Summary
We describe the evaluation of a coefficient of determination between vessel and perfusion density of the parafoveal superficial capillary plexus to identify the contribution of vessels larger than capillaries to perfusion density.
Abstract
Parafoveal circulation of the superficial retinal capillary plexus is usually measured with vessel density, which determines the length of capillaries with circulation, and perfusion density, which calculates the percentage of the evaluated area that has circulation. Perfusion density also considers the circulation of vessels larger than capillaries, although the contribution of these vessels to the first is not usually evaluated. As both measurements are automatically generated by optical coherence tomography angiography devices, this paper proposes a method for estimating the contribution of vessels larger than capillaries by using a coefficient of determination between vessel and perfusion densities. This method can reveal a change in the proportion of perfusion density from vessels larger than capillaries, even when mean values do not differ. This change could reflect compensatory arterial vasodilatation as a response to capillary dropout in the initial stages of retinal vascular diseases before clinical retinopathy appears. The proposed method would allow the estimation of the changes in the composition of perfusion density without the need for other devices.
Introduction
Retinal circulation is the combination of arteriolar, capillary, and venular flow, whose contribution can vary to meet the oxygen needs of the different retinal layers. This circulation does not depend on the autonomous nervous system regulation and has been traditionally evaluated with fluorescein angiography, an invasive method that uses intravenous contrast to delineate retinal vessels. Sequential photographs allow the evaluation of arterial, arteriolar, venular, and venous circulation, as well as sites of capillary damage in retinal vascular diseases1.
A current method to measure the macular circulation is optical coherence tomography angiography (OCTA), which uses interferometry to obtain retinal images and can outline capillaries and larger retinal vessels2. Unlike fluorescein angiography, OCTA imaging is not influenced by macular xanthophyll pigment shadowing, allowing superior imaging of macular capillaries3. Other advantages of OCTA over fluorescein angiography are its noninvasiveness and higher resolution4.
OCTA devices measure the superficial capillary plexus at the parafovea in a 3 x 3 mm map, concentric to the foveal center (Figure 1). The equipment automatically measures vessel length density (the length of capillaries with circulation in the measured area) and perfusion density (the percentage of the measured area with circulation), which includes that of vessels larger than capillaries (Figure 2)5. Vessel density has a substantial contribution to perfusion density under physiological conditions. Some devices measure vessel density as a "skeletonized vascular density" and perfusion density as "vessel/vascular density." Regardless of the device, there is usually a measurement for length (measured in mm/mm2 or mm-1) and another for the area with circulation (measured in %), which are generated automatically.
Vessel density can change in healthy people when exposed to darkness, flicker light6, or caffeinated drinks7 because of the neurovascular coupling that redistributes blood flow between the superficial, middle, and deep capillary plexuses according to the retinal layer with the highest activity. Any decrease in vessel density caused by this redistribution returns to baseline values after the stimulus ceases and does not represent capillary loss, a pathological change reported before retinopathy appears in vascular diseases such as diabetes8 or arterial hypertension9.
The decrease in capillaries could be compensated partially by arteriolar vasodilatation. Measuring only a percentage or perfused area does not provide any insight into whether there is vasodilatation, which can appear when capillaries reach a minimum threshold. Measuring vessel density would not help detect an increased circulation area resulting from vasodilatation. The contribution of arteriolar circulation to perfusion density can be estimated indirectly using a coefficient of determination between vessel density and perfusion density, and defining the percentage of the area with circulation that corresponds to capillaries or other vessels.
The rationale behind this technique is that regression analysis can identify the extent to which the changes of an independent numeric value result in changes of a dependent numeric value. In macular vessel imaging using OCTA, capillary circulation is an independent variable that influences the area with circulation because there are few larger vessels in the evaluated region. However, the parafovea has larger vessels that can dilate and change the percentage of the area with circulation, which cannot be identified directly by the current automated OCTA metrics. The advantage of using a coefficient of determination is that it measures a relationship between two existing metrics to produce two more: the percentage of the area with circulation that corresponds to capillaries, and the percentage that corresponds to other vessels. Both percentages can be measured directly using a pixel count with imaging software. However, the coefficient of determination can be calculated for a sample with the numbers that the OCTA devices generate automatically10,11.
