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Edited by: Radhakrishnan Nagarajan, University of Kentucky, United States

Reviewed by: Damian Kelty-Stephen, Grinnell College, United States; Marzieh Zare, Institute for Research in Fundamental Sciences, Iran

*Correspondence: Ali R. Mani

This article was submitted to Fractal Physiology, a section of the journal Frontiers in Physiology

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

Pulse oximetry is routinely used for monitoring patients' oxygen saturation levels with little regard to the variability of this physiological variable. There are few published studies on oxygen saturation variability (OSV), with none describing the variability and its pattern in a healthy adult population. The aim of this study was to characterize the pattern of OSV using several parameters; the regularity (sample entropy analysis), the self-similarity [detrended fluctuation analysis (DFA)] and the complexity [multiscale entropy (MSE) analysis]. Secondly, to determine if there were any changes that occur with age. The study population consisted of 36 individuals. The “young” population consisted of 20 individuals [Mean (±1 SD) age = 21.0 (±1.36 years)] and the “old” population consisted of 16 individuals [Mean (±1 SD) age = 50.0 (±10.4 years)]. Through DFA analysis, OSV was shown to exhibit fractal-like patterns. The sample entropy revealed the variability to be more regular than heart rate variability and respiratory rate variability. There was also a significant inverse correlation between mean oxygen saturation and sample entropy in healthy individuals. Additionally, the MSE analysis described a complex fluctuation pattern, which was reduced with age (

_{2}

Pulse oximetry is a technique used to measure oxygen saturation (SpO_{2}) non-invasively. It is a method commonly used clinically whether that be in intensive care, in surgery, or in some out-patient clinics (Jubran, _{2} value observed as <95% (Amoian et al.,

It has become increasingly recognized for the use of variability analysis in oxygen saturation to further gauge the regulation of blood oxygenation. However, the methods currently used are not as robust as the methods described in other physiological measurements such as heart rate variability (Garde et al., _{2} variability analysis has the potential to be used for monitoring the integrity of the cardiorespiratory control system which is involved in tissue oxygenation. Oxygen saturation variability (OSV) has also been well-characterized in pre-term infants, where it was observed that over the postnatal period there is a steady increase in OSV with no change observed in the mean SpO_{2} value (Dipietro et al., _{2} characterization adequately described the SpO_{2} modulation in order to identify those at risk of sleep disordered breathing (Garde et al.,

The main issue with previous reports on OSV is the characterization of “variability” and the lack of establishment of a “normal variability” in a healthy population. Additionally, the methods used to describe variability in these studies are primarily linear (i.e., standard deviation, Delta 12 s, saturations >2%, etc.), which to some extent miss out the pattern of SpO_{2} fluctuations (Dipietro et al.,

There exist indices that describe the pattern and complexity of fluctuations in physiological time-series. For example, sample entropy is a tool to describe regularity in time series and has been well-established in the study of the cardiovascular system dynamics (Richman and Moorman,

Multiscale Entropy (MSE) is an extension of sample entropy and has been used as a tool to describe complexity in a time series (Costa et al.,

Many physiological readings exhibit a fractal-like dynamic. Detrended fluctuation analysis (DFA) is a technique that examines scaling and fractal-like behavior in fluctuating time-series (Peng et al.,

The aim of this study is to establish how oxygen saturation varies in a healthy population and what techniques are best suited to quantifying this variability. Furthermore, we wanted to analyse the regularity, complexity, and self-similarity of these fluctuations using the aforementioned tools. Additionally, as other physical parameters such as heart rate variability (Zhang,

This study was registered and approved by the UCL Ethics committee (10525/001). The study population was made up 36 individuals, which was later split into two groups for further analysis. The “young” population, defined as members under the age of 35, consisted of 20 individuals [9 Men, 11 Women; Mean (±1 SD) age = 21.0 (±1.36 years)]. The “old” population, defined as members aged 35 and over consisted of 16 individuals [8 Men, 8 Women; Mean (±1 SD) age = 50.0 (±10.4 years)]. In order to establish a healthy study population some exclusion criteria were set; which covered Asthma, COPD, Sickle Cell Anaemia, and Pulmonary Fibrosis. Additionally, the smoking status of the participants was recorded for the possibility of retrospective analysis.

