title: A new LMS algorithm for analysis of atrial fibrillation signals.
abstract: BACKGROUND
  A 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).
  
  
  METHODS
  Equations 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.
  
  
  RESULTS
  Based 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 ± 0.49 μV(2)/sample for the new LMS algorithm versus 0.72 ± 0.35 μV(2)/sample for Widrow-Hoff LMS. The MSE for matching persistent CFAE averaged 0.55 ± 0.95 μV(2)/sample for the new LMS algorithm versus 0.62 ± 0.55 μV(2)/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.
  
  
  CONCLUSIONS
  A 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 differences in paroxysmal versus persistent AF.
authors.affiliation: Department of Medicine, Division of Cardiology, Columbia University Medical Center, New York, USA. ciaccio@columbia.edu
authors.forename: Edward J
authors.initials: EJ
authors.lastname: Ciaccio
authors.forename: Angelo B
authors.initials: AB
authors.lastname: Biviano
authors.forename: William
authors.initials: W
authors.lastname: Whang
authors.forename: Hasan
authors.initials: H
authors.lastname: Garan
mesh_terms: D000465:Algorithms; D001281:Atrial Fibrillation / Q000175:diagnosis*; D004562:Electrocardiography; D006801:Humans; D012815:Signal Processing, Computer-Assisted