**Purpose**:
To characterize macular ganglion cell layer (GCL) changes with age and provide a framework to assess changes in ocular disease. This study used data clustering to analyze macular GCL patterns from optical coherence tomography (OCT) in a large cohort of subjects without ocular disease.

**Methods**:
Single eyes of 201 patients evaluated at the Centre for Eye Health (Sydney, Australia) were retrospectively enrolled (age range, 20–85); 8 × 8 grid locations obtained from Spectralis OCT macular scans were analyzed with unsupervised classification into statistically separable classes sharing common GCL thickness and change with age. The resulting classes and gridwise data were fitted with linear and segmented linear regression curves. Additionally, normalized data were analyzed to determine regression as a percentage. Accuracy of each model was examined through comparison of predicted 50-year-old equivalent macular GCL thickness for the entire cohort to a true 50-year-old reference cohort.

**Results**:
Pattern recognition clustered GCL thickness across the macula into five to eight spatially concentric classes. *F*-test demonstrated segmented linear regression to be the most appropriate model for macular GCL change. The pattern recognition–derived and normalized model revealed less difference between the predicted macular GCL thickness and the reference cohort (average ± SD 0.19 ± 0.92 and −0.30 ± 0.61 μm) than a gridwise model (average ± SD 0.62 ± 1.43 μm).

**Conclusions**:
Pattern recognition successfully identified statistically separable macular areas that undergo a segmented linear reduction with age. This regression model better predicted macular GCL thickness. The various unique spatial patterns revealed by pattern recognition combined with core GCL thickness data provide a framework to analyze GCL loss in ocular disease.

^{1}While GCs are susceptible to a variety of disease processes,

^{2–5}GC loss is also known to occur in the absence of identified disease as a part of aging.

^{6–14}There is controversy regarding the spatial and temporal pattern of GC loss with age. Histologic studies have described GC loss to be linear,

^{6,9,15}and a model for estimating the GC population derived from visual field sensitivity has likewise suggested a linear change.

^{16}Studies using nerve fiber layer (NFL) thickness

^{10,14,17–20}and ganglion cell layer (GCL) thickness

^{12}from optical coherence tomography (OCT) as a measure of GC loss have likewise suggested linear loss with age. Gao and Hollyfield,

^{7}however, found that while the GC loss appeared to be linear for the macular area, loss metrics in the peripheral retina appeared logarithmic. Closer inspection of histologic data from Harman et al.

^{9}and Jonas et al.

^{6}suggests that there is a large variation in GC count and limited losses until after middle age. Recent studies analyzing retinal

^{21}and GCL thickness

^{11}with the OCT in the macula likewise showed greater reduction in thickness after middle age. While it is now acknowledged that peripheral retina loses GCs faster than the macula,

^{7,9}knowledge of the rate of macula change is limited. Inadequate understanding of age-related GC loss may confound the detection and diagnosis of age-related pathologies involving GC loss, namely glaucoma.

^{13,18,22}

^{23–25}allowing large-scale in vivo profiling in a normal population. Thus, we sought to reinvestigate the pattern of normal age-related GC loss in the macula using OCT. Although numerous studies have quantified GC loss via NFL thickness

^{10,14,17–20}and GCL thickness

^{11,12}by OCT, few have analyzed these entities across temporal and spatial domains of the macula. Our study uses high-density macular cube OCT scanning to assess GC changes at 64 grid locations centered at the fovea, each grid 860 × 860 μm in size. To identify areas with similar age-related changes, we applied pattern recognition, a well-established technique for computationally clustering imaging data sets over

*N*dimensions, in this case

*N*= 7 age groups defined as decades. Pattern recognition visualizes complex data associations as memberships in statistically distinct theme classes

^{26}and is traditionally used for satellite remote sensing analysis.

^{27–31}This analysis can be applied in other fields and has previously been used to successfully cluster retinal cells into unique signature classes according to small molecule content.

^{32–36}Pattern recognition has the distinct advantage of being able to analyze large data for multiobjective optimization and at the same time assess separability of the classes using statistical tests such as transformed divergence. We hypothesized that different areas within the macula could be allocated to distinct classes according to their temporal regression signature. While a gridwise analysis enables high spatial resolution, the discriminatory power may be reduced when analyzing data that are known to have high individual variability, such as GC density.

