Introduction
Pulse oximetry is a technique used to measure oxygen saturation (SpO2) non-invasively. It is a method commonly used clinically whether that be in intensive care, in surgery, or in some out-patient clinics (Jubran, 2015). The use of pulse oximetry in these settings has helped reduce the need for invasive arterial blood gases analysis and increase the detection of hypoxaemia (Jubran, 2015), as defined as an SpO2 value observed as <95% (Amoian et al., 2013).
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., 2014). The benefit of physiological variability analysis is that it can give us useful information on the integrity of physiological control system (Shirazi et al., 2013; Raoufy et al., 2017). SpO2 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 SpO2 value (Dipietro et al., 1994). Moreover, OSV has been studied to be used diagnostically. A more recent study (2016) conducted in a tertiary level hospital in Bangladesh investigated whether implementing OSV in a predictor tool could improve admission of critically ill young children (Garde et al., 2016). They found that incorporating methods that quantified OSV improved the sensitivity and specificity of the tool for identifying these children (Garde et al., 2016). In addition, OSV has been used in the diagnosis of sleep disordered breathing whereby the SpO2 characterization adequately described the SpO2 modulation in order to identify those at risk of sleep disordered breathing (Garde et al., 2014).
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 SpO2 fluctuations (Dipietro et al., 1994; Cox et al., 2011; De Jesus et al., 2011; De Oliveira et al., 2012; Amoian et al., 2013; Garde et al., 2014, 2016; Hoffman, 2016). Hence, the initial need for a study examining healthy individuals in an adult population to characterize the OSV with more sophisticated methods for variability analysis. This can then allow the subsequent comparison with patient sub-populations to garner insight into the disease pathophysiology. The tools selected for this study will be measuring the regularity, complexity, and self-similarity of the fluctuations, which have been shown to better understand biological systems (Richman and Moorman, 2000).
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, 2000). Reduction in the sample entropy of a time-series has been shown to reflect the difference between normal and diseased participants, i.e., in patients with sepsis (Ahmad et al., 2009; Gholami et al., 2012), cirrhosis (Mani et al., 2009), and in obstructive sleep apnoea (Al-Angari and Sahakian, 2007).
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., 2002). Complexity in this context can be defined as “meaningful structural richness” which incorporate correlations over multiple scales (Costa et al., 2002). This is achieved mathematically by creating several sub-time series from the main series and calculating the sample entropy of each scaled series (Costa et al., 2002). This can then be plotted to show these cross-scale correlations (Costa et al., 2002). This can be applied in a clinical setting to provide extra prognostic information (Watanabe et al., 2015). MSE has been used to analyse many bio-signals (Gao et al., 2015) such as EEG dynamics in Alzheimer's disease (Mizuno et al., 2010) and heart rate variability analysis for predicting hospital mortality (Norris et al., 2008). Entropy is linked to the concept of information content in a given time-series (Mitchell, 2009). Thus, reduced entropy in a physiological setting can be interpreted as reduced information processing or less engagement the component of within a control system (Pincus, 1994).
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., 1995). The method entails measuring the correlations in the series over several scales to determine if they fit a fractal-like pattern. In this type of analysis when something is fractal-like; it has self-similarity. Many physiological rhythms shares this trait, as they gives rise to self-similar fluctuations over different time scales (Goldberger and West, 1987).
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, 2007) differ greatly with age, the study was also set up to determine if there is a significant difference between a young and old population.
Discussion
In the present study, we used non-linear dynamics to assess the pattern of SpO2 variability. Our results showed for the first time that SpO2 exhibited a fractal-like pattern of fluctuation as assessed by DFA. We also showed that the entropy of SpO2 can be easily calculated using both sample entropy and multiscale entropy techniques.
The overall characteristics of OSV
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., 2009; Hautala et al., 2010; Raoufy et al., 2016). The mean value of sample entropy of R-R interval variability in 5-min recording of adults was close to 1 (Hautala et al., 2010). In respiratory rate variability, the sample entropy of healthy adult men was closer to 1.8 (Raoufy et al., 2016). Thus, from this study it seems that the regularity of OSV (sample entropy = 0.877) is closer to that of heart rate variability (HRV) data (Hautala et al., 2010).
