Abstract
Monitoring of arterial blood saturation with oxygen (oxygenation) has gained special significance as a result of the COVID-19 pandemic. A new method for computer processing of saturation records (so-called SaO2 signals), based on the study of differentials (increments) from signals, was proposed. Finding a differential for a time series involves calculating the difference between the pairs of its adjacent elements. The differential is non-zero only if the elements in a pair are different. The study of differentials together with primary signals for a set of records (20 subjects) shows that the spectrum of observed levels of blood saturation is discrete and limited (from 2 to 10 levels). In addition, changes in saturation levels (switches) occur only between the nearest levels. New indicators of the variability of blood saturation were proposed. These are the frequencies of saturation level switches (event intensities) and the intervals between them. It was established that these indicators are described by statistical distributions of Poisson and Erlang, respectively. Comparison of new variability indicators with the most reliable statistical – inter-quartile range – indicates that the new indicators also provide for the division of the data set into three subgroups according to the magnitude of variability. This division is statistically significant at a confidence level of 0.99 in both approaches, however, the division into sub-groups is slightly different in these methods. It was shown that the proposed indicators of the variability of SaO2 signals are scale-invariant, that is, they do not depend on the length of observation interval. This is a consequence of the fractality of the positions of differentials in the observation interval. The established switch frequencies for subgroups in order of increasing variability are (0.06, 0.11, and 0.20) Hz. These frequencies are manifested on Fourier spectra of differentials of SaO2
Highlights
Studies of the levels of blood oxygenation, that is, the percentage of oxygen saturation of hemoglobin, became increasingly active as a result of the coronavirus pandemic (COVID-19)
It was shown that the proposed indicators of the variability of SaO2 signals are scale-invariant, that is, they do not depend on the length of observation interval
They rely on the statistical distribution of data on the quartile, showing the interquartile range in the form of the boxes’ height, and the full data spread in the form of vertical lines with dashes («whiskers»)
Summary
Studies of the levels of blood oxygenation (saturation), that is, the percentage of oxygen saturation of hemoglobin, became increasingly active as a result of the coronavirus pandemic (COVID-19). Lack of oxygen, can be almost unnoticeable for saturation levels close to 90 % and below. The range of the oxygenation norm for healthy adults is (95–100) % [4]. The clinical practice mainly uses pulse oximetry – an indirect, but non-invasive, inexpensive, and convenient me thod for monitoring the oxygen level in the blood. Pulse oximeters are small devices that are fixed on fingers or on ear lobes. In this way, the so-called peripheral oxygena tion (SpO2) is measured [5, 6]
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