Interpolation of body surface potential maps

The performance of four methods for interpolation of body surface potential maps (BSPMs) for different electrode grid densities was assessed. This study is part of a research project on the influence of the variability of 12-lead electrocardiograms on computer interpretation due to small electrode position changes. Interpolated BSPMs can be used to simulate this variability. The set of BSPMs studied, derived from a 117-electrode grid with relatively many electrodes on the left precordial part of the thorax, consisted of 232 cases without abnormalities, 277 with infarction, and 237 with left ventricular hypertrophy. The interpolation methods used were fast Fourier transforms, Chebyshev polynomials, linear functions, and cubic splines (CS). In the horizontal plane, a reference signal was first interpolated and, thereafter, resampled using 11 different sets of electrodes with the number of electrodes ranging from 18 down to 8. In the vertical direction, five grids with electrodes only on the front of the thorax and nine grids with electrodes on the front and back were examined. As a performance measure for interpolation, mean absolute error (MAE) was used: the absolute differences between the reference signal and the interpolated signal, averaged over the QRS on all maps. All methods showed deteriorating performance for decreasing grid density. In the horizontal direction, CS proved to be slightly superior to other methods for the left precordial electrodes for all but the densest grid (e.g., MAE = 22.8 microV vs MAE > 24.8 microV for a 12-electrode grid). For electrodes not in that area, CS performed the best as well (MAE = 16.1 microV for the same grid), with differences with the other methods being small (MAE > 16.4 microV). In the vertical direction, CS showed the best results on the front, both for the dense nonperiodic (MAE = 19.1 microV vs MAE > 26.6 microV for a 6-electrode grid) and periodic grids (MAE = 25.1 microV vs MAE > 26.6 microV for a 12-electrode grid). Linear functions performed best for sparse nonperiodic grids and sparse periodic grids for electrodes on the back, with the difference with CS for the last case being small. The method CS performed best overall, and is recommended for interpolating BSPMs.