1. Introduction

Ocular oximetry is a technique that measures the oxygen saturation of vascular blood in the tissues of the eye fundus. Due to the central role of oxygen in multiple physiological and pathophysiological processes, oxygen supply to and oxygen regulation in the retina have been found to be important factors in ocular diseases. In fact, an increasing number of studies show that oxygen dysregulation is associated with several ocular pathologies such as glaucoma [1–6], diabetic retinopathy (DR) [1,2,7–10], retinal vessel occlusions [1,2,11,12], retinitis pigmentosa [13,14], and age-related macular degeneration (AMD) [15]. Retinal oximetry has also shown the potential for non-invasively monitoring some neurodegenerative diseases [16]. Oxygen saturation is, therefore, a key biomarker with clear potential to improve the prevention, diagnosis and management of many diseases and conditions.

Non-invasive methods for measuring oxygen saturation are generally based on the different light absorption spectra of the unbound and oxygen-bound forms of hemoglobin (deoxyhemoglobin and oxyhemoglobin, respectively). From the first description of hemoglobin by Hoppe [17], through the observation of the reversible binding of oxygen to hemoglobin by Stokes in the 19th century [18], to the invention of the pulse oximeter by Aoyagi in the early 1970s [19], much work has been done trying to measure human blood oxygenation [17,20–22]. Along with these studies, which were particularly focused on arterial blood oxygenation, studies to measure blood oxygenation in the eye took place beginning in the late 1950s. Hickam et al. proposed a method combining a camera and narrowband filters centered at two pre-determined wavelengths for the estimation of oxygen saturation in retinal arteries and veins [23]. Noting that the two-wavelengths method could be affected by light scattering due to the structures of the eye fundus, Pittman et al. developed a three-wavelengths method [24]. Delori suggested a further improvement by using wavelengths chosen exclusively in the range between $500\;\textrm{nm}$ and $600\;\textrm{nm}$, where the impact of scattering is minimal [25]. Relying on Monte Carlo simulations to justify the choice of the spectral region between $510\;\textrm{nm}$ and $586\;\textrm{nm}$, Schweitzer et al. were able to estimate the oxygen saturation in the veins and arteries of the eye fundus using a multi-wavelength method [26].

These techniques do not assess blood oxygenation in adjacent and micro-capillaries or in anatomical landmarks such as the macular region and the optic disc tissues, where early signs of disease might manifest [27].

We have developed an ocular oximetry technique for acquiring diffuse reflectance spectra from a targeted location in the retinal tissue and converting it to measurements of blood oxygen saturation ($\mathrm {StO_2}$). This technique has recently been used to compare optic disc oxygen saturation in glaucomatous and normal patients [28,29].

In all cases, despite the development and improvement of techniques for assessing oxygen saturation in the eye fundus, the validation of the oxygen saturation measurements remain a significant challenge. There is indeed no gold-standard tool or technique that can be used to assess the accuracy of these measurements in the context of the eye fundus. In vitro validation of various retinal oximetry techniques has been reported. Mordant et al. developed an eye phantom model consisting of quartz tubes, filled with blood, and a background reflectance surface [30]. This eye model was used for the validation of a hyper-spectral imaging based oximetry. Ghassemi et al. converted a segmented fundus image of the human retina into a matrix format used to 3-D print phantoms with vessel-simulating channels [31], also to validate hyper-spectral camera oximetry. A 2-layer, vessel-containing phantom could be constituted using this approach. Chen et al. designed an eye phantom model having artificial vascular pattern with varying micro-channels [32]. It consisted of two layers: a transparent top layer and a base layer simulating the reflectance of the eye fundus.

Even considering their varying levels of complexity, all these eye phantom models remain far from the complex layered-structured eye fundus.

The validation of retinal oximetry was also explored using Monte-Carlo simulation. Liu et al. assessed the accuracy of oxygen saturation measurements in a blood vessel using a simplified 4-layer fundus model [33]. They investigated the impact of blood vessel diameter and melanin concentration in the retinal pigment epithelium (RPE). Chen et al. simulated infinitely long cylindrical retinal blood vessels of various diameters [34] to assess the accuracy of visible optical coherence tomography (OCT) oximetry, focusing on the effects of vessel diameter and spectral range. Rodriguez et al. investigated the error associated with a two-wavelength oximetry algorithm using a seven-layer Monte-Carlo model of the human fundus [35]. However, these models focused on oxygen saturation in large blood vessel and do not provide information for validation in tissues containing micro-vasculatures.

In this study, we present a combination of tissue phantom models with Monte-Carlo simulations to assess the impact of several elements on measurements of oxygen saturation in the retinal tissues. This includes crystalline lens transmission, scattering, the RPE and choroidal melanin concentration, the neural retinal blood volume fraction (BVF) and the choroidal blood oxygen saturation. The phantom model is used to investigate the impact of light scattering, BVF and crystalline lens transmission, whereas the effect of the layered-structure of the eye fundus is studied using the Monte-Carlo model.

