article: We provide the first measures of foveal cone density as a function of axial length in living eyes and discuss the physical and visual implications of our findings. We used a new generation Adaptive Optics Scanning Laser Ophthalmoscope to image cones at and near the fovea in 28 eyes of 16 subjects. Cone density and other metrics were computed in units of visual angle and linear retinal units. The foveal cone mosaic in longer eyes is expanded at the fovea, but not in proportion to eye length. Despite retinal stretching (decrease in cones/mm2), myopes generally have a higher angular sampling density (increase in cones/deg2) in and around the fovea compared to emmetropes, offering the potential for better visual acuity. Reports of deficits in best-corrected foveal vision in myopes compared to emmetropes cannot be explained by increased spacing between photoreceptors caused by retinal stretching during myopic progression.
  One might expect that eye growth would stretch the photoreceptor layer and would increase the spacing between cones, causing a longer eye to more coarsely sample an image relative to a shorter eye. However the situation is not that simple; the axial elongation associated with eye growth is accompanied by magnification of the retinal image (Strang et al. , 1998). If the enlargement of the retinal image exactly matched the stretching of the cone mosaic, then eyes of different lengths would sample the visual field similarly. In fact, in large scale studies, myopes generally attain reasonably good visual acuity with optical correction (He et al. , 2004; Jong et al. , 2018). However, more careful inspection reveals that myopes generally (6 out of 9 studies) have poorer angular resolution and have uniformly (3 out of 3 studies) poorer retinal resolution. Table 1 summarizes published results from psychophysical foveal tasks. Most notably, Atchison et al. (2006) and Coletta and Watson (2006) show clear deficits in retinal resolution (cyc/mm) with increasing myopia using interferometric methods which bypass the optics of the eye and Rossi et al. (2007) show significant deficits in angular resolution (cyc/deg) in low myopes, even after using adaptive optics to correct for optical blur. All studies that find myopic visual deficits implicate retinal stretching as a possible cause, but what is actually happening structurally at the foveal center during myopic progression is not known. Therefore, the aim of the current study is to more carefully investigate how the length of the eye affects cone density at and near the foveal center. Two types of cone densities will be discussed in this study. Linear density quantifies how many cones are within a fixed area, in square mm, and serves as a way to evaluate physical retinal stretching caused by eye growth. Angular density quantifies how many cones are within one degree visual angle, (the visual angle on the retina is measured from the secondary nodal point of the eye). Angular density serves as a way to evaluate the visual implications of eye growth as it governs the sampling resolution of the eye. Figure 1 illustrates three models, along the lines of Strang et al. (1998), of how photoreceptor structure might be affected by myopic eye growth. In the first model, called the global expansion model, the retina is proportionally stretched with increasing axial length - cones are more spaced out in longer eyes - and linear density decreases with eye length. Assuming that the secondary nodal point remains at a fixed position relative to the anterior segment, the number of cones within a fixed angular area will remain constant. Therefore, angular cone density will be constant with eye length. In the second model, called the equatorial stretching model, the posterior retina simply moves axially further from the anterior segment of the eye so that the linear density does not change with eye length. Since the retina is moving further from the secondary nodal point, more cones will fall within a fixed angular area and the angular cone density will increase with eye length. The final model, called the over-development model, describes a structural photoreceptor change that mimics the changes that occur during development (Springer and Hendrickson, 2004) whereby the photoreceptors continue to migrate towards the fovea as the eye grows. In this scenario, longer eyes will show both increased linear cone density and an even steeper increase in angular cone density. The model is motivated by observations of increased linear cone density in the foveas of marmosets that underwent lens-induced eye growth (Troilo, 1998). The most definitive studies of cone spacing as a function of axial length are done through direct imaging of the retina – wherein sharp images of the cones are enabled through the use of adaptive optics, a set of technologies that actively compensate the blur caused by aberrations of the eye (Liang et al. , 1997). Combined with confocal scanning laser ophthalmoscopy (Webb et al. , 1987), adaptive optics offers the