Generation of ECG signals from a reaction-diffusion model spatially discretized

Figures

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  Figure 1. Diagram relating the cardiac natural pacemakers to the nonlinear variables x1 − x6 of the discretized BVAM model (2). Here, the action potentials of the SA node, AV node, and His-Purkinje complex are represented by coupled three oscillators, respectively.

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  Figure 2. Phase portraits for four different values of the control parameter H, after t = 500 seconds. (a) H = 7, (b) H = 2.74, (c) H = 2.72972, and (d) H = 2.7126. In the insets, the corresponding time series (in seconds) for the x4 variable are shown. Numerical simulations were carried out with C = 1.35 and β = 4.

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  Figure 3. Numerically calculated bifurcation diagram of model (3) using AUTO. (a) Supercritical Hopf (HB), period doubling (PD), and torus (TR) bifurcations are detected at H = 8.779267, 2.742524 and 2.72972, respectively. Here, red line corresponds to a family of stationary states and blue line to a set of stable limit cycles. Periodic solutions with half the frequency are indicated by the green line. Finally, the loss of stability in the period doubling gives place to the quasi-periodicity (black line). Small perturbations transform the quasiperiodic orbits into a chaotic motion. (b) Largest Lyapunov exponents as H is varied.

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  Figure 4. ECG’s corresponding to: (a) normal rhythm (H = 3), (c) quasiperiodicity (H = 2.729) and (e) VF (H = 2.164). Their corresponding power spectra, (b), (d) and (f), are shown on the right of each ECG plot, respectively.

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  Figure 5. Time series: (a) The xi variables of (3): i = 1 (blue line), i = 2 (green line), i = 3 (gray line) and i = 4 (red line). (b) Real ECG42. (c) ECG signal obtained from (4).

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  Figure 6. Comparison of ECG plots obtained from experimental observations (top panels) and the reduced system (3) (bottom panels). (a) Sinus tachycardia44, (b) Atrial flutter42, (c) Ventricular tachycardia45 and (d) Ventricular flutter46.

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  Figure 7. Block diagram of the system (3) and the linear combination (4).

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  Figure 8. Proposed analog electronic circuit.

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  Figure 9. Oscilloscope output of the proposed analog electronic circuits for the normal sinus rhythm.