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Abstract
Commercial photoplethysmography (PPG) sensors rely on the measurement of continuous-wave diffuse reflection signals (CW-DRS) to monitor heart rate. Using Monte Carlo modeling of light propagation in skin, we quantitatively evaluate the dependence of continuous-wave photoplethysmography (CW-PPG) in commercial wearables on source-detector distance (SDD). Specifically, when SDD increases from 0.5 mm to 3.3 mm, CW-PPG signal increases by roughly 846% for non-obese (NOB) skin and roughly 683% for morbidly obese (MOB) skin. Ultimately, we introduce the concept of time-of-flight PPG (TOF-PPG) which can significantly improve heart rate signals. Our model shows that the optimized TOF-PPG improves heart rate monitoring experiences by roughly 47.9% in NOB and 93.2% in MOB when SDD = 3.3 mm is at green light. Moving forward, these results will provide a valuable source for hypothesis generation in the scientific community to improve heart rate monitoring.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Obesity is commonly classified by a body mass index (BMI) of 30 or above [1] . It is estimated that a metabolically healthy 50-year-old adult has a lifetime cost savings of about $\$$36,000 when compared to an obese individual [2]. As of 2023, 31% of Americans use optical wearable sensors to track physical activities via heart rate metrics [3]. These devices have important potential health benefits, such as monitoring, storing, and sharing health data with healthcare providers in real-time. These benefits could improve health and reduce healthcare visits and costs, particularly among individuals with chronic conditions. Studies show that roughly 82% of U.S. adults are willing to share the data from wearable devices with their health care provider [4]. Users can also use the immediate feedback from wearables to adjust physical activity and energy expenditure [5].
PPG technology in the wearables requires only basic opto-electronic components: a steady state continuous-wave (CW) light source to illuminate the skin and a photodetector to measure the small variations in the reflected light intensity associated with changes in perfusion [6,7]. PPG technology can be used as a pulse oximeter and has been widely used in clinics to monitor patients’ arterial oxygen saturation [8,9]. A PPG pulse is characterized by two phases: the anacrotic phase associated with systole and the catacrotic phase associated with diastole [10,11]. For people with healthy compliant arteries, the catacrotic phase usually features a dicrotic notch [10,11]. With recent clinical applications of PPG waveforms ranging from blood pressure evaluation to cardiovascular disease (CVD) detection, it was identified that blood volume and blood vessel wall movement in skin are key factors that can affect PPG measurements [12–17]. The human skin can be divided into three layers: the stratified cellular epidermis on top, the dermis of connective tissues (where the vascular bed is found), and the subcutis of adipose tissues at the bottom [18]. To provide a useful PPG signal, optical sensors must be able to detect the vascular bed and its pulsatile activity within the dermis layer. Melanin, a pigment produced by melanocytes, is the main absorber in the epidermis. There are two types of melanin: phaeomelanin and eumelanin, whose concentration is the deciding factor of skin colors. Though superficial optical contrast may be optimized in the visible (VIS) region of the electromagnetic spectrum where blood absorption is high [19,20], epidermal melanin absorbs light strongly in this region [18] and is a major barrier for qualitative PPG in individuals with darker or thicker epidermal layers. As a compromise, common commercial wearables often consist of both green (wavelength of 520-540 nm) and near infrared (NIR) light sources (wavelength of 920-960 nm) [21].
Studies have shown that continuous monitoring of heart rate using wearable devices is more effective in increasing physical activities and decreasing body weight in individuals with obesity and chronic comorbidities than traditional interventions [22–26]. However, current wearable devices may not provide accurate heart rate measurements for obese individuals [27] with higher-than-average epidermal thickness, dermal thickness, and resting blood vessel size [18,28]. Recent studies have investigated the effects of skin tone on the accuracy of wearable PPG devices and showed that skin tones have minor effect in PPG signals [21,29–31] though it was noted that difficulties with obtaining accurate data for test subjects with dark skin were due to a low signal-to-noise ratio [32]. Overall, it was reported that variation in skin layer thickness (i.e due to obesity) has a more profound effect on PPG signals [21]
Although previous study have investigated the effects of skin tone and obesity [21], a quantitative analysis of the effect of source-to-detector distances (SDD) on PPG signals was not performed. More importantly, a solution to the poor sensitivity in commercial PPG when considering thick epidermis (morbidly obese) with larger concentration of melanin (dark skin tones) does not exist.