highest contrast en face images of the foveal photoreceptor mosaic ever recorded in vivo (Dubra et al. , 2011; Roorda et al. , 2002). Despite continued advances in image quality, previous studies investigating cone packing and eye length have not made their measurements at the foveal center, the most important region for spatial vision but the most difficult to image owing to the small size of photoreceptors. There are a number of studies on cone packing and eye length (Chui et al. , 2008; Elsner et al. , 2017; Kitaguchi et al. , 2007; Li et al. , 2010; Obata and Yanagi, 2014; Park et al. , 2013) and here we summarize the published results that are most relevant to our study. Chui et al. (2008) investigated angular and linear cone density at 1 mm and three degrees eccentricity. They found a significant decrease (p<0. 05) in linear cone density as a function of eye length at 1 mm (which, by angular distance, is closer to the fovea in a longer eye than in a shorter eye) in all directions except in the nasal retina. They found that the angular cone density at three degrees (which, by linear distance, is closer to the fovea, in a shorter eye than in a longer eye) increased with eye length, but the trends were not significant. Li et al. (2010) made similar measures, but closer to the fovea (from 0. 10 mm to 0. 30 mm eccentricity). They found that linear cone density decreased with eye length, but the trends were not significant at the smallest eccentricities (0. 1 and 0. 2 mm). When the data were plotted in angular units and angular distance from the fovea, they found that angular cone density trended toward an increase with eye length but none of the trends were significant. A more recent study measured peak cone densities in the fovea as well as axial length for 22 eyes of 22 subjects (Wilk et al. , 2017) but they did not plot peak cone density as a function of axial length, as it was not the aim of their study. We plotted the data they provided in their paper and found that the linear cone density at the foveal center dropped significantly with increases in axial length, similar to what was found by Li et al. (2010) and Chui et al. (2008), but the angular cone density had no dependency on eye length. Summary plots from previous literature are shown in Figure 2AB. Wilk et al. (2017) ’s data were consistent with a global expansion model and Li et al. (2010) and Chui et al. (2008) ’s data only leaned toward a model that falls between the global expansion and equatorial stretching models. If the trends found by Li et al. (2010) and Chui et al. (2008) near the fovea were to extend to the foveal center, then myopes would have higher foveal photoreceptor sampling resolution with a consequent potential for better performance on visual tasks compared to emmetropes. As such, the simplest explanation for visual deficits in myopes – increased separation between cones caused by retinal stretching – would have to be ruled out. With the improvements in resolution of adaptive optics ophthalmoscopes, imaging the smallest cones at the foveal center is now possible in many eyes, enabling a definitive analysis of the cone density at the fovea as a function of eye length.
  All the biometric measures used to convert angular dimensions to linear retinal dimensions are listed on Table 2. The strong correlation between refractive error and eye length (p<0. 0001) indicates that the myopia in this cohort was predominantly as a result of axial length. Images of the foveal region, the preferred retinal locus for fixation (PRL) and the fixation stability were recorded with an adaptive optics scanning laser ophthalmoscope (see Materials and methods). The image of one subject (10003L) is shown in Figure 3A. All the cones were resolved with our imaging system. The scatter plot indicates the scatter plot of fixation over the course of a 10 s video. Figure 3B shows the same image with all cones labeled and a color-coded overlay indicating the density. 16,184 labeled cones are shown on the figure. The point of maximum density is indicated by the black cross and the PRL is indicated by the yellow ellipse (best fit to the scatter plot locations in Figure 3A). This eye has a peak linear density of 204,020 cones/mm², and a peak angular density of 15,851 cones/deg². Cone density plots in linear and angular units for all eyes are shown on Figure 3—figure supplements 1 and 2. Original images and a list of the cone locations for each can be downloaded from the Dryad Digital Repository https: //datadryad. org/review? doi=doi: 10. 