=Paper=
{{Paper
|id=Vol-2762/short3
|storemode=property
|title=Blood Oxygenation Among Healthy Adults: Recurrence Plots Analysis and Quantification
|pdfUrl=https://ceur-ws.org/Vol-2762/short3.pdf
|volume=Vol-2762
|authors=Gennady Chuiko,Olga Dvornik,Yevhen Darnapuk,Olga Yaremchuk
|dblpUrl=https://dblp.org/rec/conf/ictes/ChuikoDDY20
}}
==Blood Oxygenation Among Healthy Adults: Recurrence Plots Analysis and Quantification==
https://ceur-ws.org/Vol-2762/short3.pdf
Blood oxygenation among healthy adults:
Recurrence Plots analysis and quantification
Gennady Chuikoa , Yevhen Darnapuka , Olga Dvornika and Olga Yaremchuka
a
Petro Mohyla Black Sea National University, 68 Desantnykiv, 10, 54003, Mykolaiv, Ukraine
Abstract
Authors have used Recurrence Plots analysis for a published dataset of blood oxygenation for healthy
adults. They offered a new way of the patients’ sorting regarding the subsets using the Recurrence
Plots and Recurrence Ratio for normal blood oxygenation (SpO2) trials. The Recurrence Plot of a SpO2
record turned out a quite individual portrait of a patient. We found three subsets, from which the entire
dataset consists. They vary with levels SpO2 and its recurrence ratios. The weaker subset shows the
lowest levels of oxygenation and low Recurrence of trials, hence the highest their variability. Perhaps,
the subset is riskiest for COVID-19, which mostly accompanied itself by hypoxemia. The subset is about
22 % of the full population. The most vital subset is the opposite, their recurrence ratios are highest, as
well as the level of oxygen saturation. This subset also is about 22 % of the population. The rest majority
(56 %) of healthy adults have quite a high level of oxygenation with moderate Recurrence and variability.
All differences among subsets concerning recurrence ratios ranges turned out statistically significant.
Keywords
Blood oxygenation, SpO2, Recurrence Plots, Recurrence Ratio, COVID-19, Variability
1. Introduction
Coronavirus disease 2019 (COVID-19) forces the studies of reasons and the provenance of
accompanying hypoxemia. Hypoxemia, or sharp oxygen deficiency in the arterial blood, was
pointed out in the recent studies of COVID-19 as a severe mortality factor [1, 2, 3, 4]. An element
of blood red cells, hemoglobin, is responsible for foe blood oxygen saturation. Each molecule of
hemoglobin can capture and delivery to the need place up to four oxygen molecules. Oxygen
saturations less than 92 % are associated with significant adverse events in outpatients with
pneumonia [5]. Some authors set this critical threshold even higher, up to 95 % [4].
Pulse oximetry (SpO2 data collection) is a routine medical, non-invasive rapid measurement
using small gadgets with a finger clip. There is also a more laborious and invasive method of
the saturation measuring by gas sensors introduced live inside arteries. Such data have a bit
other notation (SaO2). The divergences between these measures are minor as a rule [6]. The
reason is that pulse oximeters are calibrated mostly via the direct SaO2 data.
ICT&ES-2020: Information-Communication Technologies & Embedded Systems, November 12, 2020, Mykolaiv, Ukraine
" gennchuiko@gmail.com (G. Chuiko); yevhen.darnapuk@chmnu.edu.ua (Y. Darnapuk);
olga.dvornik@chmnu.edu.ua (O. Dvornik); olga.yaremchuk.77@ukr.net (O. Yaremchuk)
0000-0001-5590-9404 (G. Chuiko); 0000-0002-7099-5344 (Y. Darnapuk); 0000-0002-4545-1599 (O. Dvornik); 0000-
0002-0891-4216 (O. Yaremchuk)
© 2020 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
Workshop
Proceedings
http://ceur-ws.org
ISSN 1613-0073
CEUR Workshop Proceedings (CEUR-WS.org)
In [7, 8] was presented new SpO2 dataset for 36 healthy adults. The first analysis of these
data [7, 9] showed:
1. Relative small variability of data within each record. Especially it touches the short-time
variability descriptors (SD1). The long-time variability of the oxygen saturation (SD2)
does not exceed 1.1 %, while the short-time variability was less than 0.2 % [9].
