Quantitative analysis of the effect of fraction of inspired oxygen on peripheral oxygen saturation in healthy volunteers

A pulse oximeter noninvasively measures arterial blood oxygen saturation in dental care area. Respiratory management of patients is carried out by referring to the value of peripheral oxygen saturation (SpO₂) measured by the pulse oximeter [1, 2]. Therefore, it is important to ensure that pulse oximeters have high accuracy. The accuracy criteria for the pulse oximeter equipment are provided in the International Standard ISO 80601-2-61, and the U.S. Food and Drug Administration (FDA) only permits pulse oximeters that meet these criteria [3, 4]. According to the ISO 80601-2-61, the SpO₂ accuracy of a pulse oximeter should be assessed through a controlled desaturation study by comparing to the gold standard measurements of blood arterial oxygen saturation (SaO₂) obtained by a CO-oximeter [3]. In controlled desaturation studies, the range of SaO₂ is typically 70–100%, and the subjects are temporarily exposed to a fraction of inspired oxygen (FiO₂) lower than that in room air. In such situations, SpO₂ seems to decrease as FiO₂ decreases. Quantifying the relationship between FiO₂ and SpO₂ allows us to better explain the two relationships. In general, a turnover model appropriately describes the relationship between drug concentration and response [5]; particularly, the model is able to explain the concentration-response relationship when an endogenous biomarker is the response [5, 6].

The aim of this study was to characterize the relationship between FiO₂ and SpO₂ using a turnover model by retrospectively analyzing the data obtained from a controlled desaturation study.

In order to evaluate the quantitative relationship between FiO₂ and SpO₂, we utilized data obtained from a previous controlled desaturation study. Briefly, the protocol of the controlled desaturation study is as follows.

Of the 24 volunteers enrolled, four were excluded because of a technical error in FiO₂ data file storage. Hence, 20 volunteers were included in the pharmacodynamic analysis. The characteristics of these volunteers are summarized in Table 1. In total, 2899 SpO₂ data points from 20 volunteers were used to determine the pharmacodynamic characteristics. Time courses of the processed FiO₂ and SpO₂ are shown in Figure 1. As the FiO₂ decreased, the SpO₂ values tended to decrease as well. The SpO₂ values were maintained between 65–100% in each round in which hypoxic gas was supplied.

Fig. 1 Time courses of the processed fractions of inspired oxygen (FiO2, A) and peripheral oxygen saturation (SpO2, C) in all volunteers (n = 20). Processed FiO2 was defined as 100 minus FiO2. Changes in the processed FiO2 (B) and SpO2 (D) during the study period in one volunteer (ID4) are shown. Click for larger imageDownload as PowerPoint slide

Table 1 Volunteer characteristics (n = 20) Click for larger imageClick for full tableDownload as Excel file

The turnover model well described the time course of SpO₂ (Appendix). In particular, expressing the inhibitory function as a sigmoid model rather than a linear model further reduced the objective function value (OFV: 14495.97 for the linear model, 13179.24 for the sigmoidal model). No significant covariates for the pharmacodynamic parameters were observed. Figure 2 shows the plots of the predicted versus observed SpO₂ in the volunteers with the lowest or highest absolute values of the individual mean of weighted residuals. Table 2 shows the population pharmacodynamic parameter estimates, inter-individual variability, and median parameter values (2.5–97.5%) of the non-parametric bootstrap replicates of the final pharmacodynamic model of SpO₂. Predictive checks of the final pharmacodynamic model are presented in Figure 3. In total, 19.5% of the data were distributed outside of the 90% prediction intervals of the predictive check.

Fig. 2 Predicted and observed peripheral oxygen saturation (SpO2) in volunteers with the lowest (A and B) or the highest (C and D) absolute values of the individual mean of weighted residuals (A: ID2, 8.9%; B: ID4, 8.0%, C: ID8, 14.6%; D: ID7, 14.3%). The weighted residual was calculated as (measured - population predicted)/population predicted. The blue solid line and the red dotted line indicate population and individual prediction, respectively. Closed circles represent the observed SpO2 values. Click for larger imageDownload as PowerPoint slide

Fig. 3 Predictive checks of the final dynamic model of peripheral oxygen saturation (SpO2). The red solid line indicates the 50% prediction line. The blue dashed lines indicate the 5% and 95% prediction lines. +: observed SpO2. Click for larger imageDownload as PowerPoint slide

Table 2 Population pharmacodynamic parameter estimates, inter-individual variability, and median parameter values (2.5–97.5%) of the non-parametric bootstrap replicates of the final pharmacodynamic model of peripheral oxygen saturation (SpO2) Click for larger imageClick for full tableDownload as Excel file

The changes in SpO₂ due to decrease in FiO₂ under room air was well explained by the turnover model with inhibitory function as a sigmoidal model. In the setting of a controlled desaturation study, the potency of FiO₂ required to reduce SpO₂ from 100% to 70% was 14.7%.