^{6,9,37}Clustering analyses allow areas with statistically proven common features to be pooled together, which can improve the discriminatory power and allow more robust analysis of highly variable data. Furthermore, classwise data may facilitate the application of these data in future research by providing a framework with which macular areas can be classed and analyzed together. We further aimed to demonstrate the application and accuracy of these models for converting GCL thickness to an age equivalent, as well as a potential tool for in vivo estimation of GC count. This improves our understanding of normal human GC population dynamics and forms the basis for future investigations involving disease, particularly if areas of retinal space can be grouped into cohesive units.

^{38}which, in brief, included any subject with a clinical finding suspicious with regard to glaucoma on fundus appearance, imaging results, or visual fields. All eyes encompassed in this study met the following inclusion criteria: availability of a good-quality Spectralis OCT (imaging quality score > 15 dB) scan, visual acuity (VA) better than 20/25 (logMAR < 0.1) for all those under the age of 60 or better than 20/32 (logMAR < 0.2) for those older than 60, and spherical equivalent of less than ±6 diopters and astigmatism of less than 3 diopters. Unilateral ocular disease, such as central serous retinopathy, did not necessitate exclusion provided the fellow eye met the inclusion criteria. If both eyes met the inclusion criteria, one eye was randomly chosen. The scan results for the left eye were converted to right eye format. This study received ethics approval from the University of New South Wales Australia, Human Research Ethics Advisory (UNSW Australia HREA) panel. The tenets of the Declaration of Helsinki and ethics procedures put forward by the UNSW Australia HREA were observed for subject data collection.

^{39}Thus, the GCL thickness measurements were converted to decibel-micron units (dB, μm) using the following correlation:

*t*= GCL thickness in dB, μm and

_{dB}*t*= GCL thickness in microns.

_{m}^{26}As a consequence, clustering is significantly affected by the applied strategy and statistical criteria. Therefore, we have adopted a clustering paradigm that has been well established in previous studies.

^{27,28,30,34,35,40}Specifically, the data were analyzed with unsupervised classification using ISODATA clustering for each decade subgroup (PCI Geomatica, Markham, ON, Canada) (Fig. 1D, second image) generating clusters of locations within the macula with similar change in GCL thickness with age (theme classes). ISODATA clustering is a specific form of K-means clustering (a migrating means methods) and aids with feature selection by automated splitting of high variance classes and merging classes with low separability.

^{41}Unlike traditional K-means methods, this algorithm is not bound by a predefined number of classes, but allows the class numbers to be reduced or increased appropriately within a given range. The separability of identified theme classes was statistically verified using transformed divergence (D

_{T}).

^{26}D

_{T}value ranges from 0 to 2, with 0 referring to inseparable clusters and 2 indicating complete separation. A value of >1.9 corresponds to a probability of correct classification of >98%

^{42}and is commonly accepted as the cutoff for statistically significant separability for clustering studies,

^{27,28,30,32–35,40}as well as recommended by the manufacturer of the software.

^{43}Following classification and confirmation of separability, each distinct theme class was assigned a color for visualization in pseudocolor plot (Fig. 1D, third image). In the initial model, a single peripheral point was clustered together with the central four points corresponding with the fovea, which is inconsistent with an a priori assumption that the foveal pit is anatomically distinct from the rest of the retina.

^{44}Thus, in developing the final model, the central four locations corresponding to the fovea were masked and the data were reanalyzed, resulting in the reassignment of the aforementioned peripheral point with no other change in the classification. The ISODATA algorithm and statistical analysis provided the maximum number of statistically separable classes. After identifying the highest number of statistically unique theme classes using ISODATA clustering (

*N*= 8 theme classes), the K-means algorithm was used to restrict the number of classes stepwise down to the lowest separable number (

*N*= 5) to further explore the effect of total number of theme classes on the provided model.

*F*-test was conducted for each theme class to compare linear and segmented linear fit quality. The degree of freedom (df

_{1}) was defined as 1 for the numerator and 12 for the denominator (df

_{2}). The

*F*-ratio was calculated for each theme class, defined as the quotient of the absolute sum of squares (SS

_{T}) of the linear regression divided by the absolute SS

_{T}of segmented linear regression. Cutoff for statistical significance was specified as >4.75 (equivalent

*P*< 0.05). Paired

*t*-tests were conducted for the absolute SS

_{T}of the theme classes to compare the fits of the two models throughout the entire measurement area.

^{45}Specifically, this was conducted by adding a small value of

*ε*to the denominator and numerator to avoid 0 and 1 being transformed into an undefined value (i.e., −∞ and +∞) as outlined below:

*t'*= the highest non-1 proportional GCL thickness value (dB, μm) from the data set

*, t*= GCL thickness (dB, μm) as a proportion, and

_{p}*t*= proportional data after ad hoc logit transform.