2. Materials and methods

2.1 Multi-wavelength oxygen saturation algorithm

The determination of oxygen saturation is based on the wavelength-dependent absorption of oxyhemoglobin and deoxyhemoglobin within the region of spectral acquisition.

The actual spectrum acquired by the device $\mathrm {I_{RAW}}$ (which is used for oxygen saturation calculation) is affected by anatomical elements of the eye, and many factors beyond absorption. For example, the impact of the illumination light spectrum $\mathrm {I_0}$, the ambient radiation spectrum $\mathrm {I_A}$, as well as the reflections on the optical elements of the measuring device $\mathrm {I_R}$ must all be accounted for and their impact must be minimized. $\mathrm {I_{A}}$ and $\mathrm {I_{R}}$, combine with the reflected light from the eye $\mathrm {I_F}$ so that $\mathrm {I_{RAW}}$ is the sum of all these contributions :

In our experiments, $\mathrm {I_R}$ was obtained by putting a black paper (BFP1, Thorlabs) in front of the device and by acquiring a spectrum with the illumination light on. $\mathrm {I_R}$ being characteristic of the device and its optical system, it was acquired only once and was adjusted for changes in power of the illumination light. As for $\mathrm {I_A}$, it was acquired with the tissue phantom (see Section 2.2) placed in front of the device and the illumination light turned off.

$\mathrm {I_0}$ was obtained in a configuration similar to that of $\mathrm {I_R}$, by replacing the black paper with a diffuse reflectance standard (AluWhite98, Avian Technologies); $\mathrm {I_0}$ was also corrected for reflections. The optical density (OD) of the region of spectral acquisition was then calculated as:

Studies to establish a reflectance model for the eye fundus have been conducted for at least the past 50 years [36,37]. Models based on the Beer-Lambert law were generally adopted when it came to applications to oximetry. Since the path length in the fundus is not known, an empirical model was used to represent the dependence of scattering on wavelength [38–40].

We used a model based on the modified Beer-Lambert law, similar to the one used by Desjardins et al. [39], to determine the amounts of oxy- and deoxyhemoglobin. According to this model:

With five unknown variables, solving Eq. (4) by the least squares fit methods could allow for a good curve fit, but would not lead to a good approximation of the contribution of each term.

A broad spectral range allows for the best approximation of the exponentially decaying terms such as scattering and melanin, while a better accuracy on the terms related to hemoglobin can be obtained by reducing the spectral region to a range between $510\;\textrm{nm}$ and $590\;\textrm{nm}$. Moreover, by using blood samples, we found that the best approximation of oxygen saturation was obtained when the spectral region was reduced to the interval between $530\;\textrm{nm}$ and $585\;\textrm{nm}$ (Supplement 1, Figure S2).

Thus, we decided to estimate the oxygen saturation in three steps. Firstly, Eq. (4) was solved by the least squares fitting method in the spectral region between $500\;\textrm{nm}$ and $650\;\textrm{nm}$; allowing us to have a good estimate of parameters $\mathrm {c_1}$, $\mathrm {c_{Mel}}$ and $\mathrm {c_5}$. Secondly, these three parameters were set as knowns and the Eq. (4) was solved again in the spectral region ranging from $530\;\textrm{nm}$ to $585\;\textrm{nm}$. Finally, the tissue oxygen saturation was calculated as the ratio of oxygenated hemoglobin to total hemoglobin:

2.2 Retinal tissue phantom model

The eye fundus has a complex, layered structure. One can distinguish among others the neural retina, the RPE, the choroid and the sclera. Effective models for calculating retinal tissue oxygen saturation compensate for the effects of the different layers, ultimately isolating the blood absorption in capillaries.

The neural retina is organized in several superimposed layers starting from the internal limiting membrane to the photoreceptor layer, passing through the retinal nerve fiber layer (RNFL), the ganglion cells layer, the inner plexiform layer, the inner nuclear layer, the outer plexiform layer and the outer nuclear layer. The underlying layers of the neural retina have very similar optical properties, so there is very little refraction at their interfaces. The neural retina’s tissue can therefore be seen as a unique layer with microtubules, microfilaments and pericytes as main scatterers [44], and hemoglobin and macular pigments as absorbents [45]. The microvessel density in the tissue (therefore the BVF) and the RNFL thickness both vary depending on the targeted retinal region. As for anterior segment elements, Pokorny et al. evaluated the impact of aging on each one [46] and found that only crystalline lens aging seemed to affect the spectrum in the visible region.

Phantoms represent key tools for evaluating oximeters and assessing their stability and performance by controlling optical properties. The phantom used in this study took into consideration the locations for which targeted oximetry would be performed (retinal tissue with micro-capillaries, optic disc). It thus did not require the inclusion of many parameters and factors encountered in more complex eye phantoms (blood vessel topography, vessel walls density and opacity, etc.).

