Numerous metrics are used to analyze the morphometry of the foveal avascular zone (FAZ). Two such metrics, roundness and circularity, have recently shown a marked growth in their use. However, there have been inconsistencies across studies with respect to how these metrics are defined, as well as the algorithms used to calculate them. In some cases, the exact definition or algorithm is not disclosed. These issues significantly limit the translational utility of these biomarkers. We simulated FAZ shapes as circles or ellipses of differing aspect ratios and evaluated roundness and circularity with two commonly used approaches for FAZ analyses. Differing shape analysis algorithms produced conflicting results even with identical equations, and differing metric definitions produced incongruent results. Therefore caution should be used when comparing FAZ circularity and roundness metrics across studies, especially in the absence of detailed information about the algorithms used.

**Translational Relevance**:
Quantitative assessment of OCT-A images includes evaluating circularity and roundness of the FAZ. Inconsistent or inaccurate mathematical definitions of these metrics impacts their utility as biomarkers and impairs the ability to combine and compare results across studies.

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^{2}Multiple studies have characterized the size and shape of the FAZ in individuals with normal vision,

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^{9}and others have shown that the FAZ is altered in retinal pathologies such as diabetic retinopathy,

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^{5}sickle cell retinopathy

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^{11}, and retinopathy of prematurity.

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^{13}Quantitative metrics that have been examined as potential FAZ biomarkers for these and other diseases include area, perimeter, circularity, and roundness.

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^{14}Although area is perhaps the most common metric used to describe the FAZ, the enormous normal variation in the size of the FAZ

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^{9}may limit its ability to signify pathology in cross-sectional screening applications.

^{3}The regularity of the overall shape of the FAZ (measured as roundness or circularity) may enable more sensitive indication of disease because of less variation in the healthy population.

^{1}Central to the use of these metrics as FAZ biomarkers is an understanding of their mathematical definitions, as this not only impacts the sensitivity of the metric but also affects the ability to combine or compare data across studies.

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^{15}Even when included, inaccurate formulas have been reported.

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^{16}Roundness and circularity are often interpreted ambiguously and, without precise definitions, can be mistakenly used interchangeably or inconsistently between studies.

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^{15}Similarly, the use of different algorithms to calculate these metrics can introduce conflicting results based on the techniques or software being used.

*regionprops*(Mathworks, Natick, MA) and ImageJ

*Analyze Particles.*

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^{14}Additionally, the mathematical relationship between AR roundness and circularity can be found by equation manipulation of the two definitions, and is defined as

*t*, to generate the

*x*and

*y*coordinates of the points along the perimeter as defined below.

*regionprops*MATLAB function and ImageJ

*Analyze Particles*(ImageJ>Analyze>Analyze Particles). MATLAB

*regionprops*was called to measure area, two perimeter values (to account for the new and old algorithms used to calculate perimeter), circularity, major axis length, and minor axis length for each shape. These values were saved, and AR roundness was calculated by setting a ratio between the minor and major axis length. ImageJ

*Analyze Particles*was called to measure area, perimeter, circularity, roundness, major axis length, and minor axis length.

*Analyze Particles*’ roundness definition is equivalent to the AR roundness definition here.

^{18}, a Java package to connect MATLAB and ImageJ, was used in combination with Fiji

^{19}to access and run

*Analyze Particles*from the MATLAB script. To do this, an instance of ImageJ was created, navigated through, and terminated using MIJ methods and macro commands in the MATLAB script. To run

*Analyze Particles*, a mask of the shape was opened in the ImageJ instance, and the image was thresholded using default parameters (Image>Adjust>Threshold). Area, perimeter, shape, and fit were selected as measurements for

*Analyze Particles*(Analyze>Set Measurements). The results table generated by

*Analyze Particles*in ImageJ was saved into MATLAB.

*Analyze Particles*and

*regionprops*, mathematical computations performed in MATLAB included calculating theoretical values, calculating the sub-pixel perimeter using the distance formula and shape coordinates, and using MATLAB

*polyarea*to measure the sub-pixel shape area. The MATLAB functions

*ExactMinBoundCircle*

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*max_inscribed_circle*

^{21}were used to determine the diameters of the best-fit circles to calculate MIC/MCC roundness.

