A new algorithm for estimating the ν-index using sinusoidal basis functions

Recently it was shown that the spatial dispersion of ventricular repolarization (SHVR) can be assessed from the surface ECG using a metric termed ν-index. In this paper, a new algorithm is presented for estimating the ν-index, allowing the inclusion of higher order terms with ease, even in the presence of noise, leading to more accurate estimates. We first introduced a new analytical model for the derivative of the average transmembrane potentials during repolarization (the dominant T-wave) based on trigonometric functions. This functional set is closed under the operation of derivation. Therefore, the nonlinear iterative optimization required by previous methods is no longer necessary. Then, we suggested an iterative linear matrix factorization method to properly estimate the leads factors and the ν-index. Several synthetic SHVR (in the range 20 to 70 ms) were simulated, employing a publicly-available forward electrophysiological model (ECGSIM), leading to a total of 240 synthetic 8-lead electrocardiographical recordings (ECG), each composed of 128 beats. Then the ν-index was estimated with the newly introduced method and compared (root mean square error, RMSE) with the theoretical values, available for each series. The simulation results confirmed the theoretical expectations and indeed showed that the ν-index estimates were improved by increasing the number of lead factors included (RMSE=0:295±0:037 vs 0:280±0:038 for 2 and 8 lead factors respectively).