Retinal Hypoxia: Relation to Blood Flow and Oxygen Metabolic Biomarkers

Abstract

Purpose

Reduced inner retinal tissue PO₂ (tPO₂) from reduced total retinal blood flow (TRBF) often causes visual loss. We tested the hypotheses that, in ischemia, (1) tPO₂ is linearly related to TRBF and delivery rate of oxygen to the retinal circulation (DO₂), and (2) the relationships of tPO₂ with the oxygen extraction fraction (OEF) and rate of inner retinal oxygen metabolism (MO₂) are nonlinear.

Methods

The study was performed in 32 rats under either normal condition or a wide range of retinal ischemia induced by ipsilateral or bilateral common carotid artery occlusion. The tPO₂ and TRBF were determined by multimodal imaging. We also included TRBF, DO₂, OEF, and MO₂ data in 25 rats from our previous studies using identical methods, but without tPO₂ measurements.

Results

The tPO₂ was linearly related to TRBF (R² = 0.86). Based on tPO₂ derived from TRBF, tPO₂ was linearly related to DO₂ (R² = 0.97). OEF was related to tPO₂ by a sigmoid function (R² = 0.97). A critical tPO₂, 6.20 millimeters of mercury (mm Hg), was derived below which OEF = unity and MO₂ decreases linearly (phase 1). Above this value, OEF <1 and MO₂ increased as a function of tPO₂ (phase 2) according to Michaelis-Menten kinetics (R² = 0.73).

Conclusions

During graded retinal ischemia, we showed a linear relationship between tPO₂ both TRBF and DO₂. A critical tPO₂ value defined the nonlinear biphasic relationships of OEF and MO₂ with tPO₂. The relationships of these biomarkers show promise for advancing knowledge of retinal ischemia and hypoxia.

Tissue hypoxia is a significant injurious factor in many retinal conditions that lead to visual loss. Inner retinal tissue hypoxia, which can be quantified as tissue PO₂ (tPO₂), usually occurs in the context of reduced retinal blood flow, as in arterial or venous occlusions or advanced diabetic retinopathy.^1,2 Accordingly, many studies have been conducted, especially in animals, to measure retinal oxygen,^3–18 quantify retinal blood flow,^19–30 and evaluate retinal ischemia/hypoxia.^25,31–41 These studies have produced much important information. However, because of methodological limitations, it has not been possible to determine the interplay between tPO₂ and total retinal blood flow (TRBF), retinal oxygen delivery rate (DO₂), oxygen extraction fraction from the blood (OEF), and inner retinal oxygen metabolic rate (MO₂) from normal through a substantial range of reduced TRBF. Clarifying the interplay of tPO₂ with TRBF, DO₂, OEF, and MO₂ will greatly advance our understanding of the pathophysiology of retinal ischemic injury.

Currently, tPO₂ cannot be measured in humans, but methods to measure TRBF, OEF, DO₂, MO₂, are available.^{27,28,33,42–47} The most important of these is MO₂ because it indicates the adequacy of the cellular intermediary energy metabolism, which underlies numerous inner retinal physiological functions. MO₂ has been shown to become abnormal in diabetic retinopathy,^44,46–48 and it is likely to be shown to become abnormal in many conditions with retinal ischemia.

In our work, and many others, MO₂ is evaluated as the rate of exit of oxygen from the retinal circulation.^{22,25,28,33,34,41,42,49,50} Another way to evaluate MO₂ is as the rate of entry of oxygen into the cellular intermediary energy metabolic pathway. Tissue oxygen, proportional to tPO₂, is the substrate of enzymes whose reaction rates, equivalent to MO₂, are related to the level of their saturation, and, thus, conform to Michaelis-Menten (M-M) kinetics.^51–55

We have developed techniques to estimate tPO₂,^9,13,16,17 TRBF, vascular PO₂(vPO₂), DO₂, OEF, and MO₂ at essentially the same time in rats under normal conditions^22,25,56 and multiple degrees of retinal blood flow impairment.^{29,34–36,38–40,57} The purpose of the present study was to test the hypotheses that, in ischemia, (1) tPO₂ is linearly related TRBF and DO₂, and (2) the relationships of OEF and MO₂ with tPO₂ are nonlinear.

Methods

Animals

Thirty-two male, Long-Evans pigmented rats (weight = 341 ± 60g, and age = 13 ± 3 weeks) were studied. All experiments were approved by the University of Southern California Institutional Animal Care and Use Committee, complied with the guidelines of the Statement for the Use of Animals in Ophthalmic and Vision Research by the Association for Research in Vision and Ophthalmology and reported according to the Animal Research: Reporting of In Vivo Experiments guidelines.

