Human foveal cone photoreceptor topography and its dependence on eye length
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 .
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 .
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 .