Optimising low-energy defibrillation in 2D cardiac tissue with a genetic algorithm

FIGURE 1. Snapshots of voltage spiral-waves for each of the three FK parameter sets.

FIGURE 2. Snapshot of BOCF voltage dynamics. Area-wise, this domain is four times larger than the one used for the FK models, and the peak voltage of the model’s action potential is also notably higher at approx. 1.5 a.u. in comparison.

FIGURE 3. Sketch of the pacing model. Non-overlapping injection sites (green) are distributed across the voltage domain (right panel). Each site has a random efficacy coefficient to modulate the amplitude(s) of the pacing protocol to be applied (left panel). This emulates the effects of different heterogeneity geometries on a local level.

FIGURE 4. Sketch of the pacing-cost metric. The square of each pulse amplitude is integrated over its respective duration, and the sum over all pulses then yields the total cost. The squaring is done to penalise protocols with overly potent singular pulses.

FIGURE 5. The average (squared, absolute-value) Fourier spectrum (red) and the resulting ADP inter-pulse frequencies (orange) as derived from the spectrum integral (blue) for each cardiac-tissue model (rows).

FIGURE 6. ADP protocol dose-response curves for our cardiac-tissue models (bottom) with a separate detailed view of the high-TR region (top). Dots mark each model’s PC thresholds at TR values of 90%, 95%, 99%, and 100%, respectively. Each curve was sampled at 101 equidistant amplitude values with 105 termination attempts across 10 initial conditions.

FIGURE 7. Sketch of the mutation operator. A random protocol parameter (top) is selected and replaced with a randomly chosen value from a pre-defined interval (bottom). As we only considered protocols of constant pulse length, the GA implementations only ever mutated either amplitudes or recovery intervals.

FIGURE 8. Sketch of the crossover operator. Given two randomly chosen source protocols (top, columns), a random pulse (the third one in this case) beyond the first is chosen as the cutoff point for the mergers of the resulting partial protocols (colour-coded). This results in two new protocols for selection (bottom).

FIGURE 9. Overview of the GA-optimised populations for a single initial population (grey marker) per model (rows). These populations (comprising 50 protocols each) only differed in their choices of GA hyperparameters and are compared by their mean PC and TR values. Error bars indicate each metric’s standard deviation. Lastly, dashed red lines show the performance of ADP protocols at a given PC value.

FIGURE 10. Samples for each of the three recurring metric-performance patterns we observed over the course of the GA evaluations. Only PC examples are shown because TR convergence generally exhibited similar patterns (albeit mirrored horizontally).

FIGURE 11. Comparison of population convergence under different initial populations (columns) as well as models (rows). Each final population consisted of 50 pacing protocols and is placed according to its mean PC and TR values. Error bars indicate the corresponding standard deviations.

FIGURE 12. Five examples of top GA-optimised protocols for two FK models (rows). These protocols had the highest TR with the lowest PC among their respective populations. Said populations were generated by a single 104-generation application of our GA using one set of hyperparameters and initial population per model.