All of the animal procedures and methods for measuring tPO₂, vPO₂, arterial and venous oxygen contents (O_2A, and O_2V, respectively), and TRBF were the same as those that have been reported previously.^{9,22,25,36,57} The rats were kept under environmentally controlled conditions with a 12-hour light/12-hour dark cycle and free access to normal rat food and water. To obtain anesthesia, the rats received ketamine (85 mg/kg intraperitoneally [IP]) and xylazine (3.5 mg/kg IP) and were given additional doses to maintain anesthesia as needed during the procedures and imaging sessions. The rats were placed on an animal holder that incorporated copper tubing that was perfused with heated water to maintain the body temperature.

To perform common carotid artery occlusion (CCAO), an anterior, midline, cervical incision then was made, and, using blunt dissection, the salivary glands, lymph nodes, and ventral neck muscles were retracted to expose both common carotid arteries, as previously described.^36,38 Permanent ligations with silk sutures were applied to one, both, or neither of the common carotid arteries. The CCAO-induced retinal ischemia and involved both the retinal and choroidal circulations. In the normal rat, part of the outer retina usually is supplied with oxygen by the retinal circulation.⁵⁸ In addition, because the retinal circulation, as opposed to the choroidal circulation, autoregulates, dilation of the retinal vessels during ischemia results in even more supply of oxygen by the retinal circulation to the outer retina.⁴¹ Thus, in ocular ischemia induced by CCAO, there is minimal, if any, contribution of oxygen from the choroid to the inner half of the retina, that is, to tPO₂.

For tPO₂ imaging, an oxygen-sensitive phosphor (Oxyphor R2; Oxygen Enterprises, Ltd., Philadelphia, PA, USA) was dissolved in normal saline and 3 µL (0.5 mM) were injected intravitreally.^9,17 The phosphor diffused throughout the vitreous body and into the retina over 24 hours. For blood velocity imaging, the femoral artery was cannulated and a catheter was secured in place. Then, 2-µm polystyrene fluorescent microspheres (Invitrogen, Grand Island, NY, USA) were injected through the catheter. For vPO₂ imaging, an oxygen-sensitive phosphor (Oxyphor R0; Pd-porphine; Frontier Scientific, Logan, UT, USA), was injected into the femoral artery. For preparation to image, the pupil was dilated with 2.5% phenylephrine and 1% tropicamide. A glass cover slip with 2.5% hypromellose ophthalmic demulcent solution (HUB Pharmaceuticals, Plymouth, MI, USA) was applied to the cornea to minimize its refractive power and prevent dehydration.

Grouping of Animals

Both tPO₂ and TRBF imaging were performed one time in a total of 32 rats: 5 normal rats without CCAO, 3 rats at <0.5 hours after ipsilateral CCAO, 19 rats at <0.5 hours after bilateral CCAO (BCCAO), and 5 rats at 24 hours after BCCAO. In 12 of the rats (7 at <0.5 hours after BCCAO and 5 normal), vPO₂ imaging was also performed. As we accumulated data, we realized that the vPO₂ and vascular O₂ content values were lower than we had obtained in earlier studies. Formal statistical comparison of the current results to former ones led us to conclude that the dye in the vitreous for tPO₂ measurement interfered with accurate quantitation of these vascular oxygen levels. We excluded these vPO₂ and vascular O₂ content results from further analysis. Instead, to complement the data in the current study and relate tPO₂ to O_2A, DO₂, OEF, and MO₂, we also utilized data from two of our previous studies that used identical methods as in the current study, except that tPO₂ was not measured. These two studies were conducted by Karamian et al. (10 eyes after BCCAO and 4 eyes after a sham procedure)³⁶ and Leahy et al. (12 eyes after BCCAO).⁵⁷ By combining data from these 2 studies, which we will refer to as the KL data set, the relationships between tPO₂ and these four biomarkers were derived from data in 26 rats.

Imaging and Image Analysis

Imaging of tPO₂, TRBF, and vPO₂ were performed under light adapted conditions as previously described.^{9,22,25,36,57} Imaging of tPO₂ and TRBF were performed quasi-simultaneously. Briefly, an excitation laser beam at 532 nm was projected at an angle into the eye to form a slit on the retina, thus separating signals from retinal depths and the choroid laterally. The laser slit, approximately two disk diameters in height, was projected at retinal locations between one half to one optic disc diameter from the nasal and temporal edges of the optic disc. Depth-resolved phosphorescence images from R2 were generated by placing a high-pass (>650 nm) emission filter in the imaging path and captured using an intensified charge coupled device camera. The laser light and the sensitivity of the camera were modulated independently to acquire multiple phase-delayed phosphorescence images.