Our eye model (Fig. 1) was composed of a watertight black chamber and a VIS-NIR coated achromatic lens with a $\textrm{17.5 mm}$ focal length inserted through a $8\;\textrm{mm}$ diameter iris. Distilled water was used in the chamber to simulate the vitreous. A $7\;\textrm{ml}$ test tube (Covidien 8881301512) was inserted vertically into the chamber, at $22\;\textrm{mm}$ from the lens, through a dedicated opening. The test tube was filled with a mixture of phosphate-buffered saline (PBS, pH 7.4), human blood from human erythrocyte concentrate bags and lipid emulsion (intralipd, 20% w/v). Our phantom resembles in configuration the one published by Modant et al. [30], but differs from the latter by the absence of a bottom surface and quartz tubes. Instead, a liquid where the optical properties can be controlled by adjusting the composition was used to mimick the retinal tissue. The idea of a liquid phantom to adjust optical properties was previously used by Kleiser et al. to compare brain tissue oximeters [47,48].

 

Fig. 1. Sketch of the eye phantom model. (1) is the black chamber, (2) is a lens retainer, (3) is the lid with hole for test tube, (4) is an o-ring to prevent leaks, (5) and (6) are flat-head screws, and (7) is the lens. Detailed schematic available upon request.

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The mixture of PBS, lipid emulsion and sodium bicarbonate buffer was prepared separately and was deoxygenated using an oxygen reduction system (Hemanext One, Hemanext Inc.) before being introduced into a nitrogen-purged test tube, through a silicone or rubber septum cap using a gas-tight syringe. The deoxygenation of the solution was confirmed by measuring the oxygen partial pressure using a blood gas analyzer (ABL90 Flex Plus, Radiometer) before and after the process.

Red blood cell samples were deoxygenated using the same oxygen reduction system. The red blood cells were then transferred from the oxygen reduction system to empty test tubes through a sterile sampling port. The blood sample in the test tube was then exposed to the open air for varying periods of time (up to 15 minutes, depending on target $\mathrm {StO_2}$) to modulate oxygen saturation. After exposure to air, the test tube was closed and stirred to ensure homogeneity. For each exposure time, a fraction of the sample was taken for analysis with the blood gas analyzer (Supplement 1) to provide reference oxygen saturation measurements, and another fraction was transferred to the phantom. Reflectance spectra of the tissue phantom were acquired using Zilia Ocular (Zilia Inc., Quebec City, Canada).

Zilia Ocular is a device that allows the imaging of the eye fundus and the acquisition of diffuse reflectance spectra at a targeted location of the retinal tissue, simultaneously. The eye fundus is illuminated using a white light-emitting diode (LED) that emits in the range between $495\;\textrm{nm}$ to $750\;\textrm{nm}$, while a camera synchronized to the activation of the LED acquires an image of the eye fundus. Proprietary technology allows the selection of a small target region ($400\;\mu \textrm{m}$ in diameter), from which the diffuse reflectance spectra are acquired. A beamsplitter reflects, therefore, a portion of the light from this region towards a spectrometer whose sensitivity ranges from $330\;\textrm{nm}$ to $835\;\textrm{nm}$ with a resolution of $1\;\textrm{nm}$.

Oxygen saturation was calculated by post-processing reflectance spectra with Python scripts on a computer running the Ubuntu 20.04.4 LTS 64-bit operating system, using the algorithm described in Section 2.1.

2.2 Blood donation and processing

This study was approved by the research ethics committee at Héma-Québec, the blood operator in Québec, Canada. Briefly, whole blood (WB) donations were obtained from healthy volunteers who signed an informed consent form. Leukotrap RC system (Haemonetics Corp., Braintree, MA) were used to collect $485\;\textrm{ml }(\pm 10\%)$ of blood. WB was centrifuged within 24 hours of donation and component were separated using the MacoPress automated blood components separator (Macopharma, France). RCC units were suspended in AS-3 additive solution, leukoreduced using RC2D filter and processed immediately for deoxygenation with the Hemanext One device (Hemanext Inc.) for three hours at R.T. under constant agitation. RCCs were stored at $2-6^{\circ }\textrm{C}$. Donation processing is made necessary by the need for red blood cells which are used in lower concentration solutions, but above all with the aim of preserving it so that a donation can be used for experiments carried out on different days.

2.3 Monte Carlo simulations

Informed by previous work from the community [44,49–53], we developed a model for Monte Carlo simulations. Our aim was to investigate the contributions of each fundus layer to the reflectance signal and the effect of local or inter-individual variations in the optical properties of the different layers. We used the mcxyz program by Jacques, Li and Prahl [54] which uses the Monte Carlo method of sampling probabilities for the step-size of photon movement between scattering and for the angles of photon scattering events. The photons can be scattered, transmitted, reflected or absorbed as they propagate. Each layer is described by the thickness, the refractive index, the absorption coefficient, the scattering coefficient, and the anisotropy factor. Modifications were introduced to the preparation scripts to run multiple instances of the program from Python; but no modifications were made to the core of the program.