2. High Recurrence of some trials. They could be repeated hundreds and even over a
thousand times. Therefore Poincare plots turned out strongly clusterized.
3. Significantly non-Gaussian distribution for trials within every record.
The high repeatability and low variability of the blood oxygen saturation records hint that
this process is close to almost stable and hard-changing one. Poincare discovered the Recurrence
as a fundamental property of the conservative dynamical systems yet in 19 century. However,
the only three last decade it is in use as the modern computerized method of investigations
[10, 11]. Mostly it is realized via Recurrence Plots (RPs) and their quantification analysis (QRA)
[11].
Here we will be keeping in this way, studying the RPs for records of the dataset [7, 8]. Besides,
we are going to consider the maint QRA factor for them: that is the Recurrence Ratio (RR). Such
is the goal of this report.
2. Dataset and Methods of processing
The dataset [7, 8] includes 17 males and 19 females, in the age range (19 - 66) years. The patients’
body mass index (BMI) was in the range (18.5 - 28.4), which was close to the recognized norm.
The majority of participants were non-smokers (28 persons); the rest was either smokers (3)
or ex-smokers (5). The duration of every personal record of the blood oxygen saturation was
about an hour with the sampling rate equal to 1 Hz (one measuring each second). Note, that
one can get all dataset from the source [8].
The peculiar "rectangular" shape of the records [7, 8, 9] advises us a the filtering of them
by Haar wavelets as shape fittest ones. We have carried out such filtering for all records with
two-fold downsampling. We got the low-frequency (LF) and high-frequency (HF) parts of each
record as a result of such filtering. The first of them presents the filtered signal while the second
one – noises. Further, we dealt mostly with filtered LF parts of records.
Statistical Shapiro and Wilk’s W-tests, which we were applying to all 36 LF parts of records,
showed the non-Gaussian nature of them with the probability equal to 0.99. The matter is
mainly in the excess kurtosis and massive outliers within the records. Hence, such known
variability descriptors as the ranges, or even interquartile ranges, look initially as unreliable for
the dataset [7, 8]. So, one should pay attention to other descriptors. Maybe these descriptors
should be found outside of statistics.
Let pay attention to the high Recurrence of trials within SpO2 records. Consider only one
example of records (the original code is 080217B [7, 8]). The filtered LF part of this record
comprises 1793 values, but only 34 of them are unique. These unique trials were repeated from
once up to 1443 times. The most recurred saturation was equal to 98.6 %. No one can now be
surprised by the highly clusterized Poincare plots for records of this dataset [9].
Recurrence is a property opposite to variability in some sense. As intensive is the Recurrence
so smaller is the variability and reversely. The similarity matrices describe the Recurrence in a
series of trials mathematically [10, 11]. Let consider a series, the terms of which are indexed
by independent indexes 𝑜𝑛𝑒 ≤ 𝑖, 𝑗 ≤ 𝑁 . Then each pair of series’ terms (𝑖, 𝑗) corresponds to the
matrix element of the square similarity matrix. This element is either equal to 1 if the absolute
value of the difference between the pair’s terms less than some given threshold, or equal to zero
in the opposite case.
The similarity matrix has dimensioned (𝑁 𝑥𝑁 ) depending on the series length. For extensive
records, like in our case, it may be a big matrix, required the computer methods for processing
and building of RPs. Now, we can understand why the RPs have developed together with
computers [10].
The Recurrence Plot (RP) is the image of the similarity matrix [10, 11]. Let warn the reader
that there are two ways of numeration for the rows and columns of this matrix. The ordinary
matrix view suggests the numeration from the left upper corner of the matrix to down and
right. The enumeration starts from the lower-left corner to up and right in another way [10, 11].
Here we will be keeping on the matrix view.
The quantification of RPs (QRA) suggests many quantitative factors for the similarity matrix
[11]. The most useful and straightforward of them seems to be the Recurrence Ratio (RR). This
factor is the ratio between the number of matrix elements, which are equal to 1, and the total
number of matrix elements. If the similarity matrix is considering as an image, then RR meets
the mean intensity of this image. There are existing also some tules for the visual qualitative
analysis of RPs [11]. We will be using these rules below for built RPs.
