Human foveal cone photoreceptor topography and its dependence on eye length
- University of California, Berkeley, United States
- Carl Zeiss Meditec AG, Germany
- Ningbo University, China
Figures
Figure 1
Three models of myopic eye growth.
(A) Global expansion shows an eyeball that is proportionally stretched. (B) The equatorial stretching model indicates a growth model where the fovea stays rigid and unaffected as the eye grows. (C) The over-development model shows that myopic eye growth is similar with developmental eye growth where photoreceptors continue to migrate towards the fovea as the eye grows.
Figure 2
Summary of published data from Li et al. (2010), Chui et al. (2008) and Wilk et al. (2017).
In both plots, the linear fits with the solid lines indicate the data that have significant trends. (A) Linear cone density has a decreasing trend with axial length near the fovea. (B) Angular cone density (sampling resolution) of the eye generally increases with axial length although none of the data show a significant linear relationship.
Figure 3 with 2 supplements
Image, PRL, cone locations and density plot for one subject.
(A) AOSLO image of the fovea of subject 10003L. Only the central 1.5 degrees are shown here (810 × 810 pixels), which contains 16,184 cones. The white dots are a scatter plot showing the PRL, or position of the fixated stimulus over the course of a 10 s video. The red dot is the centroid of the scatter plot. (B) Same image with a color overlay indicating the density. Linear and angular cone densities are indicated on the right colorbar. Peak cone densities in this eye are 204,020 cones/mm2 and 15,851 cones/deg2. The yellow ellipse is the best fitting ellipse containing ~68% of the points in the scatterplot and indicates the PRL. The black cross indicates the position of peak cone density. Scale bar is 0.5 degrees, which in this eye corresponds to 139.4 microns.
Figure 3—figure supplement 1
Linear cone density (cones/mm2) plots over the central 450 microns for all 28 eyes.
The black cross indicates the point of maximum cone density. The black ellipse is the best fitting ellipse about the fixation scatterplot indicating the PRL. Dark blue regions indicate where no cone density estimates were made.
Figure 3—figure supplement 2
Angular cone density (cones/deg2) plots over the central 1.5 degrees for all 28 eyes.
The black cross indicates the point of maximum cone density. The black ellipse is the best fitting ellipse about the fixation scatterplot indicating the PRL. Dark blue regions indicate where no cone density estimates were made.
Figure 4 with 2 supplements
Cone density as a function of eccentricity for all eyes.
The axial length ranges of the subjects are color coded, with warmer colors for shorter eyes and cooler colors for longer eyes. In this plot, it is apparent that shorter eyes generally have higher peak cone densities.
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Figure 4—source data 1
Data for plots of cone density as a function of eccentricity for all subjects.
- https://doi.org/10.7554/eLife.47148.015
Figure 4—figure supplement 1
Plots of average cone density of all 28 eyes as a function of eccentricity in units of.
(A) cones/mm2 vs. eccentricity in microns, (B) cones/mm2 vs. eccentricity in arcminutes (C) cones/deg2 vs. eccentricity in microns and (D) cones/deg2 vs. eccentricity in arcminutes. The solid lines are the average and the upper and lower dashed lines represent ±1 standard deviation from the average.
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Figure 4—figure supplement 1—source data 1
Data for plots of average linear and angular cone density as a function of eccentricity.
- https://doi.org/10.7554/eLife.47148.012
Figure 4—figure supplement 2
Plots of density as a function of eccentricity in the vertical and horizontal directions.
(A) linear cone density (B) angular cone density. The dashed lines represent ±1 standard deviation from the mean.
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Figure 4—figure supplement 2—source data 1
Data for plots of average linear and angular cone density as a function of eccentricity in the horizontal and vertical directions.
- https://doi.org/10.7554/eLife.47148.014
Figure 5
Plots of cone density as a function of axial length at and near the fovea.
(A) Linear cone densities as a function of axial length. Longer eyes have lower linear cone density than shorter eyes. The trend remains significant out to 100 microns eccentricity. At the peak, the details for the trendline are: slope = −3,185 with 95% confidence intervals from −4,578 to −13,793. (B) Angular cone densities as a function of axial length. The peak angular cone density increases significantly with increasing axial length and this trend remains significant out to 40 arcminutes eccentricity. At the peak, the details for the trendline are: slope = 749 with 95% confidence intervals from 304 to 1193. Relationships with p-values<0.05 are labeled with asterisks and trendlines are shown as solid lines. Relationships with p-values≥0.05 have dashed trendlines.