In this paper, we will address these issues by introducing the novel concept of time-of-flight PPG (TOF-PPG) while offering a closer observation of the effect of SDD on PPG signals in both continuous-wave diffuse reflection signals (CW-DRS) and time-of-flight diffuse reflection signals (TOF-DRS). This is accomplished by simulating photon migration in skin using a commercial Monte Carlo method that records photon distribution time of flight (DTOF) in both non-obese (NOB) and morbidly obese (MOB) cases at green and NIR wavelengths.
2. Methods
Two time-variables are identified in this work: pulsatile time (τp) and time-of-flight (τs). Pulsatile time has a period of 1 second and describes the change in size of blood vessels during cardiac cycles. This cycle includes a direct current (DC) component associated with the smallest vessel size and an alternating current (AC) component associated with the range of vessel size. The time-of-flight is in the order of picoseconds to nanoseconds and describes the time for photons to travel from the source to the detector after interacting with media. In addition, the PPG signal is defined as the AC/DC ratio of a complete PPG waveform (Fig. 1). To reduce computational time and storage, we selected 25 data points to simulate a full PPG wave while maintaining its critical characters including: pulse onset, systolic peak, dicrotic notch, and diastolic peak [33].
Fig. 1. An example of CW-PPG waveform: the simulated PPG waveform is determined by the negative log of the diffuse reflectance signal (DRS). Overall, PPG signal is determined by AC-to-DC ratio. Here, we consider NOB case at SDD = 3.3 mm and wavelength of 523 nm
2.1 Optical properties for skin
Optical properties (the absorption coefficient, µa, the scattering coefficient, µs, the anisotropy, g, and the index of refraction, n) for each layer of skin at two wavelengths in Apple S5 series (green light of λ = 523 nm and IR light of λ = 940 nm) are summarized in Table 1. Although light sources in wearables have large linewidths, Ajmal et al showed that the difference between the single wavelength PPG simulation and the broadband PPG simulation was within 6.5% in extreme cases (from NOB skin tone 1 and MOB skin tone 6) [21]. Therefore, we will utilize single wavelength simulation approaches for Apple S5 LEDs to reduce computational time.
Table 1. Summary of optical properties at Apple S5 series wavelengths
As discussed by Lister et al [34], there are many factors affecting the measurement of skin optical properties in the literature such as sample preparation, methods (in vivo or in vitro), and optical techniques (diffusion approximation, adding-doubling, Monte Carlo, phase functions, etc.). Here, tissue parameters were selected so that similar optical property values can be calculated and approximated to those used in previous PPG studies [21,22].The absorption coefficient µa for a given layer is determined by the Eq (1) where B is the volume fraction of blood, S is the percent saturation of oxygen in hemoglobin, W is the volume fraction of water, and M is the volume fraction of melanin [35]. µa, oxy, µa, deoxy, µa, water, and µa, melanosome are the wavelength dependent absorption coefficients for oxygenated blood, deoxygenated blood, water, and melanin, respectively.
The values used for each of the volume fractions are shown in Table 2. For melanin, the volume fraction was approximated from the Fitzpatrick Scale of skin types. The melanin volume fraction in the epidermal layer was set at 42% [21] to produce epidermis µa = 25 cm-1 at λ = 523 nm (table 1) . Dermal oxygenation of 39% was chosen to match total dermal absorption (Eq. 1) for darker skin tone in Ajmal et al.’s studies and the dermal oxygenation in Rodriguez et al’s report [18,21]. Epidermal water content is small (W < 2.5%) [18] while water absorption in visible region is also small. Subsequently, the contribution of water content in epidermal total absorption is insignificant and thus was reduced in our study to yield best fit with Eq (1). The spectra for the absorption coefficients are presented in Fig. 2(a).
Fig. 2. Optical properties spectra in the wavelength range of 500-1000 nm: (a) absorption coefficients, µa and (b) reduced scattering coefficients, µs’. The broadband spectrum is extrapolated to meet values in table 1 and is based on parameters used in table 2.