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 (α1 = 1.30, α2 = 0.87). On very short scales the fluctuation of SpO2 seem to be very stable, thus the higher α1 value (Peng et al., 1995). While at larger scales there is more fluctuation, reflecting a more complex behavior. Noticeably though, the α of the SpO2 data is similar to the data of heart rate variability in healthy individuals (Peng et al., 1995).
Association between mean oxygen saturation level and OSV measurements
It has been reported in previous studies that OSV is inversely related to the oxygen saturation level in preterm infants (Dipietro et al., 1994). This was confirmed by our findings, where a strong linear trend existed between the two variables in healthy adults (r = −0.734). Essentially, at the higher oxygen saturation levels there was less overall variability. This relationship was stronger in the present study when compared with the results of the aforementioned study (Dipietro et al., 1994). A possible reason behind this is that DiPietro et al. were studying oxygen saturation in preterm infants, whose health may be compromised. Thus, this relationship could be an indication of health, whereby a reduction in the phenomenon could indicate compromise of the cardiorespiratory system. It could also show that the oxygenation regulatory system is not mature enough in preterm infants. Furthermore, the relationship between oxygen saturation and sample entropy was stronger (r = −0.779), where there was an increase in sample entropy at lower mean SpO2 levels. This could reflect tighter system coupling when oxygen saturation is low. According to Pincus (1994), enhanced coupling of signals within a complex system increases the overall entropy. This essentially means that a higher entropy indicates that all the components of the system are connected and in communication (Pincus, 1994). In order to correct a lower mean oxygen saturation level the system needs to be engaged. This is the advantage of using entropy analysis rather than standard deviation in describing physiological variability. The same inverse relationship was also observed between mean SpO2 and MSE, showing that entropy of pulse oximetry signals carries information about mean oxygen saturation. Entropy analysis of physiological signals has been extensively used in the last two decades. Theoretical studies initially suggested that greater physiological signal regularity indicated increased system isolation (Pincus, 1991, 1994). Thereafter, progress in computational techniques for entropy estimation led to development of approximate entropy, sample entropy and MSE. Application of these entropy indexes in physiological time-series provided evidence for a link between system connectivity and entropy in health and disease. For instance, Gholami et al. (2012) reported that impaired responsiveness of the cardiac pacemaker to cholinergic control may present a decreased sample entropy of the heart rate variability during systemic inflammation. A recent report has also shown that sample entropy (as well as MSE) analysis of body temperature time-series may represent the engagement of thermoregulatory system during systemic illnesses such as chronic liver failure (Garrido et al., 2017). A relationship between mean SpO2 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.
The effect of age on OSV
Previous studies have shown that there is a significant change in MSE of heart rate variability with age (Angelini et al., 2007). This is interpreted as a decrease in complexity that occurs with aging (Shiogai et al., 2010). Our result shows a similar relationship in SpO2 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, 2002; Gholami et al., 2012). Applying what Pincus stated (1994), a reduced entropy may describe a reduction in the system coupling and increase system isolation. Our result may be indicative of the partial uncoupling of the systems involved in the cardio-respiratory control through aging. Something that could explain the drop in Po2 with aging (Pocock et al., 2013). There is a benefit from using variability analysis in describing physiological rhythms. There is a clear limitation in using reductionistic methods to describe physiological systems, as in order to achieve meaningful results we need to disrupt the system (Shirazi et al., 2013). Thus, what you study may not display features of the original system, but rather a perturbed system (Altimiras, 1999). It is only through integrative approaches such as pattern analysis that one can truly characterize the complexities of a system (Altimiras, 1999), in this case the cardio-respiratory control system. Our study indicates that pattern analysis of SpO2 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., 2015).
Limitations of the study and future work
A potential limitation of the study is that OSV is affected by activity levels (Dipietro et al., 1994; Garde et al., 2014). During the recording, all participants were sitting down, however, their activities varied from reading to conversing. This may have affected the amount of overall variability. However, as we also used techniques less sensitive to change in activity (Hautala et al., 2010) this effect was minimalized. A larger study is needed to follow up on these results to ensure adequate coverage of a healthy population. This would also be key in comparing the effect of aging on OSV.
Future studies could look at linear and non-linear indices of SpO2 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., 1995; Ahmad et al., 2009; Donaldson et al., 2012; Raoufy et al., 2016). Additionally, novel techniques could be applied to the raw data of this study population such as memory analysis (Shirazi et al., 2013). This technique can further explain the controllability of oxygen saturation and how past fluctuations impact future fluctuations.