5061/dryad. nh0fp1b. Figure 4 shows the linear cone density as a function of linear eccentricity, where the average linear cone density was computed in 25-micron wide annuli centered around the point of peak density. Figure 4—figure supplement 1 are plots of the average cone densities in linear and angular units as a function of eccentricity in microns and arcminutes. Figure 4—figure supplement 2 are plots of the average linear and angular cone densities as a function of horizontal and vertical direction. In order to show the trends of density with axial length Figure 5A and B plot linear and angular cone density as a function of axial length where the colors indicate different eccentricity - red to purple indicate distance from the from fovea towards more parafoveal locations. Figure 5A reveals that peak linear density decreases significantly with axial length and the trend persists and remains significant from the fovea out to 100 microns eccentricity. Axial length accounts for 39% of the variance in the changes in linear cone density. Figure 5B shows the opposite trends when plotted in angular units. Peak angular density increases significantly with axial length and the trend persists and remains significant out to 40 arcminutes eccentricity. Axial length accounts for 32% of the variance in the changes in angular cone density. The plots clearly indicate that although stretching does occur (Figure 5A) it is not a simple global expansion and longer eyes have higher sampling density. The trends hold at and around fovea with statistical significance. A more relevant measure of the impact of eye length on vision is how the angular cone density changes at the PRL, which is often displaced from the location of peak cone density (Li et al. , 2010; Putnam et al. , 2005; Wilk et al. , 2017). If, for example, longer eyes had more displaced PRLs then that could diminish, or even reverse, the trend of increased angular density with eye length reported in Figure 5B. We found that the average displacement between PRL and maximum cone density was 6. 1 arcminutes and 30. 4 microns. There was no significant linear relationship found between PRL displacement in either angular or linear units vs. axial length. Therefore, the PRL was not more displaced in myopes than in emmetropes from the point of peak cone density. Plots of the cone density at the PRL with axial length show the same trend at the PRL as at the point of maximum cone density (Figure 6A and B). Finally, we explored whether fixational eye movements might have a dependency on axial length. Fixation stability around the PRL had an average standard deviation of 3. 94 arcminutes and 19. 84 microns. The average area of the best fitting ellipse containing ~68% of the points in the scatterplot (defined as the bivariate contour ellipse area, or BCEA) was 50. 7 square arcminutes and 1303 square microns. The plot of BCEA in square microns vs. axial length vs. showed a trend that approached significance (p=0. 0596) (Figure 7A), but when we plotted BCEA in square arcminutes vs. axial length, the trend was no longer apparent (p=0. 364) (Figure 7B). In other words, if there is any increase in fixational eye movements in microns, it is just a symptom of having a longer eye.
  We used our latest generation adaptive optics scanning laser ophthalmoscope (AOSLO) for foveal imaging. The system used a mirror-based, out-of-plane optical design (Dubra et al. , 2011), and employed a deformable mirror with a continuous membrane surface and shaped with 97 actuators (DM97, ALPAO, Montbonnot-Saint-Martin, France). The system scans multiple wavelengths simultaneously. Each wavelength was drawn from the same broadband supercontinuum source (SuperK EXTREME, NKT Photonics, Birkerod, Denmark) using a custom-built fiber coupler. Wave aberrations were measured with a custom-built Shack Hartmann wavefront sensor using the 940 nm channel. Images were recorded using the 680 nm channel. 512 × 512 pixel videos were recorded over a 0. 9 × 0. 9 degree square field for an average sampling resolution of 9. 48 pixels per arcminute. Eye alignment and head stabilization was achieved by using either a bite bar or a chin rest with temple pads. At least one 10 s video was recorded at the fovea and at eight more locations where the subjects were instructed to fixate on the corners and sides of the raster, to image an entire foveal region spanning about 1. 8 × 1. 8 degrees. In order to ensure the best possible focus of the foveal cones, multiple videos were taken over a range of 0. 05 D defocus steps to find the sharpest foveal cones. Focus steps were generated by adding a focus shape onto the deformable mirror. Online stabilization and registration algorithms were used to facilitate rapid feedback on the image quality. Steady fixation was achieved at the fovea center by having the subjects fixate on a dark, circular, blinking dot with a diameter of 3. 