Table 2. Summary of physical properties at each layer
The scattering coefficient µs for a given layer is determined by Eq. (2) where $\lambda \; $ is the wavelength, a’ is the scaling factor at λ = 500 nm, g is the anisotropy, fRay is the fraction of Rayleigh scattering, (1 – fRay) is the fraction of Mie scattering, and bMie is the Mie scattering power [35]. Using the values shown in Table 2 for a’, g, fRay, and bMie, scattering coefficients were derived for each layer at each wavelength. The spectra for the reduced scattering coefficients are presented in Fig. 2(b). While anisotropy factor g (dimensionless) is dependent on wavelength and is used to describe the amount of forward direction retained after a single scattering event, it is also a common practice in tissue optics to lump a constant g into the wavelength-dependent reduced scattering coefficient µs’ where µs’ = µs (1-g) [20,36,36]. Therefore, we selected g = 0.7 while matching µs’ values with those used previously for skin [21].
2.2 Monte Carlo eXtreme model
Here, we consider skin of three distinct layers: epidermis, dermis and subcutis. A GPU-based Monte Carlo eXtreme (MCX) [37] was used to save both CW-DRS and photon DTOF, and to simulate PPG (Fig. 3). The simulation launches 10 billion photons as a Gaussian beam with a beam diameter of 1.6 mm into a tissue volume of 2 × 4 × 1.1 mm3 (X-Y-Z). The size of each voxel is 2 µm and time-of-flight bin is 2.5 ps. An array of detectors with diameter of 400 µm were populated along Y dimension with SDD up to 3.3 mm. Straight cylinders along X-dimension were used to simulated blood vessels in the dermis. To simulate the effects of obesity, we consider differences in layer thickness and vessel diameter. Epidermis thickness is 100 µm for NOB and 125 µm for MOB. As reported in literature, dermal vessel size ranges between 20 µm and 120 µm [38], with an overall higher average in obese individuals [39]. In this study, the vessel diameter at rest is set at 50 µm for NOB and 75 µm for MOB with an average cross-sectional vessel density of 33.75 vessels/mm2 in the dermis, within the range used in previous studies [40,41]. Cylinder volume is changed with τp to simulate the PPG wave pulse [21,22]. Fig. 3 shows an example of MCX simulation. Comparing to recent PPG studies which simplified the vascular bed to a layer of blood [21,22,42], our model is the most accurate in allowing reasonable vessel densities in skin anatomy. Currently, each simulation takes approximately 80 minutes to complete on an NVIDIA Dual GeForce RTX 2080 GPU. Note that although dermal blood vessels may vary in shape, the effect of vessel density (or total blood optical density) on PPG signal is dominant. This is supported by previous studies where simulations of straight cylindrical vessels and of a layer of blood produced the same PPG signal when the same total blood optical density is carefully used [21].
Fig. 3. An example of MCX simulation with vessel at rest for NOB case: (a) 3-D display of the simulated volume, (b) An example of depth fluence profile in log-scale showing the arrangement of the vessels at rest across the YZ plane in NOB case. The source detector is located on the skin surface (X = 0 mm, Y = 0 mm, Z = 0 mm). Below the dermis, there is a subcutis layer which is not shown and is not of interest in our study.
3. Results
3.1 CW-PPG at λ = 523 nm
The simulations show that increasing SDDs increases CW-PPG signal in both NOB and MOB with dark skin tones. (Fig. 4) and that PPG signal in NOB case (Fig. 4(a)) is significantly higher than that in MOB case (Fig. 4(b)). More specifically, PPG signal (or AC/DC ratio) increases by approximately 9.5 times when SDD increases from 0.5 to 3.3 mm in NOB case (from 0.965% to 9.13%) and nearly 8 times in MOB case (from 0.304% to 2.38%). Notably, at SDD = 2.4 mm (smallest SDD in Fitbit Versa 2) and SDD = 3.3 mm (smallest SDD in Apple S5) [21], PPG signal in NOB is over 3.5 times higher than that in MOB.
Fig. 4. CW-PPG as a function of SDD: (a) PPG waveforms in NOB case, (b) PPG waveforms in MOB case, and (c) AC/DC ratio. Overall, PPG increases with SDD and NOB PPG is higher than MOB PPG.