The simulations were run on three identical Microsoft Azure D32s V3 virtual machines (2.3 GHz Intel XEON E5-2673 v4, 32 vCPUs, 128 GiB memory) with Ubuntu Server 20.04 LTS-Gen2 operating system. Pre- and post-processing script was written and run in python (Python 3.6.9 64-bit).

In our model, four layers of the eye fundus were considered: the neural retina, the RPE, the choroid and the sclera. The other layers were neglected, being considered to be optically thin and therefore not affecting photon propagation as much as the four ones used in the model [33]. The geometry of our model is shown in Fig. 2.

 

Fig. 2. Geometry of the eye model used in the Monte-Carlo simulations. In the figure, ROSA stands for region of spectral acquisition, i.e. only a backscattered photon having at one time or another passed through the volume of the ROSA is counted in the reconstruction of the reflectance spectrum. The neural retina, the RPE, the choroid and the sclera had thicknesses of $200\;\mu \textrm{m}$, $10\;\mu \textrm{m}$, $250\;\mu \textrm{m}$ and $700\;\mu \textrm{m}$, respectively. A thin layer of water $40\;\mu \textrm{m}$ thick was added above the retina to simulate the passage of photons from the vitreous to the retinal tissue.

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The scattering coefficients and anisotropy published by Hammer et al. [44,45] were used. Absorption in the neural retina depends on hemoglobin content (related to the density of capillaries). Using previous work on the micro-vessels density as a basis [55–57], reasonable hemoglobin concentrations were determined to be less than or equal to $\textrm{0.14 mmol/l}$ ($6\%\; \textrm{v/v}$ BVF). The simulations were therefore made by varying both the hemoglobin concentration and the oxygen saturation. The RPE consists of a single layer of cells densely filled with melanin granules. The absorption in the RPE was therefore fully modelled by the concentration of melanin, which was set at $400\;\textrm{mmol/l}$. Absorption of the choroid depends on hemoglobin and melanin content. The hemoglobin concentration in the choroid, which is not expected to change, was set to $\textrm{1.7 mmol/l}$ based on literature [45,53]. The choroidal melanin concentration on the other hand varies depending on many factors; the most important being ethnicity. In our model, the melanin concentration ranged from $50\;\textrm{mmol/l}$ to $400\;\textrm{mmol/l}$, and the average normal choroidal blood oxygen saturation was set at $95\%$. As for the sclera, the properties published by Hammer [44,45] were used. An example of parameters used in the simulations at selected wavelengths can be found in Supplement1, Table S1.

For each combination of parameters, a reflectance spectrum was obtained by propagating five million photons at each wavelength between $500\;\textrm{nm}$ and $600\;\textrm{nm}$ with steps of $2\;\textrm{nm}$, and by collecting the reflected photons while tracing all the layers that had been crossed by each photon. Thus, it was possible to reconstruct a diffuse reflectance spectrum for oximetry calculations and to know the specific contribution of each layer to the overall collected signal. The spectra were then processed with the multi-wavelength oxygen saturation algorithm described in 2.1 to obtain oximetry measurements. The results were then compared to the ground truth, the latter being the neural retina blood oxygen saturation set for the conditions tested.

3. Results

3.1 Retinal tissue phantom

Intralipid (IL) solutions are widely used in liquid phantoms that mimic biological tissues. They are biologically similar to bilipid membranes that cause scattering into tissues [58]. To determine the typical value of the IL concentration that allows mimicking the proper scattering properties of the retina, we used the properties of the $10\%$ IL solutions available in the literature [58,59] to derive the reduced scattering coefficients of a dilute solution and compared them to those determined by Hammer et al. in bovine retina [44,45]. We determined that an IL concentration of $0.77\%$ lead to scattering closest to what that encountered in the neural retina (Supplement1, Fig. S3).

To simulate the scattering variations in the eye fundus, we prepared a retinal tissue phantom where the scattering was modified by varying the concentration of IL in the solution (Supplement 1, Table S2). Four IL concentrations ($0.25\%$, $0.72\%$, $0.95\%$ and $1.80\%$) and four oxygen saturation ($29.5\%$, $56.1\%$, $72.3\%$ and $91.9\%$ as measured by the gas analyzer) levels were tested. Twenty samples (5 samples for each oxygen saturation level), whose hemoglobin concentration was $1\;\textrm{g/dl}$ (BVF of $6.67\%\; \textrm{v/v}$) and initially containing $0.25\%$ IL, were prepared. IL concentration was increased to $0.72\%$, then to $0.95\%$, and finally to $1.80\%$. A spectral acquisition was performed on each sample at each IL concentration. As illustrated in Fig. 3 and confirmed by a Friedman statistical test ($\textrm{p = 0.82}$), there is a consistency between the four sets of measurements.

