**Purpose**:
To demonstrate the applicability of a growth modeling framework for quantifying spatial variations in geographic atrophy (GA) lesion kinetics.

**Methods**:
Thirty-eight eyes from 27 patients with GA secondary to age-related macular degeneration were imaged with a commercial swept source optical coherence tomography instrument at two visits separated by 1 year. Local GA growth rates were computed at 6-µm intervals along each lesion margin using a previously described growth model. Corresponding margin eccentricities, margin angles, and growth angles were also computed. The average GA growth rates conditioned on margin eccentricity, margin angle, growth angle, and fundus position were estimated via kernel regression.

**Results**:
A total of 88,356 GA margin points were analyzed. The average GA growth rates exhibited a hill-shaped dependency on eccentricity, being highest in the 0.5 mm to 1.6 mm range and lower on either side of that range. Average growth rates were also found to be higher for growth trajectories oriented away from (smaller growth angle), rather than toward (larger growth angle), the foveal center. The dependency of average growth rate on margin angle was less pronounced, although lesion segments in the superior and nasal aspects tended to grow faster.

**Conclusions**:
Our proposed growth modeling framework seems to be well-suited for generating accurate, spatially resolved GA growth rate atlases and should be confirmed on larger datasets.

**Translational Relevance**:
Our proposed growth modeling framework may enable more accurate measurements of spatial variations in GA growth rates.

^{1}is a late stage of age-related macular degeneration characterized by contiguous regions of photoreceptor, retinal pigment epithelium, and choriocapillaris atrophy.

^{2}

^{–}

^{5}Currently, there are no approved treatments to stop or slow lesion growth and GA causes progressive vision loss.

^{6}Importantly, GA growth rates exhibit variability at multiple spatial scales

^{7}: on a global (whole lesion) scale, there is eye-to-eye and patient-to-patient variability in GA growth rates; and, on a local (margin segment) scale, there is variability in the growth rates along different lesion segments.

^{8}

^{,}

^{9}choriocapillaris status,

^{10}

^{–}

^{12}and fundus autofluorescence patterns.

^{13}Studies investigating GA lesion kinetics as a function of lesion position have found that growth rates exhibit a hill-shaped dependency on eccentricity, growing slower in the fovea and outer macula, and faster in the perifovea and parafovea.

^{14}

^{–}

^{16}In particular, the phenomenon of foveal sparing, whereby some GA lesions preferentially expand around and/or away from, rather than toward, the fovea, is well-documented.

^{7}

^{,}

^{17}Prior studies investigating spatial variations in GA growth rates have tended to use global (i.e., not spatially resolved) growth rate measurements applied to grids (grid-based),

^{14}

^{,}

^{15}or, in some cases, to particular lesion configurations (configuration-based)

^{17}—for example, lesion configurations that include residual foveal islands. However, in a local approach, Uji et al.

^{18}used Euclidean distance maps (distance-based) to study spatial variations in GA growth rates.

^{19}Because this framework allows for spatially resolved measurements along the en face lesion margin, it is naturally suited for directly quantifying spatial variations in GA growth rates. In this study, we demonstrate the applicability of our growth modeling framework for spatially resolved GA growth rate measurements in a pilot study of 38 eyes having 1-year follow-up intervals. We believe that this application of our model is important because quantifying GA growth variability may improve our understanding of GA pathogenesis, decrease measured variations in GA therapeutic trials, and refine predictive GA growth models.

^{2}or greater (1 disc area), (2) for multifocal lesions, at least one GA focus had an area of more than 1.25 mm

^{2}, and (3) the GA lesions were fully contained within the 6 mm × 6 mm field of view at both visits (see subsequent section for GA measurement and imaging details).

