Application to biomedical signals - Practical Biomedical Signal Analysis Using MATLAB - page 188

short-time fractal scaling exponent has a relatively good correlation with the ratio of
the low- to high spectral component in controlled recording conditions [Perkiomaki
et al., 2005]. It was reported that short-term scaling exponents derived from HRV
series can be predictors of vulnerability to ventricular tachycardia, ventricular fib-
rillation, arrhythmic death, and other heart conditions (review in [Perkiomaki et al.,
2005]). Power law relationship of heart rate variability was used as a predictor of
mortality in the elderly [Huikuri et al., 1998]. However the mono-fractal (scale in-
variant) behavior need not testify for the chaotic character of the data. It was reported
that surrogate data test revealed the same α and β values for original HRV series as
for the ones with randomized phases [Li et al., 2008].
In [Peng et al., 1995] by means of DFA the scaling exponent was determined
for 24 h recordings of HRV of a healthy group and patients with congestive heart
failure. Short term and long term scaling exponents α 1 and α 2 differed significantly
for normal and pathological groups, but the separation was not complete—there was
substantial overlap between both groups in parameter space (8 out of 12 healthy
subjects and 11 out of 15 pathological subjects exhibited a “cross-over” between
groups).
The same data (from PhysioNet database, Beth Israel Hospital) as those used by
[Peng et al., 1995] were subjected to wavelet analysis and DFA by [Thurner et al.,
1998]. For classification, standard deviations of wavelet coefficients at scales 4-5
(16-32 heart beats) was used, which yielded 100% classification (sensitivity and
specificity) between the groups. In the above work, from the wavelet coefficients
scaling exponentsα were also determined. The discrimination between groups based
on their values resulted in 87% sensitivity and 100% specificity, which was better
than in [Peng et al., 1995] but worse than for parametrization by wavelet standard
deviation. Thurner et al. conclude that their multiresolution approach succeeded not
only because it discriminates trends, but also because it reveals a range of scales over
which heart failure patients differ from normals.
4.2.2.4.4 Poincare and recurrence plots Other non-linear methods of analyz-
ing heart rate variability are the Poincare map (PM) and recurrence plot (RP). The
advantage of these methods is that they can be applied to short and non-stationary
data. Recurrence plots were applied to heart rate variability data by [Marwan et al.,
2002]. The examples of recurrence plots for HRV epochs before ventricular tachy-
cardia (VT) in comparison to control epochs HRV are shown in Figure 4.37. The RP
for epoch before VT onset shows big rectangular structures. Usually RP plots are
characterized by specific shape parameters, among them diagonal line lengths and
vertical line lengths, which are important for characterizing different conditions.
The study of HRV from 24 h ECG by means of entropy measures and Poincare
maps was conducted by [ Zebrowski et al., 1994]. The examples of three-dimensional
RR interval return maps (Poincare maps) are shown in Figure 4.38. One can observe
different patterns for cases: before cardiac arrest and one year later after medication.
The authors point out that although pathological patterns differ from the normal ones,
it is difficult to distinguish between different pathological cases (Figure 4.38 c and d).