Each participant was connected to a pulse oximeter connected to an AD convertor (ADInstrument Ltd, Australia). The recording was initially completed over a 1 h period at a sampling rate of 1 k/s as a pulse recording was also taken alongside. However, the resolution was reduced to 1/s for the pulse oximeter using standard desampling protocol (LabChart). The main reason for this is that pulse oximeter readings are not sampled at such a high rate, and thus at that resolution, the variability presented would not reflect true SpO_{2} variation. The data for pulse oximetry was then extracted into an ASCII file for analysis. Prior to analysis the data was visually scanned for artifacts and the artifact was replaced by the mean value of the entire data set using zero-line interpolation. We chose this method as based on previous findings, it was shown to be the most stable when compared to other methods for artifact replacement (Wejer et al., ^{1}

The linear analysis was to first establish general tendencies of the data set. The mean SpO_{2} and standard deviation were calculated for all participants using an

This method quantifies fractal-like correlation properties on the time series (Peng et al.,

This index quantifies the degree of randomness vs. the degree of regularity in a time series. It calculates that probability that an event with window length, m, and degree of tolerance, r, will be repeated at later time points (Richman and Moorman,

Multiscale Entropy (MSE) looks at the sample entropy at different scales to determine if there are any correlations. The process creates “coarse-grained” time series which are produced by averaging the time points within a given window of increasing length, Γ (Costa et al.,

Initially, sample size was calculated based on the calculated differences from the MSE data in the pilot study run in December 2016^{2}_{2}. Lastly, a two-way ANOVA analysis was used to test the effect of age on the MSE values.

No participant recruited chose to withdraw from the study so all participants were considered for analysis. However, upon partial medical history, one participant was excluded from the study due to categorization under the exclusion criteria.

It is clear that over 1 h, the oxygen saturation readings exhibit fluctuations (Figure _{2} for the population studied is 97.7%. In regards to the variability, the mean standard deviation for the pulse oximetry recording was 0.707%, showing overall a small degree of variability. Using Poincare' plot, we can see that overall there was higher variability across the line of identity (SD2 = 0.987 vs. SD1 = 0.500). This indicates that the variability was predominantly made up of long-term variations (SD2) rather than short term variations (SD1; Figure _{2} level and total variability (Figure _{2} levels there is less overall variability (

Sample SpO_{2} data collected over 1 h. The X axis is the cumulative data points, and the Y axis is the oxygen saturation.

Linear and non-linear characteristics of SpO_{2} for the study population.

_{2} (%) |
_{2} (%) |
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97.7 ± 1.25 | 0.707 ± 0.247 | 0.500 ± 0.175 | 0.987 ± 0.351 | 1.30 ± 0.11 | 0.87 ± 0.10 | 0.89 ± 0.35 |

_{2} variability, SD2 is the long-term variability. SpO2 values >95% is considered normal, DFA, Detrended fluctuation analysis. Sample size = 36

Poincaré plot showing the correlation between consecutive SpO_{2} readings in a representative participant. SD1 and SD2 represent the length and width of the plot across the line of identity.

Graph showing the linear trend that exists between mean SpO_{2} level and total variability. Each point represents a participant in the study. “r” represent the Pearson correlation coefficient.

Through DFA analysis it can be seen that OSV is fractal-like in nature. The result of this analysis can be seen below (Figure _{1} score for the participants analyzed is 1.30 (Table _{2} score is 0.87 (Table _{1} is between pink noise (1/f dynamics) and Brownian noise while the α_{2} is between white noise and pink noise. Thus, this result shows that not only is SpO_{2} variability fractal in nature, but the variation itself is complex in its constitution. The relationship between the α values and mean SpO_{2} level was tested, however, we found no statistically significant correlation between the two.

An example of DFA Analysis on SpO_{2} variability data showing the linear trend when plotting (n) and F (n) on a log-log scale. The arrow indicates the approximate point of the cross-over phenomenon.

The mean sample entropy using a window length (m) of 2 was 0.877. The relationship between Sample entropy and the mean SpO_{2} level was also tested (Figure _{2} level is indicative of a more regular pattern of variability. The multiscale entropy (MSE) analysis revealed that the sample entropy increases as the scale increases (Figure _{2} level and the sum of the MSE values (_{2} is associated with decreased complexity of pulse oximetry signals.

Graph showing the linear relationship that exists between sample entropy and the mean SpO_{2} level. The points are representative of the participants in the study, and “r” is the calculated Pearson correlation coefficient.

Multiscale entropy graph describing the overall complexity of the whole study population. The error bars are calculated sample error of the mean values.

