A new LMS algorithm for analysis of atrial fibrillation signals

Abstract

BackgroundA biomedical signal can be defined by its extrinsic features (x-axis and y-axis shift and scale) and intrinsic features (shape after normalization of extrinsic features). In this study, an LMS algorithm utilizing the method of differential steepest descent is developed, and is tested by normalization of extrinsic features in complex fractionated atrial electrograms (CFAE).MethodEquations for normalization of x-axis and y-axis shift and scale are first derived. The algorithm is implemented for real-time analysis of CFAE acquired during atrial fibrillation (AF). Data was acquired at a 977 Hz sampling rate from 10 paroxysmal and 10 persistent AF patients undergoing clinical electrophysiologic study and catheter ablation therapy. Over 24 trials, normalization characteristics using the new algorithm with four weights were compared to the Widrow-Hoff LMS algorithm with four tapped delays. The time for convergence, and the mean squared error (MSE) after convergence, were compared. The new LMS algorithm was also applied to lead aVF of the electrocardiogram in one patient with longstanding persistent AF, to enhance the F wave and to monitor extrinsic changes in signal shape. The average waveform over a 25 s interval was used as a prototypical reference signal for matching with the aVF lead.ResultsBased on the derivation equations, the y-shift and y-scale adjustments of the new LMS algorithm were shown to be equivalent to the scalar form of the Widrow-Hoff LMS algorithm. For x-shift and x-scale adjustments, rather than implementing a long tapped delay as in Widrow-Hoff LMS, the new method uses only two weights. After convergence, the MSE for matching paroxysmal CFAE averaged 0.46 ± 0.49μV2/sample for the new LMS algorithm versus 0.72 ± 0.35μV2/sample for Widrow-Hoff LMS. The MSE for matching persistent CFAE averaged 0.55 ± 0.95μV2/sample for the new LMS algorithm versus 0.62 ± 0.55μV2/sample for Widrow-Hoff LMS. There were no significant differences in estimation error for paroxysmal versus persistent data. From all trials, the mean convergence time was approximately 1 second for both algorithms. The new LMS algorithm was useful to enhance the electrocardiogram F wave by subtraction of an adaptively weighted prototypical reference signal from the aVF lead. The extrinsic weighting over 25 s demonstrated that time-varying functions such as patient respiration could be identified and monitored.ConclusionsA new LMS algorithm was derived and used for normalization of the extrinsic features in CFAE and for electrocardiogram monitoring. The weighting at convergence provides an estimate of the degree of similarity between two signals in terms of x-axis and y-axis shift and scale. The algorithm is computationally efficient with low estimation error. Based on the results, proposed applications include monitoring of extrinsic and intrinsic features of repetitive patterns in CFAE, enhancement of the electrocardiogram F wave and monitoring of time-varying signal properties, and to quantitatively characterize mechanistic diffe...

On the Preprocessing of Atrial Electrograms in Atrial Fibrillation: Understanding Botteron's Approach

“…have already reported the unsuitability of Botteron's approach for analyzing CFAEs . Indeed, these authors are currently engaged in characterizing CFAE signals , and developing optimal techniques for CFAEs analysis …”

Isolation of F-Wave From Electrocardiogram Using New LMS Algorithm

“…Suitable convergence coe±cients were derived empirically and found to be: ð b ; p ; g ; a Þ ¼ ð0:0003; 0:1; 0:135; 0:00082Þ with mesh sizes of ¼ 1 and ¼ 0:001, based upon prior observation. 6 Signals d, x, y and " were then graphed. Ideally, " will be a faithful reproduction of the synthetic F-wave with complete lack of a ventricular component.…”

“…5 Recently, a new least mean-squares (LMS) algorithm was introduced and applied as a matched¯lter to normalize extrinsic signal features. 6 Extrinsic features were de¯ned as the degree of x-axis and y-axis shift and scale, i.e. the phase lag, time duration, amplitude and baseline level of the signal.…”

Single-lead f-wave extraction using diffusion geometry

“…These algorithms can be roughly classified into two types, depending on the number of ECG channels needed for the algorithm. The first type includes blind source separation algorithms like independent component analysis and principal component analysis (PCA) [27,41,28,33,12,53,6], spatiotemporal QRST cancellation [50,31], and adaptive filtering with its variations [51,9,38,52]. These approaches typically need multiple channels; they deal frequently with the standard 12-lead ECG signal or the body surface potential map [53].…”

“…These algorithms can be roughly classified into two types, depending on the number of ECG channels needed for the algorithm. The first type includes blind source separation algorithms like independent component analysis and principal component analysis (PCA) (Langley et al 2000, Rieta et al 2004, Castells et al 2005b, Langley et al 2006, Llinares and Igual 2009, Donoso et al 2013, spatiotemporal QRST cancellation Sornmo 2001, Lemay et al 2005), and adaptive filtering with its variations (Thakor and Zhu 1991, Ciaccio et al 2012, Petrenas et al 2012. These approaches typically need multiple channels; they deal frequently with the standard 12-lead ECG signal or the body surface potential map (Zeemering et al 2014).…”