The phosphorescence lifetime (τ, µsec), which is quenched by oxygen, was measured from the phase-delayed images using a frequency-domain approach.²² The relationship between τ and PO₂ is given by the Stern-Volmer equation: τ₀ / τ = 1 + (κ_Q * τ₀ * PO₂), where τ₀ = the value of τ in a zero oxygen environment, (µsec) and κ_Q is the quenching constant for the triplet-state phosphorescence probe (µsec⁻¹ * millimeters of mercury [mm Hg]⁻¹). The values for κ_Q and τ₀ were obtained from in vitro experiments in the presence of albumin,⁵⁹ and, hence, can be used for calculation of vPO₂. However, the environment of the tissue of living animals is different, therefore we used the following approach to determine τ₀ for calculation of tPO₂. First, the Stern-Volmer equation can be rearranged to relate 1 / τ to PO₂: 1 / τ = κ_Q * PO₂ + 1/ τ₀. Second, by linear regression analysis of our experimental data, we derived an equation relating 1 / τ to TRBF: 1 / τ = 0.0015 * TRBF + 0.0064 (N = 31, R² = 0.70). When there is no blood flow, oxygen tension must be zero and the tissue is in zero oxygen environment. Therefore, by setting TRBF = PO₂ = 0 in these 2 equations, it follows that 1 / τ₀ = 0.0064 or τ₀ = 156.3 µsec. To calculate tPO₂, the Stern-Volmer equation was rearranged to tPO₂ = (τ₀ – τ) / (τ * κ_Q * τ₀). Using 156.3 µsec for τ₀ and 0.00043 µsec⁻¹ * mm Hg⁻¹ for κ_Q, we calculated tPO₂ for each value of τ.

For the purposes of this study, tPO₂ was defined as the mean of the values from the inner half of the retina, the total retina extending between the internal retinal boundary and the maximal value toward the outer retina. Measurements of tPO₂ were averaged over the entire length of the slit by depth and vertical height at retinal locations nasal and temporal to the optic disc, representing an extended retinal region.

In the KL data set, vPO₂ in each individual (ind) major artery (P_AO_2ind) and vein (P_VO_2ind), respectively, surrounding the optic nerve were measured. Means in the arteries (P_AO₂) and veins (P_VO₂) were calculated for each eye. O_2A and O_2V were calculated from P_AO₂ and P_VO₂ respectively, as the sum of oxygen bound to hemoglobin and dissolved in blood. The amount of oxygen bound to hemoglobin was calculated using the oxygen-hemoglobin dissociation curve in rats⁶⁰ and values of hemoglobin measured in previous experiments (13.8 g/dL). The amount of dissolved oxygen in blood was calculated as the product of oxygen solubility in blood (0.003 mlO₂/dL.*.mm Hg) and PO₂ measurements.

The O_2A and O_2V values would be overestimated without accounting for the Fahraeus effect which leads to a lower hematocrit in small vessels relative to the systemic hematocrit.^61–65 The amount of reduction in hematocrit is proportional to the diameter of the vessel. Using a previous publication,⁶⁵ the following empirical equation was used to determine the fraction of vessel to systemic hematocrit: fraction = Hct_v/Hct_s = Hct_s + (1-Hct_s) * (1 + 1.7.*.exp.( −0.415*D)−0.6.*.exp.( −0.011*D)), where Hct_v is the hematocrit in the retinal vessel, Hct_s is the systemic hematocrit and D is the diameter of the vessel. Hct_s was calculated to be 0.414, obtained as 3 times the hemoglobin concentration divided by 100. The O_2A and O_2V values in each blood vessel were scaled by the calculated fractions based on their respective vessel diameters. The mean fractions were 0.79 and 0.80 for arteries and veins, respectively.