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Figure 5—source data 1
Data for plots of cone density as a function of axial length at and near the fovea.
- https://doi.org/10.7554/eLife.47148.017
Figure 6
The relationship between cone density and axial length shows the same pattern at the PRL as for the peak cone density.
The numbers for the trendline in (A) are slope: 759; 95% CI: 198 to 1,320; p=0.00999. The numbers for the trendline in (B) are: slope = −8,490; 95% CI −14,600 to −2,420; p=0.00795). Axial length accounts for 24%% and 23% of the variance in linear and angular cone density, respectively.
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Figure 6—source data 1
Data for plots of cone density as a function of axial length at the PRL.
- https://doi.org/10.7554/eLife.47148.019
Figure 7
Plots of the magnitude of fixational eye movements as a function of axial length.
(A) The plot of BCEA in linear units (square microns) vs. axial length shows a trend that approaches significance (p=0.0596). (B) There is no significant relationship between BCEA in angular units (square arcminutes) and axial length (p=0.364).
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Figure 7—source data 1
Data for plots of the magnitude of fixational eye movements as a function of axial length.
- https://doi.org/10.7554/eLife.47148.021
Author response image 1
Plots of linear cone density at different retinal locations using retinal magnification factors computed using a formula from Bennett et.al., 1994.
Even though the retinal image size for myopes is underestimated for myopes and overestimated for hyperopia, there is still a significant drop in density with increasing axial length at the location of peak density.
Author response image 2
Changes in linear and angular cone density with axial length over a range of distances from the location of peak density.
The results for one eye are essentially the same as that reported in the paper.
Author response image 3
The right plot shows that the peak foveal cone density increases as the cone sampling window is decreased.
Note that the increase with reducing sampling window is linear until about 10 arcminutes. The left plot shows that the variability in the location of the peak foveal density remains consistent (within about 1.5 arcminutes of the mean) with cone sampling windows of 10 arcminutes or greater.
Tables
Table 1
Summary of studies investigating foveal spatial vision and sensitivity tasks in myopia.
https://doi.org/10.7554/eLife.47148.003| Author | Refractive error range of myopic cohort [D] | Functional tests | Results for myopes at foveal center | Suggested cause |
|---|---|---|---|---|
| Fiorentini and Maffei, 1976 | −5.5 to −10 (n = 10) | CSF | Reduced CSF | Neural insensitivity (myopic amblyopia) |
| Thorn et al., 1986 | −6 to −9.75 (n = 13) | CSF | No difference in CSF | Global expansion |
| Collins and Carney, 1990 | −2 to −11 (n = 16) | VA, CSF | No difference in VA or CSF between low and high myopic groups with contact lens correction | NA |
| Strang et al., 1998 | 0 to −14 (n = 34) | VA | Reduced VA (MAR) with increasing myopia after controlling for spectacle magnification | Retinal expansion specifically at the posterior pole; increased aberrations |
| Liou and Chiu, 2001 | 0 to >-12 (n = 105 eyes) | CSF | Reduced CSF with increasing myopia | Retinal stretching and disruption, neural insensitivity (myopic amblyopia) |
| Chui et al., 2005 | −0.5 to −14 (n = 60) | Grating resolution | Decreased resolution acuity in cyc/mm | Retinal expansion specifically at the posterior pole; global expansion along with ganglion cell loss |
| Coletta and Watson, 2006 | +2 to −15 (n = 17) | Interferometric grating resolution | Decreased resolution acuity in cyc/mm but not in cyc/deg | Retinal expansion specifically at the posterior pole |
| Atchison et al., 2006 | +0.75 to −12.4 (n = 121) | Spatial summation; interferometric grating resolution | Increased critical summation area in linear area, but not in angular area; Decreased resolution acuity in cyc/mm but not in cyc/deg | Retinal expansion specifically at the posterior pole; global expansion along with ganglion cell loss |
| Stoimenova, 2007 | −1 to −8 (n = 60) | Contrast thresholds of 20/120 letters | Lower sensitivity to contrast for letters with a fixed angular size | Morphologic changes in the retina |
| Rossi et al., 2007 | −0.5 to −3.75 (n = 10) | AO-corrected VA | Reduced acuity (MAR) compared to emmetropes | Retinal expansion, neural insensitivity; neural insensitivity (myopic amblyopia) |
| Jaworski et al., 2006 | −8.5 to −11.5 (n = 10) | Foveal summation thresholds; CSF | Increased critical summation area (angular) Decreased luminance sensitivity Reduced contrast sensitivity at high frequencies (cyc/deg) | Reduction in photoreceptor sensitivity; postreceptoral changes; increased aberrations |
| Ehsaei et al., 2013 | −2.00 to −9.62 (n = 60) | Size threshold of high and low contrast letter targets | No difference in threshold retinal image size between myopes and emmetropes. | NA |
Table 2
Subject details, biometry and cone density for all subjects.
