Novel hybrid method for interpolating missing information in body surface potential maps

Body surface potential mapping (BSPM) provides additional electrophysiological information that can be useful for the detection of cardiac diseases. Moreover, BSPMs are currently utilized in electrocardiographic imaging (ECGI) systems within clinical practice. Missing information due to noisy recordings, poor electrode contact is inevitable. In this study, we present an interpolation method that combines Laplacian minimization and principal component analysis (PCA) techniques for interpolating this missing information.

The dataset used consisted of 117 lead BSPMs recorded from 744 subjects (a training set of 384 subjects, and a test set of 360). This dataset is a mixture of normal, old myocardial infarction, and left ventricular hypertrophy subjects. The missing data was simulated by ignoring data recorded from 7 regions: the first region represents three rows of five electrodes on the anterior torso surface (high potential gradient region), and the other six regions were realistic patterns that have been drawn from clinical data and represent the most likely regions of broken electrodes. Three interpolation methods including PCA based interpolation, Laplacian interpolation, and hybrid Laplacian-PCA interpolation methods were used to interpolate the missing data from the remaining electrodes. In the simulated region of missing data, the calculated potentials from each interpolation method were compared with the measured potentials using relative error (RE) and correlation coefficient (CC) over time. In the hybrid Laplacian-PCA interpolation method, the missing data are firstly interpolated using Laplacian interpolation, then the resulting BSPM of 117 potentials was multiplied by the (117 × 117) coefficient matrix calculated using the training set to get the principal components. Out of 117 principal components (PCs), the first 15 PCs were utilized for the second stage of interpolation. The best performance of interpolation was the reason for choosing the first 15 PCs.

The differences in the median of relative error (RE) between Laplacian and Hybrid method ranged from 0.01 to 0.35 (p < 0.001), while the differences in the median of correlation between them ranged from 0.0006 to 0.034 (p < 0.001). PCA-interpolation method performed badly especially in some scenarios where the number of missing electrodes was up to 12 or higher causing a high region of missing data. The figures of median of RE for PCA-method were between 0.05 and 0.6 lower than that for Hybrid method (p < 0.001). However, the median of correlation was between 0.0002 and 0.26 lower than the figure for the Hybrid method (p < 0.001).

Comparison between the three methods of interpolation (Laplacian, PCA, Hybrid) in reconstructing missing data in BSPM showed that the Hybrid method was always better than the other methods in all scenarios; whether the number of missed electrodes is high or low, and irrespective of the location of these missed electrodes.