purpose. To develop mathematical and geometric models of the nonuniform autofluorescence (AF) patterns of foveas of normal subjects and to reconstruct these models from limited subsets of data.

methods. Confocal scanning laser ophthalmoscope (cSLO) AF fundus images of normal maculae were obtained from both eyes of 10 middle-aged subjects. They were filtered and contrast enhanced, to obtain elliptical isobars of equal gray levels (GLs) and determine the isobars’ resolutions, eccentricities, and angles of orientation. The original image data were fit with a mathematical model of elliptic quadratic polynomials in two equal zones: the center and the remaining annulus.

results. The AF images segmented into nested concentric GL isobars with GLs that increased radially from the least-fluorescent center. The mean isobar resolution was 31 ± 7 μm. The geometric eccentricity of the ellipses increased from 0.42 ± 0.12 centrally to 0.52 ± 0.14 peripherally (*P* = 0.0005), with mean axes of orientation peripherally 97.12 ± 15.46°. The model fits to the complete image data had mean absolute normalized errors ranging from 3.6% ± 3.7% to 7.3% ± 7.1%. The model fits to small subsets (1% to 2% of total image data) had mean absolute errors ranging from 3.7% ± 3.8% to 7.3% ± 7.2%.

conclusions. Normal AF fundus images show finely resolved, concentric, elliptical foveal patterns consistent with the anatomic distribution of fluorescent lipofuscin, light-attenuating macular pigment (MP), cone photopigment, and retinal pigment epithelial (RPE) pigment in the fovea. A two-zone, elliptic, quadratic polynomial model can accurately model foveal data. This model may be useful for image analysis and for automated segmentation of pathology.

^{ 1 }

^{ 2 }One of the major methods of such analysis is through the use of the confocal laser scanning ophthalmoscope (cSLO), which in its autofluorescence (AF) mode can record the complex signal predominantly from autofluorescent lipofuscin granules in the RPE.

^{ 3 }

^{ 4 }

^{ 5 }

^{ 6 }

^{ 7 }

^{ 8 }

^{ 9 }These fluoresce strongly in response to 488-nm laser light, and abnormalities of their distribution are leading indicators of the severity of AMD.

^{ 10 }

^{ 11 }

^{ 12 }

^{ 13 }

^{ 14 }

^{ 15 }This absorption is greatest in the center of the macula, which on fundus photographs and under visual observation is characterized by strong yellow color.

^{ 16 }There is similar absorption of the 488-nm light by melanin granules in the RPE,

^{ 17 }which also have greater density centrally. Finally, photopigments, particularly cone photopigments in the fovea, will attenuate the signal if they are not completely bleached.

^{ 18 }as belonging to four subtypes (phenotypes) based on relative size and intensities of the hypo- and hyperfluorescent regions. To complicate the matter further, the overall patterns are not permanent, but change with age. AF increases in older individuals, with increased lipofuscin at the posterior pole, at least to age 70,

^{ 19 }

^{ 20 }whereas the measured ratio of foveal AF to maximum AF intensity has been reported not to vary with age.

^{ 3 }Quantification of these patterns has so far been lacking and is needed to make progress in assessment of retinal disease.

^{ 21 }

^{ 22 }

^{ 23 }

^{ 24 }

^{ 25 }

^{ 26 }Clinical evaluations of increased AF and decreased AF lesions are likewise qualitative in character.

^{ 27 }Manual grading has several drawbacks, such as poor repeatability and extensive and time-consuming training necessary for adequate proficiency. Because of these drawbacks, there has been a great deal of interest in developing automated digital techniques for quantification of macular disease.

^{ 28 }

^{ 29 }

^{ 30 }

^{ 31 }

^{ 32 }

^{ 33 }Accurate mathematical models of normal images could form the basis for such techniques.

^{2}for a 30° square field. The time for acquisition was approximately 15 to 30 seconds, as would be normal in the clinical setting. As will be discussed, cone photopigment bleaching was incomplete after this exposure.

^{ 5 }After a Gaussian filter of 36-μm radius was applied to the entire image, the standard deviations in such boxes were no more than five GLs, similar to the images analyzed by von Ruckmann et al.

^{ 5 }This filter had no noticeable effect on larger image features or isobar patterns, as defined later. The image was then cropped to a 100 pixels square (1500-μm

^{2}) centered on the point of lowest foveal fluorescence, and the fovea was defined as the enclosed circle 1500 μm in diameter. All subsequent analyses were performed on these preprocessed foveal images. A typical image of the area of interest is shown in Figure 1 .

*x*,

*y*) in the

*x*–

*y*plane. The general quadratic has the following form:

*a*,

*b*,

*c*,

*d*,

*e*, constant). Thus, a quadratic,

*q*1, was fit to the data in the inner region and a second quadratic,

*q*2, to the data in the annulus (for a total of 12 coefficients). To create a smooth fit at the boundary of the two regions, we used a sigmoidal radial cubic spline function to interpolate the quadratics. An example of a foveal AF image and the associated contour graph of the smooth model fit to this foveal data are displayed in Figures 4A and 4B .

*x*,

*y*) point in two dimensions were treated as a single data set

*E*. We then calculated the mean and SD of

*E*and scaled these results by dividing by the net GL range of the original data to give the mean error ± SD as a percentage of the data range.