^{10}Briefly, eyes were imaged using a commercial swept source OCT instrument (PLEX Elite 9000; Carl Zeiss Meditec, Dublin, CA) operating at a 1050-nm central wavelength, 100-nm bandwidth, and 200-kHz A-scan rate. Full-width-at-half-maximum axial and transverse optical resolutions were 5 µm and 20 µm in tissue, respectively. Eyes were imaged over a 6 mm × 6 mm field of view using an OCTA protocol comprised of 500 A-scans per B-scan, two repeated B-scans per B-scan position, and 500 B-scan positions per volume. OCTA volumes were generated using the complex optical microangiography algorithm.

^{20}Acquisitions having a signal strength of less than 7 and/or severe motion artifacts were excluded.

^{1}

^{,}

^{10}

^{,}

^{21}The GA tracing was performed by two independent graders (Y.S. and L.W.) using commercial image analysis software (Adobe Photoshop CC; Adobe Systems, San Jose, CA) and a consensus outline was reached by the two graders. For cases in which a consensus was not reached, a senior grader (P.J.R.) acted as the adjudicator.

^{22}We opted for polynomial registration as we found that, owing to motion artifacts, affine registration was insufficiently flexible; we opted for a second-order polynomial because we found that higher order polynomials did not improve the registration quality, as subjectively assessed by retinal vasculature overlays. The position of the foveal center was approximated as the geometric center of the foveal avascular zone (FAZ), as determined by manual tracing on the visit 1 full retinal en face OCTA projections. Following prior literature,

^{16}lesions were classified as foveal center point involved or foveal center point spared according to whether the foveal center was within the region of atrophy. Lesions were also classified as foveal zone involved or foveal zone spared according to whether there was any atrophy within 750 µm of the foveal center. Global lesion growth rates were characterized by the area growth rate (mm

^{2}/year), the square root of area growth rate (mm/year),

^{21}

^{,}

^{23}and the effective radius growth rate (mm/year)

^{16}(see Supplementary Material I for definitions). Note that the effective radius growth rate is related to the square root of area growth rate by a factor of \(\sqrt \pi \). The effective radius growth rate is convenient because it has a clear physical interpretation and the same scaling as our local GA growth rate measurements, which are discussed elsewhere in this article. We report all three global growth rate metrics to facilitate comparison with prior studies.

^{19}The mathematical formulation, given in Supplementary Material II, differs somewhat from our prior study, although the effects of these differences are relatively minor. Briefly, we use a biophysical GA growth model to evolve the visit 1 GA margin to the visit 2 GA margin. The GA growth model is expressed as a partial differential equation composed of two terms: a term that causes the lesion margin to expand in the direction perpendicular to its boundary (i.e., directly outward) and a term that causes concave margin segments to expand faster than convex margin segments. The rationale for these terms is discussed in our prior study.

^{19}

*p*has a unique growth trajectory, \(\vec \ell ( p )\), and a unique growth vector, \(\vec L( p )\); however, margin points whose trajectories were involved in intrafocus or interfoci merging were excluded from the analysis. This exclusion is detailed in the Discussion, and in Supplementary Material V.

*v*, is computed as the arclength of a growth trajectory divided by the intervisit time, and is the local analogue to typical measures of global GA growth rate. In particular, for a circular lesion undergoing isotropic growth, the local growth rate is equal to the effective radius growth rate, or \(1/\sqrt \pi \) × the square root of area growth rate.

*r*; the margin angle, θ; and the growth angle, ψ (Table). For each point on the GA lesion margin, these parameters were measured with respect to a fovea-centered coordinate system, which was configured with one axis along the inferior–superior direction and the other axis along the temporal–nasal direction (Fig. 2). As shown in Figure 2, for a given margin point

*p*, the margin eccentricity was defined as the distance of the margin point

*p*from the fovea center, which is precisely equal to the length of the position vector, \(\vec s( p )\), which specifies the position of