Pathak et al. used a coefficient of determination to estimate lean muscle and fat mass from demographic and anthropometric measures using an artificial neural network. Their study found that their model had an R2 value of 0.92, which explained the variability of a large portion of their dependent variables12. O'Fee and colleagues used a coefficient of determination to rule out nonfatal myocardial infarction as a surrogate for all-cause and cardiovascular mortality because they found an R2 of 0.01 to 0.21. Those results showed that the independent variable explained less than 80% of the changes of the dependent variables, set as a criterion of surrogacy (R2= 0.8)13.
The coefficient of determination is used to assess the effect of changes of a variable, a group of variables, or a model over the changes of an outcome variable. The difference between 1 and the R2 value represents the contribution of other variables to the changes of the outcome variable. It is uncommon to attribute the difference to a single variable because there are usually more than two contributing to the outcome. However, the proportion of the macular area that has circulation can only originate from the area covered by capillaries and from that covered by larger vessels, as larger vessels dilate more than capillaries. Moreover, reactive vasodilation is considered to most probably originate from retinal arterioles, because a reduced capillary circulation could decrease oxygen supply.
Only two sources contribute to a percentage of area with circulation in the macula: capillaries and vessels larger than them. The coefficient of determination between vessel density and perfusion density determines the contribution of capillaries to the area with circulation, and the remaining changes (the difference between 1 and the R2 value) represent the contribution of the only other variable that represents an area with circulation (that within larger retinal vessels). This paper describes the method of measuring this contribution in healthy people (group 1) and how it changes in patients with retinal vascular diseases: arterial hypertension without hypertensive retinopathy (group 2) and diabetes mellitus without diabetic retinopathy (group 3).
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Protocol
This protocol was approved by Sala Uno's human research ethics committee. See Video 1 for sections 1 and 2 and the Table of Materials for details about the equipment used in this study.
1. Retinal analysis in the OCTA device
- Select the menu for retinal analysis in the OCTA device.
- Select a 3 x 3 mm retinal map; select superficial if the OCTA device measures different capillary plexuses.
- Select vessel length density (or its equivalent, e.g., skeletonized vascular density).
- Measure vessel length density in mm-1 in a 3 x 3 mm retinal map.
NOTE: The map is divided into two regions: center (within a 1 mm circle, concentric to the foveal center) and inner (outside the 1 mm center circle, Figure 3). The equipment also measures a full density (within the 3 mm circle) and subdivides the inner region into four fields: superior, inferior, temporal, and nasal (Figure 4). Each region is specified so that the vessel length densities are measured automatically. The instruments display the values for center, inner, and full densities and for superior, temporal, inferior, and nasal fields of the inner density. - Return to the menu for retinal analysis.
- Select a 3 x 3 mm retinal map; select superficial if the OCTA device measures different capillary plexuses.
- Select perfusion density (or its equivalent, e.g., vessel density).
- Measure perfusion density in % in a 3 x 3 mm retinal map.
NOTE: The map is divided into two regions: center (within a 1 mm circle, concentric to the foveal center) and inner (outside the 1 mm center circle). The equipment also measures a full density (within the 3 mm circle) and subdivides the inner region into four fields: superior, inferior, temporal, and nasal. Each region is specified so that the perfusion densities are measured automatically. The instruments display the values for center, inner, and full densities and for superior, temporal, inferior, and nasal fields of the inner density. - Verify that the density maps have a signal strength > 7; then, verify that the maps have no measurement errors resulting from artifacts or eye movements.
- Register the values of center vessel length density, center perfusion density, inner vessel length density, inner perfusion density, superior vessel length density, superior perfusion density, inferior vessel length density, inferior perfusion density, temporal vessel length density, temporal perfusion density, nasal vessel length density, and nasal perfusion density in a spreadsheet.