 

Fig. 3. $StO_2$ of blood in retinal tissue phantom with varying levels of IL. Samples at four oxygen saturation levels ($29.5\%$, $56.1\%$, $72.3\%$ and $91.9\%$) and with IL concentrations of $0.25\%$, $0.72\%$, $0.95\%$ and $1.80\%$ w/v. Five samples were prepared for each condition; $\textrm{mean }\pm \textrm{ std}$ displayed. IL concentrations were used to mimic the differences in retinal light scattering properties.

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Likewise, to mimic the variation in microvessel density in the fundus, we prepared liquid phantoms with different BVF (Supplement 1, Table S3). Five hemoglobin concentrations - $\textrm{4.5g /dl}$, $\textrm{2.25 g/dl}$, $1\;\textrm{g/dl}$, $\textrm{0.5 g/dl}$ and $\textrm{0.25 g/dl}$ (BVF of $30\%\; \textrm{v/v}$, $15\%\; \textrm{v/v}$, $6.67\%\; \textrm{v/v}$, $3.33\%\; \textrm{v/v}$ and $1.67\%\; \textrm{v/v}$) - were used. For each hemoglobin concentration, 25 samples with oxygen saturation levels ranging from $20\%$ to $100\%$ were tested, for a total of 125 samples. For all samples, the IL concentration was maintained at $0.25\%$. Mean errors on oxygen saturation measurements, compared to the blood gas analyzer for each concentration, are plotted in Fig. 4. No correlation was found between mean error and hemoglobin concentration (Kendall Tau test: $\mathrm {\tau }\textrm{ = -0.2}$, ${p = 0.817}$). Moreover, we found that, in all conditions, the absolute error compared to the blood gas analyzer was less than $5\%$; performing one-sided upper-tail Z-test on absolute error, p-values were $0.98$, $0.97$, $1.00$ and $1.00$ for hemoglobin concentration of $\textrm{4.5g /dl}$, $\textrm{2.25 g/dl}$, $1\;\textrm{g/dl}$, $\textrm{0.5 g/dl}$ and $\textrm{0.25 g/dl}$, respectively.

 

Fig. 4. Error in $StO_2$ of blood in retinal tissue liquid phantoms at five different concentrations (ranging from $\textrm{0.25 g/dl}$ to $\textrm{4.5 g/dl}$), mimicking the differences in blood vessel density in the neural retina. The absolute error is determined between values calculated using our technique and those measured by the blood gas analyzer. $\textrm{n = 25}$ for each hemoglobin concentration, error bars indicate $\textrm{mean}\pm { stdev}$.

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Finally, the robustness of measurements to lens yellowing was investigated. Fifteen samples with oxygen saturation ranging from $20\%$ to $100\%$ were prepared in three conditions: without cataract-simulating lens, and with two lenses of different levels of yellowing (lens transmission spectra in Supplement 1, Fig. S4). Hemoglobin and IL concentrations were maintained at $1\;\textrm{g/dl}$ and, $0.25\%\; \textrm{w/v}$, respectively. Figure 5 shows that the three sets of measurements were consistent, confirming the robustness of the oximetry acquisition and algorithm to lens yellowing.

 

Fig. 5. $StO_2$ of blood in retinal tissue liquid phantom with varying levels of lens yellowing (Y20 and Y60 are yellow lenses from Cantor & Nissel Ltd).

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3.2 Monte Carlo simulations

To isolate the contributions and effects of a given parameter, simulations were performed where the value of that parameter was varied while the other parameters were held at default values. Default RPE and choroidal melanin concentrations were $400\;\textrm{mmol/l}$ and $100\;\textrm{mmol/l}$, respectively; the default choroidal blood oxygen saturation was $95\%$ and the default BVF in the neural retina was $3\%\; \textrm{v/v}$. For each condition, the simulation was carried out three times. Neural retinal tissue oxygen saturation was varied between $5\%$ and $100\%$ in $5\%$ increments.

3.2.1 Choroidal melanin concentration

We performed successive simulations at five different concentrations of choroidal melanin: $50\;\textrm{mmol/l}$, $100\;\textrm{mmol/l}$, $200\;\textrm{mmol/l}$, $300\;\textrm{mmol/l}$ and $400\;\textrm{mmol/l}$.

From these simulations, the proportion of the signal collected from the target location, but having been transited by the choroid, was found to vary with the choroidal melanin concentration (Fig. 6 A). The proportion was found to be greater for the lower choroidal melanin concentrations. At $560\;\textrm{nm}$ for example, it ranged from almost $19\%$ of the total signal for a choroidal melanin concentration of $50\;\textrm{mmol/l}$ to $4\%$ when the concentration was $400\;\textrm{mmol/l}$.

