A network physiology approach to oxygen saturation variability during normobaric hypoxia

What is the central question of this study? What is the physiological interpretation of SpO2 fluctuations observed during normobaric hypoxia in healthy individuals? What is the main finding and its importance? There is a significant flow of information between SpO2 and other cardio‐respiratory time series during graded hypoxia. Analysis of the pattern of SpO2 variations has potential for non‐invasive assessment of the engagement of respiratory control system in health and disease.

S pO 2 variability data into routine clinical practice can predict the requirement of hospitalization in children with acute illness (Garde et al., 2016). Likewise a recent study has demonstrated that S pO 2 fluctuation exhibits a fractal-like pattern which can assist in the diagnosis of sleep apnoea (Vaquerizo-Villar et al., 2018).
The complexity of physiological time series data can be measured by computing the degree of irregularity of the signal (i.e. entropy) (Pincus, 1991). By applying entropy analysis to S pO 2 time series data, we have previously demonstrated that S pO 2 entropy, and not its absolute value (or mean), can distinguish older healthy individuals from their younger counterparts (Bhogal & Mani, 2017). More recently, we have demonstrated that as the concentration of inspired oxygen (F IO 2 ) is decreased, S pO 2 entropy increases, and there is a strong significant negative correlation between mean S pO 2 and its entropy during normobaric hypoxic exposure (Costello et al., 2020). In addition, S pO 2 entropy, but not mean S pO 2 , was correlated with perception of breathlessness in otherwise healthy individuals when hypoxic (Costello et al., 2020).
The entropy of a physiological time series is a measure of how much total information the signal contains (Mitchell, 2009;Pincus, 1994). Thus, it is reasonable to suggest that S pO 2 fluctuations may carry information about the integrity of the respiratory system. Although this hypothesis is plausible, it has not been systematically investigated using empirical data. Respiration is tightly controlled and requires transfer of information from chemoreceptors, which are centrally and peripherally located. Tissue oxygenation involves a complex network of feedback loops that integrate different components of both the cardiovascular and respiratory systems. Thus, respiratory rate, tidal volume, heart rate and partial pressure of oxygen and carbon dioxide interact in a non-linear fashion to maintain respiratory homeostasis (Tipton, Harper, Paton, & Costello, 2017). We have recently described the physiological response to graded normobaric hypoxia in healthy individuals and found that while S pO 2 variability is significantly increased, mean respiratory rate, tidal volume and heart rate were not markedly altered during graded hypoxia when resting (Costello et al., 2020). After completing these analyses and publishing the findings (Costello et al., 2020), we subsequently became curious to discover if useful information is present in the cardio-respiratory time series which is not reflected in their mean values. An ideal method for assessing the complex interactions in a control system is to measure the causal relationship between physiological signals. This can be achieved by measuring the flow of information between parallel time series. Schreiber developed an analytical tool (i.e. transfer entropy) to detect the directed exchange of information between two systems (Schreiber, 2000). Several groups have extended this concept and demonstrated that measures of information transfer may serve as proxies for causal interactions (Barnett, Barrett, & Seth, 2009;Wibral, Vicente, & Lindner, 2014). This motivated us to look at the interaction between S pO 2 and other cardio-respiratory time series during a hypoxic challenge using transfer entropy.
Network physiology is an emerging field that reveals the topology of functional interactions between different components of physiological

New Findings
• What is the central question of this study?
What is the physiological interpretation of S pO 2 fluctuations observed during normobaric hypoxia in healthy individuals?
• What is the main finding and its importance?
There is a significant flow of information between S pO 2 and other cardio-respiratory time series during graded hypoxia. Analysis of the pattern of S pO 2 variations has potential for non-invasive assessment of the engagement of respiratory control system in health and disease. et al., 2015). By measuring the information that is exchanged between different physiological parameters, we could potentially assess the connectivity of physiological control (Buchman, 2002;Pincus, 1994).
Transfer entropy has the potential to compute bidirectional interaction between cardio-respiratory time series and thus reveal the network of interaction between different physiological parameters (Faes, Marinazzo, Montalto, & Nollo, 2014;Marzbanrad, Kimura, Palaniswami, & Khandoker, 2015). Therefore, in this study, we tested the hypothesis that S pO 2 fluctuation carries information about cardiorespiratory control in healthy individuals using a network physiology approach. In order to address this hypothesis, the engagement of different physiological parameters, i.e. respiratory frequency (f R ), tidal volume (V T ), minute ventilation (V E ), heart rate (HR), S pO 2 , end-tidal pressure of O 2 (P ETO 2 ) and CO 2 (P ETCO 2 ) were analysed using transfer entropy in healthy volunteers who were exposed to normobaric hypoxia.

