All patients underwent video-PSG measurement for diagnosis in our sleep laboratory. The following day, those patients who were diagnosed with OSA and recommended to use CPAP therapy by clinicians were recruited and gave their written informed consent for participation in the study. Patients with unstable coronary or cerebral artery disease, severe arterial hyper- or hypotension, respiratory diseases, or a history of a sleep-related accident were excluded. Finally, 30 newly diagnosed patients with OSA (mean age 54.2, SD 13.8 years, IQR 42-65 years; male: n=27; mean BMI 35.9, SD 7.5 kg/m², IQR 31.8-42.0 kg/m²; mean AHI 53.4, SD 24.7 per hour, IQR 32-71 per hour) participated in this study. This study was approved by the local ethical commission of Northwest Switzerland, and it was in compliance with the Declaration of Helsinki.

The patients underwent incremental stepwise CPAP (AirSense 10, ResMed) titration combined with video-PSG and FDMD-NIRS recordings in one nocturnal sleep episode. This sleep episode consisted of 1 hour of baseline sleep without CPAP, followed by incremental stepwise titration of 1 cmH₂O pressure per hour starting from 5-8 cmH₂O depending on the individuals. The 1-h baseline sleep allowed us to compare arm_OD with finger_OD during natural sleep in patients with OSA. We included the CPAP titration protocol because (1) the stepwise CPAP titration protocol can increase the number of hypopneas for data analysis in our patients, since low pressures cannot fully open the airways to restore the apneas but instead cause hypopneas and (2) auto-CPAP that can automatically adjust the pressures within a given range (ie, automatic titration), and CPAP with fixed pressures are the most efficient and popular therapy for OSA [44]. Thus, the comparison between arm_OD and finger_OD in hypopneas under various CPAP pressures could allow us to test the feasibility of monitoring treatment efficacy by measuring arm_OD.

Video-PSG (Embla RemLogic, Natus Medical Incorporated) is a comprehensive recording of physiological signals during sleep, including electroencephalography at electrode locations of C3, C4, O1, O2, F3, and F4 according to 10 to 20 system, eye movements (electrooculogram), muscle activation (electromyogram), electrocardiogram, breathing functions, heart rate, fingertip SpO₂ (left index fingertip in this study), and movement during sleep. Two experienced sleep technologists independently scored the sleep stages, respiratory and limb movement events, and motion artifacts in 30-second epochs according to the 2017 American Academy of Sleep Medicine manual [12]. Sleep hypopneas were defined as an at least 30% drop in airflow lasting for at least 10 seconds with either an arousal or >3% drop in SpO₂. The discrepancy between these two technologists was resolved by discussion or recommendation by an experienced neurophysiologist. The hypopneas were excluded from analysis if their SpO₂ desaturations were larger than 15% (n=31) to exclude outliers and potentially unreliable measurements caused by instrument errors.

In this study, FDMD-NIRS (Imagent, ISS) measurements were conducted over the middle of the left biceps muscle. Imagent is currently the only commercial benchtop FDMD-NIRS device [40,42,45] and has been CE-approved for research. Its light emitters, four laser diodes at 690-nm wavelength and four laser diodes at 830-nm wavelength, are coupled into four light sources and are high frequency modulated at 110 MHz. The light can penetrate the measured tissues with a depth of several centimeters when the four light sources are aligned and placed at 2, 2.5, 3, and 3.5 cm away from an optical fiber bundle connected to the photomultiplier tube detector.

