Blood oxygen saturation (SO₂ when evaluated in blood vessels, StO₂ when evaluated in tissues) is a vital physiological measure that quantifies the proportion of oxygen-bound hemoglobin in the bloodstream relative to the total available hemoglobin molecules (Hafen and Sharma, 2018). This parameter plays a crucial role in tissue physiology (Swartz and Dunn, 2003) and serves as a diagnostic indicator for a variety of conditions, including heart, cerebral, and vascular diseases (Hoke et al., 2002; Zhang et al., 2011; McCully et al., 1994). Recent advancements have facilitated the measurement of oxygen saturation in the retina, which can be used to detect pathological changes and diseases such as diabetic retinopathy and age-related macular degeneration (Linsenmeier and Zhang, 2017). Abnormal SO₂ has been associated with a range of health issues including cancer, diabetes, choroidal disorders, and cardiovascular health (Carmeliet and Jain, 2000; Wittenberg and Wittenberg, 1989; Heitmar and Blann, 2022). Numerous research studies have indicated that irregularities in oxygen levels in the eye fundus are linked to various eye diseases including glaucoma (Boeckaert et al., 2012; Olafsdottir et al., 2014; Tobe et al., 2013), diabetic retinopathy (Jørgensen et al., 2014; Hardarson and Stefánsson, 2012; Guduru et al., 2016), retinal vessel blockages (Williamson et al., 2009; Yoneya et al., 2002), retinitis pigmentosa (Battu et al., 2015), and age-related macular degeneration (Geirsdottir et al., 2014). In addition, retinal oximetry, in which blood oxygenation is evaluated in the large retinal blood vessels, has proven to be effective in non-invasively monitoring certain neurodegenerative diseases (Stefánsson et al., 2017).

Diffuse reflectance spectroscopy (DRS) stands as a potent tool in this context and can provide molecular-level information on tissue, including evaluating StO₂ based on the reversible binding of oxygen to hemoglobin which changes its absorption spectrum (Stokes, 1864). The diffuse reflectance spectrum, obtained using an illumination light source that is commonly UV- visible and can extend to the near-infrared (NIR), is collected using a spectrometer (Delori, 1988; Sircan-Kucuksayan et al., 2015). The absorption coefficient ( μ a ), the reduced scattering coefficient ( μ s , ), and the light path length into the tissue are used to calculate the absorber concentration in a semi-infinite medium according to the modified Beer-Lambert law.

DRS has been widely applied non-invasively in biological tissues for various purposes, primarily to quantify the concentrations of chromophores such as melanin and hemoglobin (Malin et al., 1999; Bender et al., 2009; Troncoso et al., 2021; Ridder et al., 2005; Hani et al., 2011; Hernández et al., 2009). Among these, oxygenated and deoxygenated hemoglobin (oxyhemoglobin and deoxyhemoglobin, respectively) are particularly significant, as they provide critical information on StO₂ and blood volume fraction (BVF). Both parameters are essential for disease diagnosis, tissue health assessment, and cancer monitoring (Chen and Lin, 2010; Claridge et al., 2007). BVF, representing the proportion of tissue occupied by blood (Claridge et al., 2007), offers valuable insights, particularly in understanding tumor microcirculation, predicting tumor behavior, and evaluating treatment responses (Qi et al., 2008). BVF varies according to tissue type and region of interest; for instance, it ranges from 1% to 10% in colon samples (Claridge et al., 2007), 0.2%–7% in skin (Yudovsky and Pilon, 2010), and averages around 8.4% in liver tissue (Chen et al., 2011). Techniques used to measure blood oxygen saturation in the eye fundus often rely on analyzing two or more wavelengths (Hickam et al., 1963; Pittman and Duling, 1975), with the selection of these wavelengths influencing the distinction between blood vessels and surrounding tissue. These approaches typically require user-specific calibration to optimize their accuracy and performance (Delori, 1988; Harris et al., 2003; Schweitzer et al., 1999; Smith, 1999).

Despite the many algorithms developed for this purpose, achieving accurate in vivo measurements of absorber concentration in semi-infinite media, such as biological tissues, remains challenging. The presence of lipids in the tissue can have a significant effect on its absorption and scattering properties and alter the intensity and shape of the diffuse reflectance spectrum, especially in the visible and NIR range. Calculating StO₂ from the diffuse reflectance spectrum is also complicated by the sample geometry, such as thickness or curvature, or the composition of the tissue being assessed.