The pulse oximeter is an essential monitoring medical device across many fields of medicine [8]. The SpO₂ accuracy of a pulse oximeter equipment should be a root-mean-square difference of less than or equal to 4.0% SpO₂ over the range of 70%–100% SaO₂ [3],

where A_rms describes the combined bias and precision of SpO₂ readings, SpO_2ij means the j^th measured SpO₂ value of the i^th volunteer, and S_Rij refers to the j^th measured standard reference value of the i^th volunteer. The standard reference value is determined by SaO₂, which is measured by using a CO-oximeter for arterial blood collected at the same time when SpO₂ is observed. The common manufacturing literature claim for A_rms for pulse oximeters is ± 2–3% over the range of 70–100% SpO₂ [8]. The total number of acceptable SpO₂-SaO₂ pairs obtained during clinical trials should be sufficient to statistically validate the specified SpO₂ accuracy. Typically, at least 10 volunteers are recruited, and at least 20 arterial blood samples per volunteer are obtained and analyzed with at least 200 data pairs. In addition, the distribution of the SaO₂ values should have similar density over the entire required range; for example, the ranges of 70–79%, 80–89%, and 90–100% SaO₂ should each have approximately 1/3 of the total data. Particularly, the complexion of the study participants should be specified because the accuracy of SpO₂ depends on the complexion, with dark skin pigmentation resulting in an overestimation of arterial oxygen saturation especially at low saturation in some pulse oximeters [9]. With the Nellcor N-595 device (Medtronic, Boulder, CO, USA), there was a significant difference in bias, defined as SpO₂ minus SaO₂, between light skin and dark skin in the 60–100% SpO₂ range [9]. For this reason, the U.S. FDA recommended that controlled desaturation studies should have subjects across a range of skin pigmentations, including at least 2 darkly pigmented subjects or 15% of the subject pool, whichever is larger [4]. However, in Korea, such desaturation study is not required to permit the pulse oximeter equipment.

If equilibrium is quickly established between the concentration of plasma and the response, then the pharmacological effect is immediately apparent; in such case, direct pharmacodynamic models such as the linear model or sigmoid Emax model can be applied. However, several drug responses can be considered as indirect in nature [10]. The turnover model can be appropriate for use when there is a delay between concentration and response [5, 10]; accordingly, the relationship between end-tidal carbon dioxide and regional cerebral oxygen saturation with delay was also quantified by the turnover model [6]. The net baseline effect is the balance between the apparent rate of “production” of the response and the rate of “removal” of the response [5]. In situations where the production and removal of response are complex, one step is rate-limiting, and these are represented by first-order rate constants k_in and k_out, respectively [5]. The turnover model is divided into four basic models depending on whether the response increases or decreases with increasing concentration [10]. The structural formulas of the four models are as follows [10].

Model 1: inhibition of production

Model 2: inhibition of loss

Model 3: stimulation of production

Model 4: stimulation of loss

, where k_in is the turnover rate constant, k_out is the fractional turnover rate constant, and I_max and E_max are maximal inhibitory and stimulatory effects attributed to drugs, respectively. IC₅₀ and EC₅₀ are drug concentration producing 50% of maximum stimulation and inhibition at effect site, respectively. R is a response variable and γ is the sigmoidicity factor. In the current study, basic model 1 was applied. Also, the sigmoidal model was more suitable than the linear model for use as an inhibition function. Graphically, the predicted value estimated by the sigmoidal model was also closer to the observed value. Physiologically, it is difficult to interpret a linear decrease in SpO₂ as FiO₂ decreases. The oxygen–hemoglobin dissociation curve that plots the proportion of hemoglobin in its saturated form on the vertical axis against the prevailing oxygen tension on the horizontal axis has a sigmoid shape; therefore, it is also desirable to apply the sigmoidal model for inhibitory function.

The following issues should be considered as limitations of this study. First, the observed FiO₂ may be somewhat inaccurate as intubation was not used and the volunteers breathed the mixed hypoxic gas through their mouth while their noses were blocked with a clothespin. Therefore, the volunteers' exhalation may have affected the FiO₂. However, a desaturation study involving volunteers does not generally require endotracheal intubation; also, as shown in Figure 1, the changes in FiO₂ during the study period were generally acceptable. Second, interindividual variability (IIV) in pharmacodynamic parameters could not be explained by covariates. As depicted in Table 2,IC₅₀ had approximately 45% IIV. However, in volunteer-based studies, the covariates are often not included because the demographic characteristics are homogenous. Covariates may explain the IIV in pharmacokinetic and/or pharmacodynamic parameters in studies involving patients with varying characteristics [6, 11]. Importantly, the number of volunteers in this study was too small to include covariates.

In conclusion, by using the data obtained in previous controlled desaturation studies, we observed that the SpO₂ value tended to decrease as the FiO₂ decreased. The relationship between FiO₂ and SpO₂ was well described by the turnover model with inhibitory function as a sigmoidal model. The potency of FiO₂ required to reduce SpO₂ from 100% to 70% was 14.7%.