*p*relative to the given fovea-centered coordinate system. Similarly, the margin angle, θ, was defined as the counterclockwise angle between the position vector, \(\vec s( p )\), and the given fovea-centered coordinate system. Note that the coordinate system is oriented so that margin angles of 0°, 90°, 180°, and 270° correspond with the nasal, superior, temporal, and inferior aspects of the fundus, respectively. Note that, to allow data from right and left eyes to be analyzed jointly, left eyes were reflected about the inferior–superior axis. Finally, the growth angle, ψ, was defined as the smallest angle between the growth vector, \(\vec L( p )\), and the position vector, \(\vec s( p )\); that is, ψ is the arccosine of the normalized dot product of \(\vec L( p )\) and \(\vec s( p )\). With this convention, a growth angle of 0° corresponds with growth directly away from the fovea center, and a growth angle of 180° corresponds with growth directly toward the fovea center.

^{24}(Supplementary Material III). Density scatter plots, which display the relative density of the measured points falling within a particular region of the plot, were created with the ‘dscatter’ MATLAB (version 2019b; MathWorks, Inc., Natick, MA) function using default arguments.

^{25}Boxplots were created using the MATLAB function ‘boxplot’, with outliers defined as those having growth rates faster than the 75th percentile by more than the 1.5 times the interquartile range, or slower than the 25th percentile by more than the 1.5 times the interquartile range. Nadaraya–Watson kernel regression was performed with subjectively chosen bandwidths of σ = 125 µm for margin eccentricities and σ = 10° for margin and growth angles. The choice of these bandwidths is considered in the Discussion.

^{10}All 38 eyes (100%) had lesions that were classified as foveal zone involved and 31 eyes (82%) were classified as foveal center point involved (see Methods). A total of 94,870 margin points were modeled, 88,356 (93%) of which were included in the analysis, and 6514 (7%) of which were excluded owing to lesion merging. Patient and GA lesion characteristics are summarized in Figure 3 and Figure 4. Relationships between local GA growth rates and margin eccentricity, margin angle, and growth angle are shown in Figures 5 to 8. Fundus GA growth rate maps and statistical descriptions of local GA growth rates are presented in Figure 9.

^{26}

^{,}

^{27}deposits,

^{28}or other entities thought to influence GA growth. And fourth, spatial variations in GA growth rates may be helpful for more accurately evaluating the effects of potential therapeutics that slow or stop GA growth. For example, if a therapeutic decreases GA growth rates by a fixed percentage, that may manifest in different absolute average decreases in GA growth rates for eyes with lesions located in the parafovea versus perifovea—a difference that could confound the accurate evaluation of the therapeutic efficacy.

*n*= 38) in our cohort, and the limited 6 mm × 6-mm field of view. Moreover, it is important to note that, given the wide variability in lesion geometry, not all conditional growth rate estimates were computed using the same number eyes or margin points (Fig. 4). For example, the mean growth rate estimates for eccentricities in the [0 mm, 0.5 mm] and [2.5 mm, 3.0 mm] ranges were derived from fewer eyes and margin points than growth rate estimates for margin eccentricities in the (0.5 mm, 2.5 mm) range. Because it is reasonable to expect that the generalizability of a growth estimate for a particular spatial covariate (e.g., margin eccentricity) is a function of both the number of eyes and the number of margin points used to make the estimate, we should be particularly cautious when interpreting growth rate estimates made with relatively few eyes and margin points. With these caveats in mind, and also making note of our different measurement approach, the results of our study are reasonably congruent with those of prior studies.

^{14}

^{–}

^{16}In particular, as in prior studies, we found that GA growth rates exhibit a hill-shaped dependency on eccentricity. In our study, we found the highest growth rates at eccentricities in the approximate range of [0.5 mm, 1.6 mm] range (Fig. 5), which agrees well with the report from Mauschitz et al.,

^{14}who reported the highest median area growth rates at eccentricities in the [0.6 mm, 1.8 mm] range. Our results agree less well with those from Sayegh et al.,

^{15}who report the highest mean area growth rates at eccentricates in the [1.5 mm, 3.0 mm] range, although the large grid spacing makes the extent of disagreement difficult to assess. Our results also differ somewhat from those of Shen et al.,