One approach is to simplify all the equations by ignoring the contribution of the non-blood layer in the tissue. Therefore, the computational complexity is reduced. However, the accuracy is decreased by considering that the reflected light would only travel from the blood layer and neglecting the effect of the tissue pigment (Delori and Pflibsen, 1989; Rajaram et al., 2010). If we incorporate the optical properties of the non-blood components, this method can provide a more comprehensive explanation of the tissue, yet there needs to be prior knowledge of the concentration of the non-blood part of the tissue (Cui et al., 1990). Many algorithms are mostly based on parameters depending on the optical setup and numerical computations of coefficients (Middelburg et al., 2011; Reif et al., 2008; Akitegetse et al., 2022).

Here, we propose a principal component analysis (PCA)-based algorithm to evaluate the blood oxygen saturation in retinal tissue using DRS. PCA is used to find independent bases associated with the variations in the dataset. Consequently, the oxygen saturation is calculated by the projection of the dataset in the independent bases onto the spectrum of the compounds of the dataset. The method’s performance was evaluated by using both simulated data and data collected on a liquid phantom mimicking retinal properties, showing consistent performance on both datasets. This novel approach is poised to improve the assessment of blood oxygen saturation in the eye and in other tissues. It is expected to strengthen our grasp of a wide range of health conditions and facilitate the development of more precise and comprehensive diagnostic procedures.

To evaluate the performance of the developed PCA-based algorithm, StO₂ values were calculated on the simulated dataset and the root-mean-square error (RMSE) was calculated for each condition tested and for each algorithm tested. The average value of RMSE and the standard deviation are shown in Figure 2. Figure 2A shows that the RMSE values for all simulations with different melanin content evaluated with the PCA-based algorithm were under 1% while the estimated values were highly correlated with the true values in all cases (r-value >0.99, p-value <0.05). Figure 2B demonstrates the RMSE for different BVF values between the calculated StO₂ and the true values. All calculated values in each simulation were highly correlated with the real values (r-value >0.99, p-value <0.05). The error in StO₂ values decreased with a higher content of blood. Additionally, the algorithm was robust to different blood volume fractions or melanin contents, since in all cases the standard deviation of the RMSE was less than 0.15%.

Afterward, the model’s performance was compared against three alternative methods—namely, the 4-wavelength method, the 3-wavelength method, and the NNLS method. We generated 5000 simulated spectra five times. The RMSE values were computed and depicted in Figure 2C for each dataset. For the 4-wavelength method, the RMSE was approximately 30%, with a Pearson correlation coefficient of 0.69 between estimated StO2 values and actual values. In contrast, the three-wavelength algorithm showed an average RMSE of 12.9% and a higher Pearson correlation coefficient of 0.83 with the actual StO2 values. Furthermore, the NNLS algorithm yielded an average RMSE of 3.85% with a correlation coefficient of 0.97, while the PCA-based algorithm demonstrated the lowest RMSE at 1.68% and the highest correlation coefficient of 0.99 among all algorithms tested. These results indicate that the PCA-based algorithm achieves the highest accuracy compared to the other algorithms assessed.

The performance of the PCA-based algorithm was evaluated on the fourth simulated dataset. Using the same fitted PCA on the simulated data, the StO₂ values of the phantom data with different intralipid concentrations were estimated. The coefficient of determination for the calculated oxygen saturation with the PCA-based algorithm on the simulated data (shown in Figure 3A) was 0.98 and the overall RMSE was 2.78%. The results of using the same fitted PCA on the data from the tissue phantom model with various intralipid concentrations are shown in Figure 3B. Samples at different StO₂ values (29.5%, 56.1%, 72.3%, and 91.9%) and intralipid contents (0.25%, 0.72%, 0.95%, and 1.80% IL) were assessed through five acquisitions each (49 spectra per acquisition). Figure 3 shows the calculated StO₂ values for tissue phantom blood samples at different StO₂ levels and lipid contents. The average RMSE between the StO₂ values of each acquisition and the real values of all acquisitions made with the PCA-based algorithm was 7.38%.

To evaluate the performance of the algorithm with tissues having different micro-vessels densities, samples at five different concentrations of hemoglobin (0.25 g/dL, 0.50 g/dL, 1.00 g/dL, 2.25 g/dL, and 4.50 g/dL) were prepared and assessed in the tissue phantom. A total of 100 acquisitions were performed with samples at different StO₂ values. The absolute error between the calculated StO₂ and the value obtained from a blood gas analyzer is shown in Figure 4 for the range of hemoglobin concentrations. The average error, accounting for all cases tested, was less than 6.3%, and we found there was no correlation between the error on the StO₂ values and the concentration of hemoglobin (r = 0.69, p-value = 0.19).

