Abstract
Theil entropy is a statistical measure used in economics to quantify income inequalities. However, it can be applied to any data distribution including biological signals. In this work, we applied different spectral methods on heart rate variability signals and cellular calcium oscillations previously to Theil entropy analysis. The behavior of Theil entropy and its decomposable property was investigated using exponents in the range of [−1, 2], on the spectrum of synthetic and physiological signals. Our results suggest that the best spectral decomposition method to analyze the spectral inequality of physiological oscillations is the Lomb–Scargle method, followed by Theil entropy analysis. Moreover, our results showed that the exponents that provide more information to describe the spectral inequality in the tested signals were zero, one, and two. It was also observed that the intra-band component is the one that contributes the most to total inequality for the studied oscillations. More in detail, we found that in the state of mental stress, the inequality determined by the Theil entropy analysis of heart rate increases with respect to the resting state. Likewise, the same analytical approach shows that cellular calcium oscillations present on developing interneurons display greater inequality distribution when inhibition of a neurotransmitter system is in place. In conclusion, we propose that Theil entropy is useful for analyzing spectral inequality and to explore its origin in physiological signals.
Highlights
Biological signals are diverse and of great value as they can be used to understand physiological processes [1,2]
Theil entropy analysis performed on synthetic signals showed that the intra-band component is the one that contributes the most to the total value, this means that the origin of the spectral inequality is found in the energy difference that exists within each band and not in the differences between the bands (Figure 2)
The present study used Theil entropy in the analysis of inequality of the spectrogram of biological signals. From this analysis we conclude that: (1) the suggested spectral decomposition method to analyze spectral inequality is the Lomb–Scargle; (2) the exponents that provide the most information to describe the spectral inequality are zero, one, and two; (3) the additive decomposition of generalized entropy provides important information about the origin of this, with the intra-band component being the one that contributes the most to total inequality; (4) in the state of mental stress inequality increases with respect to the state of rest; (5) in developing interneurons, spectral inequality is greater when there is inhibition of calcium dynamics by blocking glycine receptors
Summary
Biological signals are diverse and of great value as they can be used to understand physiological processes [1,2]. Like most signals in the real world, they have irregularities and various shapes, and they are neither purely periodic nor can they be expressed with an analytical formula These irregularities are signs of the uncertainty in the evolution of the observed physiological processes. This uncertainty limits the predictability of the signals analyzed and carries important information [3,4]. The discrete Fourier transform is an adaptation used in most scenarios for the digitization of a continuous natural phenomenon in finite samples uniformly spaced The problem with this approach is that it only provides a discrete description of the phenomenon and does not provide complete information regarding its evolution
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