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Abstract
Photoplethysmography (PPG) is an optical technique that monitors blood oxygen saturation levels, typically with the use of pulse oximeters. Conventional pulse oximetry estimates the ratio of light absorbed at two wavelengths. Attempts have been made to improve the precision of these measurements by using polarized light, with the tradeoff of requiring multiple sequential measurements. We demonstrate a novel PPG technique that uses radially polarized light generated by a light-emitting diode (LED) to obtain single-shot, blood oxygen-saturation measurements using a single wavelength at a rate of 50 fps. Our work, to the best of our knowledge, presents both a novel use of a vector beam and a first demonstration of vector-beam generation using LEDs.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Oxygen saturation in arterial blood is a critical measure of the efficiency of the lungs’ ability to transmit oxygen to blood vessels through capillaries [1]. This can be measured using arterial blood gas analysis, which is the most accurate and precise technique, with the tradeoff of being invasive and time intensive [2]. A common noninvasive approach is based on photoplethysmography (PPG), an optical technique used to measure blood volume changes in the microvascular bed of tissue [3]. Typically implemented through pulse oximetry, [4,5] the level of blood oxygen saturation (SpO2) is determined by comparing the PPG waveforms recorded at two different wavelengths emitted from light-emitting diode (LED) sources [6,7]. This allows for a more convenient and safe continuous monitoring of SpO2 in peripheral blood from cardiac-induced absorption. SpO2 readings above 95% are considered normal while those in the range 90-94% imply the patient is hypoxic, and those below 90% may be indicative of a clinical emergency requiring immediate life-saving intervention [8]. However, pulse oximeters are known to have a 2% error in readings [9]. Several factors that reduce the accuracy of readings include temperature, motion artifacts, nail polish/texture, skin pigmentation, and increased carbon monoxide for smokers [10,11,12]. Thus, there have been several studies seeking to improve the accuracy of pulse oximetry. A particularly promising approach employs a polarization model for measuring SpO2 [13].
Researchers have leveraged polarization techniques to improve the accuracy of SpO2 measurements [13,14]. Mishra et al. make use of polarization gating to differentiate between reflected components from deep and superficial layers of skin [13]. Sun et al. implement a cross polarization imaging technique to measure SpO2 complemented with a multi-linear regression algorithm to improve the accuracy of their measurements [15]. The algorithm considers the ratio of ratios (RoR) between the green and red channels of a smartphone light, as well as the reflectance images recorded at these channels. RoR is usually based on the different optical absorption rates of oxygenated hemoglobin (HbO2) and deoxygenated hemoglobin (Hb) at the red and infrared wavelengths. The method used by Sun et al. leads to a 43% improvement when compared to traditional RoR analysis. This approach however requires multiple, sequential measurements to determine SpO2 values [15]. An alternative method would be to parallelize the polarization state generation process using polarization vector beams, which exhibit spatially varying polarization states across their wavefront and a concomitant polarization singularity (intensity null) at the geometric center of the beam [16,17,18]. The most common vector beams are radially and azimuthally polarized light, which are often represented as a superposition of orthogonally polarized Hermite-Gauss HG01 and HG10 modes [19].
In this work, we present a novel polarization imaging-based technique to measure SpO2 values in five volunteers. Our experimental setup for radially polarized oximetry (RPOX) involves illuminating the finger with a radially polarized vector beam [20], derived from a partially coherent LED source, and measuring the response at a single wavelength for co- and cross-polarization states simultaneously. The ratio of the intensities are directly encoded into the beam profile leading to a single-shot method for SpO2 detection [13]. A statistical analysis is applied to compare our results to those obtained using two commercial devices. The work builds on the polarization model proposed by other researchers and simultaneously brings to the fore, a new application for vector beams as well as the first demonstration of LED-based vector-beam generation. This work is organized as follows. Section 2 depicts the theory based on reflection pulse oximetry. Section 3 exhibits the experimental approach. Section 4 presents the results and discussions. Finally, the conclusion of our proof-of-concept work is summarized in Section 5.