2. Calculation of the coefficients of determination using a spreadsheet
- Select the variables to be evaluated (e.g., center vessel length density and center perfusion density). Select the values of both variables for a defined group (e.g., group 1).
- In the toolbar, click on insert.
- Click on the recommended charts button in the graphs section. Wait for a scatter chart to appear as a suggestion in a window. Click the OK button to accept the suggestion.
- Inspect the scatter chart of the data. Right-click on the series to display an options menu.
- Select the add trendline option. Wait for a linear trendline to be added to the chart and for a menu on the right side of the screen.
- Displace the menu downwards to find the Display R-squared value on chart option. Select this option to display the R-squared value on the chart. Select the R-squared-value.
- Select Home on the toolbar and then click on the copy button.
- Prepare a chart of coefficients of determination on a new page.
- Select a destination cell (e.g., center coefficient of determination for group 1). Click on the right mouse button. Select paste with keep source formatting.
- Prepare a new chart to show the percentage of perfusion density changes explained by changes in vessel density.
- Select the cell with the coefficient of determination in the previous chart. Click on the right mouse button. Select copy.
- Select a destination cell in the new chart (e.g., center in group 1). Click on the right mouse button. Select paste.
- Select the cell with the pasted value; then, in the toolbar, select home | percent style in the number menu.
- Select increase decimal in the number menu and click it once.
NOTE: The resulting number is the percentage of changes in perfusion density explained by the changes in vessel density. - Prepare another table to show the percentage of perfusion density explained by the changes in vessels larger than capillaries.
- Select a destination cell (e.g., center in group 1). Subtract the last result from 1.
- Select this cell. Select home in the toolbar.
- Select percent style in the number menu.
- Click once on increase decimals in the number menu.
- Format the charts to display the contribution of capillaries (vessel density) and vessels larger than capillaries to the changes in perfusion density.
- Repeat the procedure to obtain the values of inner vessel/perfusion densities and superior, inferior, temporal, and nasal vessel/perfusion densities in group 3.
3. Comparison of the coefficients of determination
- Compare the coefficients of determination in three groups: 1, healthy people; 2, patients with arterial hypertension without hypertensive retinopathy; and 3, patients with type 2 diabetes mellitus without diabetic retinopathy. In group 3, also compare the coefficients of determination between fields: superior, inferior, temporal, and nasal.
4. Compare the percentage differences in the contribution of capillaries and vessels larger than capillaries to perfusion density, between groups and between fields in group 3
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Representative Results
There were 45 subjects in group 1, 18 in group 2, and 36 in group 3. Table 1 shows the distribution of age and densities by group; only vessel and perfusion densities in group 1 were lower than in group 2. The coefficients of determination of center vessel and perfusion densities are shown in Figure 5. There was no significant difference between the groups.
The coefficient of determination between the inner vessel and perfusion densities was 0.818 in group 1, 0.974 in group 2, and 0.836 in group 3. The contribution of vessels larger than capillaries accounted for 18.2% in healthy subjects, 2.6% in patients with arterial hypertension, and 16.4% in patients with diabetes (Figure 6).
In group 3, the coefficients of determination between vessel and perfusion density were 0.722 in the superior field, 0.793 in the inferior field, 0.666 in the temporal field, and 0.862 in the nasal field. Although the inner region had a contribution of vessels larger than capillaries that accounted for 16.4% of perfusion density, this contribution was 27.8% in the superior field, 20.7% in the inferior field, 33.4% in the temporal field, and 13.8% in the nasal field (Figure 7).
Figure 1: Distribution of an optical coherence tomography 3 x 3 mm density map of the right eye. The map is centered in the fovea and measures 3 mm in diameter; the center metrics correspond to a region 1 mm in diameter. The inner metrics correspond to the ring between the central 1 mm and the 3 mm diameter circles. The full metrics correspond to the whole area within the boundaries of the map. The inner ring is divided into fields: superior, temporal, inferior, and nasal; the map for the left eye switches the positions of the temporal and nasal fields. Please click here to view a larger version of this figure.