Each subject’s refractive error was self-reported at the time of the study. Axial Length, corneal curvature and anterior chamber depth were measure by IOL Master, and retinal magnification factor (microns/deg) was calculated from biometry data. Linear and angular cone densities are reported for a 10 arcminute sampling window (see Materials and methods).
| Subject ID | Eye | Gender | Age | Ethnicity | Spherical equivalent refraction (D) | Axial length (mm) | Corneal curvature (mm) | Anterior chamber depth (mm) | Retinal magnification factor (microns/deg) | Angular cone density (cones/deg2) | Linear cone density (cones/mm2) | PRL distance from fovea (minutes) | PRL distance from fovea (microns) | PRL angular cone density (cones/deg2) | PRL linear cone density (cones/mm2) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 20165 | L | F | 28 | Caucasian | 0.500 | 22.26 | 7.37 | 3.86 | 261.79 | 13316 | 194625 | 2.83 | 12.34 | 12470 | 181952 |
| R | F | 28 | Caucasian | 0.500 | 22.64 | 7.44 | 3.80 | 267.79 | 12714 | 177692 | 5.30 | 23.66 | 11758 | 163965 | |
| 20177 | L | F | 18 | Mixed | 0.000 | 23.04 | 7.80 | 3.24 | 273.59 | 12211 | 162890 | 7.25 | 33.06 | 11476 | 153319 |
| R | F | 18 | Mixed | 0.000 | 23.23 | 7.91 | 3.20 | 275.85 | 11999 | 159027 | 4.57 | 21.00 | 11317 | 148721 | |
| 10003 | L | M | 50 | Caucasian | 1.000 | 23.30 | 7.80 | 3.12 | 278.81 | 15851 | 204020 | 7.23 | 33.59 | 13961 | 179594 |
| R | M | 50 | Caucasian | 1.000 | 23.50 | 7.81 | 3.14 | 282.00 | 15358 | 193090 | 6.45 | 30.32 | 14869 | 186972 | |
| 20176 | L | F | 18 | Asian | 0.000 | 23.45 | 7.98 | 3.65 | 276.50 | 12515 | 163676 | 18.16 | 83.71 | 8813 | 115273 |
| R | F | 18 | Asian | 0.000 | 23.58 | 8.01 | 3.62 | 278.52 | 12312 | 158356 | 4.05 | 18.78 | 11913 | 153566 | |
| 20172 | L | F | 25 | Caucasian | −0.750 | 23.56 | 7.71 | 3.90 | 280.13 | 15516 | 196844 | 1.23 | 5.72 | 15210 | 193824 |
| R | F | 25 | Caucasian | −0.500 | 23.65 | 7.72 | 3.96 | 281.33 | 14976 | 189377 | 3.13 | 14.66 | 14636 | 184921 | |
| 20147 | R | M | 26 | Caucasian | −0.375 | 24.16 | 7.73 | 2.36 | 298.73 | 15537 | 174122 | 4.68 | 23.29 | 14839 | 166278 |
| L | M | 26 | Caucasian | 0.000 | 24.17 | 7.81 | 4.03 | 288.94 | 14994 | 178435 | 11.57 | 55.72 | 13894 | 166422 | |
| 20124 | L | F | 26 | Asian | −3.000 | 24.67 | 7.70 | 4.05 | 298.82 | 13973 | 153998 | 5.17 | 25.77 | 13334 | 149334 |
| R | F | 26 | Asian | −4.250 | 25.29 | 7.68 | 4.07 | 309.88 | 13927 | 145588 | 2.38 | 12.30 | 13543 | 141033 | |
| 20174 | L | F | 43 | Caucasian | −1.750 | 24.80 | 7.79 | 3.57 | 302.57 | 13775 | 150204 | 7.78 | 39.21 | 11671 | 127480 |
| R | F | 43 | Caucasian | −2.750 | 25.37 | 7.83 | 3.62 | 311.85 | 12857 | 132443 | 6.00 | 31.19 | 11848 | 121826 | |
| 20173 | R | F | 22 | Caucasian | −2.750 | 24.96 | 7.81 | 3.68 | 304.64 | 16648 | 179779 | 7.11 | 36.08 | 15989 | 172286 |
