Three-dimensional MRI study of the relationship between eye dimensions , retinal shape and myopia

We investigated changes in eye dimensions and retinal shape with degree of myopia, gender and race. There were 58 young adult emmetropes and myopes (range –1.25D to −8.25D), with 30 East-Asians (21 female/9 male), 23 Caucasians (16/7) and 5 SouthAsians (1/4). Three-dimensional magnetic resonance imaging was undertaken with a 3.0 Tesla whole-body clinical MRI system using a 4.0 cm receive-only surface coil positioned over the eye. Automated methods determined eye length, width and height, and curve fitting procedures determined asymmetric and symmetric ellipsoid shapes to 75%, 55% and 35% of the retina. With myopia increase, eye dimensions increased in all directions such that increase in length was considerably greater than increases in width and height. Emmetropic retinas were oblate (steepening away from the vertex) but oblateness decreased with the increase in myopia, so that retinas were approximately spherical at 7 to 8D myopia. Asymmetry of eyes about the best fit visual axis was generally small, with small differences between the vertex radii of curvature and between asphericities in the axial and sagittal planes. Females had smaller eyes than males, with overall dimensions being about 0.5mm less for the former. Race appeared not to have a systematic effect. ©2017 Optical Society of America OCIS codes: (330.4460) Ophthalmic optics and devices; (330.7326) Visual optics, modeling. References and links 1. B. A. Holden, M. Jong, S. Davis, D. Wilson, T. Fricke, and S. Resnikoff, “Nearly 1 billion myopes at risk of myopia-related sight-threatening conditions by 2050 time to act now,” Clin. Exp. Optom. 98(6), 491–493 (2015). 2. C. W. Pan, D. Ramamurthy, and S. M. Saw, “Worldwide prevalence and risk factors for myopia,” Ophthalmic Physiol. Opt. 32(1), 3–16 (2012). 3. S. M. Saw, A. Shankar, S. B. Tan, H. Taylor, D. T. Tan, R. A. Stone, and T. Y. 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Introduction
Myopia is the most common refractive anomaly in children and young adults [1].It is particularly prevalent in East Asian communities where it affects up to 60-90% of teenagers, and its incidence is increasing worldwide [2,3].High myopia (refraction < -6.00 D) is a leading cause of blindness in later life through association with an increased risk of retinal disease, retinal detachment and glaucoma [4][5][6].Myopia is associated with axial elongation of the eye, but although causes and treatment of myopia have been debated for decades, the mechanism of elongation of the eye remains unclear.Both environmental and genetic factors have been associated with the onset and progression of myopia [7,8].Developing spectacle or contact lenses to slow or stop the progression of myopia would be of great interest and benefit [9].Achieving this objective requires a rigorous understanding of the stimuli that cause myopia progression.
Previously, much attention was given to the central retina and the state of focus along the visual axis, but since the foveal area forms only a small part of the visual field, peripheral retinal areas might be of importance in driving refractive status.Retinal shape may play a causative role in this, with particular eyeball shapes more vulnerable to subsequent distortion and axial stretch, leading to myopia [10].
Retinal shape can be estimated by indirect optical methods that are based on peripheral refraction [11][12][13], partial coherence interferometry [14][15][16][17][18][19][20][21][22][23][24] and optical coherence tomography [25,26].However such methods rely on assumptions concerning shape and refractive index distribution through the lens and other structures within the eye, in order to convert optical path lengths into geometrical dimensions.There have been some studies of retinal shape using the more direct method of magnetic resonance imaging (MRI) [27][28][29].In this study we have used MRI to investigate changes in overall eye dimensions and in retinal shape with degree of myopia.There is little information on effect of gender on these parameters, and so we considered the influence of gender.Because of the high prevalence of myopia in East Asian (Chinese) communities, we considered also the influence of race.

Participants
The study involved 38 females and 20 males with a mean age 22.3 ± 3.1 years and an age range of 18 to 28 years, giving 58 participants in total after two had been removed because of poor retinal fitting associated with motion artefacts.Refraction was determined with a SRW-5000 auto refractor (Shin-Nippon, Tokyo, Japan).There were 28 emmetropes with right eye spherical equivalent refraction in the range + 0.75 D to −0.62 D and 30 myopes (-0.75 D to −8.25 D).Some results for the participants have been reported previously [22].Table 1 shows refraction characteristics related to race and gender.The study followed the tenets of the declaration of Helsinki, and experimental protocols were approved by the Human Research Ethics Committees of the Queensland University of Technology and the University of Queensland.The nature of experimental procedures was explained to participants and written informed consent was obtained before taking measurements.