2. Theory
Conventional pulse oximetry makes use of the RoR method to calculate SpO2. Arterial blood oxygen saturation is a ratiometric measure of oxyhemoglobin to total hemoglobin. SpO2 can be determined from
Comparison of the optical extinction of deoxyhemoglobin and oxyhemoglobin in the red and infrared regions of the light spectrum, allows discrimination between these two compounds. Thus, the typical wavelengths used for pulse oximetry are 660 nm and 940 nm. When light is emitted through the peripheral site, there are several other absorbers of light (including water and melanin) with different path lengths, concentrations and extinction coefficients that contribute to light attenuation. Equation (2) can be divided into 3 components: attenuation due to arterial Hb, attenuation due to arterial HbO2, and attenuation due to tissues other than the arterial blood. These contributions are overall additive [22] and their expressions differ depending on whether the derived PPG waveform intensity corresponds to a valley Iv or a peak Ip in the waveform. Thus, the corresponding function for the valley intensity is defined as
The concentration of Hb and HbO2 can then be isolated by dividing Eq. (3) and (4), which removes the dependence on the non-arterial blood tissues and the power of the incident light such that
Using Eq. (5) for two separate wavelengths and finding the ratio of these equations we obtain Eq. (6) below [15]
Rewriting Eq. (1) and solving for ${{{C}}_{{{Hb}}}}$ gives Eq. (7)
Substituting Eq. (7) into (6) and simplifying the equation leads to the following expression for R
Finally, Eq. (8) can be rewritten so that SpO2 is a function of R
We see that SpO2 varies linearly with R, where the gradient of the line describing this relationship can be assigned to the variable ${\beta}$ and the y-intercept to ${\alpha}$
The calibration coefficients ${\alpha}$ and ${\beta}$ are determined by regression analysis or selected from look-up tables based on calibration curves [22].
Light traversing through scattering media, such as biological tissue, succumbs to changes in the state-of-polarization (SoP) where depolarization increases with depth of penetration through the finger as shown in Fig. 1(a) [13,14]. The depth of penetration of the light depends on the wavelength as shown in Fig. 1(b) [14]. Human skin consists of three main layers—the epidermis, dermis, and hypodermis [23]. Within these layers, the protein hemoglobin found in red blood cells, binds reversibly to oxygen forming HbO2. This molecule breaks down to form Hb and O2 in regions of the body in need of O2. An incoming optical field can be predominantly absorbed by either HbO2 or Hb, depending on whether the light reflected arises from blood vessels located in the deep or superficial layers of the skin, respectively [13]. The incident light is typically polarized and its reflected response (after interacting with the tissue) is recorded by a polarization-sensitive optical detection system. Detection is carried out for two polarization-analyzer scenarios, parallel (Ipar) and perpendicular (Iper) to the input polarization, in order to isolate the light reflected from the superficial and deep layers, respectively [13,14]. Ipar is described as [21]
where the polarization analyzer is oriented parallel to the incident illumination I0, Rs represents the superficial component of the light, and Rd refers to the deeply reflected light component. Tmel acts as a spectrally sensitive absorption filter representing the absorption due to melanin on the skin’s surface. In Iper, the superficial reflected light is rejected and as a result Iper is described as [21]
Fig. 1. (a) Reflection model of light penetrating the fingertip. The dashed black arrows indicate the propagation direction of the incoming transmitted, and reflected light, while the red arrows indicate the output polarization response. (b) The primary layers of the skin and the corresponding penetration depths of light at different wavelengths.
A relationship analogous to (1) between the polarization intensities and SpO2 can be determined by
To parallelize the measurement of Ipar and. Iper, a cylindrical vector beam is used. The radially polarized electric field used to illuminate the finger is described by [20]
where ${\vec{e}_x}$ and ${\vec{e}_y}$ are unit vectors, respectively, for the horizontal x and vertical y directions in Cartesian coordinates [20]. The component reflected off the finger subsequently passes through an analyzer that is oriented along the y-polarized direction. This approach thereby permits the following: simultaneous detection of the co-polarized HG01 mode corresponding to the maximum intensity, the cross-polarized with minimum intensity, and the unpolarized contributions emanating from the deep layers in the tissue. As a result, the data collection procedure is expedited.3. Experiment
3.1 Incoherent vector field generation and characterization
The combined experimental and calibration setup system for RPOX is shown in Fig. 2(a). An LED light source (Thorlabs M780L3-C1) spectrally centered at 780-nm wavelength, where tissue absorption is low [24], is first collimated by a lens (L1) and then impinges on a neutral density (ND) filter, which attenuates the power to 431 µW. Next, a spatial filtering system comprising an aspheric lens (L2), iris (I1), and collimating lens (L3) arranged in a 2f system generates an aberration-free, circularly symmetric beam. A linear polarizer (LP1) is subsequently used to ensure that vertically polarized light propagates through a zero-order vortex wave plate (Thorlabs WPV10L-780) for radially polarized vector field generation. For calibration, a silvered mirror (not shown) is used to direct the vector field to a CMOS camera (Edmund Optics 2122M) located at position 1, as indicated in Fig. 2(a). Conversely, the camera is moved to position 2 when SpO2 measurements are carried out, and the mirror is replaced by the individual’s finger.