| 20170 | R | M | 26 | Asian | −2.250 | 25.00 | 7.69 | 3.90 | 305.54 | 14485 | 153681 | 8.98 | 45.73 | 12244 | 131153 |
| L | M | 26 | Asian | −3.750 | 25.66 | 7.65 | 4.15 | 316.25 | 14853 | 147115 | 1.70 | 8.96 | 14708 | 147060 | |
| 20138 | R | F | 29 | Caucasian | −5.000 | 25.26 | 7.95 | 3.14 | 311.22 | 13874 | 141971 | 6.32 | 32.76 | 12449 | 128530 |
| L | F | 29 | Caucasian | −5.000 | 25.28 | 7.91 | 3.15 | 311.92 | 14776 | 151699 | 5.36 | 27.87 | 14060 | 144506 | |
| 20114 | R | F | 24 | Asian | −5.500 | 25.83 | 8.72 | 3.47 | 310.94 | 14615 | 152657 | 7.00 | 36.29 | 13787 | 142601 |
| L | F | 24 | Asian | −6.000 | 26.16 | 8.98 | 3.58 | 313.31 | 15634 | 159228 | 4.48 | 23.40 | 15287 | 155729 | |
| 20160 | R | F | 25 | Asian | −5.375 | 25.83 | 7.81 | 3.60 | 320.25 | 15885 | 155083 | 8.25 | 44.06 | 14409 | 140492 |
| 20143 | R | F | 23 | Asian | −6.875 | 25.91 | 7.42 | 2.10 | 334.12 | 17258 | 153560 | 3.01 | 16.77 | 16562 | 148354 |
| 20158 | R | F | 34 | Asian | −6.500 | 26.60 | 7.84 | 3.51 | 333.78 | 13147 | 118491 | 11.82 | 65.76 | 10876 | 97623 |
| 20163 | R | F | 25 | Asian | −7.125 | 26.84 | 7.89 | 3.65 | 336.60 | 18114 | 159397 | 3.82 | 21.42 | 17481 | 154287 |
| L | F | 25 | Asian | −7.125 | 27.06 | 7.89 | 3.65 | 340.44 | 19001 | 163731 | 5.02 | 28.50 | 17899 | 154437 |
Author response table 1
Retinal Magnification Factors (microns/degree) computed three different ways.
https://doi.org/10.7554/eLife.47148.024| Subject | Eye | RMF (2-surface lens) | RMF (4-surface lens) | RMF (Bennett et.al., 1994) |
|---|---|---|---|---|
| 20165 | L | 261.73 | 263.60 | 266.95 |
| R | 267.81 | 269.64 | 271.91 | |
| 20177 | L | 273.56 | 275.04 | 277.13 |
| R | 275.86 | 277.29 | 279.61 | |
| 10003 | L | 278.75 | 280.19 | 280.53 |
| R | 282.02 | 283.46 | 283.14 | |
| 20176 | L | 276.44 | 278.03 | 282.49 |
| R | 278.54 | 280.11 | 284.19 | |
| 20172 | L | 280.15 | 281.93 | 283.92 |
| R | 281.29 | 283.09 | 285.10 | |
| 20147 | R | 298.76 | 299.90 | 291.76 |
| L | 288.94 | 290.74 | 291.89 | |
| 20124 | L | 298.86 | 300.71 | 298.42 |
| R | 309.82 | 311.68 | 306.52 | |
| 20174 | L | 302.60 | 304.23 | 300.12 |
| R | 311.83 | 313.46 | 307.56 | |
| 20173 | R | 304.58 | 306.24 | 302.21 |
| 20170 | R | 305.52 | 307.31 | 302.73 |
| L | 316.23 | 318.13 | 311.35 | |
| 20138 | R | 311.19 | 312.58 | 306.13 |
| L | 311.93 | 313.33 | 306.39 | |
| 20114 | R | 310.96 | 312.19 | 313.57 |
| L | 313.35 | 314.53 | 317.88 | |
| 20160 | R | 320.19 | 321.82 | 313.57 |
| 20143 | R | 334.10 | 335.25 | 314.62 |
| 20158 | R | 333.78 | 335.36 | 323.63 |
| 20163 | R | 336.64 | 338.26 | 326.76 |
| L | 340.48 | 342.10 | 329.63 |
Additional files
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- https://doi.org/10.7554/eLife.47148.022
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Human foveal cone photoreceptor topography and its dependence on eye length
eLife 8:e47148.
https://doi.org/10.7554/eLife.47148