The effect of lens yellowing on the performance of the algorithm is shown in Figure 5. There were 15 samples for each level of StO₂, with three different levels of yellowing of the lens (without yellowing, Y20, and Y60). The concentration of hemoglobin and intralipid content were constant (at 1 g/dL and 0.25%, respectively) in the samples. The statistical equivalency of the values obtained for each of the three groups of measurements showed the algorithm is robust to the yellowing of the lens.

A PCA-based algorithm to estimate the blood oxygen saturation in a semi-infinite tissue, specifically micro-vascularized regions of the retina, using DRS has been introduced. The error on StO₂ calculated by the algorithm was lower than that of previously established algorithms based on four-wavelength, three-wavelength, and NNLS analyses. The accuracy of values measured by 2-, 3- or 4-wavelength methods can be affected by artifacts, signal-to-noise ratio, optical interference, and the accuracy of the oxygen standard that is used for calibration (Sinex, 1999). The 4-wavelength method uses absorbance values at four different wavelengths to estimate SO₂ or StO₂, three of them are for transforming the measured spectrum and only one wavelength is used for quantification (Pittman and Duling, 1975). Hence, this approach is vulnerable to noise, especially at 560 nm. While multi-wavelength techniques optimize regressors, they can result in overfitting or underfitting when considering missing or excessive components in regression, leading to less accurate estimates of oxygen saturation (Su et al., 2012).

The performance of the PCA algorithm on the simulated dataset with different concentrations of melanin shows a slight decrease in accuracy as the melanin content increases. It is important to note that the relationship between melanin content and the accuracy of the algorithm may vary depending on the specific algorithm. Melanin is a pigment responsible for absorbing light in the visible and NIR spectrum. When the melanin content is higher, it absorbs more light, leading to a decrease in the intensity of light reaching deeper tissue layers and returning from the eye. Reducing the fraction of captured light that has undergone interaction with hemoglobin typically results in the attenuation of the characteristic peaks observed in hemoglobin (Damodaran et al., 2018).

Based on the results of our simulations, the calculated errors for different BVF values demonstrate a slight increase in the accuracy of StO₂ estimation (less than 1%) as the volume of blood increases. This can happen for several reasons. When blood volume is greater, there is a greater amount of hemoglobin available to absorb light which provides more robust spectral information, making it easier for the algorithm to estimate oxygen saturation accurately. This causes the backscattered signal from blood cells to become stronger compared to the background tissue. This improved signal-to-noise ratio makes it easier for the algorithm to extract the oxygen saturation information from the spectral measurements, leading to increased accuracy.

The performance of the algorithm on the data acquired from samples placed in tissue phantoms, using different levels of intralipid and hemoglobin concentration, is evaluated in systems with different optical properties including scattering and absorption. This approach allows us to assess how well the performance of the algorithm under varying conditions and provides a benchmark for understanding the algorithm’s limitations and strengths. Moreover, phantoms provide controlled experimental conditions where the actual oxygen saturation values can be precisely determined using a blood gas analyzer, the gold standard in the field. By comparing the algorithm’s measurements with known values, researchers can validate its accuracy and identify any discrepancies or biases that need to be addressed.

The PCA-based algorithm showed that when the volume of blood is greater, we observe consistent results when the intralipid and hemoglobin contents are changing. Unlike simulations, experiments conducted on phantoms do not exhibit a decrease in error as the hemoglobin content increases, and it is confirmed by the literature that the blood volume does not affect the accuracy of SO₂ estimation (Chen et al., 2015).

Measurements made from simulated spectra showed superior performance than those from phantom experiments, with errors smaller than 1%. In addition, in phantom experiments, the error increased with greater intralipid contents. This difference in performance can be attributed to several factors. Simulations provide a highly controlled environment in which scattering and absorption are assumed to be homogeneous, whereas phantom experiments introduce variability due to factors such as uneven intralipid mixing, surface scattering effects, and the optical heterogeneity of the phantom material. These complexities make light-tissue interactions in phantom models more intricate than in simulations. Moreover, the algorithm used to estimate oxygen saturation assumes a homogeneous scattering and absorption environment, which is an oversimplification in simulations. In contrast, phantom data exhibit more variable scattering properties that may deviate from the idealized model, thus reducing algorithm accuracy. Consequently, phantom data serve as a more realistic proxy for real tissues, offering a more representative assessment of performance in in vivo applications.