_{logit}*F*-test was conducted on the classwise normalized GCL thickness data to determine if all of the classes could be fitted to a single regression curve.

*n*= 34, Table 1) to assess for accuracy.

^{3}) was determined as previously described in Raza and Hood.

^{46}In short, GC density per mm

^{2}for the horizontal and vertical meridians was linearly interpolated with polar coordinates for each of the 64 grid locations using currently available histologic data of GC density per area (mm

^{2}).

^{37}A group of age-equivalent subjects to the histologic data was selected from our cohort (

*n*= 31, Table 1), and the gridwise GCL thickness was obtained from this group. GC density per mm

^{2}value was divided by the GCL thickness in mm to obtain the GC density in mm

^{3}. Furthermore, gridwise estimate of the GC count for our age-equivalent subgroup was derived by multiplying the GC density per mm

^{3}to the average GCL thickness and grid area (860 × 860 μm).

^{2}was interpolated from previous histologic data

^{37}as described in Methods (Fig. 2A). From this, GC density per mm

^{3}(Fig. 2C) and the GC count (Fig. 2D) within the macular area were obtained, resulting in an estimated GC count for the total grid area of 4.68 × 10

^{5}cells, or 3.53 × 10

^{5}cells if restricted to the central 2.8-mm radius area.

*R*

^{2}± SD: 0.648 ± 0.20). However, high variance was observed for both the rate of regression (range, −0.003 to −0.141 dB, μm per decade) and coefficient of determination (range

*R*

^{2}: <0.01–0.88) throughout different regions of the measurement area. In general, the central and paracentral points showed greater rate of regression with a bias toward the nasal quadrant and areas with the lowest statistical significance, and

*R*

^{2}values were primarily located peripherally, although no clear trend could be identified (Fig. 3C). Segmented linear regression analysis for the gridwise data was unsuccessful as inflection point could be identified successfully for only 23 of the 64 grid locations, while the remaining 41 locations could not be adequately described using this model.

_{T}> 1.9) representing macular locations with similar GCL thickness and change with age (Fig. 4A). These classes were arranged in concentric configurations, which were retained even when the number of theme classes was reduced (Fig. 5). The location provided theme maps (Figs. 4A, 5), which, when combined with the average thickness data (e.g., Supplementary Fig. S1), allowed the generation of theme class–derived data sets of GCL thickness change over time (e.g., Figs. 4B, 4C) for any theme–map combination. Theme classes plotted with the segmented linear regression exhibited negligible change in GCL thickness until the inflection point at middle to high age range (48.41–72.11 years of age; Table 2), after which greater regression rates were seen (average rate of regression before inflection: −1.79 × 10

^{−3}dB, μm/decade, after inflection: −3.45 × 10

^{−3}dB, μm/decade; Table 2). The average coefficient of determination for each of the regression models was found to be higher for segmented linear regression (

*R*

^{2}= 0.917) compared to linear regression models (

*R*

^{2}= 0.663; Table 2, Figs. 4B, 4C). This difference in coefficients of determination is to be expected, however, when comparing a simple model to a more complex one. To determine if the more complex model (segmented linear regression) is appropriate,

*F*-test and paired

*t*-test of the absolute SS

_{T}was conducted.

*F*-test exhibited

*F*-ratios of greater than 4.75 (equivalent to

*P*< 0.05) for the first four theme classes, demonstrating that segmented linear regression is a more appropriate model for these measurement areas (Table 3). The paired

*t*-test did not reach statistical significance for all theme classes together (

*P*= 0.0543), likely due to the high absolute SS

_{T}exhibited by theme class 1, despite reaching significance by itself. When this class was excluded from the analysis, the relationship was found to be highly statistically significant (

*P*< 0.01), thus suggesting that a segmented linear regression may be applied as a whole.

*F*-test was conducted on the normalized GCL thickness data to determine if all of the classes could be fitted to a single regression curve. Class 1 was analyzed independently on the a priori assumption that the foveal area, which it corresponds to, reflects an anatomically distinct entity. A model consisting of a different regression curve for each class was rejected by this analysis (

*P*= 0.983), indicating that a single curve can adequately describe the observed regression pattern (Table 4).

^{23–25}and the advancement in image analysis enables the GCL to be assessed independently from the inner plexiform layer (IPL), which arguably allows for better assessment of GC integrity as the GCL undergoes greater absolute thinning than the IPL.