Figure 2: A 3 x 3 mm optical coherence tomography angiography density map of the superficial macular capillary plexus. The device uses the representation of the retinal vessels to measure vessel length density in mm-1 and perfusion density in %. Vessel length density corresponds to the sum of the length of vessels with circulation within the boundaries of the map; perfusion density corresponds to the percent area of the macula with circulation. The broader vessels correspond to arterioles and venules, which are larger than capillaries and have a higher contribution to perfusion density. The vertical magenta and horizontal lines are references of the scan used to center the map. Please click here to view a larger version of this figure.
Figure 3: Vessel length density maps. The OCT device outlines the area with circulation (upper left image), the retinal structure (lower left image), the retinal surface (upper right image) and generates the metrics automatically (lower right image). Maps of (A) a healthy individual and (B) a diabetic patient without retinopathy. The vessels at the level of the superficial capillary plexus are shown in white in the upper left images; there is a larger number of vessels in A than in B, a difference that is confirmed as a reduction in all the densities, especially center density. Interna = inner density; completa = full density. Please click here to view a larger version of this figure.
Figure 4: Vessel length density map in a diabetic patient without retinopathy, analyzed by field. The upper left image outlines the area with circulation; the lower left image shows the retinal structure; the upper right image shows the retinal surface; the lower right image shows the automatically generated metrics. The figure corresponds to the left eye and shows the automatic measurements for the superior, temporal, inferior, and nasal fields of the inner density in the upper left image. Abbreviations: S = superior; T = temporal; I = inferior; N = nasal. Please click here to view a larger version of this figure.
Figure 5: Comparison of the coefficients of determination between center vessel (mm-1) and perfusion (%) densities in the three groups. There are few capillaries in the center region and almost no vessels larger than capillaries, which explains the slight differences between the groups. Please click here to view a larger version of this figure.
Figure 6: Comparison of the coefficients of determination between inner vessel (mm-1) and perfusion (%) densities in the three groups. The contribution of vessels larger than capillaries to perfusion density was lower in patients with arterial hypertension and did not change in patients with diabetes, compared with healthy subjects. Please click here to view a larger version of this figure.
Figure 7: Comparison of the coefficient of determination between vessel (mm-1) and perfusion (%) densities by field, in group 3. The contribution of vessels larger than capillaries was greater in the temporal field, which was 20 percentage points higher than that of the nasal field. Please click here to view a larger version of this figure.
| Variable | Group 1 (n= 45) | Group 2 (n=18) | Group 3 (n= 36) | p* | |
| Age | 57.16±1.01 | 55.89±1.82 | 55.33±1.16 | 0.495 | |
| Center vessel density (mm-1) | 8.86±0.44 | 8.12±0.79 | 8.66±0.59 | 0.713 | |
| Inner vessel density (mm-1) | 21.14±0.29 | 19.84±0.91 | 20.52±0.27 | 0.116 | |
| Superior vessel density (mm-1) | 20.98±0.35 | 20.33±0.82 | 20.27±0.34 | 0.392 | |
| Inferior vessel density (mm-1) | 21.18±0.32 | 19.31±1.17 | 20.64±0.31 | 0.057 | |
| Temporal vessel density (mm-1) | 21.06±0.31 | 19.95±0.91 | 20.50±0.30 | 0.229 | |
| Nasal vessel density (mm-1) | 21.36±0.30 | 19.72±0.99 | 20.69±0.36 | 0.076 | |
| Center perfusion density (%) | 15.74±0.77 | 14.54±1.40 | 15.13±1.02 | 0.734 | |
| Inner perfusion density (%) | 39.12±0.48 | 38.85±1.58 | 37.95±0.49 | 0.108 | |
| Superior perfusion density (%) | 38.54±0.62 | 37.72±1.40 | 37.59±0.58 | 0.578 | |
| Inferior perfusion density (%) | 39.38±0.56 | 35.57±2.11 | 37.95±0.57 | 0.026 | |
| Temporal perfusion density (%) | 39.05±0.61 | 37.99±1.36 | 38.19±0.61 | 0.561 | |
| Nasal perfusion density (%) | 39.53±0.55 | 35.99±1.96 | 38.10±0.77 | 0.049 | |
Table 1: Comparison of variable distribution by group (mean ± standard error). *One-way analysis of variance.