For TRBF measurement, red-free retinal images were analyzed to determine retinal arterial (D_Aind) and venous (D_Vind) diameter, respectively, for each major vessel. Image sequences obtained at high frequency (>100 hertz [Hz]) displaying the motion of fluorescent microspheres were analyzed to provide measurements of blood velocity (V_ind) in each major vein. Imaging of tPO₂ in the current study preceded imaging of the injected fluorescent microspheres. TRBF was calculated by V_ind, * π * (D_Vind)² / 4, summed over all major veins. DO₂ was calculated as TRBF * O_2A, MO₂ was calculated by TRBF * (O_2A – O_2V) and OEF was calculated as MO₂ / DO₂.⁵⁶

Data Analysis

Statistical analyses were performed using Excel in Microsoft Office Professional 2016 (Microsoft, Redmond, WA, USA) and IBM SPSS Statistics, version 29.0, (IBM Corp., Armonk, NY, USA). To determine whether data from different groups could be combined, tPO₂ and TRBF were compared between (1) subgroups in which only tPO₂ versus both tPO₂ and vPO₂ were imaged; (2) subgroups imaged <0.5 hours versus 24 hours after occlusion. Unpaired Student’s t-test was used to compare the means of the two groups. Linear and nonlinear regression were used to relate parameters. One outlier data point was removed for regression of tPO₂ versus TRBF based on falling over 2 standard deviations above the regression line, yielding 31 data points for the current data set. One outlier data point (high TRBF with unity OEF) was removed, resulting in 25 for the KL data set. Significance was accepted at P ≤ 0.05.

Results

Relating tPO₂ to TRBF

First, tPO₂ and TRBF measured in the current study were compared between eyes in which only tPO₂ was imaged (N = 12) and those in which both tPO₂ and vPO₂ were imaged (N = 7). TRBF were 1.23 ± 1.06 and 1.51 ± 0.97 µL/min (P = 0.57), respectively. The tPO₂ measurements were 15.5 ± 3.8 and 16.4 ± 3.6 mm Hg (P = 0.63), respectively. Therefore, we combined the TRBF and tPO₂ data from the two sets of experiments, yielding a total of 19 data points at 0.5 hours after BCCAO.

Second, to combine data in the current study obtained from eyes with different durations of ischemia, TRBF and tPO₂ measured <0.5 hours (N = 19) and 24 hours (N = 5) after occlusion were compared. TRBF were 1.33 ± 1.01 and 2.2 ± 0.79 µL/min (P = 0.06), respectively. The tPO₂ measurements taken <0.5 hours or 24 hours after BCCAO, were 15.8 ± 3.7 and 17.2 ± 4.8 mm Hg, respectively (P = 0.47). Thus, we combined the TRBF and tPO₂ data from the two post-occlusion durations in the further analyses.

Linear regression of tPO₂ on TRBF yielded tPO₂ = 3.42 * TRBF – 0.112. Because the regression line should pass through the origin, the y-intercept was set to zero, thus giving the following relationship: tPO₂ = 3.39 * TRBF (N = 31, R² = 0.86, P < 0.001), as shown in Figure 1.

Figure 1.

Relationship of tPO₂ to TRBF, based on the current study data set (N = 31). The tPO₂ is the partial pressure of oxygen in the inner retinal tissue (mm Hg) and TRBF is the total retinal blood flow (µL/min). The best linear fit to the data is shown, and the equation and the associated R² value are indicated.

Relating tPO₂ to DO₂

Because tPO₂ is physiologically dependent on DO₂, we report tPO₂ as a function of DO₂, using the KL data set. Because we knew that tPO₂ must equal zero when DO₂ equals zero, we set the negligible y-intercept (1.6 mm Hg) of the regression line to zero, which insignificantly altered the slope. The result of the linear regression was: tPO₂ = 0.0414 * DO₂ (N = 25, R² = 0.97, P < 0.001), as depicted in Figure 2. Equivalently, linear regression analysis yields: DO₂ = 23.5 * tPO₂.

Figure 2.

Relationship of tPO₂ to DO₂. DO₂ and TRBF were obtained from the KL data set (N = 25) and tPO₂ was calculated as TRBF * 3.39 (see Fig. 1). DO₂ is the rate of oxygen delivery into the retinal circulation (nLO₂/min), and tPO₂ is the partial pressure of oxygen in the inner retinal tissue (mm Hg). The best linear fit to the data is shown, and the equation and the associated R² value are indicated.

Relating tPO₂ to OEF

OEF is defined as MO₂ / DO₂ or (O_2A – O_2V) / O_2A, and it represents the fraction of the oxygen in the retinal circulation that is removed for metabolism.⁵⁶ Because O_2V cannot either exceed O_2A or be negative, OEF ranges from 0 to 1. On inspection of Figure 3, showing the relationship between OEF and tPO₂ based on values from the KL data set, at low values of tPO₂, OEF was unity or near it, whereas at higher values it had a negative slope. However, at extremely high values of tPO₂, OEF would have to approach zero. Accordingly, we fit the data to the sigmoid equation: OEF = 1 – exp (a – (b / tPO₂)). The best values for a and b were 0.298 and 29.0 mm Hg, respectively (N = 25, R² = 0.97).