16 arcminutes (30 pixels) in the center of the AOSLO scanning raster. The fixation target was generated by modulating the same 680 nm scanning beam used for imaging and, as such, the target’s location was encoded directly into each frame of the video (Poonja et al. , 2005). A scatter plot of the positions of the blinking dot relative to the retina was generated and was fit with a bivariate ellipse using free online MATLAB scripts downloaded from http: //www. visiondummy. com/wp-content/uploads/2014/04/error_ellipse. m. The bivariate contour ellipse area (BCEA), which is the area of the best-fitting ellipse encompassing 68% of the points in the scatterplot (Castet and Crossland, 2012) was used to quantify the fixation stability (Figure 7) and the exact location of the PRL within the imaged cone mosaic (Table 2, Figure 3—figure supplements 1 and 2). High quality images were generated from the recorded videos offline using custom software (MATLAB, The MathWorks, Inc, Natick, MA) to measure and correct for distortions caused by eye movements (Stevenson and Roorda, 2005). An open source version of the code is posted at https: //github. com/lowvisionresearch/ReVAS (Agaoglu et al. , 2018; copy archived at https: //github. com/elifesciences-publications/ReVAS). Poor-quality frames were manually excluded and registered frames were averaged into a single high signal-to-noise image. The processed images were stitched together (Photoshop; Adobe Systems, Inc, Mountain View, CA) to create an approximately 1. 8-degree montage of the foveal cone mosaic. We used custom software to identify and label individual cones in the AO retinal images. The program allows the user to select a region of interest and manually add and delete cone labels. A combination of both manual and automated methods (Li and Roorda, 2007) were used to identify cone locations as the current version of the program does not adequately recognize cones in the foveal center where they are dim and smaller (Li et al. , 2010). All the cone coordinates were selected and reviewed by two of the authors. In some cases cones were too dim to be seen but there was only a gap in the mosaic (Bruce et al. , 2015). If a space that might have been occupied by a cone was dim or dark, we would assume it was a cone and mark its location. We rationalize this for two reasons: First, if there is a gap in the mosaic, then it is likely that a cell is occupying that space, otherwise the adjacent cells would migrate to fill it in (Scoles et al. , 2014). Second, in our experience and of others (Pallikaris et al. , 2003), cones that appear dark in one visit, can often appear bright in the next. In other cases (uncommon) the contrast was low in some regions or there were interference artifacts in the images (Meadway and Sincich, 2018; Putnam et al. , 2010), making the cone locations slightly ambiguous. In these instances, we made manual cone selections based on the assumption that the cones were all similar in size and close-packed into a nearly hexagonal array (Curcio et al. , 1990). Continuous density maps were generated by computing cone density within a circular cone sampling window of 10 arcminutes in diameter around every pixel location across the image. All cones whose centers fell on or within the boundary of the sampling window were counted. The size of the cone sampling windows was chosen for several reasons. First, it encompasses the typical range of eye motion during a typical fixation task. Second, the area was large enough to generate smooth maps, but small enough to resolve local changes. Smaller cone sampling windows showed slightly higher densities (see Discussion) but were also associated with more variability in the identification of the location of peak cone density. Changes in density with eccentricity were generated by computing the density in five-arcminute annuli surrounding the point of peak cone density. For linear density measures we used annuli with 25-micron widths. The exact angular dimensions of the AOSLO images were computed by imaging a calibrated model eye in the AOSLO system, but the conversion to linear dimensions on the retinal image requires additional measurements, since the dimensions of each eye governs the actual size of the image on its retina. The conversion from visual angle to retinal distance requires a measurement of the axial length of the eye and an estimation of the location of the secondary nodal point. We did paraxial ray tracing, described by Li et al. (2010), in a four-surface schematic eye model to estimate the location of the secondary nodal point. The corneal first surface radius of curvature, the anterior chamber depth and the axial length were measured for each subject with an IOL Master (Zeiss Meditec, Dublin, CA). The radius of the curvature of the back surface of the cornea was computed as 88. 31% of the front surface as per the Gullstrand eye model (Bennett et al. , 1994). The indices of refraction of the media and the radii of curvature of the front and back lens surface were taken from the Gullstrand schematic eye (Vojniković and Tamajo, 2013). Once determined, retinal image size is related to visual angle by the equation: I=tan (1∘) (x−AN′) θ Where I is retinal image size, x is axial length, AN’ is the distance from the corneal apex to the eye’s second nodal point, and θ is the visual angle. As can be seen in Table 2, myopic eyes, which generally have longer focal lengths, have proportionally larger retinal images. Other methods to compute the retinal magnification factor (RMF) might have been used. We did a paraxial ray trace to find the secondary nodal point using lens