 

Fig. 6. Effect of choroidal melanin concentration. Melanin concentrations of $50\;\textrm{mmol/l}$, $100\;\textrm{mmol/l}$, $200\;\textrm{mmol/l}$, $300\;\textrm{mmol/l}$ and $400\;\textrm{mmol/l}$ were simulated. A) Rate of collected light from the region of spectral acquisition having passed through the choroid as a function of wavelength. B) Calculated $\mathrm {StO_2}$ at different level of melanin concentration, as a function of the actual neural retinal $\mathrm {StO_2}$.

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Considering this, even though the region of spectral acquisition of the Zilia Ocular is located in the neural retina, the oxygen saturation calculated from the collected spectra is expected to be affected by the choroidal melanin concentration. This is indeed what was observed when calculating the oxygen saturation from the spectra collected during the simulations using our oximetry model. Decreasing choroidal melanin concentration led to greater deviations in calculated $\mathrm {StO_2}$ values compared to the expected values. A linear correlation exists between the calculated and the expected values, but the slope tends to decrease from $1.0$ (perfect agreement) with decreasing melanin concentration (Fig. 6 B, Supplement1 Table S4). For example, for an $\mathrm {StO_2}$ of $25\%$ in the neural retina, the determined $\mathrm {StO_2}$ varied from about $26\%$ for a choroidal melanin concentration of $400\;\textrm{mmol/l}$ to reach $40\%$ for a concentration of $50\;\textrm{mmol/l}$.

3.2.2 Neural retina blood volume fraction

In order to investigate the impact of the blood volume fraction on the calculated $\mathrm {StO_2}$, simulations were run at four different BVFs in the neural retina: $6\%\; \textrm{v/v}$, $3\%\; \textrm{v/v}$, $1.5\%\; \textrm{v/v}$ and $0.75\%\; \textrm{v/v}$.

Results show that $\mathrm {StO_2}$ calculated from collected spectra displayed greater deviation from the expected values as the neural retina BVF decreased. The same trend as for choroidal melanin concentration is observed; i.e. a linear correlation exists between the calculated and the actual values, the slope tends to decrease from $1.0$ (perfect agreement) with decreasing BVF (Fig. 7, Supplement1 Table S5). For example, for an $\mathrm {StO_2}$ of $50\%$ in the neural retina, the calculated value varied from about $52\%$ for a BVF of $6\%\; \textrm{v/v}$ to reach $62.5\%$ for a BVF of $0.75\%\; \textrm{v/v}$.

 

Fig. 7. Calculated $\mathrm {StO_2}$ at different level of retinal BVF, as a function of the actual neural retinal $\mathrm {StO_2}$. Four values of BVF were simulated: $0.75\%\; \textrm{v/v}$, $1.5\%\; \textrm{v/v}$, $3\%\; \textrm{v/v}$ and $6\%\; \textrm{v/v}$.

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3.2.3 Choroidal blood oxygen saturation

Since early simulations showed that part of the collected reflectance signal passed through the choroid, we investigated the implications that a change in the oxygen saturation of the choroidal blood ($\mathrm {StO_{2-ch}}$) could have on the determination of $\mathrm {StO_2}$ in the neural retina. Simulations with varying $\mathrm {StO_{2-ch}}$ from $55\%$ to $95\%$ in steps of $10\%$ were performed. We found that, for a given oxygen saturation in the neural retina, the calculated $\mathrm {StO_2}$ differed by approximately $7\%$ when $\mathrm {StO_{2-ch}}$ was at $95\%$ compared to that at $55\%$, as illustrated on Fig. 8 A. The deviation between calculated $\mathrm {StO_2}$ values at different $\mathrm {StO_{2-ch}}$ level seems invariant to the retinal $\mathrm {StO_2}$ value; i.e. the slope of the trend line is the same for all $\mathrm {StO_{2-ch}}$ values, but the bias increases with increasing $\mathrm {StO_{2-ch}}$ (Supplement 1, Table S6).

 

Fig. 8. Calculated $\mathrm {StO_2}$, at different level of $\mathrm {StO_{2-ch}}$, as a function of the actual neural retinal $\mathrm {StO_2}$. A) Five different values of $\mathrm {StO_{2-ch}}$ were simulated: 55%, 65%, 75%, 85% and 95%. There was a linear correlation between calculated and actual $\mathrm {StO_2}$. The trend line was shifted up as the $\mathrm {StO_{2-ch}}$ value was increased, meaning that a change in the $\mathrm {StO_{2-ch}}$ value impacts only the bias. B) Impact of $\mathrm {StO_{2-ch}}$ fine changes on the calculated retinal $\mathrm {StO_2}$.

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To determine whether smaller variations in $\mathrm {StO_{2-ch}}$ would have a noticeable impact on the calculated $\mathrm {StO_2}$ values, additional simulations were performed with $\mathrm {StO_{2-ch}}$ ranging from $90\%$ to $100\%$. In these cases, very little variation in the estimated retinal $\mathrm {StO_2}$ was observed, as shown in Fig. 8 B.