^{12,47}While a number of past studies have investigated age-related retinal tissue loss with OCT,

^{48–51}to the best of our knowledge this is the first investigation that not only analyzed the gridwise GCL thickness changes but also clustered them into statistically separable theme classes according to temporal regression signatures. This study demonstrated that pattern recognition can be applied to retinal thickness measurement, with the advantage of allowing a large number of data points to be analyzed for multiobjective optimization over

*n*dimensions and, at the same time, statistically test the separability of the clusters.

^{6,9,37}the discriminatory power may be reduced. Our result demonstrated this to be the case; the spatial and temporal patterns of regression were not readily apparent with the gridwise regression data, and only a third of the measurement area could be modeled with segmented linear regression curve. Classwise analysis of pattern recognition–derived classes, on the contrary, allowed for a more powerful analysis by enabling statistically similar areas to be analyzed together and revealing that GCL regression was better modelled with a segmented linear regression than with linear regression. It has also indicated the spatial signatures to be arranged in a concentric pattern with a slight bias toward the nasal side: This is consistent with histologic data.

^{8}Furthermore, these data may be able to be applied in place of gridwise regression potentially without appreciable reduction in accuracy or spatial resolution: The predicted 50-year-old equivalent GCL thicknesses with linear regression model derived from both the gridwise and classwise analysis were identical (Supplementary Figs. S2B, S2C, S2F, S2G), and the bias and confidence intervals were also similar (Figs. 6A, 6B).

^{18}To further verify the pattern of cluster found, supplementary pattern recognition analysis was conducted on selected age groups (20–29, 40–49, and 60–69) of the cohort to determine if similar classes are still present through different age groups when classified with GCL thickness alone instead of multiobjective classification. The result demonstrated similar clustering patterns to be present for all three age subgroups, with only a few points being classified differently from the original class (Supplementary Fig. S3). While a reduction in D

_{T}is expected due to the smaller sample size, it dropped below 1.9 on only one to three occasions for each subgroup, predominantly for the peripheral-most theme classes (data not shown). Furthermore, the concentric pattern persisted when clusters with similar characteristics were merged together with the restriction of the number of theme classes using the K-means algorithm (Fig. 5). Thus, these results lend support to the concentric pattern of theme classes found on the initial ISODATA analysis as having biological meaning. Additionally, we present a schema with varying number of concentric theme classes, which allows macular area with statistically similar GCL characteristics to be analyzed together.

^{52}and GCL

^{37}count reduced the density of the sampling windows and increased window size with eccentricity, and a similar approach with OCT measurements needs to be explored.

^{6,9,10,12,14–20}although there were some indications that they may follow a segmented linear regression.

^{6,9,11}Comparison of the theme classes' temporal regression pattern with

*F*-test suggested that segmented linear regression was a more suitable model than linear regression for the determined classes. Alternatively, the GCL thickness regression can be expressed as a normalized percentage change, in which case, the one formula can be applied to the entire macular area (except the fovea). Both of these models demonstrated accurate conversion of GCL thickness value to a given age; the classwise model demonstrated greater accuracy (less bias) while the normalized model showed greater precision (smaller confidence interval). Depending upon the intended purpose, models with greater accuracy or precision may be desired: For instance, if converting a cohort's GCL thickness data to a desired age to facilitate direct comparison to another cohort with a different age, the former may be preferable, although in cases such as repeated measurements on the same subject, the latter may be preferred. We therefore developed two alternate segmented linear regression models, each of which could be applied for different purposes. Combined with a spatial clustering schema with variable number of theme classes as shown in Figure 5, we present a framework with which future investigation of GCL can be conducted. In particular, it may be advantageous for application in structure–function studies, as it may assist in the spatial translation of data to visual field, which has different spatial distribution of data. The GCL thickness measurement was represented as a decibel scale to further facilitate future comparative study, as visual field data are also expressed in decibel scale. While a linear scale has the advantage of direct applicability to clinical scenario and a uniform scale, it was shown by previous studies that a linear relationship exists between structure and function when decibel scale was used for both variables

^{16}and better correlation may be achieved compared to linear scale.