^{16}who, in a meta-analysis that included data from Mauschitz et al. and Sayegh et al., concluded that the effective radius growth rates, which are, of the three measurement types (Supplementary Material I), the closest to our metric, were highest in the [0.6 mm, 3.5 mm] range. The results of Shen et al. are somewhat challenging to interpret in the context of our results because (1) they treat the measurements of Mauschitz et al. as being mean area measurements, when they are actually median area measurements. (2) Owing to the relatively large number of eyes in Mauschitz et al., and because Shen et al. weight the studies according to the number of eyes, the Mauschitz et al. results have substantial influence on the estimated means. However, in Mauschitz et al. the median lesion area in the [1.8 mm, 3.6 mm] range is 0.6 mm

^{2}, whereas in Sayegh et al., the mean lesion area in the [1.5 mm, 3.0 mm] range is substantially higher, at 2.65 mm

^{2}. Thus, weighting by lesion area or perimeter, rather than number of eyes, may change the Shen et al. estimates by decreasing the weighting of the Mauschitz et al. data in the [1.5 mm, 3.0 mm] range. (3) Finally, the Mauschitz et al. sector-wise (nasal, superior, temporal, and inferior) median growth rates in the [1.8 mm, 3.6 mm] range are individually all very low (≤0.03 mm

^{2}/year), substantially less than the pooled median in the [1.8 mm, 3.6 mm] range of 0.42 mm

^{2}/year. Thus, further studies are needed to understand to what extent the differences in our results are attributable to differences in measurement approaches and to what extent they are attributable to our limited cohort size, or other factors, such as our limited 6 mm × 6-mm field of view.

^{18}found no statistically significant differences in growth

*distances*as a function of margin angle.

^{17}In that study, GA growth rates were compared along the inner and outer margin segments in eyes with residual foveal islands. Owing to the particular spatial configurations of these lesions, GA growth directions along the outer margin segments were inferred to be growing away from the fovea, whereas growth directions along the inner margin segments were inferred to be growing toward the fovea. Their analysis found a 2.8 times faster square root of area growth rate along the outer margin segments (away from fovea growth direction) compared with the growth rates along the inner margin segments (toward fovea growth direction). In our analysis, average GA growth rates were approximately 1.9 times faster in segments growing away from the fovea than in segments growing toward the fovea (Fig. 7). Importantly, in Lindner et al., the examined lesion configurations were such that segments growing toward the fovea were necessarily closer to the fovea than segments growing away from the fovea. In our analysis, although lesion segments farther from the fovea were found to also be more likely to be growing away from the fovea, as discussed elsewhere in this article, this was not prespecified.

^{29}Future studies with larger patient cohorts may add further insight into the statistical distribution of local GA growth rates.

^{14}

^{,}

^{15}configuration-based,

^{17}and distance-based

^{18}strategies for spatially resolved GA growth rate measurements, we believe that our approach offers substantial advantages. First, grid-based and configuration-based techniques use either area growth rates, which are dependent on lesion perimeter,