Figure 3.

Relationship between OEF and tPO₂. OEF and TRBF were obtained from the KL data set (N = 25) and tPO₂ was calculated as TRBF * 3.39 (see Fig. 1). OEF is the fraction of the oxygen in the retinal circulation that is extracted for metabolism and not returned to the systemic circulation. The tPO₂ is the partial pressure of oxygen in the inner retinal tissue (mm Hg). The curve (solid) generated using the sigmoid function: OEF = 1 – exp (0.298 – (29.0 / tPO₂)) (N = 25, R² = 0.97) is shown. The vertical line (dotted) indicates the value of tPO₂ (6.20 mm Hg, tPO₂crit), which divides the relationship into two phases.

Defining the Critical tPO₂

As tPO₂ increases from zero, there is a relatively abrupt change in OEF from virtually unity to a moderate, quasilinear, negative slope (see Fig. 3), we estimated the value of tPO₂ that marked the change in trajectory. This critical tPO₂ was called tPO₂crit and was determined by the following steps. First, we selected data points such that OEF <0.995 in the sigmoid function, thus marking a biphasic transition point set on the basis of the fitted data. Second, we performed linear regression on these points, which yielded OEF = −0.0214 * tPO₂ + 1.13 (N = 14, R² = 0.998, P < 0.001). Third, using this equation, we determined tPO₂ at OEF = 1, which yields tPO₂crit = 6.20 mm Hg. Because tPO₂crit is the point below which essentially all the vascular oxygen has been extracted, tPO2crit also estimates the point above which O_2V becomes more than zero. Thus, tPO₂crit divides the values of OEF into two phases: in phase 1, for tPO₂ ≤ tPO₂crit, OEF is essentially unity, and, in phase 2, for tPO₂ > tPO₂crit, OEF displays a moderate, quasilinear, negative slope on tPO₂.

Relating tPO₂ to MO₂

It is widely accepted that, in neural tissue, the relationship of the rate of oxygen consumption (e.g., MO₂) to oxygen concentration (proportional to tPO₂) is nonlinear, conforming to M-M kinetics.^51–55 M-M kinetics describe the situation in which the rate of metabolism of a substance varies according to the degree of saturation of the enzyme that limits the rate of the reaction. The general M-M equation for MO₂ is:

$$\begin{array}{c}\hfill \mathrm{M}{\mathrm{O}}_2=\mathrm{M}{\mathrm{O}}_2\max *\mathrm{tP}{\mathrm{O}}_2/\left(\mathrm{Km}+\mathrm{tP}{\mathrm{O}}_2\right)\end{array}$$ (1)

where MO₂max is the maximum rate of the reaction, that is, the maximum value for MO₂, and Km is the value of tPO₂ when MO₂ is half maximum. Whereas oxygen is metabolized in several ways, the great majority is used as the final electron acceptor by cytochrome c oxidase (complex IV) in the cellular intermediary energy metabolic pathway that generates adenosine triphosphate (ATP).⁶⁶

Only the data on MO₂ in phase 2 conforms to M-M kinetics. This is because in phase 1, because OEF is essentially unity, MO₂ virtually equals DO₂, which declines linearly with tPO₂ (see Fig. 2). Thus, whereas our goal is to fit the MO₂ data from KL in phase 2, we also must constrain the fit so that when tPO₂ equals tPO₂crit the value of MO₂ equals DO₂. We accomplished this as follows: at tPO₂ = tPO₂crit = 6.20 mm Hg, MO₂ = DO₂. Thus, MO₂max * 6.20 / (Km + 6.20) = 23.5 * 6.20. Based on this equation, the following relationship between MO₂max and Km is derived: MO₂max = 23.5 * Km + 146. This constraint was imposed on the nonlinear regression model parameters to fit MO₂ data using the M-M equation for tPO₂ > tPO₂crit = 6.20 mm Hg. A relationship between MO₂ and tPO₂ was estimated: MO₂ = 556 * tPO₂ / (17.5 + tPO₂) (N = 14, R² = 0.73). We note that, because MO₂max was 556 nLO₂/min, increasing tPO₂ above normal theoretically could lead to values of MO₂ up to 556 nLO₂/min. Figure 4 shows MO₂ as a function of tPO₂ (that is, TRBF * 3.39). Both MO₂ and TRBF were obtained from the KL data set. For tPO₂ > tPO₂crit, a curve was generated according to the M-M equation above and for tPO₂ < tPO₂crit, a line with the following equation was generated for MO₂ = DO₂ = 23.5 tPO₂. In the four normal eyes in the current study, the mean calculated MO₂ (from the M-M equation) was 331 ± 38 nLO₂/min.

