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Three-dimensional MRI study of the relationship between eye dimensions, retinal shape and myopia JAMES M. POPE,1,2 PAVAN K. VERKICHARLA,2,3,4 FARSHID SEPEHRBAND,2,3 MARWAN SUHEIMAT,2,3 KATRINA L. SCHMID,2,3 AND DAVID A. ATCHISON2,3,* 1
School of Chemistry, Physics and Mechanical Engineering, Queensland University of Technology, Brisbane, Australia 2 Institute of Health and Biomedical Innovation, Queensland University of Technology, Brisbane, 4059 Australia 3 School of Optometry and Vision Science, Queensland University of Technology, Brisbane, 4059 Australia 4 Brien Holden Institute of Optometry and Vision Sciences, L V Prasad Eye Institute, Hyderabad 500034, India *[email protected]
Abstract: 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. 2. 3. 4. 5. 6. 7. 8. 9.
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). C. W. Pan, D. Ramamurthy, and S. M. Saw, “Worldwide prevalence and risk factors for myopia,” Ophthalmic Physiol. Opt. 32(1), 3–16 (2012). S. M. Saw, A. Shankar, S. B. Tan, H. Taylor, D. T. Tan, R. A. Stone, and T. Y. Wong, “A cohort study of incident myopia in Singaporean children,” Invest. Ophthalmol. Vis. Sci. 47(5), 1839–1844 (2006). S. M. Saw, G. Gazzard, E. C. Shih-Yen, and W. H. Chua, “Myopia and associated pathological complications,” Ophthalmic Physiol. Opt. 25(5), 381–391 (2005). Y. Timothy, “Retinal complications of high myopia,” The Hong Kong Medical Diary 12(9), 18–20 (2007). P. K. Verkicharla, K. Ohno-Matsui, and S. M. Saw, “Current and predicted demographics of high myopia and an update of its associated pathological changes,” Ophthalmic Physiol. Opt. 35(5), 465–475 (2015). A. Wilson and G. Woo, “A review of the prevalence and causes of myopia,” Singapore Med. J. 30(5), 479–484 (1989). M. Feldkämper and F. Schaeffel, “Interactions of genes and environment in myopia,” Dev. Ophthalmol. 37, 34– 49 (2003). N. Charman, “Myopia: its prevalence, origins and control,” Ophthalmic Physiol. Opt. 31(1), 3–6 (2011).
#285601 Journal © 2017
https://doi.org/10.1364/BOE.8.002386 Received 24 Jan 2017; revised 19 Mar 2017; accepted 22 Mar 2017; published 5 Apr 2017
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10. R. A. Stone and D. I. Flitcroft, “Ocular shape and myopia,” Ann. Acad. Med. Singapore 33(1), 7–15 (2004). 11. M. C. M. Dunne, D. A. Barnes, and R. A. Clement, “A model for retinal shape changes in ametropia,” Ophthalmic Physiol. Opt. 7(2), 159–160 (1987). 12. M. C. M. Dunne, “A computing scheme for determination of retinal contour from peripheral refraction, keratometry and A-scan ultrasonography,” Ophthalmic Physiol. Opt. 15(2), 133–143 (1995). 13. N. S. Logan, B. Gilmartin, C. F. Wildsoet, and M. C. M. Dunne, “Posterior retinal contour in adult human anisomyopia,” Invest. Ophthalmol. Vis. Sci. 45(7), 2152–2162 (2004). 14. G. F. Schmid, “Axial and peripheral eye length measured with optical low coherence reflectometry,” J. Biomed. Opt. 8(4), 655–662 (2003). 15. G. F. Schmid, “Variability of retinal steepness at the posterior pole in children 7-15 years of age,” Curr. Eye Res. 27(1), 61–68 (2003). 16. G. F. Schmid, “Association between retinal steepness and central myopic shift in children,” Optom. Vis. Sci. 88(6), 684–690 (2011). 17. E. A. H. Mallen and P. Kashyap, “Technical note: Measurement of retinal contour and supine axial length using the Zeiss IOLMaster,” Ophthalmic Physiol. Opt. 27(4), 404–411 (2007). 