Video 1: Calculation and comparison of coefficients of determination between variables, using a spreadsheet. Please click here to download this Video.
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Discussion
The contribution of vessels larger than capillaries to perfusion density changes in retinal vascular diseases before the development of retinopathy. It decreased in the inner region of patients with arterial hypertension and varied between fields in patients with diabetes. There are direct methods for measuring vascular reactivity in the retina, which depend on the exposure to a stimulus14,15. The measurement proposed in this paper uses two metrics, automatically generated by OCTA devices, to estimate the contribution of vessels larger than capillaries to the percentage of the evaluated area with circulation.
The critical step in the method is obtaining adequate measurements of vessel and perfusion densities in the 3 x 3 mm map. Images with a signal strength > 7 and without artifacts produce reliable numbers for use in a scatterplot. Although there are protocols for correcting segmentation errors in OCTA measurements16, this study worked only with images with high quality, without artifacts or measurement errors. The coefficient of determination is calculated using a usual spreadsheet or any other statistical package; the contribution of vessels larger than capillaries requires only subtraction and a conversion to a percent expression.
A limitation of the technique is that it currently evaluates only samples because it requires several subjects to assess the dispersion of changes in the outcome variable. Further studies should address cut points that allow the use of the information in an individual patient or eye. The significance of the results of this method is that it can be of value for detecting population clusters with a particular alteration of retinal circulation, which can then be evaluated with direct, more expensive, or invasive methods.
The change in the percent contribution of vessels larger than capillaries may reflect a compensatory event when a decrease in permeable capillaries induces arteriolar dilatation. It has been reported that capillaries dilate by 1% and arterioles by up to 6% in response to flicker light stimulation17. However, patients with arterial hypertension may not show the same dilatation because of the increased arteriolar constriction, which could explain the reduction in the contribution of vessels larger than capillaries to perfusion density, which was found in this group.
Compensatory changes in vessels larger than capillaries have not received the same attention as capillary density in retinal vascular diseases. However, they may show a condition where the reduction of capillary density is critical and where local hypoxia requires another source of blood flow. There is insufficient data to define whether this finding may occur simultaneously to the loss of neurovascular coupling, reported early in diabetic patients without retinopathy18.
The changes found in this study may not apply to every patient with arterial hypertension or diabetes. Although the estimation proposed is indirect, it revealed differences worth comparing with direct methods and that show the composition of parafoveal circulation at a particular time point. The potential application of this measurement is the future identification of threshold values of capillary dropout that induce arteriolar dilatation in various stages of retinal vascular diseases. Those thresholds have not been reported and might be helpful as biomarkers for disease progression and responses to treatments.
In conclusion, a method is proposed to evaluate the contribution of vessels larger than capillaries, which requires only the usual measurements that the OCTA devices produce and that may go unnoticed with the automatic metrics. The changes found in people with vascular diseases before retinopathy appears suggest reactive vasodilation, which may be useful to evaluate therapeutic interventions without using other equipment.
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Disclosures
The authors declare that they have no conflicts of interest to disclose.
Acknowledgments
The authors would like to thank Zeiss Mexico for the unrestricted support to use the Cirrus 6000 with AngioPlex equipment.
Materials
| Name | Company | Catalog Number | Comments |
| Cirrus 6000 with Angioplex | Carl Zeiss Meditec Inc., Dublin CA | N/A | 3 x 3 vessel and perfusion density maps |
| Excel | Microsoft | N/A | spreadsheet |
| Personal computer | Generic | N/A | for running the calculations on the spreadsheet |
References
- Ong, J. X., Fawzi, A. A. Perspectives on diabetic retinopathy from advanced retinal vascular imaging. Eye. , (2022).
