S. Schuler, A. Wachter, and O. Dössel. Electrocardiographic Imaging Using a Spatio-Temporal Basis of Body Surface Potentials—Application to Atrial Ectopic Activity. In Frontiers in Physiology, vol. 9:1126, 2018
Electrocardiographic imaging (ECGI) strongly relies on a priori assumptions and additional information to overcome ill-posedness. 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. 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. Measured BSPs are projected onto this basis and reconstructions are expressed as linear combinations of corresponding transmembrane voltage (TMV) basis vectors. The novel method was applied to simulations of 100 atrial ectopic foci with three different conduction velocities. Three signal-to-noise ratios (SNR) and bases of six different temporal lengths were considered. Reconstruction quality was evaluated using the spatial correlation coefficient of TMVs as well as estimated local activation times (LAT). The focus localization error was assessed by computing the geodesic distance between true and reconstructed foci. 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. Mean LAT correlation could be improved by up to 5, 7, and 19% for the three SNRs. For 0 dB, the average localization error could be halved from 15.8 to 7.9 mm. For the largest basis length, the localization error was always below 34 mm. In conclusion, the new method improved reconstructions of atrial ectopic activity especially for low SNRs. Localization of ectopic foci turned out to be more robust and more accurate. 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.
Conference Contributions (2)
S. Schuler, A. Loewe, and O. Dössel. Forcing Transmembrane Voltages to Decrease Slowly: A Temporal Regularization for ECG Imaging. In Computing in Cardiology, vol. 45, 2018
ECG imaging aims to reconstruct the cardiac electrical activity from non-invasive measurements of body surface potentials (BSP) by finding unique and physiologically meaningful solutions to the inverse problem of electrocardiography. This can be accomplished using regularization, which reduces the space of admissible solutions by demanding solution properties that are already known beforehand. Messnarz et. al. proposed a regularization scheme that requires transmembrane voltages (TMV) to not decrease over time. We suggest a generalization of this method that forces TMVs to decrease only slowly and as a result can also be applied to irregular cardiac activity. We first develop the method using a simplified spherical geometry and then show its benefit for imaging fibrillatory activity on a realistic geometry of the atria.
The human heart is an organ of high complexity and hence, very challenging to simulate. To calculate the force developed by the human heart and therefore the tension of the muscle fibers, accurate models are necessary. The force generated by the cardiac muscle has physiologically imposed limits and depends on various characteristics such as the length, strain and the contraction velocity of the cardiomyocytes. Another characteristic is the activation time of each cardiomyocyte, which is a wave and not a static value for all cardiomyocytes. To simulate a physiologically correct excitation, the functionality of the cardiac simulation framework CardioMechanics was extended to incorporate inhomogeneous activation times. The functionality was then used to evaluate the effects of local activation times with two different tension models. The active stress generated by the cardiomyocytes was calculated by (i) an explicit function and (ii) an ode-based model. The results of the simulations showed that the maximum pressure in the left ventricle dropped by 2.3% for the DoubleHill model and by 5.3% for the Lumens model. In the right ventricle the simulations showed similar results. The maximum pressure in both the left and the right atrium increased using both models. Given that the simulation of the inhomogeneously activated cardiomyocytes increases the simulation time when used with the more precise Lumens model, the small drop in maximum pressure seems to be negligible in favor of a simpler simulation model.