18. D. A. Atchison and W. N. Charman, “Can partial coherence interferometry be used to determine retinal shape?” Optom. Vis. Sci. 88(5), E601–E607 (2011). 19. A. Ehsaei, C. M. Chisholm, I. E. Pacey, and E. A. H. Mallen, “Off-axis partial coherence interferometry in myopes and emmetropes,” Ophthalmic Physiol. Opt. 33(1), 26–34 (2013). 20. M. Faria-Ribeiro, A. Queirós, D. Lopes-Ferreira, J. Jorge, and J. M. González-Méijome, “Peripheral refraction and retinal contour in stable and progressive myopia,” Optom. Vis. Sci. 90(1), 9–15 (2013). 21. X. Ding, D. Wang, Q. Huang, J. Zhang, J. Chang, and M. He, “Distribution and heritability of peripheral eye length in Chinese children and adolescents: the Guangzhou Twin Eye Study,” Invest. Ophthalmol. Vis. Sci. 54(2), 1048–1053 (2013). 22. P. K. Verkicharla, M. Suheimat, J. M. Pope, F. Sepehrband, A. Mathur, K. L. Schmid, and D. A. Atchison, “Validation of a partial coherence interferometry method for estimating retinal shape,” Biomed. Opt. Express 6(9), 3235–3247 (2015). 23. P. K. Verkicharla, M. Suheimat, K. L. Schmid, and D. A. Atchison, “Peripheral refraction, peripheral eye length and retinal shape in myopia,” Optom. Vis. Sci. 93(9), 1072–1078 (2016). 24. P. K. Verkicharla, M. Suheimat, K. L. Schmid, and D. A. Atchison, “Differences in retinal shape between East Asian and Caucasian eyes,” Ophthalmic Physiol. Opt., doi:10.1111/opo.12359. 25. A. N. Kuo, R. P. McNabb, S. J. Chiu, M. A. El-Dairi, S. Farsiu, C. A. Toth, and J. A. Izatt, “Correction of ocular shape in retinal optical coherence tomography and effect on current clinical measures,” Am. J. Ophthalmol. 156(2), 304–311 (2013). 26. A. N. Kuo, P. K. Verkicharla, R. P. McNabb, C. Y. Cheung, S. Hilal, S. Farsiu, C. Chen, T. Y. Wong, M. K. Ikram, C. Y. Cheng, T. L. Young, S. M. Saw, and J. A. Izatt, “Posterior eye shape measurement with retinal OCT compared to MRI,” Invest. Ophthalmol. Vis. Sci. 57(9), OCT196 (2016). 27. J. F. Chen, A. E. Elsner, S. A. Burns, R. M. Hansen, P. L. Lou, K. K. Kwong, and A. B. Fulton, “The effect of eye shape on retinal responses,” Clin. Vis. Sci. 7(6), 521–530 (1992). 28. D. A. Atchison, N. Pritchard, K. L. Schmid, D. H. Scott, C. E. Jones, and J. M. Pope, “Shape of the retinal surface in emmetropia and myopia,” Invest. Ophthalmol. Vis. Sci. 46(8), 2698–2707 (2005). 29. B. Gilmartin, M. Nagra, and N. S. Logan, “Shape of the posterior vitreous chamber in human emmetropia and myopia,” Invest. Ophthalmol. Vis. Sci. 54(12), 7240–7251 (2013). 30. S. Kasthurirangan, E. L. Markwell, D. A. Atchison, and J. M. Pope, “In vivo study of changes in refractive index distribution in the human crystalline lens with age and accommodation,” Invest. Ophthalmol. Vis. Sci. 49(6), 2531–2540 (2008). 31. P. K. Verkicharla, A. Mathur, E. A. H. Mallen, J. M. Pope, and D. A. Atchison, “Eye shape and retinal shape, and their relation to peripheral refraction,” Ophthalmic Physiol. Opt. 32(3), 184–199 (2012). 32. D. A. Atchison, “Optical models for human myopic eyes,” Vision Res. 46(14), 2236–2250 (2006). 33. D. A. Atchison, C. E. Jones, K. L. Schmid, N. Pritchard, J. M. Pope, W. E. Strugnell, and R. A. Riley, “Eye shape in emmetropia and myopia,” Invest. Ophthalmol. Vis. Sci. 45(10), 3380–3386 (2004). 34. D. A. Atchison, N. Pritchard, and K. L. Schmid, “Peripheral refraction along the horizontal and vertical visual fields in myopia,” Vision Res. 46(8-9), 1450–1458 (2006). 35. D. A. Berntsen, D. O. Mutti, and K. Zadnik, “Study of theories about myopia progression (STAMP) design and baseline data,” Optom. Vis. Sci. 87(11), 823–832 (2010).