MRI protocols
MRI was undertaken at the University of Queensland Centre for Advanced Imaging on a 3.0 Tesla Siemens Magnetom Trio whole-body clinical MRI system using a standard Siemens 4.0 cm receive-only surface coil positioned over the eye, following procedures based on those used by Kasthurirangan et al. [30].A checklist (standard survey form) was used to select suitable participants and to screen for heart pacemakers, bionic implants or other metallic objects that might cause localized heating or degrade image quality.Female participants were requested not to wear eye make-up on the day of the examination, in order to reduce susceptibility artefacts.Patients were instructed to blink as little as possible.All imaging was carried out under the supervision of a qualified MRI radiographer.Scanning was performed with participants lying supine and fixating on a small white cross projected onto a translucent screen mounted in the end of the magnet bore at a viewing distance of 0.93 meters.Participants looked upwards to view the target through the receiver coil, via an adjustable mirror mounted at 45° to the vertical.For myopes, best correcting spherical and cylindrical lenses on top of the coil provided a clear target.Transverse axial and sagittal 2-dimensional images with 0.25mm in-plane resolution were acquired using a multi slice turbo spin-echo (TSE) imaging sequence (64 mm FOV; 256 × 256 matrix; 2mm slice thickness (no gaps); repetition time (TR) = 4000 ms; echo time (TE) = 16 ms; echo train length 12, imaging time 128 s).Following this, a T2-weighted Half-Fourier-Acquisition Single-Shot Turbo Spin-Echo (HASTE) sequence was employed to generate 3D isotropic images of the eye with 0.5 mm cubic voxels (128 × 128 × 64 matrix; TR = 2500 ms; TE = 56 ms; imaging time 4 min).Limitations of the method associated with the dimensions of voxels have been discussed previously [22].

MRI image analysis and fitting
MRI data were analyzed using custom written MATLAB (Mathworks, Natick, MA) software in three major steps detailed previously [22]: 1. Image rotation to a common z-axis (visual axis), 2. Image segmentation to extract retinal boundaries, and 3. Data fitting to estimate vertex radii of curvature and asphericities.
The retinal boundary was segmented in each slice by applying a Canny edge detection algorithm to determine the transition between voxels that are in both the vitreous and sclera.The retinal boundary was separated from the rest of the detected edges by applying morphological filters about the approximate size and shape of the retina.An advanced segmentation technique, "active contour" was applied when low contrast to noise ratio or blinking artefacts limited the conventional edge detection accuracy.In this technique, a mask is initiated, with the algorithm growing the mask outwards, based on the image gradient, until it strikes the retinal boundary.To decrease the influence of partial volume effects, the retina was segmented in all three planes (axial, sagittal and coronal).All acquired boundary points were concatenated to build an N × 3 matrix in the coordinate system, where N is the number of segmented voxels.Coordinates of the back of the eye were found by exploring the extreme point in the slice that contained the central plane of the eye.Before fitting ellipsoids, the 'corneal bulge' was removed from the image and the resulting outline of the retina was segmented into fractions F ranging from 25% to 75%, the latter corresponding to the maximum eye proportion that could be fitted for all participants.The relationship between fractional area F and angle (θ) subtended at the center of the scleral globe was given by ( ) Automated measurements of overall eye length (average of those in axial and sagittal planes), width (in the axial plane) and height (in the sagittal plane) were made from 3D HASTE image data sets (Fig. 1).Co-ordinates of 3D HASTE data identified as defining the shape of the retina were fitted with an asymmetric ellipsoid where C X = 1/R X , C Y = 1/R Y and C Z = 1/R Z and with R X , R Y and R Z being the principal radii of ellipsoids.The data were also fitted with the axially symmetric equation ( ) where -1 < Q < 0 for prolate ellipsoids, Q = 0 for spheres and Q > 0 for oblate ellipsoids.
Retinal shape can be quantified also in terms of vertex radius of curvature and asphericity.For asymmetric ellipsoids are the vertex radii of curvatures in the XZ and YZ planes respectively, with corresponding asphericities [31]

Statistics
Multiple linear regressions using the backward variant (IBM SPSS Statistics, version 21, Armonk, NY) were conducted for length, width, height, R X , R Y and R Z , R v , R Xv , R Yv , Q, Q X and Q Y , with independent variables of refraction, race (East Asians = -1, Caucasians = + 1), and gender (females = -1, males = + 1).Since there were only 5 South Asians in the cohort, they were omitted.Simple linear regressions with refraction as the independent variable were conducted for all participants.For the retinal shape factors, F = 75%, 55% and 35% were considered separately in multiple and simple regressions.