Figure 4.

Relationship between MO₂ and tPO₂. MO₂ and TRBF were obtained from the KL data set (N = 25) and tPO₂ was calculated as TRBF * 3.39 (see Fig. 1). MO₂ is the rate of inner retinal oxygen metabolism (nLO₂/min), and tPO₂ is the partial pressure of oxygen in the inner retina (mm Hg). For tPO₂ > tPO₂crit (= 6.20 mm Hg), a curve (dashed) was generated according to the Michaelis-Menten equation: MO₂ = 556 * tPO₂ / (17.5 + tPO₂) (N = 14, R² = 0.73). For tPO₂ < tPO₂crit, a line (solid) was generated with the following equation: MO₂ = DO₂ = 23.5 * tPO₂.

Discussion

In this work, we were able to confirm our hypotheses that tPO₂ was linearly related to TRBF and DO₂, and nonlinearly related to OEF and MO₂. Of note, the latter relationships were also found to be biphasic. Several points about the new findings of the relationships between tPO₂ and these biomarkers deserve further consideration, as discussed below.

Tissue PO₂

The tPO₂ quantifies retinal hypoxia and thereby can reveal degrees of its severity. From the perspective of the retinal cells, tPO₂ represents the access they have to oxygen and the ability to generate energy for the work they do to enable cellular survival and vision. Anaerobic glycolysis can add ATP, but at the associated low TRBF levels in ischemia, glucose availability is also limited. There are substantial fine spatial variations in local measurements of PO₂ in the normal inner retina, depending on the proximity to blood vessels. However, to relate PO₂ in the inner retina to global measures of TRBF, DO₂, OEF, and MO₂, necessitates a tPO₂ measured in a substantial retinal region. After all, it would not be possible to attribute the oxygen supply to a certain local inner retinal location to a specific location in the blood stream. Thus, in the current study, the measured tPO₂ was global, characterizing oxygen in an extended region of the inner retina.

tPO₂ Versus TRBF and DO₂

Although it seems reasonable that there would be some close relationship between tPO₂ and TRBF, to the best our knowledge, this is the first time that data has been obtained to demonstrate a statistically significant linear relationship between the two under physiologically normal and a wide range of reduced TRBF induced by CCAO. In the current study, we also found a linear relationship between tPO₂ and DO₂. As opposed to TRBF, which indicates the rate at which blood enters the retinal circulation, DO₂ indicates the rate at which oxygen enters the retinal circulation. As such, DO₂ more directly relates to retinal tissue oxygenation and consumption than TRBF. On the other hand, because DO₂ equals TRBF * O_2A, DO₂ and TRBF often provide similar information.

OEF Versus tPO₂ and Defining tPO₂crit

We previously have shown that the relationships between OEF and both TRBF and DO₂ are nonlinear with a progressively steeper negative slope as TRBF or DO₂ is reduced from normal.^34,36 In addition, He et al.⁶⁷ presented evidence that the oxygen extraction ratio (equivalent to OEF) as a function of blood flow was not linear, and the slope became progressively more negative (steeper) as blood flow decreased. Yi et al. also found increasing OEF with decreasing systemic P_AO₂.⁴¹ However, although both studies induced ischemia/hypoxia, O₂ deprivation was not enough for OEF to approach or equal unity. The current study confirms these findings and further demonstrates for the first time a nonlinear, sigmoid relationship between OEF and tPO₂. The nonlinear, progressively steeper negative slope of OEF as tPO₂ is reduced applies to higher levels of tPO₂, such that with progressive reductions in tPO₂, OEF can increase and serve as a compensatory mechanism to counteract reduction of MO₂ (phase 2). At low levels of tPO₂, OEF becomes maximized at unity and no more oxygen can be extracted from the retinal circulation (phase 1). We found a value for tPO₂crit of approximately 6.2 mm Hg that defines this biphasic characteristic of the relationship between OEF and tPO₂. To the best of our knowledge, tPO₂crit has not been quantified before in the retina.