Fig. 2. (a) Experimental and calibration setup based on reflection pulse oximetry. Radial vector beam (b) SOP and (c) Stokes parameters. Intensity vector distributions generated from an LED after the beam has passed through a polarization analyzer oriented (d) parallel and (e) perpendicular to the direction of the first. Red and green regions of interest indicate spatial dependent co- and cross- polarization states. ND: Neutral Density Filter, L1, L2, L3, L4, L5: Lenses, LP1, LP2, LP3: Linear Polarizers, I1, I2: Irises, and VWP: Vortex Wave Plate.
We begin our experiment by calibrating the radially polarized vector beam from an incoherent source. We measure the Stokes parameters of the vector field by inserting polarization analyzer LP2 and a quarter-wave plate (QWP) into the beam path immediately preceding the camera, as shown in Fig. 2(a). The relative intensity contributions of the various polarization components to the SoP of the vector field are then determined by the Stokes parameters defined as
3.2 Data collection procedure
Prior to carrying out measurements, informed consent is given by the volunteers. At this time, the volunteers are asked to fill a survey that collects information regarding their level of physical activity, caffeine consumption, smoking habits, and whether they are wearing nail-polish. This data set consists of five healthy volunteers of varying skin tones, (I – VI on the Fitzpatrick scale [25]. Of these 5 volunteers aged between 23 and 34 years, 3 are males and 2 females. Two trials per individual are carried out in a dark room at 65°F ambient temperature, each trial being 2 hours apart to account for intrapersonal variations. At the time of the study, volunteers are required to wear a face mask over their nose and mouth in order to comply with Brown University COVID policy. After 10 minutes of acclimatization to the lab environment, volunteers are asked to breathe under normal, deep, held, and shallow breathing conditions, which are synchronized by an audible metronome for 160 seconds. Normal breathing conditions entail volunteers breathing at a rate of 17 breaths per minute while deep breathing entails a rate of 6 breaths per minute. This is followed by breathing at a rate of 17 breaths per minute, occurring after the volunteer have held their breath for 30 seconds. Finally, the volunteers are asked to perform shallow breathing at 30 breaths per minute. Note that for this study, a waiver for IRB approval was received because the work focuses on calibrating the device, and thus does not meet the federal definition of generalizability.
3.3 Vector-beam pulse oximetry
As shown in Fig. 2(a) volunteers insert their finger into the optical setup after the generation of the vector beam where an iris (I2) is used to aperture the size of the beam. The non-specular light reflected from the deep and diffuse layers of the finger is collected by a 4f system comprising lenses L4 (focal length = 30 mm) and L5 (focal length = 30 mm), and subsequently imaged onto the camera at position 2. A linear polarization analyzer LP3 is placed after the finger and is set to be parallel to the illumination polarization produced by LP1. A series of 8000 frames is collected at 50 frames per second (fps), where Figs. 2(d) and 2(e) depict typical intensity profiles when LP3 is oriented parallel and perpendicular to LP1, respectively. These frames are then processed in MATLAB to generate the regions of interest as depicted by the red and green boxes in Figs. 2(d) and 2(e). This experiment makes use of Fig. 2(d). The red box represents Ipar and the green box represents Iper. Equations (1)–(4) are then applied to calculate SpO2 for RPOX, where the SpO2 value is averaged across 8000 frames. In tandem, two commercial pulse oximeters (Metene JPD500D and Masimo MightySat) are attached to a volunteer’s middle and index finger, respectively, on the right hand, where reference SpO2 measurements are recorded. Each commercial pulse oximeter has a reported accuracy of 2%.
3.4 Statistical methods
Participant-level characteristics are summarized with descriptive statistics. The main objective is to evaluate the performance of RPOX compared to the Metene and Masimo pulse oximeters. A linear regression model is used which regresses SpO2 on device type (effect-coded to allow for pairwise comparisons between RPOX vs. Metene and RPOX vs. Masimo), controlling for confounders identified a priori. Interest was in estimating effect sizes and confidence intervals, rather than strict statistical hypothesis testing. Data was analyzed using R statistical software.
4. Results
As shown in Table 1, our results suggest no significant difference in mean SpO2 between the Masimo oximeter and RPOX (p = 0.2078) as well as between the Metene oximeter and RPOX (with p = 0.0918) as summarized by the multiple linear regressions analysis shown in Table 1.
Table 1. Multiple linear regression analysis comparing RPOX to Masimo and Metene
Unadjusted outcomes are summarized in Table 2 across breathing conditions and participants. Participant outcomes are collapsed within individuals across conditions. From Table 2 we note that RPOX has the lowest standard deviation (SD) for each volunteer (1.21 × 10−4 for participant 1, 4.15 × 10−6 for participant 2, 3.23 × 10−6 for participant 3, 5.26 × 10−6 for participant 4 and 3.0 × 10−6 for participant 5) indicating that the measurements taken by RPOX are the most consistent when considering each participant separately.