Results
Table 2 shows the simple linear regression results for spherical equivalent refraction (henceforth referred to as refraction), including slopes and corresponding R 2 and p values.Table 3 shows multiple linear regression results, with the values in brackets being standard errors of the coefficients found to be significant and with dashes indicating non-significance.

Influence of refraction on overall dimensions
Figure 2 shows eye length, width and height, and the ratios width/length, height/length and height/width as a function of refraction for all participants.With considerable inter-participant variability, eye dimensions increased with increasing myopia (more negative refraction), with length increasing at a faster rate (0.

Influence of fraction of retina on retina shape estimates
For the 75% fraction, most variables were significantly affected by refraction, with increasing dimensions, decreasing vertex radii of curvature and decreasing asphericities with increasing myopia (Tables 2 and 3 and Fig. 3).For the 55% fraction, the data were scattering more than for the 75% fraction, but the fits were similar and many of the slopes were still significant.However for the 35% fraction, data were very scattered and the fits were different from the other fractions and lacked significant trends.The 75% fraction fits are used to describe retinal shape in the rest of the Results section.Consistent with overall dimensions, as shown in Fig. 3 the principal radii increased with increase in myopia, with R z increasing at a more rapid rate than R x and R y .With increase in myopia, despite eyes becoming larger, vertex radii of curvature became smaller in both meridians; there was a greater rate of change in the horizontal than in the vertical meridian (+ 0.12 v. + 0.06 mm/D -see Table 2).For emmetropic eyes, mean asphericity was Q = + 0.2 (oblate shape) in both horizontal and vertical meridians, but with increase in myopia there was a negative shift so that retinas were predicted to become prolate beyond 7 D myopia.
Rotationally symmetric fits gave similar results to the asymmetric fits, with vertex radius of curvature becoming smaller with increase in myopia and asphericity becoming less positive so that it was predicted to become negative beyond about 8 D myopia.

Effects of gender and race on dimensions and retinal shape (East Asians and Caucasians)
The multiple linear regressions showed that male eyes were 0.4 to 0.5 mm bigger than female eyes (note that the gender coefficients in Table 3 should be multiplied by 2 to obtain the average difference in overall eye dimensions between males and females).The only significant influences of gender on shape were in the vertical meridian with principal radius and vertex radius of curvature being larger in males than in females.2.  2.
There were some indications that race affected retinal shape, but not for the overall dimensions.Where significant effects occurred in the vertical meridian with principal radius and vertex radius of curvature, these were in the opposite direction to those for gender.We think that this is at least in part due to the greater number of females in the East Asian group.With females having smaller eyes and a tendency towards more curved retinas, it is not surprising that there are significant effects of race.When race is removed as a factor, gender is significant only for the overall dimensions and not for the retinal shape factors.