^{39}

^{46}a mismatch in age between the OCT and histology cohort potentially leads to overestimation of the GC count. To address this, we conducted a similar analysis with age-matched OCT and histology data

^{37}(Table 1). The total GC count was estimated to be 3.53 × 10

^{5}cells within the central 2.8-mm radius, which was comparable to another OCT study (3.81 × 10

^{5}cells)

^{46}and histology (3.69 × 10

^{5}cells)

^{37}-derived estimates. To further ascertain the impact of mismatch in age, the GC count was recalculated with a cohort with similar characteristics to that in Raza and Hood's

^{46}study (52.1 ± 9.14 years of age,

*n*= 135,

*P*= 0.2024, unpaired

*t*-test), which did not considerably affect the estimate (3.57 × 10

^{5}cells). This is perhaps not surprising given the nature of segmented linear regression, which showed slower regression until middle age. Disparities in GC count estimates may instead be attributed to other sources such as differences in OCT analysis methods, instrumentation, grid size, and analysis area. Additionally, the impact of nonneural elements (glia)

^{53}and displaced amacrine cells must be considered.

^{37,54–56}As acknowledged in the original paper,

^{37}the histologic data utilized for this study also did not account for displaced amacrine cells and hence potentially overestimate GC density, although the impact within the macular region is expected to be low.

^{57}Likewise, they did not account for the presence of glial cells within the GCL.

^{53}Further investigation of displaced GC and glial cell density in the GCL of human retina may be required to refine the model further.

^{58}While age-related loss of contrast sensitivity is commonly acknowledged, controversy exists regarding the extent to which optical and neural changes drive the losses.

^{58–65}Similarity in the temporal pattern of GC loss in our data and contrast sensitivity loss suggests that age-related neural loss could be a fundamental source of visual sensitivity loss. On the other hand, comparison to visual field sensitivity with age showed a disparity in the rate of regression; visual field sensitivity within the central 10° regressed between −0.36 and −0.77 dB per decade,

^{66}while the rates of GC loss were less when expressed as a linear model (approximately −0.1 dB, μm per decade, Table 2). These conflict with histology studies suggesting a direct relationship between GC count and visual field sensitivity,

^{16}and a more recent investigation directly comparing GCL thickness measured with OCT likewise finding a direct relation between the two, albeit with a significant floor effect limiting the range where this is applicable.

^{67}A possible explanation is a compensatory increase in the nonneuronal component, leading to a reduction of neural component density per unit volume.

^{10,14,22}While there are studies that show the average GC soma diameter to decrease with glaucomatous neuropathy, which may lead to reduction in neural density,

^{15,68,69}it does not alter significantly with age.

^{9}Furthermore, recent studies have highlighted the limitation of conventional visual field strategy utilizing stimulus size not scaled for spatial summation area,

^{70–72}a potential confounding factor for any such structure–function comparison. Thus, a structure–function study comparing GC density to appropriately scaled visual stimulus and further analysis of GC density per volume may be required to clarify the relationship.

^{73}While the variability does not alter with eccentricity, this is expected to have a greater impact on the peripheral areas than the central area due to the decreased initial thickness and is likely to impact the analysis of regression pattern peripheral locations, especially if rate of regression is proportional to the baseline thickness.

^{27,28,30,34,35,40}and we have further confirmed the separability of the clusters using a validated statistical method and cutoff value (D

_{T}> 1.9).

^{27–35,40}Using this paradigm, we identified a maximum of eight clearly distinct classes arranged in a concentric pattern. This was consistent with the GCL thickness pattern, which was also arranged concentrically and, given that GCL regression rate is proportional to the initial thickness, the concentric arrangement of the theme classes likely reflects the biology of the GCL rather than an artefact caused by the clustering process or criteria. The robustness of these classes could be further supported if they are reproducible using different measures of separability, such as ΔK,

^{74}which will be an important future step in this area once larger sample sizes are available.

^{66}used in previous studies.

^{70,75–77}The spatial theme class schema may be implemented in structure–function concordance study by allowing multiple measurement areas to be analyzed together and facilitate spatial translation of GCL data to visual field data points. A preliminary result on similar pattern recognition study on visual field revealed a similar spatial pattern to be present when stimulus size was adjusted for spatial summation area (Kalloniatis M, et al.

*IOVS*2016;57:ARVO E-Abstract 4745), and further comparison of spatial and temporal characteristics of the two modalities may shed further light onto structure–function concordance. Finally, similar to a previous study,

^{46}our study presents a framework with which GC population estimates can be derived from Spectralis OCT measurement.

**N. Yoshioka**, None;

**B. Zangerl**, None;

**L. Nivison-Smith**, None;

**S.K. Khuu**, None;

**B.W. Jones**, None;

**R.L. Pfeiffer**, None;

**R.E. Marc**, None;

**M. Kalloniatis**, None

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