Development of a method for differential analysis of data on the arterial blood oxygenation in healthy adults




arterial blood oxygenation, variability, differential analysis, Poisson and Erlang distributions, COVID-19


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

Author Biographies

Gennady Chuiko, Petro Mohyla Black Sea National University

Doctor of Physical and Mathematical Sciences, Professor

Department of Computer Engineering

Yevhen Darnapuk, Petro Mohyla Black Sea National University

Postgraduate Student

Department of Computer Engineering


Herrmann, J., Mori, V., Bates, J. H. T., Suki, B. (2020). Modeling lung perfusion abnormalities to explain early COVID-19 hypoxemia. Nature Communications, 11 (1). doi:

Kashani, K. B. (2020). Hypoxia in COVID-19: Sign of Severity or Cause for Poor Outcomes. Mayo Clinic Proceedings, 95 (6), 1094–1096. doi:

Xie, J., Covassin, N., Fan, Z., Singh, P., Gao, W., Li, G. et. al. (2020). Association Between Hypoxemia and Mortality in Patients With COVID-19. Mayo Clinic Proceedings, 95 (6), 1138–1147. doi:

Hypoxemia (low blood oxygen) (2018). Mayo Clinic. Available at: Last accessed: 21.09.2021

Niknafs, P., Norouzi, E., Bahman, B. B., Baneshi, M. R. (2015). Can we Replace Arterial Blood Gas Analysis by Pulse Oximetry in Neonates with Respiratory Distress Syndrome who are Treated According to INSURE Protocol? Iranian Journal of Medical Sciences, 40 (3), 264–267. Available at: Last accessed: 21.09.2021

Jubran, A. (2015). Pulse oximetry. Critical Care, 19 (1). doi:

Mack, E. (2007). Focus on Diagnosis: Co-oximetry. Pediatrics in Review, 28 (2), 73–74. doi:

Chushkin, M., Popova, L., Shergina, E,, Krasnikova, E., Gordeeva, O., Karpina, N. (2020). Comparative analysis of the arterial oxygen saturation (SaO2) and pulse oximetry measurements (SpO2) in patients with pulmonary tuberculosis. European Respiratory Journal, 56. doi:

Wilson-Baig, N., McDonnell, T., Bentley, A. (2021). Discrepancy between SpO2 and SaO2 in patients with COVID‐19. Anaesthesia, 76 (S3), 6–7. doi:

Shenoy, N., Luchtel, R., Gulani, P. (2020). Considerations for target oxygen saturation in COVID-19 patients: are we under-shooting? BMC Medicine, 18 (1). doi:

Fossion, R., Fossion, J. P. J., Rivera, A. L., Lecona, O. A., Toledo-Roy, J. C., García-Pelagio, K. P. et. al.; Olivares-Quiroz, L., Resendis-Antonio, O. (Eds.) (2018). Homeostasis from a Time-Series Perspective: An Intuitive Interpretation of the Variability of Physiological Variables. Quantitative Models for Microscopic to Macroscopic Biological Macromolecules and Tissues. Cham: Springer, 87–109. doi:

Chuiko, G., Dvornik, O., Darnapuk, Y., Baganov, Y. (2021). Devising a new filtration method and proof of self-similarity of electromyograms. Eastern-European Journal of Enterprise Technologies, 4 (9 (112)), 15–22. doi:

Yoshida, M., Onda, K., Wada, Y., Kuwahara, M. (2015). Influence of sickness condition on diurnal rhythms of heart rate and heart rate variability in cows. Journal of Veterinary Medical Science, 77 (3), 375–379. doi:

Bhogal, A. S., Mani, A. R. (2017). Pattern Analysis of Oxygen Saturation Variability in Healthy Individuals: Entropy of Pulse Oximetry Signals Carries Information about Mean Oxygen Saturation. Frontiers in Physiology, 8. doi:

Frost, J. (2019). Introduction to Statistics: An Intuitive Guide for Analyzing Data and Unlocking Discoveries. Available at: Last accessed: 21.09.2021

Chuiko, G., Darnapuk, Y., Dvornik, O., Kraynik, Y., Yaremchuk, O., Haab, R. (2021). A New Way of Data Analysis and Rating of the Blood Oxygen Saturation Variability. 2021 IEEE 12th International Conference on Electronics and Information Technologies (ELIT), 51–54. doi:

Chuiko, G., Darnapuk, Y., Dvornik, O., Kraynik, Y., Yaremchuk, O., Davidenko, A. (2021). "Devil`s stairs", Poisson`s Statistics, and Patient Sorting via Variabilities for Oxygenation: All from Arterial Blood Gas Data. doi:

Goldberger, A. L., Amaral, L. A. N., Glass, L., Hausdorff, J. M., Ivanov, P. C., Mark, R. G. et. al. (2000). PhysioBank, PhysioToolkit, and PhysioNet: Components of a new research resource for complex physiologic signals.. Circulation, 101 (23), e215–e220. doi:

Ghassemi, M., Moody, B., Lehman, L., Song, C., Li, Q., Sun, H. et. al. (2018). You Snooze, You Win: The PhysioNet/Computing in Cardiology Challenge 2018. 2018 Computing in Cardiology Conference (CinC). doi:

Bernardin, L., Chin, P., DeMarco, P., Geddes, K. O., Hare, D. E. G., Heal, K. M. et. al. (2020). Maple Programming Guide. Maplesoft, a division of Waterloo Maple Inc. Available at: Last accessed: 21.09.2021

Karlis, D., Xekalaki, E. (2007). Mixed Poisson Distributions. International Statistical Review, 73 (1), 35–58. doi:

Scott, D. W. (2010). Averaged shifted histogram. Wiley Interdisciplinary Reviews: Computational Statistics, 2 (2), 160–164. doi:

Weglarczyk, S. (2018). Kernel density estimation and its application. ITM Web of Conferences, XLVIII Seminar of Applied Mathematics, 23 (2). doi:

Tetrax: Fourier transformation of postural sway, Sunlight. Available at: Last accessed: 21.09.2021

Amaral, L. (2012). A Brief Overview of Multifractal Time Series. Available at: Last accessed: 21.09.2021

Banerjee, S., Easwaramoorthy, D., Gowrisankar, A. (2021). Fractal Functions, Dimensions and Signal Analysis. Cham: Springer. doi:



How to Cite

Chuiko, G., & Darnapuk, Y. (2021). Development of a method for differential analysis of data on the arterial blood oxygenation in healthy adults. Eastern-European Journal of Enterprise Technologies, 6(4 (114), 37–43.



Mathematics and Cybernetics - applied aspects