*P*= 0.0005). The axes of orientation of the outer ellipses clustered around 90°. The mean axis of orientation was 97 ± 15°, with 17 of 20 within 90 ± 30°. The average foveal isobar resolution was 31 ± 7 μm (range, 21–47 μm). The isobar resolutions centrally were even finer, usually ∼15 μm (1 pixel) in width. We did not find any major differences in the patterns themselves or their isobar resolutions when analyzed according to age, race, or sex in this small sample.

*t*-test). A similar finding of elevated mean GLs temporally held for right eyes, with radii greater than 585 μm. When the line scans were renormalized by dividing by the lowest GL, the results were almost identical. The mean GL ratio temporally in the left eyes was significantly higher than nasally with radii greater than 515 μm, and in right eyes, with radii greater than 600 μm. There were no significant differences between GL ratios superiorly and inferiorly in the left or right eyes, or between left eyes temporally compared with right eyes. In our 20 eyes, the maximum GL ratios were always temporal and ranged from 1.2 to 2.6 (mean, 1.72 ± 0.37). The means of 10 horizontal and vertical line scans, normalized by division, through the foveas of left and right eyes are shown in Figure 5 .

^{ 19 }A simple noise filter and contrast enhancement revealed geometry of convex GL isobars, with isobar resolutions averaging 30 μm in the periphery, but in the central foveal area closer to single-pixel resolution (15 μm).

^{ 14 }The distribution of this pigment peaks centrally and tapers radially. Its anatomic density drops to half-maximum within a diameter of 500 to 600 μm, reaches a quarter-maximum at a diameter of approximately 1000 μm, and from there tapers slowly outward to a low constant level.

^{ 34 }There is considerable variation in the central optical density (compared with an eccentric reference point) of MP, reported to range from 0.21 to 0.77 (median 0.53) density units in one group of seven normal subjects at the peak absorption.

^{ 14 }Another group found an MP density of 0.0 to 0.64 (mean, 0.32 ± 0.24) in 34 normal control subjects aged 20 to 65 years.

^{ 35 }Because the relative optical density of macular pigment at 488 nm is approximately 0.8, the corresponding central optical densities of the former subjects would range from 0.17 to 0.62 (median, 0.42) density units, and in the latter from 0.0 to 0.51 (mean, 0.25). If we estimate the densities at 750-μm radius to be a quarter of these values,

^{ 34 }then the change in density from the center to 750 μm would range from 0.13 to 0.47 (median, 0.32) in the former group, and from 0.0 to 0.38 (mean, 0.19) in the latter. The corresponding AF images would thus have central minima deeper by factors ranging from 1.3 to 3.0 (median, 2.1) or from 1.0 to 2.4 (mean, ∼1.5).

^{2}) and thus contribute to the patterns obtained in clinical image acquisition. The main contribution is from cones (37% bleached at 15 seconds, 56% at 30 seconds), rather than rods (density 0.3 at 12°, negligible centrally, 78% bleached after 15 seconds).

^{ 36 }With a cone density of 0.8 density units centrally at the absorption peak of 550 nm, one can calculate (for cone absorption at 488 nm equal to 0.49 relative to 550 nm) that the optical density of cone photopigment to 488 nm centrally after 15 to 30 seconds is 0.25 to 0.17 density units. The cone density at the foveal periphery (approximately 2.5°), by two-way density measurements, is approximately 0.25,

^{ 37 }and so the change in optical density from center to periphery is approximately 0.55 density units. After bleaching and correction for absorption at 488 nm, the difference in optical density between center and periphery would thus range from 0.17 (15 seconds) to 0.12 (30 seconds). These density differences would give deeper minima (ratio of peak to trough) in measured AF at the center relative to the periphery by factors of 1.5 and 1.3, respectively, and a greater gradient centrally than if bleaching were complete. For rods, the corresponding optical density maximum would be 0.06 density units at 12° to 15° from the fovea, negligible in the fovea itself. The cone bleaching in clinical settings is thus likely to be somewhat variable and necessarily incomplete, because, even after 90 seconds of exposure, the cone bleaching plateaus at 78%. This yields a deeper central minimum in AF by a factor of 1.15. If the cones are contributing a factor of 1.3 to 1.5 and if MP contributes factors between 1.0 and 2.4, as just calculated according to Davies and Morland,

^{ 35 }one would expect the peripheral fovea to central AF peak-to-trough ratios on the HRA to vary between 1.3 and 3.6 in these subjects. In our 10 subjects, these ratios ranged from 1.2 to 2.6 (mean, 1.72 ± 0.37), a range that is quite consistent. The peak-to-trough ratios expected from the data of Bone et al.

^{ 14 }would be somewhat higher (1.7–4.5).

^{ 19 }This distribution pattern also contributes to central hypofluorescence. The melanin in RPE has a broad absorbance across the visible spectrum and also has highest density centrally.

^{ 38 }

^{ 39 }

^{ 40 }For example, foveal hyperfluorescence,

^{ 20 }

^{ 27 }embedded in the darker central pattern, could be delineated and quantified more accurately than is possible at present.

**Figure 1.**

**Figure 1.**

**Figure 2.**

**Figure 2.**

**Figure 3.**

**Figure 3.**

**Figure 4.**

**Figure 4.**

**Figure 5.**

**Figure 5.**