The most common commercially available NIRS devices, including wearable NIRS devices (eg, Humon [30,31], Moxy [32,33], and PortaMon [34]), are continuous-wave NIRS (CW-NIRS), which measure the hemodynamic changes in human tissues based on the modified Beer–Lambert law (MBLL) [46-48]. As illustrated in Figure 1A, in the original Beer–Lambert law, the light extinction is proportional to the concentration C multiplied by the constant extinction coefficient ε for the particular absorber and the length d of the absorbing media when light passes through a nonscattering but absorbing media [49]. C × ε is also called the absorption coefficient µ_a of the absorbing media. However, biological tissues are highly scattering media, and scattering will increase the path-length of light, thus increasing the probability of both light absorption and loss of light. Scattering also makes it possible that some light can go out of the tissue from the same side of the light source (ie, backscattering light), as shown in Figure 1B. Thus, reflectance photoplethysmography (R-PPG) pulse oximeter [50-52] and the NIRS device in which the light source and detector are placed on the same side of the measured tissues were developed based on MBLL. In MBLL, the light propagation due to scattering is taken into account by introducing the differential path-length factor (DPF). The real path-length of light in the tissue is then calculated as DPF multiplied by the source-detector distance r. DPF varies between different biological tissues and different individuals, and it also depends on other factors such as light wavelength and age and gender of the individual [48,53]. CW-NIRS devices use fixed value of DPF in the range of 3 to 6 for different light wavelengths [53]. They can only estimate the relative changes in the main absorbing chromophores, that is, oxygenated hemoglobin (HbO₂) and deoxygenated hemoglobin (HHb) in the measured biological tissues. R-PPG and T-PPG pulse oximeters usually use two near-infrared wavelengths that are mainly absorbed by HbO₂ and HHb respectively. The influences of scattering on light attenuation are approximately assumed to be cancelled out in the calculation of SpO₂ that is derived from the ratio of the light intensities of the two wavelengths, ie, assuming the path-lengths of the two wavelengths are identical in the tissues [50-52]. However, this assumption is actually not valid because DPF varies between different wavelengths. Experimental calibrations against in vitro measurement of arterial oxygen saturation (SaO₂) in extracted arterial blood (ie, invasive co-oximetry) thus must be performed in commercial pulse oximeters during their research and development period to correct measurement errors [50-52]. Several calibration-free methods were also proposed, including calculating the real light path-length and absorption by using the frequency-domain NIRS algorithm [52,54-57].

As illustrated in Figure 1C, in FDMD-NIRS, the light emitted from light source can be detected by detectors placed at different distances away from the source. The light intensity (I_DC) and modulation amplitude (I_AC) of the detected light decrease, and a phase delay (φ) occurs between the detected light and the source light due to absorption and scattering. The detected I_DC and I_AC are smaller but theφ is larger at the detector further away from the light source. The I_DC, I_AC and φ from different light source-detector distances vary linearly [42,45]. Therefore, to submit the measured I_DC, I_AC and φ to linear regression, we can obtain the following equations derived from the photon diffusion equation in a semi-infinite geometry [40,45,58-60]:

ln (r²I_AC) = rS_AC + C_AC (1)

ln (r²I_DC) = rS_DC + C_DC (2)

φ = rS_φ + C_φ (3)

Where r is the known source-detector distance, S_AC, S_DC and S_φ are the slopes and C_AC, C_DC and C_φ are the intercepts. The linearity of the equation is monitored by the R² of the fitted linear regression. By combing any two of these three slopes (eg, we chose S_AC and S_φ in the following equations), we can calculate the absorption coefficient µ_a and the reduced scattering coefficient µ_S^’ of the measured tissue [40,45,58-60]:

µ_a = ω/2v × (S_φ / S_AC − S_AC / S_φ) (4)

µ_S^’ = (S_AC² − S_φ²) / 3µ_a − µ_a (5)

where ω/2π is the modulation frequency and v is the velocity of light in the tissue. FDMD-NIRS uses two wavelengths. The µ_a and µ_S^’ of both these wavelengths can be calculated individually by using the same equations (4) and (5). Equation (4) gives us the absorption coefficient of the measured tissues calculated by taking the influence of scattering into account. It is equal to C × ε as mentioned above. In NIRS, the main contributions to absorptions in tissues are HbO₂ and HHb, so we have the following equation:

µ_a^λ = ε_HHb^λ C_HHb + ε_HbO2^λ C_HbO2 (6)

where µ_a^λ is the absorption coefficient of the measured tissue at wavelength λ. ε_HHb^λ and ε_HbO2^λ are the known extinction coefficients at wavelength λ for HHb and HbO₂, respectively. C_HHb and C_HbO2 are the concentrations of HHb and HbO₂, respectively. Using two wavelengths λ1 and λ2, we can then calculate C_HHb and C_HbO2 with the following equations:

C_HbO2 = (μ_a^λ1 ε_HHb^λ2 − μ_a^λ2 ε_HHb^λ1) / (ε_HbO2^λ1 ε_HHb^λ2 − ε_HbO2^λ2 ε_HHb^λ) (7)

C_HHb = (μ_a^λ2 ε_HbO2^λ1 − μ_a^λ1 ε_HbO2^λ2) / (ε_HbO2^λ1 ε_HHb^λ2 − ε_HbO2^λ2 ε_HHb^λ1) (8)

Therefore, Sto₂ can be further derived as:

StO₂ = 100 × C_HbO2 / (C_HbO2 + C_HHb) (9)

The FDMD-NIRS algorithm can calculate the absolute values of HbO₂, HHb, and StO₂ in the measured tissue and it is superior to the simple CW-NIRS algorithm, because of its sophisticated mathematical frameworks calculating µ_a and µ_S^’ that can best estimate the real light propagation distance in the measured tissues based on the diffusion equation in complex geometries. The robustness, precision, and accuracy of measuring HbO₂, HHb, and StO₂ of the Imagent system used in this study have been well validated in different physical blood-lipid models [45,58,61] and in vivo studies [59,62-64]. It has been used as a gold-standard reference measurement of StO₂ for validations or calibrations of wearable CW-NIRS armbands [31] and portable CW-NIRS oximeters [61,65] including those that have received FDA clearance [66,67].

In this study, the sampling rate of FDMD-NIRS recording was 5.2 Hz. The reliability and accuracy of FDMD-NIRS measurements depend on the linearity of the measured optical signals on distances, because µ_a and µ_S^’ are derived from the slopes of equations (1-3). The linear dependence R² of the modulated light amplitude and phase shift over the measured distances should be highly close to 1 in each light wavelength. Thus, before the start of the recording, our Imagent system was calibrated on an optical phantom block with known µ_a and µ_S^’, that is, the light intensity of each light source was adjusted so that R² was equal to 1 and the measured µ_a and µ_S^’ of the optical phantom block were equal to their known values. This calibration step can exclude the uncertainty of our measurements due to machine errors such as light source and detector errors. The raw optical data were discarded if the R² was smaller than 0.95 in either modulated light amplitude or phase shift in any wavelength to exclude poor-quality data arising from improper probe-skin contact and shunted light reaching the detector without travelling through the tissue [68,69]. The NIRS data were then subjected to a low-pass (<0.08 Hz), zero-phase filter designed using Hanning window to remove the physiological noises, including heart rate, respiratory noise, and spontaneous slow hemodynamic oscillations [70,71]. The filtered data were smoothed with moving average smooth method (robust locally weighted scatter plot smoothing [70,72]).

Bland-Altman plots were used to illustrate the agreements between arm_OD and finger_OD during baseline sleep and under CPAP, respectively. We used t test to determine whether the differences between arm_OD and finger_OD were significantly different from 0. In order to check whether arm_OD could replace finger_OD in subgroups of hypopneas (ie, hypopneas with different degrees of desaturations), we used Spearman correlation to evaluate the relationship between arm_OD and finger_OD in different subgroups defined by finger_OD greater than or equal to specific cut-offs. The cut-offs ranged from 2% to 8%. P values <.05 indicated statistical significance for both analyses. Pre-processing of FDMD-NIRS signals was carried out in MATLAB (MathWorks, Inc.). All statistical analyses were performed using R statistical software (version 3.2.4; R Foundation for Statistical Computing).

