**Purpose**:
The purpose of this study was to investigate the spatial distribution of human cone photoreceptors and examine cone density differences between the retinal meridians and quadrants.

**Method**:
Using adaptive optics scanning laser ophthalmoscopy, the maculae were imaged in 17 eyes of 11 subjects with normal chorioretinal health aged 54 to 72 years. We measured cone density at 325 points within the central 10 degrees radius of the retina. Cone density spatial distributions along the primary retinal meridians and in four macular quadrants (superior-nasal, superior-temporal, inferior-temporal, and inferior-nasal) were analytically modeled using the polynomial function to assess the meridional and quadrantal difference.

**Results**:
The mean and 95% confidence interval for the prediction of cone density along the primary retinal meridians was modeled with a 7-degree one-variable polynomial (R^{2} = 0.9761, root mean squared error [RMSE] = 0.0585). In the 4 retinal quadrants, cone density distribution was described by a 2-variable polynomial with X degree 3 and Y degree 4 (*R*² = 0.9834, RMSE = 0.0377). The models suggest no statistically significant difference between medians and between quadrants. However, cone density difference at corresponding spatial locations in different areas can be up to 25.6%. The superior-nasal region has more areas with high cone density, followed by quadrants of inferior-nasal, inferior-temporal, and superior-temporal.

**Conclusions**:
Analytical modeling provides comprehensive knowledge of cone distribution across the entire macula. Although modeling analysis suggests no statistically significant difference between medians and between quadrants, the remarkable cone density discrepancies in certain regions should be accounted for in applications requiring sensitive detection of cone variation.

^{1}The spatial distribution of these cells dictates the spatial information conveyed to higher stages of visual processing.

^{2}In a seminal work, Curcio and co-workers systematically quantified the two dimensional (2D) distribution of the human photoreceptor (including cones and rods) using the whole mounts of the fixed donor retinas, establishing the basic knowledge of the human cone topography.

^{3}

^{4}The fundamental spatial properties of cone density have been studied in eyes with normal chorioretinal health, including density variation with retinal eccentricity,

^{5}

^{–}

^{8}the influence of the eye length,

^{5}

^{,}

^{9}

^{,}

^{10}refractive error, gender, race/ethnicity and ocular dominance,

^{5}the aging effect,

^{5}

^{,}

^{11}

^{,}

^{12}the variability of foveal cone density,

^{13}the interocular symmetry of the foveal cone mosaic,

^{13}

^{–}

^{15}cone density distribution differences between the fovea and the periphery,

^{16}and the foveal cone packing mosaic pattern.

^{17}These studies replicated the cone spatial distribution characteristics obtained by histology, such as a peak of density at the foveal center, a sharp density drop in the fovea and parafovea, and then a mild decline with increasing eccentricity, wide variability of foveal cone density, isodensity contours elongated along the horizontal meridian, and higher density in the nasal than the temporal periphery.

^{5}

^{,}

^{7}

^{,}

^{9}

^{–}

^{11}

^{,}

^{13}

^{,}

^{15}

^{–}

^{24}In vivo cone density measured in the normal eyes by AO imaging not only enriched our knowledge of visual sampling and limit, but also provided a reference for assessing cone loss in various retinal diseases.

^{4}

^{,}

^{25}

^{–}

^{28}

^{11}

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^{16}

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^{20}

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^{23}

^{,}

^{28}

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^{29}and hinted a statistically isotropic distribution in the macula, despite the histologic and in vivo finding of the anisotropic cone density along different meridians.

^{5}

^{–}

^{11}

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^{13}

^{,}

^{15}

^{–}

^{24}The incomplete characterization of the cone density distribution and variability within individual eyes can obscure the study of cone density variation between subjects.

^{30}

^{,}

^{31}in a group of older participants.

^{32}The subject enrollment, image acquisition and process, and cone density measurement methods have been reported elsewhere.

^{12}

^{,}

^{32}For the readers’ convenience, we summarize the procedures here.

^{33}Subjects deemed with healthy macular health were rated as having AREDS2 grade 1 in both eyes.

^{30}

^{,}

^{32}

^{,}

^{34}

^{,}

^{35}through a dilated pupil (with 1.0% tropicamide and 2.5% phenylephrine hydrochloride) in all participants. The AOSLO images were continuously recorded across the macula. Post-processing corrected the nonlinear distortion caused by the resonant scanner, registered successive frames to enhance the signal-to-noise ratio, and montaged all individual images with cell-to-cell precision using custom and commercial software (Photoshop, Adobe Systems Inc., Mountain View, CA).

^{36}A sampling grid of 20 degrees × 20 degrees divided into a lattice of 1 degree × 1 degree was overlaid on the AOSLO image. Cone density was measured at 325 mesh points, including 317 grid nodes in 10 degrees radius macula (Fig. 1, left panel) and 8 points at 0.2 degrees and 0.5 degrees meridian eccentricity (zoomed in the white box on the top left corner of Fig. 1), using the “find Maxima” function of ImageJ (version 1.53c; http://imagej.nih.gov/ij). Cone density was expressed in cells/degree

^{2}.

