A New Scientific Study towards Distinction of ECG Signals of a Normal healthy person and of a Congestive Heart Failure Patient

Abstract

First of all, ECG signals of healthy persons and of Congestive heart failure patients are collected from MIT-BIH database in Physionet.
Next the data are tested for non-stationarity by QQ-plot method and for nonlinearity by surrogate hypothesis test. Being sure about the nonlinearity of the signals we next test for positive Lyapunov exponents prior to three dimensional attractor reconstruction of the signals. Now to reconstruct the attractors we find out proper time delay by a standard nonlinear method and then its proper embedding dimension. It is found that in all cases the embedding dimensions exceed three. Also the attractors thus reconstructed are not at all well formed. So they are not fit for the purpose of differentiation. Therefore we try for getting proper time delay under our newly developed method of generalized auto-correlation with same and different time-delays. In these cases also the embedding
dimensions are found to be larger than three. Also in almost all cases the attractors are not still well formed. In fact, the three dimensional attractors are seldom well formed, as the embedding dimensions are always greater than three. However for geometrical clarity we like to stick to three dimensional attractors only. So question of distinction of the signals through their reconstructed three dimensional attractors does not arise. Thus time domain analysis to differentiate the signals in three dimensions fails. Therefore, we try for a new approach of analyzing the signals in the frequency domain in the form of ‘frequency-delay plot’ and its quantification. The analysis is completely new and is different from the standard periodogram analysis in the frequency domain. In frequency
delay plots it is found that for normal persons the plots are really well formed and prominent too, under both cases of same delay and different delays. For Congestive heart failure patients the plots are, no doubt, so prominent but they maintain the basic feature of being dense. So these are also workable for the purpose of differentiation. In fact, the frequencydelay plots for both categories of persons are easily differentiable visually. So we try for scientific confirmation of the differences of the plots in the two categories of persons. For this purpose, we develop a new concept of three dimensional quantification procedure, known as ‘ellipsoid fit’ in a three dimensional cluster. It is found that the lengths of the axes of the ellipsoids taken together behave as proper quantifying
parameters, as they differ significantly in the two cases. But the results do no differ significantly if only the lengths of SD1 and SD2 are considered. Hence the main role of the parameters is played by the axis SD3 only. This establishes that for proper distinction of the signals, three dimensional ‘frequency-delay plots’ and their quantifications are essential. No significant result can be achieved from two dimensional considerations only.