Finally, the performance of the algorithm was evaluated using lenses that simulate various degrees of yellowness. Yellowing of the eye significantly alters the illumination of the fundus by filtering the blue and green light. Comparing the results of two lenses with different yellowing levels and a lens without yellowness demonstrates that the algorithm remains robust when the blue and green light are filtered out. These promising results are a positive step forward toward assessing StO₂ in patients with cataracts, although it's worth acknowledging that they do not provide an absolute guarantee of the algorithm’s robustness against all types of cataracts. In particular, cortical cataracts, which not only alter the light spectrum but also cause clouding of the lens, are expected to pose significant challenges. The reduced amount of light reaching and returning from the eye’s fundus can lower sensitivity and introduce more errors in StO₂ measurements. In this scenario, the problem extends beyond merely adjusting the oximetry algorithm—it also involves identifying a more effective method to allow sufficient light transmission and collection to ensure accurate measurements.

Our evaluation of the algorithm’s performance involved two distinct approaches. In the first approach, depicted in Figures 2, 3, we utilized simulated data for training PCA, subsequently evaluating its performance on novel data not encountered during training. Conversely, for the outcomes presented in Figures 4, 5, we employed phantom data for both training PCA and assessing algorithmic performance. Remarkably, the algorithm exhibited robust performance in both scenarios, underscoring its versatility. PCA, in this context, is not employed for conventional feature extraction; rather, it serves to establish a new basis for spectral analysis. Consequently, the algorithm’s efficacy is upheld when trained with a dataset showcasing variations in the concentration of a target component, whether simulated or experimental (phantom).

The PCA-based method introduced here has the benefit of having no fit and weights to estimate, so it could be run on whole datasets without the need to exclude noisy spectra. The method is easy to implement and there is less computational complexity compared to methods with numerical or network-based AI analysis. More importantly, using PCA in the algorithm mitigates overfitting issues. To further prevent overfitting or underfitting, we ensured that the dataset included sufficient variability to represent real-world scenarios. Yet the algorithm needs to be validated with the results from real eyes since the simulations and the phantom do not perfectly represent a real tissue; however, this is a complex endeavor as there is no gold standard to establish a ground truth for blood oxygen saturation in the tissues of the retina.

The tests conducted with tissue phantoms allowed us to evaluate the strength and accuracy of our oximetry algorithm, even in the presence of interfering elements. While the phantom incorporated key structural features of the eye, it remains a simplified representation of its actual complexity. This model provided a controlled environment to isolate specific factors, facilitating real-life mimicking measurements and validating the data collection process. However, it does not account for critical variables such as varying thickness, optical properties, or the composition of different layers in the eye’s fundus. Furthermore, using red blood cells in saline solution combined with components like intralipids presents limitations in the modeling of real tissues. The assumption of homogeneous tissue properties made in both phantom and simulation models overlooks the influence of factors such as variable blood flow velocities and red blood cell aggregation in capillaries, which can significantly affect the tissue’s optical properties, including light absorption and scattering, and potentially impact StO₂ measurements. Future studies should focus on developing more complex phantoms that better mimic the eye and incorporate realistic parameters, as well as simulating blood flow with whole blood and employing advanced models to accurately represent tissue behavior.

Our study introduces a PCA-based algorithm for estimating StO₂ using DRS in the retina. The algorithm demonstrates superior performance compared to existing methods, such as 4-wavelength, 3-wavelength, and NNLS algorithms, with reduced errors in estimated values. Our evaluations encompassed simulated data, experimental measurements on tissue phantoms, and assessments under various conditions, highlighting the algorithm’s robustness and versatility.

The discussion emphasizes the impact of confounding factors, such as melanin content, blood volume fraction, and optical properties of tissues, on the algorithm’s accuracy. It is crucial to recognize the limitations of the algorithm, particularly in the presence of increased melanin content and higher intralipid concentrations, where accuracy may diminish. Additionally, the study scrutinizes the algorithm’s performance under conditions simulating different degrees of yellowing of the lenses, showcasing its resilience against alterations in the light spectrum.

The comparison between simulated and phantom data reveals nuances in error rates, emphasizing the challenges associated with real-world tissue complexities. The algorithm’s efficacy is upheld in both scenarios, demonstrating its adaptability and robustness. Importantly, our technique employs a simplified tissue model, acknowledging its limitations in capturing the full complexity of real tissue. Recommendations for future improvements include incorporating capillary contributions, simulating blood flow, and utilizing more complex tissue models.

Despite these considerations, the PCA-based algorithm offers several advantages, including no need for fitting or weight estimation, ease of implementation, and lower computational complexity compared to alternative methods. However, it is crucial to validate the algorithm using real eye data, as simulations and phantom models may not perfectly represent the intricacies of actual tissue.

In conclusion, our findings underscore the potential of the PCA-based algorithm as a valuable tool for non-invasive monitoring of oxygen saturation in clinical and research settings. With proper optimization, validation, and consideration of its limitations, the PCA-based approach holds promise for advancing the field of DRS and enhancing our ability to accurately estimate tissue oxygen saturation.