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.

There has been a rapid increase in prevalence of myopia, of all magnitudes, in the period between 1971–1972 and 1999–2004 (Vitale, 2009). Across sub-populations grouped by race, ethnicity and gender, several studies report axial length of the eye to be the primary variable related to myopia (González Blanco et al., 2008; He et al., 2015; Iyamu et al., 2011). Increased axial length is associated with retinal stretching and thinning of posterior segment layers and the choroid (Fujiwara et al., 2009; Harb et al., 2015) and is associated with sight-threatening, often irreversible pathologies of the retina (Morgan et al., 2012; Verkicharla et al., 2015). Even without any detectable pathology, the structural changes associated with eye growth ought to have functional consequences for vision.

Models for how photoreceptors change with eye growth

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).

Figure 1

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Previous studies of cone spacing with axial length

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.

Figure 2

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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.

The experiments were approved by the University of California, Berkeley Committee for the Protection of Human Subjects. All subjects provided informed consent prior to any experimental procedures. Subjects self-reported their eye health so that only healthy individuals with no ocular conditions were included in the study. All eyes were dilated and cyclopleged with 1% Tropicamide and 2.5% Phenylephrine before imaging. We report data from 28 eyes of 16 subjects with a wide range of refractive error and axial length. Age, sex and ethnicity are listed on Table 2.

Imaging data

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 3 with 2 supplements see all

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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.

Figure 4 with 2 supplements see all

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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

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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.

Figure 5

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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

Download elife-47148-fig5-data1-v1.csv

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).

Figure 6

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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

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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.

Figure 7

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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

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In this paper, we measure the cone density at and near the foveal center and investigate how it changes as a function of axial length. This is the first comprehensive study of cones in living eyes at the foveal center, the area solely responsible for a human’s fine spatial vision. Our results show that although some expansion does occur (linear cone density decreases with axial length) the angular sampling resolution actually increases, on average, with axial length. Prior to this study, the relationships between cone density and axial length were only made outside of the fovea, the closest being 0.1 mm, or 0.3 degrees (Li et al., 2010). Although an eccentricity of 0.3 degrees might seem close, it is noted that the cone density drops precipitously just outside of the location of peak density (Curcio et al., 1990) as does human vision (Poletti et al., 2013) (Rossi and Roorda, 2010b). There are other factors that govern peak cone density, however; eye length accounts for anywhere between 31% and 39% of the variance in cone density at the foveal center.

Our finding that the slopes of cone density vs. axial length are in opposite directions when plotted in linear (negative slope) and angular (positive slope) units, supports an eye growth model that lies between the global expansion model and an equatorial stretching model. Previous studies from our lab (Li et al., 2010) and also from Chui et al. (2008) leaned in the same direction. None of the cone density studies provide insight into the reasons why the photoreceptor density would behave this way with eye growth, but the results do align with other observations reported in the literature. Specifically, Atchison et al. (2004) used magnetic resonance imaging and found that eyeball dimensions in axial myopes are variable but are generally larger in all directions with a weak tendency to be preferentially greater in the axial direction. Their reported eye growth patterns lie between that illustrated for the global expansion and equatorial stretching models in Figure 1.

Our results differ from Wilk et al. (2017) whose data support a global expansion model (i.e. there is no detectable change in angular cone density with axial length; Figure 2B). But it is important to point out that their study did not set out to address the same question and the number of subjects with long axial lengths was disproportionately low.

Our results also differ from Troilo (1998) who studied retinal cell topography in a marmoset animal myopia model. Higher cone packing densities were observed in the experimentally enlarged eyes compared to normal eyes in the fovea. Their result followed the overdevelopment model, which is the reason why we included it as one of the possible outcomes of our study. In fact, the overdevelopment model is an extension of Springer’s model of development (Springer and Hendrickson, 2004), which offers a biomechanical explanation for how cone packing increases at the foveal center in a developing eye. While our data do not support the overdevelopment model, it does not preclude the existence of biomechanical factors working in opposition to simple global expansion.

