The organization of the cone photoreceptor mosaic measured in the living human retina

Abstract

The cone photoreceptors represent the initial fundamental sampling step in the acquisition of visual information. While recent advances in adaptive optics have provided increasingly precise estimates of the packing density and spacing of the cone photoreceptors in the living human retina, little is known about the local cone geometric arrangement beyond a tendency towards hexagonal packing. We analyzed the cone mosaic in data from 10 normal subjects. A technique was applied to calculate the local average cone mosaic structure which allowed us to determine the hexagonality, spacing and orientation of local regions. Using cone spacing estimates, we find the expected decrease in cone density with retinal eccentricity and higher densities along the horizontal as opposed to the vertical meridians. Orientation analysis reveals an asymmetry in the local cone spacing of the hexagonal packing, with cones having a larger local spacing along the horizontal direction. This horizontal/vertical asymmetry is altered at eccentricities larger than 2 degrees in the superior meridian and 2.5 degrees in the inferior meridian. Analysis of hexagon orientations in the central 1.4° of the retina shows a tendency for orientation to be locally coherent, with orientation patches consisting of between 35 and 240 cones.

Keywords: Adaptive optics imaging; Anisotropy; Average cone photoreceptor; Clustering; Hexagonal packing; Organization.

Figure 1

Example of the calculation process for an average-cone image. (A) Foveal cone montage (from a 28yo female, with 0.5μm/pixel sampling, scale bar represents 100μm) and a sliding 50×50 pixel window (25×25 microns) at 0.43° nasally. (B) Example of the 50×50 pixel window selected for analysis where cones inside a 25×25 pixel (12.5×12.5μm) region (centered dashed square) were automatically detected and ROI’s of 25×25 pixels (12.5×12.5μm) centered on the detected cones were extracted. The ROI’s were rescaled after extraction (C1, C2 and Ci, examples of three ROI’s (150×150pixels, 12.5×12.5μm)) and averaged, producing an average-cone image (D, scale bar represents 3μm).

Figure 2

Schematic of the four step analysis procedure applied to the average cone images (see figure 1). We first computed the radial intensity profile and then the circumferential intensity profile (step 1). From the circumferential profile, we used FFT (step 2) to determine the degree of hexagonality and the rotation of the local hexagons (step 3), and the maxima to extract the angle of the principle axis (θ₁ to θ₆) and local spacing anisotropy (variation in distances, r1 to r6) (step 4).

Figure 3

Foveal (top) and parafoveal (bottom) montages for subject S7 (a 28 yo. Female). Scale bars represent 50μm for foveal and 200μm for parafoveal montages. Lines of isoeccentricity are drawn and average cone images are shown for selected locations along the four primary meridians. Average cone images are 12.5×12.5μm for the foveal montage and 25×25μm for the parafoveal montage.

Figure 4

Average cone spacing (panel A) and cone density (panel B) computed using the local cone average technique for the four primary meridians (Temporal, Nasal, Superior and Inferior). Error bars represent plus or minus one standard deviation across subjects.

Figure 5

Local axis of the best fitting ellipse of the normalized local spacing along the four primary meridians and for oblique meridians in the foveal region. For illustration purposes, we superimposed the average results across subjects on the parafoveal montage of S7. The white lines indicate the ellipse orientation (orientation of longest axis) and the magnitude of the ellipse eccentricity (length of white line). Scale bar represents an ellipse eccentricity of 0.5.

Figure 6

Color-coded hexagon orientation maps for the 10 subjects. Scale bar represents 100μm. For representation, each colored square (12.5×12.5μm) corresponds to the orientation of local hexagon in this region.

Figure 7

Ratio a_x/b_y, (semi axis of the X and Y axis respectively of the non-tilted best fitting ellipse of the normalized local spacing) along the four primary meridians and for oblique meridians in the foveal region.

Figure 8

Top row: Foveal montage (S7, 28yo female, scale bar represents 100μm) with color-coded orientation map, random permutation of the oriented local hexagons. Bottom row: (middle) examples of one local hexagon (+) and its 4 adjacent, 4 diagonal, 4 second-ring and 4 third-ring neighbors. (A) Change in degree of rotation of each hexagon from region to region for subject S7 (* stands for a statistically significantly difference from random) and (B) average degree of rotation change as a function of average distance.