MO₂ Versus tPO₂

There are several ways to estimate retinal oxygen consumption. Whereas the consumption rate of oxygen has been derived in the outer retina from tPO₂ data based on a one-dimensional oxygen diffusion mathematical model,^{3–5,7,12,13,16,68,69} the multidirectional fluxes from its ramifying capillary bed preclude this approach in the inner retina. The exception is the estimate of oxygen consumption from tPO₂ in the avascular inner plexiform layer by Cringle and coworkers.⁷⁰ One-directional flux has been established in the inner retina by eliminating retinal blood flow with an intraocular probe or laser/heat coagulation while simultaneously administrating high fractions of oxygen in the inspired gas.^8,71,72 The resulting high choroidal vascular PO₂ yields substantial diffusion of oxygen to the nonperfused inner retina. Although this method allows estimations of normal inner retinal O₂ consumption rates from tPO₂, it does not permit estimation of consumption with incomplete reductions of blood flow. More recently, MO₂ has been evaluated as the rate that oxygen exits the retinal circulation according to the Fick principle. The equation underlying this method is MO₂ = TRBF * (O_2A – O_2V), which can be written as DO₂ * OEF. This equation was used in previous studies,^{22,28,41,49,50} as well as for deriving the KL data set.^36,57 In the current work, we showed how MO₂ can be evaluated from tPO₂ as the rate of entry of oxygen into the cellular intermediary energy metabolic pathway. This method is based on evidence that, in phase 2 (tPO₂ > tPO₂crit), MO₂ is related to tPO₂ according to M-M kinetics (Equation 1) in which enzymatic saturation occurs at high values of tPO₂.^51–55 We were able to derive the constants (MO₂max and Km) by using MO₂ values from the KL data set that had been obtained as the rate of exit of oxygen from the retinal circulation. No estimates of the M-M constants for the retina in living mammals during retinal ischemia have been reported previously.

We showed that the relationship between MO₂ and tPO₂ has two phases. In phase 1, it is linear (tPO₂ ≤ tPO₂crit). This follows from the fact that, in phase 1, MO₂ equals, and cannot exceed, DO₂, which we showed is linearly related to tPO₂. In phase 2, we modeled MO₂ as a function of tPO₂ on the basis that the rate of the cellular intermediary energy metabolic pathway is governed by M-M kinetics, which is nonlinear. This relationship has experimental support based on data obtained in the brain.⁵¹ Whereas the M-M fit to our data has a high R² value, we do not have enough experimental data points to assert with complete certainty that this function best describes the relationship. Nonetheless, we believe this is the first time that derivation of MO₂ from tPO₂ in either phase 1 or 2 has been described in the retina in vivo.

The reported MO₂ in the literature that is most comparable to our measurement is from Yi et al.⁴¹ They inferred rMRO₂ (the same as MO₂) in rats based on the Fick principle, using visible light optical coherence tomography. Rearranging their equations, we can derive an equation relating MO₂ to TRBF. The mean TRBF in the 4 normal eyes in the current study was 6.9 µL / min, which is within the normal range for rats.^41,73–78 Inserting the mean TRBF, into this equation gives an MO₂ value of 333 nLO₂ / min, which is almost the same as the value of 331 nLO₂/min determined by the M-M equation derived in the current study. A comprehensive review of the inner retinal oxygen consumption was previously published by Linsenmeier and coworkers.⁷⁹ In two studies, the means and SD of oxygen consumption values were 3.6 ± 2.2 and 3.7 ± 1.5 mLO₂ * min⁻¹ 100gm⁻¹.^72,79 Assuming the weight of the inner retina to be 6 mg, in the 4 normal eyes in the current study, we calculated oxygen consumption to be 5.5 ± 0.63 mLO₂ * min⁻¹ 100gm⁻¹. This value is within or near a single SD of the means previously reported. Whereas our estimated oxygen consumption value is higher than those in previous studies, it is still comparable considering the methodological, biological, and physiological variabilities among studies.

It would seem that a reduction in MO₂ would have to be associated with an inability to fully conduct some energy requiring processes, so compensatory mechanisms are needed. When tPO₂ is near the normal level, effective compensatory mechanisms of autoregulation of retinal blood flow and varying extraction of O₂ from the vasculature maintain a relatively constant MO₂ (zero-order function). As the level of ischemic challenge becomes more severe, the range of compensation by vasodilation and the amount of increased extraction of O₂ from the vasculature are exceeded, resulting in impairment of MO₂. In fact, when tPO₂ approaches tPO₂crit, there clearly is decreased MO₂ despite the availability of O₂ in the vasculature, as indicated by the fact that OEF is less than unity. Based on the data in the current study, it is difficult to identify a junction between a zero-order region and one controlled by M-M kinetics. To the extent that it is applicable, a study by Buerk and Saidel⁵¹ that examined the relationship between oxygen metabolism and tPO₂ measured by microelectrodes in the brain and liver concluded M-M kinetics provides the most accurate fit of experimental data as compared to zero-order and first-order kinetics.

