Occurrence of excitation conduction block in a 1D myocardial model at 15 min of ischemia is shown under three conditions: without reduction in the diffusion coefficient (IM115 model) and with the diffusion coefficient D reduced by factors of 1.5 and 2 (IM215 models), from left to right. The panels display events occurring between the 18th and 23rd simulated stimuli. (Upper panels) Membrane potential traces for cardiomyocytes within the 1D strand. Depending on the model used and the coefficient D, some stimuli trigger action potentials, whereas some stimuli elicit only short-lived, low-amplitude spikes that are incapable of triggering an action potential. These transient depolarizations are similar to the electrotonic responses of non-excitable tissue to external electrical stimulation. (Middle panels) Membrane potential along the 1D strand. The vertical axis shows the position along the strand’s length. In this representation, the strand is shown in its unstretched state, where each point on the axis corresponds to a single cell. The horizontal axis represents time. Regions where the membrane potential is above the resting potential are shown in white, while gray indicates…

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  Figure 1. Changes during ischemia at 0, 5, 10, and 15 min of the acute ischemia in simulated isometric contractions of a single cell. (a) Time course of action potential (AP) generation; (b) active force generated by the cardiomyocyte; (c) intracellular Ca2+ concentration (Cai); (d) ATP-sensitive potassium current (iK,ATP). All presented signals are steady states for the corresponding stage of ischemia. Force in panel (b) is normalized to the peak value in the healthy myocyte (0 min).

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  Figure 2. Changes during ischemia at 0, 5, 10, and 15 min of the acute ischemia in the 1D strand simulation. (Left) Changes in action potential duration at 90% repolarization level (APD90) in cells along the strand. (Middle) Active force generated by the strand in isometric contractions (normalized to its peak value for the healthy state). (Right) Arrival time of the depolarization wave to each cell. The traces for the 15 min ischemia correspond to the first 18 stimuli following the onset of this ischemic phase. Subsequently, a conduction block occurred.

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  Figure 3. Time course of the fast Na+ current iNa (a) and its components according to Equation (5) at 0 (solid lines), 5 (dash-dotted lines), 10 (dotted lines), and 15 (dashed lines) minutes of the acute ischemia during simulated isometric contractions of a single cell within the first 5 ms after stimulus, when iNa is active. V represents the action potential (b); m, h and j are voltage-dependent gating variables of iNa (c); and V-ENa is the driving force for Na+ (d).

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  Figure 5. Comparison of Ca2+ transients (a), intracellular Na+ concentration dynamics (b), Na+-Ca2+ exchange current (c), and action potential (d) in the first cell of the 1D IM115 model during the last twitch before the onset of the block (solid lines), and in a specially tuned model of the single isolated cell with identical parameters (dashed lines), which is stimulated with the same initial conditions as this cell in the 1D strand (see the text for more details). Time on the axes of the panels is shown starting from the moment of the last stimulus before the onset of the block in the IM115 model.

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  Figure 6. Fast sodium current iNa in the tuned virtual isolated cell (trace 1) and in the first cell of the 1D IM115 model immediately before the block (trace 2) and during the block onset (trace 3).

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  Figure 7. Safety factor (SF, upper panel) and contractile element force (FCE, bottom panel) in cardiomyocytes of a 1D strand during local ischemia at 15 min. The traces show the response to the 36th stimulus applied to the left edge of the strand (pacing rate 1 Hz). The bar under the panels indicates the strand regions: normal areas (white), border zone (light gray), and ischemic area (black). All parameters in the border zone change linearly from normal to ischemic values. Symbols on the curves mark the cells for which SF and FCE values were measured (values normalized to the strand force in normal conditions). The vertical dotted line marks the cell where the conduction block occurs.

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  Figure 8. Schematic representation of (a) single-cell mechanics and (b) mechanics of a 1D virtual strand of cardiac tissue under isometric conditions. The inset in panel (b) shows the rheological scheme of a single cardiomyocyte (cell x) used at point x of the strand. (a,b): The contractile element CE (CEx) is connected in series and parallel to passive elastic elements (SE, SEx and PE, PEx, respectively). A viscous element VS (VSx) is placed in parallel with the parallel elastic element PE (PEx). XSE is an external in-series elastic element (relative to the cells). Current changes in the lengths of PE, CE (PEx, CEx) and XSE normalized to their slack lengths are denoted as l(t), l1(t) (l(x,t), l1(x,t)) and lex(t), respectively. (b): The distance [0, xF] corresponds to the slack length of the virtual 1D strand. The variable l^(x,t) represents the displacement of cell x from its initial position in the unstretched and relaxed strand. The excitation wave propagates from the left to the right end of the 1D strand (as indicated by the arrow).

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  Figure 9. Schematic representation of ionic membrane currents and intracellular Ca2+ handling in the single cardiomyocyte model (TP+M model). Ion translocation across the sarcolemma involves voltage- and time-dependent currents: L-type Ca2+ current (iCaL), background Ca2+ current (ibCa), fast Na+ current (iNa), background Na+ current (ibNa), inward rectifier K+ current (iK1), transient outward current (ito), rapid and slow delayed rectifier K+ currents (iKr, iKs), and plateau K+ current (ipK). The model also includes the specific ATP-sensitive K+ current (iKATP) to simulate ischemic conditions. Additional modeled currents include the sarcolemmal Ca2+ pump (ipCa), Na+-K+ pump (iNaK), and Na+-Ca2+ exchanger (iNaCa). In the 1D tissue model, the electrical propagation between cardiomyocytes is mediated by non-selective ionic currents across gap junctions (GJs). Specific ionic currents through GJs are not explicitly included in either the isolated single cardiomyocyte model or the cellular submodels of the continuous 1D model. The GJ conductance in the 1D model is represented by the electrodiffusion coefficient (Equation (4)). Intracellular Ca2+ dynamics comprise release from the sarcoplasmic…