Effect of myocyte-fibroblast coupling on the onset of pathological dynamics in a model of ventricular tissue

Figures

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  Figure 1. Pseudocolor image of the transmembrane potential V for the two-dimensional system of size 512 × 512 describing protocols P1: Initiating a wavefront from a position slightly off the center of the simulation domain (a–c) and P2: Creating a spiral wave via S1–S2 stimulation (d–f). Once S1 wave propagates over half the domain, the first quarter of the domain is stimulated (d), creating a curved wavefront (e) that slowly evolves into a complete spiral wave of excitation (f).

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  Figure 2. The effect of M-F coupling on single cell action potential, for Gs = 0 nS (solid line), Gs = 0.5 nS (broken line) and Gs = 2.0 nS (dot-dash) for fibroblasts (a,b) and myofibroblasts(c,d) using resting membrane potentials VFR = −49.7 mV for (a and c) VFR = −24.5 mV for (b and d). Myocyte parameters used (xGCaL = 3 and yGKr = 0.75) do not produce EADs in the absence of coupling.

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  Figure 3. The value of parameter xGCaL at which the transition from NO EAD to EAD state occurs is plotted as a function of the strength of M-F coupling for values of yGKr = 0.4 (a,d), 0.8 (b,e) and 1.2 (c,f) respectively for C = 6.3 pF (circles) and C = 50 pF (square). Panels (a–c) correspond to resting membrane potential VFR = −49.7 mV, while panels (d–f) correspond to the case when VFR = −24.5 mV.

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  Figure 4. Characterizing the different possible dynamical states and their corresponding time series, due to M-F coupling for stimulation P2. The columns correspond to spiral wave (SW), spiral fibrillation (SFb and SFa) and oscillatory dynamics respectively. The rows correspond to voltage, state of L-type Ca gates (=dff2fCass) and Na gates (=m3hj) respectively. Fully open gates have a value of 1, while fully closed gates have value 0. Parameters used are yGKr = 0.2, Gs = 0.5, with fibroblasts occupying 10% of the randomly chosen lattice points. The values of x (multiples of GCaL) are 2.25, 3.0, 3.5 and 4.75 for SW, SFa, SFb and OSC states respectively.

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  Figure 5. Two-parameter phase diagram of the steady state dynamics for a 2D system with 30% fibroblasts inserted randomly between myocytes and stimulated via protocol P2. The x and y axis correspond to the factor by which GCaL and GKr are multiplied. The phase portraits are shown for three different coupling strengths Gs = 0.5 nS, 2.0 nS and 4.0 nS. While (a) corresponds to the case with no fibroblasts, (b–d) are portraits for Fibroblast-1(C = 6.3 pF, VFR = −49.7 mV) and (e–g) are phase diagrams for Fibroblast-2 (C = 50 pF and VFR = −24.5 mV). The colormap indicates the different dynamical states observed, viz. stable rotating spiral wave (SW), spiral fibrillation driven by sodium waves (SFb), spiral fibrillation driven by calcium waves (SFa) and fibrillation due to phase waves (OSC).

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  Figure 6. Two-parameter phase diagram of the steady state dynamics for a 2D system with 30% fibroblasts inserted randomly between myocytes and stimulated via protocol P1. The axes correspond to the factors by which GCaL and GKr are multiplied. The phase portraits are shown for three different coupling strengths Gs = 0.5 nS, 2.0 nS and 4.0 nS. While (a) corresponds to the case with no fibroblasts, (b–d) are portraits for Fibroblast-1(C = 6.3 pF, VFR = −49.7 mV) while (e–g) are phase diagrams for Fibroblast-2 (C = 50 pF and VFR = −24.5 mV). The colormap indicates the different dynamical states observed, viz. wave propagation without any oscillation in action potential (NO EAD), a propagating wave with oscillations in action potential but no persistent activity (EAD), spiral fibrillation consisting of many sources of activation (SF includes both SFb and SFa) and oscillatory fibrillation (OSC).

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  Figure 7. Effect of M-F coupling on the percentage of cases that result in non-trivial pathological dynamics (such as SFa or SFb or OSC) as a function of strength of coupling. N1 and N2 are the number of non-trivial cases resulting from protocol P2 and P1 respectively. The results are shown for both Fibroblast-1 (a) and Fibroblast-2 (b).

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  Figure 8. Pseudocolor images of transmembrane potential highlighting the location of initiation of reentrant activity for fibroblast fractions 10% (a,b) and 20% (c,d). For panels (a,b,d) Fibroblast-2 (C = 50 pF and VFR = −49.7 mV) is used, while for panel (c) Fibroblast-1 (C = 6.3 pF and VFR = −24.5 mV) is used.