Fast Characterization of Inducible Regions of Atrial Fibrillation Models With Multi-Fidelity Gaussian Process Classification

Figures

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  Figure 1. Overview of the methodology. We predict the regions where AF can be induced using a multi-fidelity Gaussian process classifier. We use the Laplacian eigenfunctions of the atrial geometry to efficiently construct a Gaussian process covariance function that operates directly on the manifold surface. We pace different sites in computational models of AF with low and high resolution to create a dataset to train our classifier. In the end, we obtain an inducibility map that can be used to assess treatments.

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  Figure 2. AF models. Fibrosis distribution in 3 different scenarios: moderate fibrosis [(A), 50% fibrotic tissue], and severe fibrosis (70%) in two different patterns (B), (C). (D) shows PVI and BOX ablation lines.

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  Figure 3. Inducibility of AF in the computer model. Two simulations with different pacing sites (grey stars) and inducibility outputs. The middle plot illustrates the pacing protocol. Top: transmembrane potential resulting from a successful induction of AF and corresponding lead II ECG recording. The stimulation results in a self-sustained activity. Bottom: transmembrane potential resulting from an unsuccessful induction of AF and corresponding lead II ECG recording. The stimulation results in a vanishing wave.

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  Figure 4. Numerical assessment of the Gaussian process classifier. We create different random examples with different correlations lengths (first column) and train a nearest neighbor classifier (second column), a Gaussian process classifier trained with the same data-set as the nearest neighbor classifier (third column), and Gaussian process classifier that adaptively selects the training points through active learning (fourth column). The black bars represent the size of the length scale relative to the atrial geometry.

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  Figure 5. Accuracy of the numerical assessment. We quantify the improvements in accuracy when using a Gaussian process classifier versus the nearest neighbor classifier (top row) and when using a Gaussian process classifier with active learning, versus the baseline nearest neighbor classifier (middle row) for different length scales. The gray lines show the balanced accuracy improvements of the 10 examples for each length scale and the black line shows the mean improvement. The bottom row shows how the average balanced accuracy changes with length scale when the classifiers are trained with 100 samples. The dashed vertical line represents the average geodesic distance between training points of the fixed design.

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  Figure 6. Inducibility maps for the three cases. The performance of the classifiers is analyzed for three cases: a case with no ablation (A), a case with PVI ablation (B) and a case with PVI+BOX ablation (C). In each panel, the leftmost column shows the training set (top) and the single-fidelity Gaussian process classifier trained with 100 low fidelity samples (bottom). In the remainder panels, we show the nearest neighbor, single-fidelity Gaussian process classifier, and multi-fidelity Gaussian process classifier trained with 50 and 100 high fidelity samples. The ground truth points are also shown in these panels.

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  Figure 7. Performance of the classifiers. In (A), the agreement between the low fidelity and the high fidelity model is reported as a confusion matrix, as resulting from 1,800 simulations (900 per fidelity). Moreover, each point is colored according to the case of fibrosis. In (B), we compare the balanced accuracy for the nearest neighbor, single-fidelity, and multi-fidelity classifier, for all nine model scenarios and with a fixed budget of 40 high fidelity simulations.

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  Figure 8. Accuracies for 9 different cases. We show how the balanced accuracy evolves as more samples (from 20 to 100) are available for the multi-fidelity, single-fidelity, and nearest neighbor classifiers. The samples are represented as the cost of running a high fidelity model and the multi-fidelity curve is shifted to the right to account for the cost of 100 low fidelity simulations. The dashed horizontal line represents the accuracy of a Gaussian process classifier trained with 100 low fidelity simulations predicting the high fidelity test set.