Ethics
All participants provided their written informed consent before taking part in this study. The experimental procedures adhered to the standards set by the latest revision of the Declaration of Helsinki, except for registration in a database, and were approved by the Science Faculty Ethics Committee of The University of Portsmouth (project number 2017-025).

Experimental design
This study was part of a larger project investigating effects of normobaric hypoxia on physiological and cognitive function and the experimental design has been described in detail elsewhere (Costello et al., 2020;Williams et al., 2019). A convenience sample of 12 healthy males participated in this study, with mean (SD) age 22 (4)

Physiological recording
Participants' cardiorespiratory parameters, including f R , V T ,V E , HR, S pO 2 (using an ear clip), P ETO 2 and P ETCO 2 , were measured and monitored non-invasively for 45 min using a metabolic cart MA, USA, R2019b) and applied to remove any missing data and replace them with the overall average value of the data thread. Data were discarded if missing data equated to more than 5% of total length of the time series. Accordingly, one participant had more than 5% missing data and was subsequently discarded from the analyses.

Sample entropy calculation
Sample entropy of physiological time series was calculated using an algorithm developed in MATLAB (Goldberger et al., 2000). Sample entropy is a measure of irregularity of a time series by calculating the logarithmic likelihood that a sequence with window length, m, and degree of tolerance, r, will be repeated at a later time. In the present analysis, m and r were set at 2 (window length) and 0.2 (0.2 × SD) as described previously (Bhogal & Mani, 2017;Richman & Moorman, 2000).

Transfer entropy
Transfer entropy reflects the measures of causal relationship between two parallel time series (Barnett et al., 2009;Schreiber, 2000). In this study, it was employed to quantify the level of directed influence and information transfer that a data segment

Statistical analysis
Data are presented as the mean (SD), unless otherwise stated. The distribution of data was assessed using descriptive methods (skewness, outliers and distribution plots) and inferential statistics (Shapiro-Wilk test). A one-way ANOVA followed by Tukey's post hoc test was used to compare the physiological indices at different F IO 2 values.
Statistical analyses were carried out using MATLAB and GraphPad Prism (version 7, GraphPad Software Inc., San Diego, CA USA). P < 0.05 was considered statistically significant.

Network visualization
The directed transfer entropy values that physiological time series (i.e. f R , V T ,V E , HR, S pO 2 , P ETO 2 and P ETCO 2 ) exerted on each other following exposure to an F IO 2 of 0.17, 0.145, 0.12 were compared against those at sea level (F IO 2 : ∼0.2093-0.21). With the values obtained, any significant value in transfer entropy calculation was then compiled to form an adjacency matrix for each F IO 2 . If there was no statistically significant difference in transfer entropy in comparison of with F IO 2 0.21, a transfer entropy of zero was considered in the adjacency matrix.
This matrix was used to plot a directed graph. The codes for calculation of transfer entropy and plotting the network were written in MATLAB.

RESULTS
Eleven participants completed the study (45 min conditions × 4 sessions). One participant was removed from the chamber in F IO 2 0.12 (P ETO 2 fell below 45 mmHg). A sample representing 30 min recording of physiological signals during hypoxia is demonstrated in Figure 1. Data are presented as means ± SD (n = 11). Post hoc analysis: a P < 0.05 in comparison with F IO 2 = 0.21, b P < 0.05 in comparison with F IO 2 = 0.17, c P < 0.05 in comparison with F IO 2 = 0.145. f R , respiratory frequency; HR, heart rate; P ETCO 2 , end-tidal pressure of CO 2 ; P ETO 2 , end-tidal pressure of O 2 ; S pO 2 , peripheral capillary oxygen saturation;V E , minute ventilation; V T , tidal volume.
change during the hypoxic challenge, there were significant changes in mean S pO 2 , P ETO 2 and P ETCO 2 during normobaric hypoxia.
Sample entropy of the physiological time series are detailed in Table 2. S pO 2 sample entropy, calculated from S pO 2 signals using an ear clip oximeter with a resolution of one sample per respiratory cycle, increased as the concentration of inspired oxygen decreased (P < 0.0001). This finding is in agreement with our previous report where S pO 2 was recorded using a finger pulse oximeter with a sampling rate of 1 Hz (Costello et al., 2020). None of the other measured physiological time series exhibited any alteration in their sample entropy following the hypoxic challenge.  Figures 2b,c) Data are presented as means ± SD (n = 11). Post hoc analysis: a P < 0.05 in comparison with F IO 2 = 0.21, b P < 0.05 in comparison with F IO 2 = 0.145. f R , respiratory frequency; HR, heart rate; P ETCO 2 , end-tidal pressure of CO 2 ; P ETO 2 , end-tidal pressure of O 2 ; S pO 2 , peripheral capillary oxygen saturation;V E , minute ventilation; V T , tidal volume.