*regionprops*and

*Analyze Particles*resulted in identical shape area values, the

*polyarea*function resulted in better agreement with theoretical values (Mann-Whitney U = 2672,

*P*< 0.0001). Similar to

*polyarea*, the sub-pixel perimeter was most accurate to theoretical values (Kruskal-Wallis H(4) = 371.0,

*P*< 0.0001). The Table describes the percent difference between theoretical calculations and area and perimeter measurement methods along with their mathematical relationships in which theoretical value is represented as

*y*and measurement value is represented as

*x*.

*regionprops*and

*Analyze Particles*selected best-fit ellipses for the shapes with differing methods to find AR roundness, both ultimately calculated identical values of AR roundness. The relationship between AR roundness and MIC/MCC roundness for circles and ellipses resulted as

*regionprops*and

*Analyze Particles’*calculations of circularity for circles and ellipses resulted as

^{15}and the FAZ pixel diameter can be increased to fit into the relationships mentioned above. Figure 1C depicts an example of upsampling.

^{9}The OCT images were acquired with the AngioVue OCTA system (Optovue Inc., Fremont, CA) and the angiogram images were extracted using a slab of the superficial plexus layer (between 3 µm below the internal limiting membrane to 16 µm above the inner plexiform layer) 304 × 304 pixels in size. The images were of the right eye from 175 participants with no known ocular or systemic pathologies and were measured through a modified section of the MATLAB script described earlier. The area of the FAZs, measured with

*polyarea,*ranged from 0.07 mm

^{2}to 0.66 mm

^{2}with an average of 0.28 mm

^{2}and standard deviation of 0.1 mm

^{2}. Perimeter measured via the distance formula ranged from 1.14 mm to 3.69 mm with an average of 2.24 mm and standard deviation of 0.43 mm. As in the simulation, area, perimeter, and circularity results varied across the algorithms. Likewise, AR roundness values calculated using

*regionprops*and

*Analyze Particles*were the same despite having different major and minor axis lengths. Differences between the measurements were calculated by

*regionprops*and

*Analyze Particles*generated discordant circularity values, with differences ranging 6.3% to 13.2% with an average of 9.2% and 1.3% standard deviation. Between AR roundness and MIC/MCC roundness, the percent difference, independent of algorithm used, was 24.6% to 113.9% with an average of 59.4% and 17.6% standard deviation. For all FAZs, AR roundness was greater than MIC/MCC roundness (Fig. 4). Similarly, 131/148 of the simulated shapes had AR roundness values greater than the MIC/MCC roundness value (Fig. 4). This is due to AR being derived from the best-fit ellipse, so minor irregularities in the FAZ border have less impact, whereas the MIC/MCC roundness value is more significantly impacted by small irregularities in the FAZ border (as explained in Fig. 2). When assessing trends of the differences versus the FAZ shape, we found that as the average roundness value increased, the difference between AR roundness and MIC/MCC roundness decreased (

*r*= −0.7463, 95% confidence interval = −0.8055 to −0.6725,

*P*< 0.0001). In contrast, as the average circularity value increased, the difference between circularity values derived from

*regionprops*and

*Analyze Particles*increased (

*r*= 0.3966, 95% confidence interval = 0.2637 to 0.5146,

*P*< 0.0001), although the effect was smaller. These relationships demonstrate a non-uniform offset between methods, further illustrating the challenge of comparing results derived from different methods.

^{22}Although the change induced by different calculation methods may be small relative to some of these other sources of error, they do limit the ability to combine data across studies.

*regionprops*or ImageJ

*Analyze Particles*to analyze shapes, our analysis does not suggest that one is necessarily more accurate than another, just that there are differences. Choosing which approach to use will factor into many considerations. For example, MATLAB has extensive documentation, and changes to algorithms or formulas are generally well tracked; however it is a paid subscription application. Although ImageJ is a free open-source software, it does not have the same level of documentation and it may be difficult to find information about algorithm changes. As for area and perimeter calculations, we recommend using MATLAB

*polyarea*and the distance formula using the shape coordinates.

**J. Grieshop**, None;

**M. Gaffney**, None;

**R.E. Linderman**, None;

**R.F. Cooper**, US Patent 16/389,942 (P), Translational Imaging Innovations (I,C);

**J. Carroll**, AGTC (F), MeiraGTx (F), Optovue (F), Translational Imaging Innovations (I), US Patent 9,427,147 (P)

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