4. Discussion

The method and algorithm for the measurement of oxygen saturation in the retinal tissue presented here is based on the analysis of the diffuse reflectance spectrum of the eye fundus. The analysis aims to extract information on oxygen saturation in the neural retina. The complex structure of the fundus, inter-region unevenness and inter-individual differences all have an effect on the diffuse reflectance spectrum and therefore could lead to deviations in the calculated oxygen saturation value. In the present study, we show that the combination of a retinal tissue liquid phantom reproducing some geometrical aspects of the eye fundus with Monte Carlo simulations provides valuable information towards the validation of ocular oximetry measurements. This makes it possible to explore an array of important parameters (oxygen saturation levels, blood volume fraction, scattering, melanin concentration, multi-layer thicknesses, etc.) over physiologically relevant ranges. Since there is currently no gold standard to provide accurate real-time in vivo information on oxygen saturation in the eye fundus, this combined approach proves to be a powerful mean to validate measurements. Because of this lack of gold standard tool, target values for accuracy and sensitivity are not yet established. Studies of different pathologies, based on relative measurements of oxygen saturation in arteries and veins, have however shown that the significant variations observed were not necessarily large in amplitude. For example, global saturation in arteries was found to be about $10\%$ higher for Retinis Pigmentosa affected eyes compared to control eyes [13]. Moreover, oxygen saturation in retinal venules was found to increase by $0.45\%$ per year in patients with exudative AMD while it decreased by $0.13\%$ in healthy individuals [15]. Jørgensen et al. showed that vessels’ oxygen saturation depended on the severity of DR [7]; the difference in saturation in retinal arterioles between a healthy subject and a severe case of DR was approximately $5\%$. It is therefore obvious that good accuracy and good sensitivity are required. Although the method presented here does not, by itself, allow for a complete validatation of accuracy under real in vivo conditions, it provides an efficient approach to the evaluation of the contributions of important physiological factors and clearly improves on the validation methods used to date. As clinical evidence accumulates, diagnostic protocols will establish the levels of accuracy required for different conditions.

In the anterior segment, the crystalline lens is the element that has the most impact on the spectrum of visible light reaching the eye fundus [46,60,61]. Indeed, yellowing significantly modifies the illumination of the fundus by filtering blue and green light. The results of tests using two lenses simulating two levels of yellowing presented here show that the oximetry algorithm is robust to these changes. This was made possible by inserting contributions of a yellowing component into the calculation model. Although these results are promising, they do not prove that the method would be robust to all cataracts. In particular, cortical cataracts do not only modify the light spectrum, but they also render the lens cloudy. Thus, in advanced cortical cataracts, the amount of light reaching the fundus would be extremely reduced, likely leading to reduced sensitivity and increased deviation in $\mathrm {StO_2}$. Under these conditions, it is not a question of finding an adjustment to the oximetry algorithm, but of finding a better way to pass and collect enough light.

The erythrocytes, the retinal nerve fibers and the capillary walls have the greatest contributions to scattering of the neural retina [38,62]. Since density varies throughout tissues, scattering varies accordingly. The phantom tests carried out in this work further show the robustness of the presented ocular oximetry algorithm. Since the blood from which oxygen saturation is measured is in the capillaries, a change in the capillary density has the same impact as changing the blood volume fraction in the targeted region. The observed lack of correlation between the blood volume fraction and the error on the measurements made in the tissue phantom tells us that the accuracy of our measurement has no correlation with the capillary density.

We observed some variability between replicates of the same experiment. We can for example observe the error bars in the Fig. 3, which have a fairly large amplitude. This is due to small discrepancies during samples preparation. It is indeed not easy to introduce the ingredients into the solution without letting some air in (and therefore increasing the StO2). The hypothesis is confirmed by the presence of the same error bars when looking at the partial pressure of oxygen, measured by the gas analyzer ( Fig. S5). The significant variations are due neither to the acquisition process nor from the algorithm, but come from the sample preparation.

The tests performed in tissue phantoms allowed us to study the robustness and accuracy of our oximetry algorithm in the presence of interfering elements. However, despite containing important geometrical considerations of the eye, the phantom model used herein remains simple compared to the high complexity of the eye. It did, however, provide a controlled environment where factors could be isolated providing real-life measurements with the hardware, thus allowing the validation of the acquisition process. The fact remains that our phantom model does not take into account other complex elements such as the thickness, varying optical properties and composition of the different layers of the eye fundus. Monte-Carlo simulations allowed us to address these concerns and to study the effect of changes in the choroid (oxygen saturation and melanin content), a layer showing very different properties from those of the neural retina.