An RP enables us to investigate the multi-dimensional phase space trajectory through a
two-dimensional and visual representation of its recurrences [11]. The recurrence threshold
value mentioned above is a critical thing for the RPs building Authors [11] pointed out that
recurrence threshold selection is a trade-off. On one hand, we intend to a threshold as small
as possible, but on the other hand, a sufficient number of recurrences need a higher threshold.
We choose the recurrence threshold equal to 0.1 %, which is about equal to the short-time
variabilities of records [9]. This value also roughly meets the standard deviation of HF parts of
records.
3. Results
3.1. RPs for the vital subset
Those people from the dataset [7, 8], who showed the highest RR in the range (0.537 – 0.742),
were included in the vital subset. It was eight persons or about 22 % of the population. The
mentioned above Shapiro and Wilk’s W-test shows the distribution of RR values close to the
standard (Gaussian) one with the probability 0.99. Gaussian distribution without any outliers
turned out as fit also for the other two subsets. Fig. 1 shows the collection of RPs for this subset.
The mean value for RR is equal to 0.636, with the standard deviation equal to 0.081 for this
subset. Thus, the Recurrence is relatively high and concentrated within the higher range. That
means that the variability of the oxygenation is lowest for these people. The oxygen saturation
process is stable enough and hard-changing.
(a) 𝑅𝑅 = 0.563 (b) 𝑅𝑅 = 0.559 (c) 𝑅𝑅 = 0.742 (d) 𝑅𝑅 = 0.537
(e) 𝑅𝑅 = 0.719 (f) 𝑅𝑅 = 0.597 (g) 𝑅𝑅 = 0.685 (h) 𝑅𝑅 = 0.689
Figure 1: Recurrence Plots for the persons from the more vital subset. Note that all RPs are unique by
their textures.
However, this process is significantly non-stationary, which confirms by inhomogeneity of
plots. Periodic patterns (block-like textures) show that the process can have characteristic cyclic
ties. Dark rectangles are signs that some states do not change or change slowly for some time
intervals (that is so-called laminar states) [11].
3.2. RPs for the riskier subset
People from the riskier subset have RR values from other, palpably lower ranges (0.217 –
0.298) with a mean value equal to 0.250, and the standard deviation about 0.027. Participants
demonstrate significantly higher variability and much fewer recurrence ratios. Fig. 2 presents
their RPs. The difference of mean intensities of plots is quite evident if one compares Fig. 1 and
Fig. 2.
Thus, the oxygen saturation process is here less stable and easier to change. That is why
we called this subset riskier to COVID-19. Besides, the saturation process for the people from
the subset is non-stationary, though the cyclic ties and laminar states are less expressed as for
the previous subset. Pay attention to the "fading" of corners for some RPs of Fig. 2. That is an
additional quantitative sign of a non-stationary process [11].
3.3. The main subset
This subset comprises 20 participants or 56 % of the total population. The range of RR is (0.327
– 0.568) with a mean equal to 0.430 and a standard deviation of about 0.065. Thus this range
(a) 𝑅𝑅 = 0.298 (b) 𝑅𝑅 = 0.281 (c) 𝑅𝑅 = 0.237 (d) 𝑅𝑅 = 0.217
(e) 𝑅𝑅 = 0.228 (f) 𝑅𝑅 = 0.249 (g) 𝑅𝑅 = 0.234 (h) 𝑅𝑅 = 0.258
Figure 2: Recurrence Plots for the persons from the riskier subset.
lightly overlays with the previous vital subset, while the border with the riskiest subset looks
clearer.
The participants demonstrate middle variabilities and recurrences. The conclusions made
above for smaller subsets remain valid for the main subset. We mean here the Gaussian
distribution, unique textures of RPs, non-stationarity, and presence of cyclic ties and laminar
states in the blood oxygen saturation process.
Fig. 3 presents the statistical box-and-whisker plot for RR ranges of all three subsets. The
hight of boxes reflects the interquartile ranges (the distance between upper and lower quartiles).
The "whiskers" shows the ranges of each subset. The lines inside the boxes are the medians.
Statistical Two-Sample T-test confirms the statistical significance of the differences between
means of RRs for all possible pairs of subsets with the probability equal to 0.99.