3.2 TOF-PPG at λ = 523 nm
The principle of time-resolved or time-of-flight diffuse reflectance spectroscopy (TOF-DRS) is based on the injection of a short light pulse into the sample and on the temporal detection of the re-emitted light (Fig. 5). Time-resolved or time-of-flight diffuse reflectance spectroscopy (TOF-DRS) outperforms continuous-wave steady state DRS (CW-DRS) in different circumstances: TOF-DRS can assess absolute optical properties of various human tissues with high accuracy, is less prone to source-detector distance (SDD) and detector size, and has better depth sensitivity than CW-DRS [43–45]. These advantages are due to the ability of time-gating technology to target the observed photon groups (relative to their path-lengths in the tissue) [46–48]. While TOF-DRS has been used extensively to measure optical properties of layered tissues [49–51], it has not been used to compute PPG. Fig. 5 demonstrates the advantages of TOF-DRS in tagging the group of photons from certain depth being collected at a specific SDD. Like other models of time-resolved reflectance [52,53], we are only interested in simulating the sample response function or distribution time of flight (DTOF). The contribution of pulsed laser response function in the measured DTOF will be handled experimentally (depending on the laser) using several different deconvolution approaches [54]. In general, longer time gate is applicable for photons travelling deeper in skin (Fig. 5(d&e)). A similar concept is applied to optimize PPG signal for specific SDD so that longer τs is used for larger SDD (Fig. 5(g&h)).
Fig. 5. Principle of TOF-DRS considering τp = 0: (a) A demonstration of TOF - depth relationship to show that longer time gate τs is applicable for photons travelling deeper in skin, (b) An example of DTOF at SDD = 2 mm, (c-e) 2-D images of depth fluence and (f-h) 2-D images of surface reflectance in CW and at τs = 5 ps and 10 ps. Here, MOB case is shown when λ = 523 nm and when vessel is at rest. Pixel intensity is normalized and plotted in log-scale (c-h).
MCX saves DTOF as a function of SDD, optical properties (wavelengths), vessel size and density as well as epidermal thickness (NOB case and MOB case) (Fig. 5(b)). At each SDD, we select τs values so that reflectance (and PPG) is optimized. In general, the simulations show that the PPG dependance on SDD is insignificant when SDD is larger than 2 mm (Fig. 6), especially in MOB case (Fig. 6(b)). Most notably, the AC/DC increases about 70% as SDD increases from 1 mm to 2 mm in the NOB case (Fig. 6(a)). Beyond SDD = 2 mm, AC/DC fluctuates between 12% and 14% in NOB, and between 3.8% and 4.3% in MOB (Fig. 6(c)).
Fig. 6. TOF-PPG as a function of SDD at optimized τs values: (a) PPG waveforms in NOB case, (b) PPG waveforms in MOB case, and (c) AC/DC ratio as a function of SDD for both NOB and MOB. Like Fig. 4, MOB reduces PPG signal. Unlike Fig. 4, PPG signal is less affected by SDD, specifically when SDD > 2 mm.
Fig. 7 compares TOF-PPG to CW-PPG considering the full waveform in NOB and MOB case at SDD = 2 mm (Fig. 7(a)) and SDD = 3.3 mm (Fig. 7(b)), as well as AC/DC ratio (Fig. 7(c)). Though the difference between TOF-PPG and CW-PPG becomes smaller as SDD increases, TOF-PPG outperforms CW-PPG in all simulated cases. Notably, AC/DC in TOF-PPG improves by about 100% in both NOB case at SDD = 2.4 mm and in MOB case at 3.3 mm.
Fig. 7. Comparison between CW-PPG and TOF-PPG in NOB and MOB cases: (a) PPG waveform at SDD = 2 mm, (b) PPG waveform at SDD = 3.3 mm, and (c) AC/DC as a function of SDD. TOF-PPG significantly improves AC/DC signal in all cases.
3.3 CW-PPG and TOF at λ = 945 nm in MOB case
Fig. 8 compares PPG signal at green wavelength (in green color) to that at IR wavelength (in red color) when using CW (Fig. 8(a&b)) and TOF technique (Fig. 8(c&d)), considering MOB case (epidermal thickness = 125 µm).