The fact that angular cone density (visual sampling resolution) increases with eye length (myopia), at the peak density and at the PRL, means that poorer performance by myopes on resolution tasks cannot be explained by a decrease in photoreceptor sampling. The deficit must arise at a post-receptoral level.

Low-level causes for myopic visual deficits might arise from differences in the connectivity between cones and ganglion cells. Atchison et al. (2006) suggested that abnormal eye growth may be associated with a loss of ganglion cells. Alternately, if ganglion cells pool signals from multiple cones, then they will impose the retinal sampling limit and reduce certain aspects of visual performance (acuity, for example). Recent electron microscopy studies of a human fovea have revealed extensive convergence and divergence connections between photoreceptors and ganglion cells, albeit in an eye from an individual who was born prematurely (Dacey, 2018). These discoveries challenge our current understanding of neural connectivity in the foveal center and force us to consider the possibility of interindividual differences in foveal cone wiring. More experiments are necessary to explore these ideas.

To explain why low myopes did not perform as well on an acuity task as emmetropes, even after correction or bypassing of high order aberrations, Rossi et al. (2007) and Coletta and Watson (2006) both raised the possibility that myopes might have become desensitized to high frequency information (low level myopic amblyopia) as a result of having less exposure to a high contrast visual environment. In this case, it might be possible to train myopes to take advantage of their higher sampling resolution, but one myope in a follow up study by Rossi and Roorda (2010a) never reached the acuity levels of emmetropes in the same study.

The following data are available for download at the Dryad Digital Repository: https://dx.doi.org/10.5061/dryad.nh0fp1b. 1. All original images and cone locations. 2. A table of scaling parameters (pixels per degree and retinal magnification factors) for each image. 3. A MATLAB script that can be used to plot cone locations on the original image.

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Author details

1. Yiyi Wang

   School of Optometry, University of California, Berkeley, Berkeley, United States

   Contribution

   Data curation, Formal analysis, Investigation, Visualization, Writing—original draft, Writing—review and editing

   Competing interests

   No competing interests declared

2. Nicolas Bensaid

   Carl Zeiss Meditec AG, Berlin, Germany

   Contribution

   Software, Significant engineering support

   Competing interests

   No competing interests declared

3. Pavan Tiruveedhula

   1. School of Optometry, University of California, Berkeley, Berkeley, United States
   2. Vision Science Graduate Group, University of California, Berkeley, Berkeley, United States

   Contribution

   Software, Significant engineering support

   Competing interests

   No competing interests declared

4. Jianqiang Ma

   Department of Mechanical Engineering, Ningbo University, Ningbo, China

   Contribution

   Software, Significant engineering support

   Competing interests

   No competing interests declared

5. Sowmya Ravikumar

   1. School of Optometry, University of California, Berkeley, Berkeley, United States
   2. Vision Science Graduate Group, University of California, Berkeley, Berkeley, United States

   Contribution

   Conceptualization, Data curation, Investigation, Writing—original draft

   Competing interests

   No competing interests declared

6. Austin Roorda

   1. School of Optometry, University of California, Berkeley, Berkeley, United States
   2. Vision Science Graduate Group, University of California, Berkeley, Berkeley, United States

   Contribution

   Conceptualization, Data curation, Software, Formal analysis, Supervision, Funding acquisition, Validation, Investigation, Visualization, Methodology, Writing—original draft, Project administration, Writing—review and editing

   For correspondence

   aroorda@berkeley.edu

   Competing interests

   has a patent (USPTO#7118216) assigned to the University of Houston and the University of Rochester which is currently licensed to Boston Micromachines Corp (Watertown, MA, USA). Both he and the company stand to gain financially from the publication of these results. No other authors have competing interests.

   "This ORCID iD identifies the author of this article:" 0000-0002-3785-0848

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