Table 2. Summary of the mean, and standard deviation of SpO2 across breathing conditions for each participant.
Figure 3 are box and whisker plots of the results obtained for each participant under four different breathing conditions (shown by four different colors) for each device. We observe that RPOX provides oxygen saturation levels close to a baseline defined by the commercial devices for the normal, deep, held, and shallow breathing cases. The highest mean SpO2 value recorded for RPOX and Masimo for person 2, 3 and 4 was recorded under shallow breathing conditions. According to Fig. 3 the Masimo and Metene devices are more likely to record large variation in the SpO2 measurements collected over 160 seconds as shown by the range of values in the box and whisker plots. The value for participant 1 is below the expected range for healthy patients (95-100%) for the normal, deep, and shallow breathing conditions.
Fig. 3. Box and whisker plots for the 5 participants under, normal, deep, held, and shallow breathing conditions. While RPOX collects frames, the Metene and Masimo devices simultaneously records the SpO2 values of the participants.
Figure 4 depicts the combined-data box and whisker plots across participants for each device while the mean and standard deviation values for this data are summarized in Table 3. The purpose of combining the participant data is to evaluate the overall performance of RPOX when compared to Masimo and Metene. It is evident from Table 3 that RPOX shows the most variation for all breathing conditions except that of the held breathing condition, where RPOX shows the least variation. RPOX shows the most variation under shallow breathing condition (2.26%). From Fig. 4 and Table 3 we note that the SpO2 readings recorded by RPOX are (0.4-0.9%) lower than those recorded by Masimo and Metene. Additionally, RPOX shows the largest interquartile range in measured SpO2 values under the deep, held, and shallow breathing conditions in person 4.
Table 3. Summary of the mean, and standard deviation of SpO2 across breathing conditions across participants.
To investigate the influence of the data obtained for participant 1 on the combined participant data across devices, participant 1 is omitted from the data set summarized in Table 4. Consequently, RPOX shows the least variation in the normal and held breathing conditions.
Table 4. Summary of the mean, and standard deviation of SpO2 across breathing conditions across participants 2-5.
5. Discussion
There are two immediate observations from our work. The first is that the parallelization of the polarization degree-of-freedom allows for single-shot pulse oximetry, yielding SpO2 mean values consistent with those obtained using commercial devices. Our results suggest that a larger sample size will see the Metene pulse oximeter and RPOX tending towards having a difference in mean SpO2 measured as indicated by the low p value of 0.00918. The results of this experiment are significant as the RPOX approach could mitigate some of the artifacts associated with data acquisition over extended durations. The obvious tradeoff is the complexity associated with using a vector-beam mode converter. Another observation is the contribution of participant 1 to the data set. We clearly observe that the commercial devices are less sensitive to participant 1 than RPOX, as indicated by the generally lower standard deviations in measures for the former devices. This could result from the fundamental difference in method for RPOX compared to the other approaches. Any variations in skin textures or tones across participants would be mitigated using polarization-based approaches, such as RPOX, because of the polarization-gating method allows for improved separation of skin and subsurface contributions. As a result, RPOX would be more sensitive to underlying variations in SpO2 from an individual than the commercial instruments, where the skin contributions could mask such variations. For example, in the survey taken prior to the experiments participant 4 indicated that they had eaten between trials 1 and 2. This may have caused more considerable variations in the SpO2 values measured by RPOX compared to Masimo and Metene in person 4 when compared to the SpO2 values measured by RPOX for the other participants. However, a further study requiring a clinical trial would need to be carried out.
6. Conclusion
We have presented the first demonstration of pulse oximetry carried out using a radially polarized vector beam. Compared to conventional commercial pulse oximetry devices by Masimo and Metene, our approach permits single-shot data acquisition at a single wavelength. Our results showed no significant difference between the mean SpO2 readings measured by the commercial devices and our RPOX approach. Experiments were carried out at a rate of 50 fps, but ultimately the speed is limited only by the frame rate of the camera. Moreover, our work is the first demonstration of vector field generation using a partially incoherent light source, and a new application domain for vector beams, in general. Future experiments will be carried out on a much larger set of participants and will explore the role of melanin as a confounder in SpO2 readings.
Funding
Brown University Office of the Vice-President for Research; MURI award, Office of Naval Research (N00014-20-1-2789).
Acknowledgments
This work was supported by a seed award from the Brown University Office of the Vice-President for Research. This work is also partially supported by a MURI award from the Office of Naval Research (N00014-20-1-2789). J.A.B. acknowledges support from the Hibbitt Post-Doctoral Fellowship award. We would like to thank the members of the PROBE lab for participating as volunteers for this experiment. Lastly, Fig. 1 was adapted from the “Anatomy of Skin” BioRender.com (2022), retrieved from https://app.biorender.com/biorender-templates.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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