In this study, we compare, for the first time, event-by-event finger_OD to arm_OD in sleep hypopneas during naïve sleep and CPAP therapy sleep. We choose the gold-standard reference methods for both arm_OD and finger_OD—advanced FDMD-NIRS for arm_OD and PSG fingertip transmission photoplethysmography for finger-OD. Arm_OD is 2% to 3% smaller than finger_OD, probably because finger_OD is caused only by arterioles, whereas arm_OD is physiologically determined by mixed sources of arterioles, venules, and capillaries [42,73,74]. The lower value of arm_OD is thus most likely due to the contribution of the venous blood pool. The significant difference between finger_OD and arm_OD and their broad LoA (Figure 4) suggest that arm_OD cannot directly replace finger_OD to define hypopneas. If the standard criterion of ≥3% drop is applied, it will cause a high rate of false-negative results in diagnosing OSA and in assessing the efficacy of CPAP treatment. The poor agreement between finger_OD and arm_OD and the low sensitivity of arm_OD in measuring hypopneas cannot essentially be improved even after normalization, in which raw arm_OD is normalized to its baseline before the start of hypopnea. The poor correlations (Figure 5) between finger_OD and arm_OD across hypopnea severity further suggest that the arm_OD cannot be used to define hypopneas, that is, correlations remain low even in severe hypopneas that are associated with much larger finger_ODs.

The armband and smartwatch are two of the most popular wearable technologies. Our results have direct implications for wearable armbands and portable oximeters using NIRS techniques to measure OSA, as we discuss below.

First, the FDMD-NIRS system used in our study is well recognized as the most robust and reliable reference NIRS technique [31,42,61]. Arm StO₂ measured by our device should be identical to that measured by consumer-grade wearable NIRS armbands (eg, Humon [30,31], Moxy [32,33], and PortaMon [34]). It should also be equal to that measured by FDA-cleared medical-grade portable NIRS oximeters, such as INVOS 5100C (Medtronic) [66], FORE-SIGHT (CAS Medical Systems) [67], SenSmart (Nonin Medical Inc) [75], Hutchinson InSpectra (Hutchinson Technology Inc) [76], and ViOptix ODISsey (ViOptix Inc) [77]. Our results suggest that the absolute or relative (ie, normalized to baseline) OD at arm muscle measured by these aforementioned devices cannot be directly used to define sleep hypopnea.

Second, the NIRS StO₂ is the proportion of HbO₂ in arterial, capillary, and venous compartments of the measured tissue. It can be expressed by its two major compounds as StO₂ = (a × SaO₂) + (b × SvO₂), where SaO₂ and SvO₂ are the arterial and venous oxygen saturation [68,73]. Fingertip SpO₂ is the best noninvasive estimate of SaO₂ [50,52]. The ratio of the coefficients a/b is called the arterio-venous ratio (AVR). The AVR of different tissues (eg, brain and muscles) and different populations (eg, healthy people and patients, adults, and children) has been determined by invasive measurements under different conditions but not during sleep [73,78-88]. Commercially available NIRS oximeters, including the aforementioned FDA-certificated medical devices take the fixed AVR value as either 0.25/0.75 or 0.30/0.70 but have not validated it in OSA [78-88]. Our results of poor correlations between arm_OD and finger_OD (Figure 5) indicate that such an uncritical AVR adoption is not justified. According to the mathematical model of fixed relationship between StO₂ and SaO₂, we expect a strong correlation between StO₂ and SpO₂ that we could not confirm using our data. These conflicting results suggest that the model is not valid for OSA. Therefore, developers of wearable or portable NIRS devices should first study the AVR in muscle tissues and validate it against invasive blood sample measurements before using their devices commercially for OSA diagnosis.