- Tan, A. C. S., et al. An overview of the clinical applications of optical coherence tomography angiography. Eye. 32 (2), 262-286 (2018).
- Elnahry, A. G., Ramsey, D. J. Optical coherence tomography angiography imaging of the retinal microvasculature is unimpeded by macula xanthophyll pigment. Clinical and Experimental Ophthalmology. 48 (7), 1012-1014 (2020).
- Elnahry, A. G., Ramsey, D. J. Automated image alignment for comparing microvascular changes detected by fluorescein angiography and optical coherence tomography angiography in diabetic retinopathy. Seminars in Ophthalmology. 36 (8), 757-764 (2021).
- Rosenfeld, P. J., et al. Zeiss AngioPlex spectral domain optical coherence tomography angiography: technical aspects. Developments in Ophthalmology. 56, 18-29 (2016).
- Nesper, P. L., et al. Hemodynamic response of the three macular capillary plexuses in dark adaptation and flicker stimulation using optical coherence tomography angiography. Investigative Ophthalmology and Visual Science. 60 (2), 694-703 (2019).
- Zhang, Y. S., Lee, H. E., Kwan, C. C., Schwartz, G. W., Fawzi, A. A. Caffeine delays retinal neurovascular coupling during dark to light adaptation in healthy eyes revealed by optical coherence tomography angiography. Investigative Ophthalmology and Visual Science. 61 (4), 37 (2020).
- Barraso, M., et al. Optical coherence tomography angiography in type 1 diabetes mellitus. Report 1: Diabetic Retinopathy. Translational Vision Science and Technology. 9, 34 (2020).
- Xu, Q., Sun, H., Huang, X., Qu, Y. Retinal microvascular metrics in untreated essential hypertensives using optical coherence tomography angiography. Graefe's Archive for Clinical and Experimental Ophthalmology. 259 (2), 395-403 (2021).
- Yeh, R. Y., Nischal, K. K., LeDuc, P., Cagan, J. Written in blood: applying grammars to retinal vasculatures. Translational Vision Science & Technology. 9, 36 (2020).
- Corvi, F., Sadda, S. R., Staurenghi, G., Pellegrini, M. Thresholding strategies to measure vessel density by optical coherence tomography angiography. Canadian Journal of Ophthalmology. 55 (4), 317-322 (2020).
- Pathak, P., Panday, S. B., Ahn, J. Artificial neural network model effectively estimates muscle and fat mass using simple demographic and anthropometric measures. Clinical Nutrition. 41 (1), 144-152 (2022).
- OFee, K., Deych, E., Ciani, O., Brown, D. L. Assessment of nonfatal myocardial infarction as a surrogate for all-cause and cardiovascular mortality in treatment or prevention of coronary artery disease: a meta-analysis of randomized clinical trials. JAMA Internal Medicine. 181 (12), 1575-1587 (2021).
- Kushner-Lenhoff, S., Ashimatey, B. S., Kashani, A. H. Retinal vascular reactivity as assessed by optical coherence tomography angiography. Journal of Visualized Experiments: JoVE. (157), e60948 (2020).
- Sousa, D. C., et al. A protocol to evaluate retinal vascular response using optical coherence tomography angiography. Frontiers in Neuroscience. 13, 566 (2019).
- Falavarjani, K. G., et al. Effect of segmentation error correction on optical coherence tomography angiography measurements in healthy subjects and diabetic macular oedema. British Journal of Ophthalmology. 104 (2), 162-166 (2020).
- Warner, R. L., et al. Full-field flicker evoked changes in parafoveal retinal blood flow. Scientific Reports. 10 (1), 16051 (2020).
- Zhang, Y. S., et al. Reversed neurovascular coupling on optical coherence tomography is the earliest detectable abnormality before clinical diabetic retinopathy. Journal of Clinical Medicine. 9 (11), 3523 (2020).