To our knowledge, there are no reported values for Km in the retina. Our estimation of Km in the rat retina is 17.5 mm Hg, which is substantially higher than Km measured in the gerbil brain (3.3 mm Hg).⁵² A notable difference between studies is the methods used for deriving Km. Our method measured retinal MO₂ = TRBF × (O_2A – O_2V) according to the Fick principle and a derived relationship between TRBF and global tPO₂ (see Fig. 1). Consequently, as described by phase 1, when OEF = (O_2A – O_2V) / O_2A reaches the maximum value of unity at O_2V = 0 (tPO_2crit ≤ 6.2 mm Hg), clearly global tPO₂ and MO₂ will have progressively lower values, becoming zero only when TRBF = 0 (or theoretically O_2A = O_2V). In contrast, the method used for deriving brain oxygen consumption was based on measuring local tissue PO₂ using oxygen microelectrodes. One possibility is that these measurements may not have recognized phase 1 in the brain data. Local tissue PO₂ (and MO₂) was zero, which could occur adjacent to the venous end of the microvessels when O_2V = 0. However, global tPO₂ and MO₂ still may have been greater than zero. To simulate this possibility, we ignored data in phase 1, subtracted the value of 6.2 mm Hg from each of the global tPO₂ values, and then fit the data to a M-M equation. We found Km and MO₂max to be 3.2 mm Hg and 389 nLO₂/min, values nearly the same as those reported by Nair et al.⁵² Therefore, differential measurements of global and local tissue PO₂ likely accounts for the difference in findings. Recently, Milej and coworkers used hyperspectral near-infrared spectroscopy combined with diffuse correlation spectroscopy to determine the relationship between ΔCRMO₂ (percent loss in cerebral metabolic rate of oxygen) and ΔCBF (percent loss in cerebral blood flow) under ischemia induced by bilateral carotid artery occlusion in piglets.⁸⁰ The data were fit to a power function (Δy = (kΔx)^a). Because we found that global tPO₂ is related to TRBF by a constant, the percent losses for ΔtPO₂ and ΔTRBF (or ΔCBF) would be the same. To compare our results with those of Milej et al., we simulated a relationship between MO₂ and tPO₂ using a M-M function with our derived constants (MO₂ = 556 * tPO₂ / (17.5 + tPO₂) and then calculated ΔMO₂ and ΔtPO₂ to mirror the brain data. The results showed the exponent of the fitted power function for our data (a = 1.42) is very close to the value published in the brain (a = 1.37). Overall, the results of this published data in the brain are consistent with and supportive of our finding of Km = 17.5 mm Hg in the retina. Nevertheless, we recognize that there may be other factors that could contribute to the estimated Km value in the current study. The effective Km value could be elevated if there are two cytochromes, one with low-affinity and one with high-affinity for oxygen. In one study, the net effect of the 2 cytochromes was equivalent to a Km of 24.4 mm Hg under certain conditions.⁸¹ Moreover, our estimated Km value was based on nonlinear regression analysis of a limited dataset, particularly in the intermediate tPO₂ levels. It is possible that another function, such as sigmoid, may better describe the relationship in the retina than the M-M function.

Limitations

There were several limitations of this study. First, this study was conducted in a small sample size of male Long-Evans rats, so the generalizability of the findings may be limited. In addition, because the current sample predominately has eyes with low blood flow, a larger sample, especially having eyes with higher levels of blood flow, are needed to augment the robustness of the relationships we have presented. Second, although we combined data on TRBF from eyes having BCCAO for <0.5 hours and 24 hours, the P value of the difference between groups was 0.06. The possibility of type two errors was suggested, warranting additional data to confirm the findings. Third, we treated the M-M constants to be independent of tPO₂, although there is some conflicting evidence.⁵³ Fourth, we also note that the biomarkers TRBF, DO₂, OEF, and MO₂ are global measurements, and localized effects may be obscured. In contrast, our tPO₂ measurements may not represent conditions away from the measurement sites, although the retinal regions evaluated were substantial and the ischemia-induced changes likely affected the retinal tissue relatively uniformly.

Conclusions

Over a range of retinal blood flow conditions, from normal to severe reduction, we showed a linear relationship between tPO₂ and TRBF. We derived a critical tPO₂ level (6.2 mm Hg), such that below this value, MO₂ equals DO₂ and increases from zero linearly with tPO₂. Above this value, MO₂ increases according to M-M kinetics. The relationships of tPO₂ with TRBF, DO₂, OEF, and MO₂ help clarify the pathophysiology of ischemic retinal injury and eventually may contribute to better care of people with retinal ischemia and hypoxia.