Following on from the previous results, the effects of aging on the OSV were studied. Statistically there was a significant difference between the mean ages in both groups (_{2} and standard deviation of SpO_{2}, there was no significant difference between the two groups (Table

The effect of age on the measures of SpO_{2.}

_{2} (%) |
_{2} (%) |
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Participants < 35 | 21.1 ± 1.4 | 98.02 ± 0.81 | 0.68 ± 0.22 | 1.28 ± 0.098 | 0.87 ± 0.11 | 0.86 ± 0.29 |

Participants > 35 | 49.9 ± 10.4 | 97.31 ± 1.59 | 0.75 ± 0.28 | 1.34 ± 0.11 | 0.88 ± 0.086 | 0.90 ± 0.42 |

0.000^{*} |
0.090 | 0.408 | 0.102 | 0.78 | 0.739 |

The multiscale entropy analysis showed a significant [_{Age} (1, 19) = 99.02; _{Scale} (19, 19) = 65.44;

The graph is depicting the effect of aging on the complexity of the oxygen saturation variability. The error bars are the standard error of the mean at each scale, and each point is the mean value at that scale from all the participants in the age group.

In the present study, we used non-linear dynamics to assess the pattern of SpO_{2} variability. Our results showed for the first time that SpO_{2} exhibited a fractal-like pattern of fluctuation as assessed by DFA. We also showed that the entropy of SpO_{2} can be easily calculated using both sample entropy and multiscale entropy techniques.

From the raw data, it is clear that OSV is apparent in a healthy population. However, the amount of overall variability changes from person to person. When analysing the pattern of OSV, the time series appears to be regular when compared with other physiological time series (Cuesta-Frau et al.,

Through Poincaré analysis, the variability was characterized to be more long term rather than short term (SD2 > SD1). Both DFA and MSE analysis uses scaling and it enables us to study oxygen saturation dynamics from both long-term and short-term views. DFA showed that the pattern of OSV is fractal-like. However, the slope seems to show a crossover effect (α_{1} = 1.30, α_{2} = 0.87). On very short scales the fluctuation of SpO_{2} seem to be very stable, thus the higher α_{1} value (Peng et al., _{2} data is similar to the data of heart rate variability in healthy individuals (Peng et al.,

It has been reported in previous studies that OSV is inversely related to the oxygen saturation level in preterm infants (Dipietro et al., _{2} levels. This could reflect tighter system coupling when oxygen saturation is low. According to Pincus (_{2} and entropy of the pulse oximetry signals is an interesting finding that goes along with these lines of research. However, details of the significance of this relationship, await further investigations.

Previous studies have shown that there is a significant change in MSE of heart rate variability with age (Angelini et al., _{2} variability with the use of MSE analysis. The scaled values for the young population was significantly higher than that of the older population. The lower sample entropy values at each scale does not only suggest reduced complexity, but also might suggest increased system isolation, which may reflect partial “uncoupling” of the control system (Buchman, _{2} with aging (Pocock et al., _{2} variability carries information on the integrity of body oxygenation with potentials to be used in clinical practice. It may also provide a tool to study dynamic interactions of organ systems in the emerging field of network physiology (Bartsch et al.,

A potential limitation of the study is that OSV is affected by activity levels (Dipietro et al.,

Future studies could look at linear and non-linear indices of SpO_{2} variability and whether these indices can be assigned clinical significance in the context of disease, as it has done in other physiological variables (Peng et al.,

The present study has established the pattern of OSV in a normal healthy population. The total variability predominantly consists of long term variations, and is dependent on the mean SpO_{2} level. The application of sample entropy analysis and MSE analysis to the data has provided novel information about the regularity and complexity of this variability. The fractal nature of OSV, as provided through DFA analysis suggests that structurally, physiological variables may all share this trait. Furthermore, by investigating the effect of aging on OSV, we have garnered insight into the control of oxygen saturation, and how this control system is impaired with aging.

The study was Conceptualized by AB and AM. The Data was collected by AB. Formal analysis was conducted by AB. Software was developed by AB and AM. AM supervised the study. AB wrote the initial draft. Reviewing and editing was completed by AM.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

We would like to express our gratitude to all the participants involved, for their support and patience, in contributing their time to help with our study. We would also like to acknowledge Dr. Tara Dehpour for data collection and Ms. Dougal (UCL Research Ethics Committee) for her guidance.

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