Non-Invasive Electroanatomical Mapping: A State-Space Approach for Myocardial Current Density Estimation

Figures

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  Figure 1. Schematic overview of the current density estimation algorithm.

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  Figure 2. Block diagram of the assumed connectivities between the six considered voxel types and the input function u. The input function u is connected to the sinoatrial node. The other arrows indicate allowed connections between neighboring voxels. For example, a direct connection from atrium to ventricleis not allowed. Instead, the propagation has to pass through the atrioventricular node and the HIS-Purkinje system before reaching the ventricles. Voxels of type pathological are not connected to other voxels in this model and, therefore, never excited. (Figure adapted from [24]).

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  Figure 3. Overview of the used simulation setup. (a) Voxel types of the ground truth model: The colors of the voxels correspond to their type as depicted in Figure 2. A region of pathological tissue is present in the right ventricle. (b) Voxel types of the initial model: The initial model assumes a healthy heart without any pathological regions. (c) The difference in voxel types: red regions stand for differences between the ground truth and initial model. Green regions stand for equalities. (d–i) The L1-norm of the current densities in each voxel. (d–f) During the time of the maximal difference between ground truth and initial model (t=0.3675 s). (g–i) The maximum of this L1-norm over the complete cardiac cycle. (j–l) The simulated magnetic fields z around the time of the QRS-complex. The black dashed line corresponds to the time of the maximum difference between the ground truth and the initial model (t=0.3675 s).

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  Figure 4. The results of applying the pseudoinverse solution to the data generated by the ground truth model introduced in Figure 3. (a) The estimated measurements in pT. (b) The difference between the predicted measurements and the ground truth measurements (cf. Figure 3j). (c) Maximum of the L1-norm of the current densities in each voxel over the complete cardiac cycle. (d) The difference between these maxima and those of the ground truth (cf. Figure 3g).

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  Figure 5. The results of the nested state-space optimization procedure after 2000 epochs. (a) The loss over the first 500 epochs. (b) The estimated magnetic measurements in pT. (c) The difference between these estimates and the ground truth (cf. Figure 3j). (d) Maximum of the L1-norm of the current densities in each voxel throughout the cardiac cycle. (e) The difference between these maxima and those of the ground truth (cf. Figure 3g). (f) The DICE score for different segmentation thresholds. A threshold of 0.88 achieves the maximum DICE score of 0.84. (g) The predicted voxel types for a threshold of 0.88. The color-coded regions stand for: green—true positive (TP), blue—true negatives (TN), orange—false positive (FP), and red—false negatives (FN).