Therefore, the intervals of Recurrence Ratios pointed out for each of subsets are a relatively
reliable tool for the separation of patients, concerning subsets. Some uncertainty may arise
on the border between the upper-middle and the lower-vital subgroup, but the riskiest one is
entirely separable via the RR measuring.
3.4. The negative correlation between RRs and standard deviations
(variabilities)
Let consider the bond between the RRs and standard deviations for each record of the dataset
[7, 8]. Here we reckon the standard deviation as the most reliables indicator of the total
variability of each record [12]. Fig. 4 shows this correlation.
The correlation showed by Fig. 4 is quite vital that the correlation coefficient is equal to about
Figure 3: Statistical box-and-whisker plot for Recurrence Ratios intervals, which characterizes each of
subsets. Note that RR data are free of outliers in contrast to the dataset [7, 8].
Figure 4: The negative correlation between Standards Deviations and Recurrence Ratios. As higher
is the Recurrence as lower is the variability (the Standard Deviation). Thus the vital subgroup demon-
strates the lowest variabilities while the riskiest has the highest ones.
-0.88. Table 1 show some other correlation coefficients.
Note that we have to accept as essential non-zero correlation any correlation coefficients
exceed the critical value equal to ± 0.39 if we take confidence on the level 0.99 and use well-
known Student’s critical tables. Thus, all coefficients in Table 1 are statistically significant. The
sole positive correlation of Table 1 tells us that as higher is the Recurrence as higher is and
oxygen saturation of a patient. Although this correlation is moderate enough, the connection
sounds as essential for us.
It is visible that the correlation coefficients are lower for the ranges and interquartile ranges
than for standard deviations. We can explain this fact by numerous outliers in the dataset [7, 8].
They have a noise-like effect on the veracity of these ranges, what was said above.
Table 1
The correlation coefficients between Recurrence Ratios (RR) and some statistical indicators of the
dataset variability [7, 8]
RR and modes
RR and RR and
(most probable values RR and ranges
Standard Deviations interquartile ranges
of the oxygen saturations)
-0.88 -0.83 +0.73 -0.61
4. Discussion and conclusions
Processes and systems, which are ubiquitous, also in medicine and physiology besides, mostly
are non-linear and non-stationary ones. They usually exist in noisy mediums. Of course, all
of that is conditions breaking to use the arsenal of powerful linear methods and tools [11].
The reader could see how the non-Gaussian nature of the signals, especially the presence of
numerous outliers, inhibit the use of statistical tools (ranges and interquartile ranges analysis)
or the Poincare plots technique concerning the dataset.
The RPs and QRA are relatively new methods of non-linear dynamics, permitting the study
of such processes and systems successfully [10, 11]. We have used here only one of the many
qualifications within QRA [10, 11]. However, even that was enough for the straight separation
of the dataset on three subsets. Quantification of Recurrence Plots can be continued and looks
promising.
It is worthy to point out that RPs are individual portraits of the patients. We did not found
even two identical among all of them. The qualitative analysis of their textures, much more
profound, than in this paper, also looks like a coming way.
The correlations between Recurrence Ratios and statistical parameters, which shows Table 1,
permit us a few conclusions:
1. Recurrence and statistical descriptors of variability, such as standard deviation, ranges,
and interquartile ranges [12, 13], have the essential negative correlations. It means, as
higher is Recurrence as lower is the variability, as we assumed it above.
2. The vital subset, for instance, has not only the lowest variabilities but and highest oxygen
saturation levels. The riskiest subset, reversely, have not only much highest variability,
but and the lowest oxygenation. It follows from the positive correlation in Table 1 between
Recurrence and the most probable values of oxygenation (modes).
3. The Recurrence Ratios, as the measure for the variability, are free from dataset drawbacks
because they have Gaussian distribution and have no outliers. Therefore, they are more
reliable, as we believe.
We suppose that healthy adults, incoming to either the vital subset or in riskiest one, should
have different chances of arising and deepness, if it has begun, of the hypoxemia accompanying
COVID-19.
Acknowledgments
This report is a part of the research project entitled "Development of hardware and software
complex for non-invasive monitoring of blood pressure and heart rate of dual purpose" (regis-
tration number 0120U101266) Ukrainian Ministry of education and science financially support
this project, and the authors are grateful for that.
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