Our findings also indicate that appropriate arterial oxygen saturation measurement is not possible with armbands using the R-PPG method. As mentioned in the Methods section, R-PPG essentially has the same theoretical limitations as CW-NIRS, such that the scattering of light in the human tissues cannot be calculated. R-PPG and T-PPG pulse oximeters estimate SpO₂ under the assumption that changes in blood volume only occur in arterial but not in the venous compartment. SpO₂ is measured from the fingertip or the superficial forehead because these locations are well perfused by arteries [36,52,89]. It is not recommended to measure SpO₂ by using R-PPG at the wrist or the arm, because of its low signal-to-noise ratio. Compared to the more precise fingertip T-PPG method, the low signal-to-noise ratio of R-PPG at the wrist or arm is about 10 times weaker due to various factors such as relative low blood perfusion and sensitivity to pressure and ambient light sources [51,89]. Additionally, the key assumption of constant venous blood volume is no longer valid at the wrist or arm [89,90]. Although recently, some smartwatches [26-29] and a few armbands [35-37] claimed that they can measure SpO₂ at the arm or wrist by using R-PPG, they actually measure both arterial and venous blood [89,90] similar to NIRS. A main difference between NIRS and R-PPG is the measurement depth. Whether R-PPG measures the blood only in the skin or in both the skin and muscle depends on the distance between the light source and detector [91]. The detector can detect the light passing through deeper tissues at a larger separation distance. In vivo studies suggest that R-PPG can obtain its best signal-to-noise ratio at a separation distance of 3 to 6 mm [92]. Thus, a separation distance of several millimeters is used in the design of R-PPG pulse oximetry [36]. A recent study modeled the R-PPG light propagation in human skin [37]. The authors found that even at a separation distance of only 0.6 mm, many light rays reaching deeper into the muscle can still be received by the detector because of the random nature of light scattering [37]. Therefore, similar to NIRS armbands, armband devices using R-PPG capture the oxygen saturation in both skin and muscle. There are challenges in using both techniques to differentiate SaO₂ and SvO₂ desaturations from the measured StO₂ desaturation to define sleep hypopneas.

We did not include a smartwatch in this study, although recently, leading smartwatch companies like Apple, Fitbit, Garmin, Huami, and Huawei have all added the function of measuring oxygen saturation in their products. This is because these commercially available products cannot or are unwilling to export their raw data for analyses, or their temporal resolutions are simply too low for an event-by-event comparison necessary for our study because usually these consumer-grade smartwatches upload their data to their cloud servers in minute resolution. Nevertheless, our results may have indirect implications for smartwatches. R-PPG smartwatch is different from the fingertip T-PPG in measuring SpO₂. Lee et al [89] found that the raw light signals measured by wrist R-PPG and fingertip T-PPG change differently during breath-holding, indicating different SpO₂ values are calculated by these two techniques. Abay et al [36] reported that wrist R-PPG results in lower SpO₂ values than fingertip T-PPG at rest, and during venous occlusion, fingertip T-PPG SpO₂ does not exhibit desaturation but wrist R-PPG SpO₂ drops similarly as the simultaneously measured NIRS StO₂ at the same arm. Their findings also indicate that although smartwatches measure the wrist and NIRS measures the arm muscle, the measured changes in oxygen saturation by these two techniques are likely to be the same. Thus, the venous blood influences in our NIRS StO₂ measurements are also likely to be observed in smartwatch measurements.

Our study warns consumers, health care insurance companies, and sleep clinicians and scientists to interpret the AHI provided by smartwatches and armbands with caution until those products are clinically and experimentally validated. An AHI >5/hour suggests the diagnosis of OSA [12]. Our results suggest that AHI is likely to be underestimated if using the criterion of arm_OD ≥3% to define hypopneas. Wearable technology developers who are validating their products can learn from this study and take into account the mismatch between the ODs measured by their products and by the gold-standard technique fingertip pulse oximetry. Developing new parameters (eg, estimated-oxygen-variation provided by Fitbit smartwatches [26]) or combining smartwatches with external fingertip T-PPG sensors [93] may be a more promising strategy to measure OSA. Nevertheless, validations of these new approaches are necessary before releasing them for clinical use. In addition, our finding of a weak correlation between finger_OD and arm_OD indicates that (1) prediction of finger_OD using arm_OD may be possible but will require development and implementation of sophisticated data-mining, such as machine learning algorithms [90], and (2) as previous studies have validated NIRS oximeters as medical devices, protocols that quantify the arterial and venous contributions to the arm_OD are needed. Arm_OD can then be calibrated to indicate the changes in the arterial ODs at the arm or wrist.