Discussion
We performed 3-D magnetic resonance imaging on a group of young adult emmetropic eyes.As myopia increased in adult eyes, the dimensions of the eye increased in all directions such that increase in length was considerably greater than increase in width and height.Accompanying this were corresponding changes in the asphericity of the retina.Emmetropic retinas were oblate (steepen away from the vertex) but this oblateness decreased with increase in myopia, so that retinas were approximately spherical at 7-8 D myopia.The asymmetry of the eyes about the best fit visual axis was generally small, with small differences between the vertex radii of curvature and between asphericities in the axial and sagittal planes.Females had smaller eyes than males, with overall dimensions being about 0.5 mm less for the former.Race appeared not to have a systematic effect.
Previously we conducted 2-D magnetic resonance imaging with a 1.5 T machine for a larger group of 88 participants, 84% of whom were Caucasian [28,33].Influences of gender and race were not explored.In that study, dimensions were determined and retinal fits were made for approximately 75% of the retina.Overall, the results of this study confirm the previous findings.The common finding was the reduction in oblateness of retinal shape as myopia increases.Gilmartin et al. [29] used MRI with both eyes of 55 young adults and found less oblateness in a myopic group than in an emmetropic group, but did not conduct regressions as we have done.They made the interesting suggestion that a spherical retinal shape provides a biomechanical limitation to further elongation of the eye.
The main contrast with our previous study [28,33] was that, overall, there were similar refraction-dependent rates of change in the horizontal and vertical meridians in this study, whereas previously the rates of change were considerable greater in the vertical than in the horizontal meridian.This study is more consistent with Gilmartin et al.'s study, whose results indicate similar retinal widths and heights in myopia.
Our results suggest that for emmetropes, the Q values characterizing asphericity decrease as the fraction of the eye fitted was decreased from F = 75% through F = 55% to F = 35% (Tables 2 and 3, Fig. 3(C)), implying that the rear part of the retina (surrounding the fovea) tends to be approximately spherical, independent of degree of myopia.Due to the limited resolution of images (the 3D HASTE data were acquired with 0.5mm cubic voxels), the fits may tend to make the rear part of the retina appear 'flatter' than it actually is, because eye edge points with a Z-coordinate within 0.5mm of the vertex are all assigned the same Z value.This will particularly affect fits corresponding to smaller F values, because the overall number of data points fitted is reduced, so these voxels make up a larger proportion of the total.It will tend to make the central part of the retina appear more oblate, whereas our data imply the reverse of this, although this result is difficult to confirm as the scatter is much greater at the lower fraction.
The retinal shape results can be related to peripheral optics of the eye.Peripheral refraction has different patterns in the horizontal and vertical visual field meridians [24,31,34,35].For the horizontal field, emmetropes tend to have peripheral myopia, while myopes have reduced myopia in the periphery (termed relative peripheral hyperopia).For the vertical field, both emmetropes and myopes have relative peripheral myopia with our recent study indicating that this is less in myopes than in emmetropes [23].Using the retinal shape derived from our previous study, our eye modelling predicted only a small part of the difference between the refractive patterns for the horizontal and vertical meridians (Table 2 [28]); as the meridional differences in this study were less than in the earlier work, changing the retinal shapes would give even less meridional effect on the peripheral optics modelling.
There are two possible explanations for the failure of the modelling.One is that there are meridional differences in peripheral optics due to the ocular components that have not been recognized yet in biometry investigations.The second is that there are asymmetries in the retina close to the fovea that cannot be picked up by fitting curves to more than 50% of the retina, or the scatter in the data over a small posterior region makes it difficult to recognize these differences.We note that our "partial coherence interferometry" method for estimating retinal shape by combining peripheral axial length measurements with symmetric ocular modelling found meridional differences, with retinas being steeper by about 1.5 mm vertex radius of curvature in the horizontal meridian than in the vertical meridian in an East Asian group, and with the shapes being strongly correlated with peripheral refraction (steeper retinas accompanying higher relative peripheral hyperopia) [23].A further study with a combined East Asian/Caucasian group found a difference in vertex radius of curvature of 1.2 mm between meridians [24].
A further difference between the current study and the partial coherence interferometry method is that in the latter, race was found to affect shape, with East Asians having steeper retinas than Caucasians with a mean difference in vertex radii of curvature of -0.7 ± 0.5 mm [24].
A limitation of our modelling is that it provides no information about nasal/temporal or superior/inferior asymmetries.The previous study [28] included tilts and decentrations; ellipsoids were tilted about the vertical axis by 11 ± 13° nasally in retinal space, and ellipsoid centers were decentered by 0.5 ± 0.4 mm nasally and 0.2 ± 0.5 mm inferiorly relative to the fovea.

Funding
Johnson & Johnson Vision Care, Inc.

Fig. 2 .
Fig. 2. a) Eye length, width and height as a function of refraction.b).Ratios width/length, height/length and height/width as functions of refraction.Linear regression coefficients are given in Table2.

Fig. 3 .
Fig. 3. Retinal shape parameters as a function of refraction for different retina fractions for all participants.Column A: principal radii R X , R Y and R Z ; Column B: vertex radii of curvature R xv and R yv ; Column C: Asphericities Q x and Q y .Note different vertical scales for the 35% fraction than for the other two fractions for principal radius.Linear regression coefficients are given in Table2.