Reconstructing the heart's electrical activity from non-invasively measured body surface potentials (BSP) is known as the inverse problem of electrocardiography ( Pullan et al., 2010). Preliminary experiments indicate that the basis generalizes to some extent from the training data and may even be applied for reconstruction of non-ectopic activity. Localization of ectopic foci turned out to be more robust and more accurate. In conclusion, the new method improved reconstructions of atrial ectopic activity especially for low SNRs. For the largest basis length, the localization error was always below 34 mm. For 0 dB, the average localization error could be halved from 15.8 to 7.9 mm. Mean LAT correlation could be improved by up to 5, 7, and 19% for the three SNRs. Compared with an optimally parameterized Tikhonov-Greensite method, the BSP basis reconstruction increased the mean TMV correlation by up to 22, 24, and 32% for an SNR of 40, 20, and 0 dB, respectively. The focus localization error was assessed by computing the geodesic distance between true and reconstructed foci.
Reconstruction quality was evaluated using the spatial correlation coefficient of TMVs as well as estimated local activation times (LAT). Three signal-to-noise ratios (SNR) and bases of six different temporal lengths were considered. The novel method was applied to simulations of 100 atrial ectopic foci with three different conduction velocities. Measured BSPs are projected onto this basis and reconstructions are expressed as linear combinations of corresponding transmembrane voltage (TMV) basis vectors.
In this work, we attempt to address this problem by constructing a spatio-temporal basis of body surface potentials (BSP) from simulations of many focal excitations. The major challenge of obtaining good reconstructions consists in finding ways to add information that effectively restricts the solution space without violating properties of the sought solution.