Abstract:
Fractal is an object whose Housdorff dimension is greater than its Euclidean dimension.
This report presents the application of fractal theory to the analysis of Electrocardiogram
(ECG). Three methods for calculating fractal dimension (FD) namely, relative dispersion
(RD), rescaled range (RS) and power spectral density (PSD) methods are applied here. At
first, the three methods are applied to simulated data with known FD. The FD by all the
methods depends on data length which is taken as 1024, 2048 and 4096. The RS and PSD
methods are less biased to data length and give more consistent result than RD method.
The best result is obtained for a data length of 4096.
The same three methods are applied to calculate FD of instantaneous heart rate (IHR)
derived from ECG of both normal and abnormal records of MIT-BIH data base. The
abnormalities considered here are premature ventricular contraction (PVC), bundle branch
block (BBB) and atrial premature beat (APB). The number of data sets for whose ECG
are taken is 3 in each case except for BBB where 4 data sets are taken. The FD of IHR of
normal ECG is by RD, RS and PSD methods are found as 1.46±0.071, 1.66±0.006 and
1.80±0.025, respectively, where FD is provided as mean ± standard deviation. The
respective values of FD for records containing PVC are 1.43±0.035, 1.51±0.029 and
1.71±0.010 while that for left BBB are 1.28±0.015, 1.74±0.017 and 1.70± 0.043. The FD
values for APB data are 1.35±0.015, 1.56±0.015 and 1.74±0.006. It is seen that the FD of
ECG containing PVC, BBB and APB type abnormalities is different from that of normal
ECG. Hence, it is can be said that fractal analysis can distinguish these types of
abnormalities from the normal ones. However, due to small number of data sets studied
here, absolute conclusion regarding the applicability of FD analysis to detect cardiac
abnormality can not be made. This study shows the potential use of fractal analysis in the
estimation of cardiac condition.