^{8}

^{,}

^{9}

^{,}

^{21}

^{,}

^{23}

^{,}

^{30}or square root transformed area growth rates,

^{21}

^{,}

^{23}which assume circular lesions. In contrast, because our growth modeling approach measures growth at each margin point, it is less dependent on lesion geometry. Second, for grid-based approaches, estimated growth rates are strongly influenced by the lesion and grid geometry, which can result in both overestimates and underestimates of the true growth rate. Indeed, as illustrated in Figure 10, even simple variations in lesion geometry can lead to wide variations in the estimated growth rates. Although Figure 10 shows the effect of gridding for the case of the effective radius growth rate metric, similar effects occur when using the area growth rate metric. In contrast, our growth modeling approach is grid-free and therefore avoids these challenges. Third, because configuration-based approaches use particular lesion configurations (e.g., residual foveal islands), they are not applicable to general lesion geometries. In contrast, as mentioned elsewhere in this article, our growth modeling approach is applicable to arbitrary lesion geometries. Fourth, both grid-based and configuration-based approaches lack spatial resolution, which for grid-based approaches is determined by the grid spacing, and for configuration-based approaches is binary. Note that although the grid-based approaches can improve spatial resolution by decreasing grid spacing, this practice exacerbates the gridding artifacts. In contrast, spatial resolution in our growth modeling approach is limited only by the resolution at which the lesions can be traced, and by the spatial coverage of the margin points. Fifth, the distance-based approach relies on a closest point computation, wherein every visit 2 margin point is associated with the closest visit 1 margin point.

^{18}This process implicitly models GA growth as occurring along straight line growth trajectories, which, depending on the lesion configuration, may be nonphysical and can result in growth trajectories intersecting regions of nonatrophy (Fig. 11). In contrast, our model generates physically plausible growth trajectories that never intersect regions of nonatrophy.

^{31}used mixed effects logistic regression to study variations in the local likelihood of atrophy development in eyes with type 1 choroidal neovascularization. While estimating likelihoods—and not growth rates, per se—we believe that their approach is promising and could be used to study relative trends in GA growth rate variations with respect to, for example, margin eccentricity and angle (it is less clear how applicable the method is to estimating trends with respect to growth angle). However, in our present article, we have not focused on this approach because it has yet to be applied to studying spatial variations in GA growth rates in the more general context.

^{32}Therefore, it is unlikely that the use of autofluorescence imaging would yield more accurate GA boundaries or different results, given that autofluorescence imaging has limitations of its own. In particular, the bright light associated with autofluorescence imaging may lead to more movement artifacts, which results in blurred lesion boundaries. Moreover, the luteal pigments can obscure GA margins within the central macula and cataracts may impact the accurate detection of GA boundaries, although these limitations have largely been resolved with green autofluorescence imaging.

^{33}Even if the results differ when using autofluorescence imaging, which is unlikely, it is likely that the OCT-defined boundaries are more accurate.

^{34}For this reason, we eschewed data-driven approaches in selecting our kernel bandwidths and instead chose bandwidths that we believe correspond with physiologically plausible and relevant scales of variation—that is, scales on which we would expect, on the basis of clinical observation and previous growth rate studies, there to plausibly be variations in mean GA growth rates. Although more sophisticated techniques for the data-driven kernel bandwidth estimation exist,

^{34}given the added complexity, the purpose of our study, and our limited cohort size, we did not pursue them. Correlations in our data also complicate the estimates of confidence intervals for the kernel regression estimates, which is why we did not report confidence intervals in our analysis. In future studies with larger datasets, we hope to address these limitations.

**E.M. Moult,**VISTA-OCTA (P), Gyroscope (C);

**Y. Hwang,**None;

**Y. Shi,**None;

**L. Wang,**None;

**S. Chen,**None;

**N.K. Waheed,**Allegro (C), Regeneron (C), Apellis (C), Optovue (device to institution, R), Heidelberg (device to institution, R), Nidek (device to institution, R, C), Zeiss (R), Stealth (C), Genentech (C), Astellas (C), Gyroscope (E), Ocudyne (I), Boehringer Ingelheim (C);

**G. Gregori,**Carl Zeiss Meditec (F);

**P.J. Rosenfeld,**Apellis (C, I) Biogen (C), Bayer (C), Boehringer-Ingelheim (C), Carl Zeiss Meditec (F, C) Chengdu Kanghong Biotech (C), EyePoint (C) Iveric bio (F), Ocunexus (C, I), Ocudyne (C, I), Regeneron (C) Stealth BioTherapeutics (F) Valitor (I), Verana Health (I).

**J.G. Fujimoto,**Optovue (I, P), Topcon (F), VISTA-OCTA (P)

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