Fig. 8. PPG Comparison between green wavelength and NIR wavelength in MOB case: (a&b) CW-PPG (c&d) TOF-PPG. Overall, green wavelength is more advantageous than NIR wavelength in studying heart rate, particularly when SDD > 2 mm, in our simulation geometry where epidermal thickness = 125 µm.
In CW-PPG, IR wavelength produces higher AC/DC ratio than green wavelength when SDD < 2.3 mm and lower AC/DC ratio when SDD > 2.3 mm (Fig. 8(a&b)). The maximum AC/DC ratio of 2.25% is observed with NIR wavelength when SDD = 1.25 mm (Fig. 8(b)). In TOF-DRS, green wavelength produces better PPG signal than IR wavelength regardless of SDD (Fig 8(c&d)). More specifically, when SDD = 3.3 mm, AC/DC ratio in green wavelength is about 160% better than in IR wavelength.
In TOF-PPG, IR wavelength produces lower AC/DC ratio than green wavelength at any SDD (Fig. 8(c&d)). In addition, AC/DC dependance on SDD is insignificant, particularly for NIR wavelength. It is noted that CW-NIR and TOF-NIR produce similar AC/DC at SDD = 3 mm.
4. Discussion and conclusion
In this study, we showed that CW-green AC/DC ratio is higher in NOB than that in MOB, and is higher than CW-IR AC/DC ratio when SDD > 2.3 mm. These trends agree with previous studies which focused on SDD > 2.4 mm [21]. This phenomenon is likely due to the dominant effect of high blood absorption at green wavelength over the penetrating power of NIR wavelength in PPG analysis at long SDD. In addition, green CW-PPG increases with SDD (Fig. 4) whereas IR light PPG decreases with SDD when SDD > 1.25 mm (Fig. 8(a&b)). Most notably, CW-IR is more advantageous than CW-green in detecting PPG signal at short SDD, producing up to 240% better signal (when SDD = 1.25 mm, as shown in Fig. 8(b)).
Ultimately, we were able to simulate and optimize PPG waveform in TOF domain (Fig. 6) and showed that TOF AC/DC ratio is higher than CW-PPG AC/DC ratio in all cases for green light (Fig. 7) and under certain conditions for IR light (Fig. 8). In addition, TOF AC/DC is less affected by SDD. Furthermore, TOF AC/DC ratio is less affected by SDD, and remains stable at SDD > 2 mm for all cases. Though the simulations indicated that increasing SDD may be more beneficial for CW-PPG, signal-to-noise ratio also decreases at larger SDD, particularly for green light in MOB case (Fig. 4(b) and Fig. 8(b)). As shown in Fig. 7&8, the selection of SDD for best discrimination between CW-PPG and TOF-PPG is dependent on obese status and wavelengths. In statistics, it is most common to accept a p-value (the probability under the assumption of no effect) at 0.05. For example, if we set the limit of 5% difference, then SDDs that do not allow differentiating TOF-PPG from CW-PPG in dark skin tones are: SDD < 1 mm at 523 nm (both NOB and MOB) and SDD = 0.5 and 2.5 mm at 945 nm (MOB). In addition, one can increase signal-to-noise ratio (SNR) by increasing the number of photons launched. The acceptable SNR level is achieved when the number of detected photons at each SDD is at least the square root of number of photons launched (Poisson distribution). In this study, the cut-off is roughly at SDD = 3.4 mm for λ = 523 nm. In any future experimental measurement, SNR can be increased by increasing the number of detection fibers at the same SDD.
Overall, the paper provides three options to improve optical heart rate monitoring including: (1) the selection of source-detector distance (not all short SDDs are bad), (2) the selection of wavelengths, (3) the use of time-resolved reflectance. While the latter is a challenge for wearable applications due to instrument bulkiness, our simulations provided promising results for clinical application. Ultimately, an artificial neural network model combining experimental measurements of TOF-PPG and CW-PPG can be developed to correct current wearable errors without the burden of pulsed laser system. Altogether, this work supports that heart rate in obese individuals is much more assessable and more reliable in TOF-resolved PPG provided that gated time is optimized.
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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