^{37}with these functions along four primary retinal medians (superior, inferior, nasal, and temporal) and four macular quadrants (Q1 = superior-nasal; Q2 = superior-temporal; Q3 = inferior-temporal; and Q4 = inferior-nasal), we selected a 7-degree one-variable polynomial to model cone density along the primary retinal meridians and a two-variable polynomial with X degree 3 and Y degree 4 accurately for cone density in the 4 retinal quadrants (Supplementary Tables S1, S2). The modeling analysis was performed using Matlab Apps Curve fitter (Matlab R2023a; The MathWorks, Inc. Natick, MA, USA).

^{12}To avoid the correlation of the cone densities between the fellow eyes, the pointwise mean was calculated for modeling analysis if both eyes of a subject were imaged.

^{3}

^{,}

^{40}Visual acuity = 0.05 ± 0.12 (logarithm of the minimum angle of resolution, ranging from −0.1 to 0.3), and refraction error = 0.03 ± 1.38 D (ranging from −3.25 D to 1.75 D).

*R*

^{2}(>0.95), the residuals exhibited a distinctive “fan in” pattern from left to right rather than a random spread around the zero line. Meanwhile, the Q-Q plots manifested significant nonlinearity aberrating from the 45 degrees line. The non-stable variances and the aberrating Q-Q plots indicate poor modeling, which can also be perceived by the negative cone density in the models beyond 6-degree eccentricity. In contrast, the logarithmic transformation of the raw data stabilized the variance (see Fig. 2, middle column) and corrected for the skewness (see Fig. 2, right column) of the measurements, making the residuals follow a normal distribution.

^{41}

^{–}

^{44}

^{4}

^{,}

^{25}

^{,}

^{26}Albeit the importance, cone density modeling was inexplicitly and inadequately studied. Duncan and associates used a quadratic function to model cone spacing with data measured at retinal locations from 0.5 degrees to 3.5 degrees eccentricity.

^{29}Song and co-workers adopted an exponential function to fit the cone density acquired in the primary retinal medians.

^{11}Zayit-Soudry et al.,

^{20}Qin et al.,

^{23}and Cooper et al.

^{45}described cone spacing in normal human subjects using an exponential function. In a recent publication, Duncan and colleagues modeled the mean spacing of the cones as a function of location using a double exponential function to account for the spatial position of the region of interest in the macula.

^{28}In these pioneering studies, cone density or spacing was modeled either in one direction and did not consider potential directional differences, or along the primary retinal meridians and did not account for possible two-dimensional inhomogeneity across the macula. Our study addressed these inadequacies by examining the cone density in the primary medians and in four macular quadrants. Furthermore, in a recent study, Elsner and colleagues found cone densities at 0.63 mm retinal eccentricity were uncorrelated to those at 2.07 mm. This fact rules out models with a constant or proportional relation of cone density to eccentricity,

^{16}indicating that the spatial variation of the cone photoreceptors should be modeled with higher-order mathematical functions. We thus modeled cone density with high-order polynomials based on an evaluation of different mathematical functions, including exponential, Fourier, Gaussian, and rational functions (see Supplementary Table S1).

^{3}and partially measured by in vivo AO imaging studies.

^{7}

^{,}

^{8}

^{,}

^{11}

^{,}

^{17}

^{3}which defines the spatial locations of the sampling points. Histological

^{3}and in vivo imaging studies

^{10}

^{,}

^{12}

^{,}

^{13}have found a dramatic density drop from the fovea. Thus, precisely determining the foveal center location is critical. We have identified this point by the peak cone density

^{3}

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^{9}

^{,}

^{10}

^{,}

^{12}

^{,}

^{13}and checked with the OCT B-scans of the fovea.

^{36}Further, we made a continuous montage of the cone photoreceptor images and registered it to the fundus photograph, thereby establishing the retinal coordinates system to model the spatial distribution of the cone photoreceptors with rigorous mathematical functions. Furthermore, we carefully assessed the modeling correctness by evaluating the residual error distribution and correcting for the data abnormality, thereby avoiding inappropriate modeling only judged by the

*R*

^{2}. It is also worth mentioning that our data were derived from an older population, providing valuable age-matched comparisons for the diseased populations. The study also identified limitations to be addressed in future investigations. We used data acquired in a small number of subjects only. The spatial locations do not have an equal number of measurements. There are fewer measured data at 10 degrees eccentricity, which may be the contributory factor resulting in cone density at some edge points outside the common confidence interval. Another weakness is that all measurements were only performed at the integer grid points (see Fig. 1). A more random sampling is preferable for proper modeling. Future measurement in more subjects incorporated with split-detection imaging is warranted.

**X. Wang**, None;

**S. Hoshi**, None;

**R. Liu**, None;

**Y. Zhang**, None

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