Vectorcardiography (VCG) can evaluate the vector loops of electrocardiographic waves, being a time-spatial representation of the heart vector into the three orthonormal leads. During atrial fibrillation (AF), F waves reflect the disorganized depolarization of the atria, replacing the organized P wave. Usually, paroxysmal AF (PAF) spontaneously terminates, differently from chronic AF (CAF), possibly due to the still-preserved main direction of the P-wave vector loop. To investigate this hypothesis, this study aims to evaluate the similarities between the P-wave vector loop and F-wave vector sway in subjects affected by PAF and CAF. Overall, 10-s VCG were acquired from 10 healthy (HEA) subjects showing normal sinus rhythm, 10 subjects affected by PAF (one during normal sinus rhythm and one during AF), and 10 subjects affected by CAF. P waves were extracted using ECGdeli software, while F waves were extracted after QRST cancellation. Ellipse axes and eccentricities were calculated as the root mean square of VCG components and the ratio between axes, respectively. Overall, 84 beats of HEA, 205 beats of PAF (89 beats during normal sinus rhythm and 116 during fibrillation), and 103 beats of CAF were analyzed. Distributions of axes and eccentricities of PAF are not statistically different (P-value>0.05) than normal sinus rhythm but features related to the Z axis of CAF were statistically lower than PAF (P-value〈10-3). F-wave vector sway in PAF resembles the P-wave vector loop, suggesting the maintenance of the atrial depolarization main direction in subjects with self-terminating AF. Moreover, the F-wave vector sway is more manifest in PAF than in CAF.

Spatial heterogeneity of ventricular repolarization (SHVR) is related to the development of arrhythmias. To assess SHVR, we introduced the V-index, a metric which needs computation of the Dominant T-Wave (DTW) and its derivatives. Theoretically, the larger the number of derivatives, the better the adherence to the modelled T-wave. In practice, only the first derivative is included, as the numerical computation of higher derivatives is corrupted by computation noise. Here, we introduce a parametric method (PM), based on analytic definitions of the DTW, to allow analytical computation of its derivatives. Three analytic forms, based of combination of sigmoidal (S), Gaussian (G) or exponentials (E) functions, were considered. A set of simulated ECGs were generated using a forward ECG model (Matlab version of ECGSIM). SHVR was varied from 5 to 40 ms (5 ms-steps). To simulate real recordings, noise available from the MIT-BIH Noise Stress Test Database was added with different peak-to-peak amplitudes (30, 60, 120 and 180μV). The use of PM allowed the inclusion of a larger number of derivatives in the model and reduced the difference between actual and estimated T-waves, especially for larger SHVR. This reduction was more pronounced for model S and G. However, the model E resulted in a lower estimation bias of V-index with respect to the actual SHVR.

The V-index is a recently-proposed metric related to repolarization heterogeneity (RH) across the myocardium, a key quantity for the development of arrhythmias. The metric is derived from multi-leads ECG recordings and this paper investigates two of its properties: i) the dependency on the lead system (Frank's orthogonal vs. 12 standard leads); ii) the influence of errors in the location of the T-end position. The first investigation was performed by simulations, using a forward ECG model (ECGSIM). In the lead system of interest, the V-index was computed varying the standard deviation of RH (sv). The results showed that the average bias in the estimate of RH (at σφ = 1 ms) ranged from -20.4±4.0% (sv = 20.6 ms) to -26.3±4.0% (sv = 70.9 ms) for the standard system and from -7.0 ± 4.2% to - 19.0 ± 4.2% for the Frank's one. While the bias diminished, the vulnerability to noise slightly increased. Secondarily, 68 ECGs from the E-OTH-12-0068-010 THEW database were analyzed. To simulate mislocation, the T-end point was consistently moved (±20 ms) around its correct position and the V-index computed. The average differences in the V-index estimates across the population were always smaller than 1%. This is a desirable property, given the discrepancies across methods in locating T-end positions.

The cancellation of ventricular activity (VA) from atrial electrogram (AEG) is commonly performed by template matching and subtraction (TMS): a running template, built by adaptive averaging of AEG segments in correspondence of QRS, is subtracted from AEG to uncover atrial activity (AA). In our approach, before subtraction, templates are modulated by a set of coefficients which are estimated by maximizing, via Multiple Particle Swarm Optimization (MPSO), a fitness function based on: 1) the energy of the estimated and measured AA; 2) the first derivative of the estimated and measured AA; 3) the similarity between the template and its modulated version. To validate the method, three datasets of 500 synthetic AEG were built. Each signal included background AA, localized AA and VA. We observed that TMS+MPSO provided better performances then TMS alone when the ratio of VA/AA amplitude is large (VA/AA ≥ 3), while the performances get closer when the ratio decreases.

Recently, the research efforts in the context of electrocardiographical recording during atrial fibrillation (AF) has been directed to broaden the understandings on the electrophysiological and structural remodelling occurring during the arrhythmia and on characterizing the different types of AF. Following this line, both surface ECG and endocardial electrograms have been thoroughly studied and a series of linear and non-linear parameters were computed either directly on the electrograms or on the derived activation series. In this paper, we reviewed some signal processing methods used to characterize surface ECG and endocardial electrograms during AF, focusing on spectral and non-linear analysis. In particular, parametric and non-parametric methods for spectral analysis of the residual ECG, i.e. atrial waves obtained from surface ECG after removing ventricular activity, and endocardial recordings are described. The different purposes of spectral analysis (exploring autonomic functions, analysis of spontaneous AF behaviour and predicting therapeutic effects) are illustrated with some examples. In addition, we described some more recent non-linear methods applied to AF, assessing the organization of atrial signals as well as ventricular response in AF. In particular, methods derived from embedding time series and based on entropy computation are illustrated and exemplified.