A correlation between neural retina blood volume fraction and oxygen saturation estimation error was observed in the Monte-Carlo simulations, while the phantom tests suggested the opposite. This shows the relevance of the tests in the tissue phantom, because the disagreement of the observations suggests that the differences are not due to the BVF but to other factors, in particular the layers considered in the two models. Using a phantom model as simple as the one we used has made it possible to highlight the low impact that BVF has on the oximetry algorithm and facilitates the interpretation of the Monte-Carlo simulation results. Recalling that the tissue phantom is a simplified model consisting of only one layer whereas the Monte-Carlo model consists of four layers, the inconsistency of the results of the phantom model with those of the Monte-Carlo model suggests that the observed difference comes from the contribution of the other layers, in particular the choroid. By varying the neural retina blood volume fraction, the weight of the choroidal hemoglobin in the optical density varies. It is therefore not surprising that the error on the measurement of oxygen saturation increases with decreasing blood volume fraction in the neural retina. To illustrate this, we rewrite Eq. (4) to obtain a spectrum depending mainly on hemoglobin content.

Let then replace the weights of oxygenated $\mathrm {c_{HbO}}$ and reduced hemoglobin $\mathrm {c_{HbR}}$ with the contributions of the neural retina $\mathrm {W_{nr}}$ and the choroid $\mathrm {W_{ch}}$:

Since we are interested in the oxygen saturation in the neural retina, the contribution of the choroid is not desired and affects the accuracy of the $\mathrm {StO_2}$ calculated values, as we have shown. By decreasing the blood volume fraction of the neural retina, the weight of the $\mathrm {W_{ch}}$ term relative to the weight of the neural retina $\mathrm {W_{nr}}$ term in the model increases, thus decreasing the accuracy of the measurement.

Our results show that choroidal melanin concentration impacts collected reflectance signal. The lower the melanin concentration, the higher the ratio of the reflectance signal having passed through the choroid. This is in agreement with previous studies, which had shown that the amplitude and shape of eye fundus reflectance spectra are strongly affected by the choroidal melanin concentration [37,63,64]. This is explained by the fact that with less melanin, the light absorption by the choroid is reduced, resulting in more back-scattered light from the choroid. In this case, the $\mathrm {StO_2}$ calculated from reflectance spectra deviates from the ground truth as the melanin concentration decreases. Consequently, it is not surprising that the choroidal blood oxygen saturation impacts the accuracy of the calculated $\mathrm {StO_2}$. The absolute difference in calculated $\mathrm {StO_2}$ values between the two extreme simulation conditions ($\mathrm {StO_{2-ch}}$ values at $55\%$ and $95\%$) is about $7\%$. For the simulations carried out with choroidal blood oxygen saturation values varying from $90\%$ to $100\%$, the difference between calculated StO2 and ground truth was much reduced to less than $2\%$. So, even if choroidal blood impacts the accuracy of the calculated $\mathrm {StO_2}$, the technique and algorithm presented can still be used for the assessment of neural retinal oxygen saturation, unless the subject has a condition that would cause choroidal blood oxygen saturation to vary by more than $5\%$. It is challenging to know if variations of such amplitude can occur in the choroid, given the limited literature available on the assessment of the choroidal $\mathrm {StO_2}$. In a healthy subject, the $\mathrm {StO_2}$ in the choroid is considered high and close to arterial saturation, given that the arteriovenous difference is approximately $3\%$ [49,53,63]. Certain diseases such as AMD and DR may cause abnormalities in choroidal blood flow [65,66] but, to our knowledge, there are no studies that have highlighted and quantified changes in choroidal $\mathrm {StO_2}$ in human eyes.

Our technique does have some limitations. Firstly, red blood cells suspended in saline solution are used in the tissue phantom. Secondly, both the phantom and the Monte-Carlo model consider the tissue as a homogeneous medium. In reality, whole blood circulates in capillaries with a certain velocity and, under these conditions, there can be aggregation of red blood cells under the influence of shear and proteins in the plasma [67]. Blood flow and aggregate formation have been reported to significantly influence the optical properties of blood by decreasing both absorption and scattering of light [68]. A subsequent step to this study should be to make the two models (phantom and Monte-Carlo) more complex by incorporating contributions from capillaries. In phantom testing, whole blood would be used and flowed through capillaries. This improvement would also allow us to study the effect of blood pulsation on our measurements. The cardiac cycle induces blood pulsation in blood vessels and could influence the variation of diffuse reflectance spectra [25], and consequently the variation of the determined $\mathrm {StO_2}$ values.

5. Conclusion

In this study, we combined in vitro experiments and Monte-Carlo simulations to assess the performance and the robustness of our retinal tissue oxygen saturation model. The use of the two-step method for the resolution of the model equation offers the necessary robustness to scattering and lens yellowing, while keeping good accuracy. The performance of the algorithm is however impacted by the choroidal circulation, highlighting the need for further efforts to develop algorithms that account for the choroidal contribution to the diffuse reflectance spectrum. The results show the ability of our strategy to isolate and study the impact of each parameter on the diffuse reflectance spectra; which will be useful to anyone involved in the development of technologies for the study of the eye fundus based on diffuse reflectance.