F I G U R E 2
Graphical presentation of directed transfer entropy between different physiological parameters as the concentration of inspired oxygen decreases (n = 11). (a) F IO 2 = 0.17, (b) F IO 2 = 0.145, and (c) F IO 2 = 0.12. Each node represents a physiological time series. Network edges (links) represent the link between two variables if there is a statistically significant difference in transfer entropy in comparison with F IO 2 = 0.21. The number on each edge represent transfer entropy (bits). f R , respiratory frequency; HR, heart rate; P ETCO 2 , end-tidal pressure of CO 2 ; P ETO 2 , end-tidal pressure of O 2 ; S pO 2 , peripheral capillary oxygen saturation;V E , minute ventilation; V T , tidal volume Data are shown as means ± SD. f R , respiratory frequency; HR, heart rate; P ETCO 2 , end-tidal pressure of CO 2 ; P ETO 2 , end-tidal pressure of O 2 ; S pO 2 , peripheral capillary oxygen saturation;V E , minute ventilation; V T , tidal volume.

TA B L E 4
Adjacency matrices representing transfer entropy of physiological signals at different fraction of inspired oxygen (F IO 2 ) A: F IO 2 = 0.17; B: F IO 2 = 0.145; C: F IO 2 = 0.12. Zero value means that there is no statistically significant difference in transfer entropy in comparison with F IO 2 = 0.21. f R , respiratory frequency; HR, heart rate; P ETCO 2 , end-tidal pressure of CO 2 ; P ETO 2 , end-tidal pressure of O 2 ; S pO 2 , peripheral capillary oxygen saturation;V E , minute ventilation; V T , tidal volume.
in F IO 2 of 0.145 and 0.12 bits respectively (Table 4). Moreover, this enhanced connectivity displayed a bidirectional flow of information as shown in Figure 2. While, bidirectional interactions were observed between various cardio-respiratory parameters at an F IO 2 of 0.145, S pO 2 exhibited the highest connectivity in the network (Figure 2b). In

