An LMS Algorithm for Characterization of BioSignal Shape

Dr. Edward J. Ciaccio,Columbia University, USA

Abstract: Shape is an important biomedical signal component which is often overlooked in feature extraction, signal classification, and matching schemes. Presently, simple statistical and syntactic metrics are often used to capture signal morphology, such as mean and variance calculation and peak-counting. However, the essence of signal shape is not well elucidated by these methods. It would therefore be useful to improve the calculation paradigm. A biomedical signal can be defined by its extrinsic shape (x-axis and y-axis shift and scale) and intrinsic shape (shape after normalization of extrinsic features). To increase efficacy for morphologic characterization, a least mean squares (LMS) algorithm can be implemented to adaptively seek optimal performance criteria using the method of differential steepest descent. Equations for normalization of x-axis and y-axis shift and scale should be formulated to normalize and measure extrinsic signal shape, enabling the remaining, intrinsic signal shape to be identified.

As an example, fractionated atrial electrograms, which are signals with multiple random deflections obtained from the endocardial heart surface with a standard ablation catheter during electrophysiologic study, can be utilized to demonstrate the new algorithm efficacy. These signals were acquired with a standard ablation catheter at a 977 Hz sampling rate in 10 paroxysmal and 10 persistent atrial fibrillation patients. Each original signal was matched with a version of itself that had been altered in x-axis and y-axis shift and scale. Over 24 trials, adaptation of the altered to the original signals, using the new algorithm with four weights, was compared to adaptation using the Widrow-Hoff LMS algorithm with four tapped delays. Time for convergence and error after convergence were compared. The new LMS algorithm was also applied to electrocardiograms acquired from atrial fibrillation patients, for atrial wave enhancement and for monitoring of extrinsic changes in signal shape.

Based on the mathematical formulation of the new LMS algorithm, y-shift and y-scale adjustments were shown to be equivalent to the scalar form of the Widrow-Hoff LMS algorithm. However, for x-shift and x-scale adjustment, rather than implementing a long tapped delay line as is utilized by the Widrow-Hoff LMS algorithm, the new method is comprised of a two-weight system. After convergence, the matching error for paroxysmal electrograms averaged 0.46 ± 0.49μV2/sample for the new LMS algorithm versus 0.72 ± 0.35μV2/ sample for the Widrow-Hoff LMS. The matching error for persistent electrograms averaged 0.55 ± 0.95μV2/sample for the new LMS algorithm versus 0.62 ± 0.55μV2/sample for the Widrow-Hoff LMS. The mean convergence time was approximately 1 second (977 discrete sample points) for both algorithms. The new LMS algorithm was useful for electrocardiogram F wave enhancement by subtraction of an adaptively weighted prototypical reference. The extrinsic weighting over 25s demonstrated that patient respiration and other time-varying functions can be identified and monitored.

Based on the comparative analysis, the new LMS algorithm is able to normalize extrinsic electrogram signal shape and to enhance the electrocardiogram F wave in atrial fibrillation patients. The new LMS weighting at convergence provides an estimate of the degree of similarity between any two signals in terms of x-axis and y-axis shift and scale. The algorithm is computationally efficient with low estimation error. Applications for this implementation include monitoring of extrinsic and intrinsic signal shape, as well as enhancement of low-level signal components when a reference can be used for adaptive cancellation of larger masking features.