parameters from a 6-surface Gullstrand eye model, and found that the RMFs were essentially identical. When we computed the RMF using an equation proposed by Bennett et al. (1994) we found that the RMF was overestimated for hyperopic eyes and underestimated for myopic eyes. This discrepancy arises from the fact that Bennett’s equation is based on the assumption that the focal point of the eye’s optics coincides with the retina, which it does not (Li et al. , 2010). Despite this known error, when we redid the analysis using RMFs computed using the Bennett et al. (1994) equation, we still found a significant trend of reducing linear density with axial length, but only at the position of peak cone density. Of course, all the angular density calculations are unaffected by differences in the RMF. Given the trends of increased angular density as a function of axial length that Li et al. (2010) observed at the location closest to the fovea (slope = 531 cones/deg2 for each mm increase in axial length; standard deviation of the regression errors = 1377 cones/deg2), we estimated that data from approximately 32 eyes, evenly distributed across a range of axial lengths would be sufficient to show if there was a true effect at the fovea. The targeted number was computed using methods outlined by Dupont and Plummer (1998) implemented using free online software (Power and Sample Size Program Version 3. 0, January 2009, downloaded from http: //biostat. mc. vanderbilt. edu/wiki/Main/PowerSampleSize) with type one error probability of 0. 05 and a power of 0. 95. All data collected in this study were analyzed using simple linear regression models in Excel. p-values for all linear regressions are reported and linear trendlines with p-values less than 0. 05 are plotted as solid lines and p-values greater than 0. 05 as dashed lines. In this study, we included both the right and left eyes of some of the subjects. When we reran the statistics with a single eye from each subject (n = 16), the results were essentially the same and the same conclusions could be drawn.
summary: The human eye has many different parts that enable sight. The retina is the light sensitive tissue at the back of the eye, and it contains the fovea, the region that provides the clearest vision. Light must be focused on the retina to create images, a feat achieved by the transparent parts at the front of the eye called the cornea and lens. These parts of the eye are called the optics. Between birth and adulthood, significant changes take place in the eye. Most noticeably, the distance between the optics and the fovea grows by about seven millimeters. Cells called cone photoreceptors, which provide light sensitivity, migrate and pack into the fovea. Finally, the eye’s optics adjust to maintain a sharp focus. At the same time, the brain is learning how to process inputs from the eyes to generate mental images that realistically correspond to the physical world around it. The development of the eye is fascinating in its complexity, but for more and more people, the process does not go as expected. Specifically, a growing proportion of the population has eyes that are too long. This means that, for light reflected by far away objects, the eye’s optics form an image in front of the retina instead of on it. As a result, images of distant objects cannot be seen clearly, a condition known as myopia or nearsightedness. Researchers have also discovered that nearsighted people see less clearly than those who do not use glasses, even when given a sharp image to examine at close range. It has been hypothesized that these deficits result from stretching of the retina as the eye becomes bigger. Until recently, testing this hypothesis by looking at cone photoreceptors directly in the eye was impossible. This is because the optics of all eyes have small imperfections that distort the light passing through them, including any light used to take high resolution microscopic images of the fovea. This hurdle can be overcome using adaptive optics, which means adding a deformable mirror to the instrument being used to image the eye that can adjust to correct the distortion. Wang et al. use a new generation Adaptive Optics Scanning Laser Ophthalmoscope to check the density of cones at the fovea in relation to the size of the eye. They show that although the center of the fovea has fewer cones when the eye is bigger, this effect is more than offset because the longer eye increases magnification. So, if a near-sighted person wearing contacts and someone who does not need glasses stood side-by-side admiring the full moon, the near-sighted person would most likely have more cones sampling the image and should therefore have a higher resolution view. These findings rule out reductions in the density of cone photoreceptors as the cause or effect of visual deficits associated with near-sightedness, adding to the understanding of this common condition.
keywords: neuroscience
title: Human foveal cone photoreceptor topography and its dependence on eye length