DISCUSSION
The main finding of this study, in support of the hypothesis, was that Control of respiration requires transfer of information from central and peripheral chemoreceptors to ensure a rigorous balance between supply and use of oxygen. If oxygen availability is reduced, the respiratory centres in the brainstem respond to this flow of information by changing their firing pattern to alter breathing rate and volume (Jubran & Tobin, 2000). Such physiological responses require optimum transfer of information between the different components involved in the homeostatic control of tissue oxygenation (e.g. respiratory centres in the brainstem, autonomic and cardiovascular centres, cardiac pacemaker, vasculature, airways, respiratory muscles, etc.). Previous reports have indicated that hypoxia leads to the development of subtle ventilatory oscillations which have not been thoroughly examined in the existing literature (Jubran & Tobin, 2000). Some investigators have suggested that the engagement of the respiratory control system in the response to environmental or pathological challenges can be quantified by studying the pattern of respiratory rhythm and volume (Jubran & Tobin, 2000;Satti et al., 2019;Shirazi et al., 2013;Tipton et al., 2017). The current findings have further extended our understanding of this process by demonstrating that there is a higher degree of information transfer between different components of the respiratory control system, despite the absence of a significant change, or increase, in average f R , V T , orV E . Our findings also highlight that this bidirectional flow of information can be quantified by transfer entropy, a tool which shows merit in network visualization of the respiratory control during hypoxia.
A novel finding in the present study was the existence of a causal relationship between S pO 2 fluctuations and respiratory control.
Although previous observational and experimental studied have shown that S pO 2 instability is associated with pathophysiological and environmental challenges, the interpretation of such observations had remained speculative (Costello et al., 2020;Dipietro, Caughy, Cusson, & Fox, 1994;Garde et al., 2016;Roe & Jones, 1993). In general, investigating the causal relationship between physiological signals has largely been limited to reductionistic approaches (i.e. in vitro, ex vivo studies) (Altimiras, 1999). However, novel analytical methods have provided reliable tools to assess causal inference in multivariate time series data. Barnett and colleagues showed that the transfer entropy between two time series is equivalent to the Granger causality and can be used for data-driven causal inference (Barnett et al., 2009). Thus, transfer entropy has potential for the assessment of the respiratory control system based on multivariable recording of physiological signals, which is often available in acute clinical settings (e.g. intensive care units). Alternative methods that measure flow of information between parallel time series (e.g. mutual information and cross-entropy), do not reveal bidirectional relationship between time series (Raoufy et al., 2016;Richman & Moorman, 2000). This makes transfer entropy a unique method to non-invasively study the feedback loops responsible for autonomic control of the cardio-respiratory system.
In the present study, we observed that during exposure to F IO 2 0.17, S pO 2 had a causal influence on V T andV E , but not f R (Figure 2a).
This corroborates previous literature showing that the ventilatory response to normobaric hypoxia is influence by V T more than f R (Tipton et al., 2017). However, at a lower F IO 2 , the flow of information between S pO 2 and other variables (f R , V T ,V E , P ETO 2 , P ETCO 2 ) exhibits a bidirectional relationship. This may indicate tighter regulation as the physiological challenge or stimulus is increased. The presence of bidirectional relationships in the network suggests that S pO 2 is not only influenced by ventilatory parameters, but also has an impact on respiratory variables, possibly through feedback regulation. As expected, the strongest causal link was related to P ETO 2 → S pO 2 (Figure 2b,c). This corroborates a recent observation on mechanically ventilated pigs, which demonstrated that variations in the arterial partial oxygen pressure (P aO 2 ) is related to cyclic fluctuations of alveolar oxygen tension during respiratory cycles (Formenti et al., 2017). Thus, the information derived from physiological fluctuations in alveolar oxygen tension can be transmitted to the systemic arteries and hence be reflected in haemoglobin saturation and its fluctuations.
We also observed a reciprocal association between HR and S pO 2 time series in F IO 2 0.145 and 0.12 ( Figure 2). This relationship was weaker than that observed between S pO 2 and the respiratory variables, and is consistent with previous reports on the relationship between S pO 2 and HR variability at high altitude or during normobaric hypoxia (Krejčí, Botek, & McKune, 2018;Saito, Tanobe, Yamada, & Nishihara, 2005).
Understanding integrated physiological function is the focus of network physiology (Bartsch, Liu, Bashan, & Ivanov, 2015 While reciprocal interactions were observed between different cardio-respiratory parameters during hypoxia, S pO 2 remained the main hub of the network (Figure 2). This may indicate that indices derived from S pO 2 variability analysis have potential for non-invasive field and clinical studies to measure the connectivity of the respiratory control system. For example, application of fractal analysis of S pO 2 signals has been suggested as an alternative in paediatric sleep apnoea (Vaquerizo-Villar et al., 2018). Future studies are therefore warranted to investigate the application of non-invasive S pO 2 fluctuation analysis in monitoring individuals exposed to terrestrial altitude or patients who are susceptible to respiratory failure (e.g. patients with COVID-19). Despite extensive literature describing the physiology of respiration in health and disease, our understanding is not complete (Bunn & Poyton, 1996;Tipton et al., 2017;West, 2004

Study limitations and future perspectives
This study uses a convenient sample of healthy young males to test the feasibility of the proposed method. First, in order to generalize the findings, future research is required to expand these findings to females and older individuals. Second, all of the participants were healthy and did not have any comorbidities that would affect the dynamics of the cardio-respiratory network. Therefore, the application of S pO 2 fluctuation analysis to the general population may show different results. For example, we have previously shown that S pO 2 entropy is affected by ageing (Bhogal & Mani, 2017). Other underlying conditions (e.g. respiratory diseases) are likely to impact the network and require attention in future research.
Pulse oximeter technology has recently expanded beyond measurement of S pO 2 to other applications, including detection of pulsus paradoxus and fluid responsiveness based on variability analysis of the plethysmography waveform (Hess, 2016). However, the potential application of analysing the variability in the S pO 2 signal per se has only recently been appreciated (Costello et al., 2020;McGrath, Perreard, MacKenzie, & Blike, 2020). To the best of our knowledge, this was the first time that the transfer of information between S pO 2 , f R , V T ,V E , P ETO 2 , P ETCO 2 and HR time series during graded normobaric hypoxia has been demonstrated.
It appears that S pO 2 fluctuations during graded normobaric hypoxia exposure carries information about cardio-respiratory control.
Implementations of the algorithms developed in the present study could be utilized as physiological signal predictors incorporated into smart devices and fitness equipment, making them suitable for monitoring changes in aerobic fitness and physical health beyond the infrequent monitoring of patients during clinical interventions and rehabilitation programmes. Future studies should also examine if S pO 2 variability analysis could be used to improve monitoring in intensive care settings (e.g. need for or step-down from mechanical ventilation) in a similar way that is described for respiratory rate variability analysis (Seely et al., 2014).

Conclusion
S pO 2 fluctuations during graded hypoxia exposure carry information about cardio-respiratory control. S pO 2 entropy analysis has potential for non-invasive assessment of the engagement of the respiratory control system.