1. 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 [4–6]. Myopia is associated with axial elongation of the eye, but although causes and treatment of myopia have been debated for decades, the
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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 [11–13], partial coherence interferometry [14–24] 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) [27–29]. 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. 2. Methods 2.1 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 SRW5000 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. Table 1. Participant characteristics (right eyes) Gender/Race Female/East Asian Female/Caucasian Female/South Asian Male/East Asian Male/Caucasian Male/South Asian
Number 21 16 1 9 7 4
Mean refraction ± SD –2.81 ± 2.52 –1.30 ± 1.93 –0.75 –1.57 ± 2.04 –1.00 ± 1.75 + 0.19 ± 0.18
Range (D) + 0.31 to –8.15 + 0.75 to –4.18 N/A + 0.37 to –5.75 + 0.56 to –3.52 + 0.44 to + 0.01
2.2 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
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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]. 2.3 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 F ( % ) = 100[1 – cos(θ / 2)] / 2
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 C X 2 X 2 + C Y 2 Y 2 + C Z 2 Z 2 – 2C Z Z = 0
Solving for Z gives Z=
CX 2 X 2 + CY 2Y 2 CZ 1 ± 1 − CX 2 X 2 − CY 2Y 2
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where CX = 1/RX, CY = 1/RY and CZ = 1/RZ and with RX, RY and RZ being the principal radii of ellipsoids. The data were also fitted with the axially symmetric equation X 2 + Y 2 + (1 + Q ) Z 2 – 2ZRv = 0
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
RXv = RX 2 / RZ , RYv = RY 2 / RZ are the vertex radii of curvatures in the XZ and YZ planes respectively, with corresponding asphericities [31] QX = CZ 2 / Cx 2 – 1, QY = CZ 2 / CY 2 – 1
Fig. 1. Eye length and width measurements from 3D HASTE image data (0.5 mm isotropic resolution).
2.4 Statistics
Multiple linear regressions using the backward variant (IBM SPSS Statistics, version 21, Armonk, NY) were conducted for length, width, height, RX, RY and RZ, Rv, RXv, RYv, Q, QX and QY, 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. 3. Results
Table 2 shows the simple linear regression results for spherical equivalent refraction (henceforth referred to as refraction), including slopes and corresponding R2 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. 3.1 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 (0.30 mm/D) than eye width and height (0.14mm/D and 0.10mm/D, respectively). The height/width ratio was constant at ≈1.02.
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Table 2. Simple linear regressions with spherical refraction for all participants. Fraction (%)
variable
constant
slope
R2
P
75 75 75 75 75 75 75 75 75
Length Width height Height/width Height/length Width/length Rz Rx Ry Rxv Ryv Qx Qy Rv Q
24.16 23.56 24.14 1.025 1.000 0.975 10.87 11.86 11.74 12.98 12.72 + 0.199 + 0.174 12.90 0.193
–0.297 –0.138 –0.099 + 0.0018 + 0.0076 + 0.0059 –0.19 –0.04 –0.07 + 0.12 + 0.06 + 0.030 + 0.024 + 0.08 + 0.025
0.44 0.11 0.06 0.01 0.24 0.17 0.37 0.05 0.12 0.07 0.02 0.22 0.19 0.05 0.18
< 0.001 0.01 0.06 0.46 < 0.001 0.001
Three-dimensional MRI study of the relationship between eye dimensions, retinal shape and myopia JAMES M. POPE,1,2 PAVAN K. VERKICHARLA,2,3,4 FARSHID SEPEHRBAND,2,3 MARWAN SUHEIMAT,2,3 KATRINA L. SCHMID,2,3 AND DAVID A. ATCHISON2,3,* 1
School of Chemistry, Physics and Mechanical Engineering, Queensland University of Technology, Brisbane, Australia 2 Institute of Health and Biomedical Innovation, Queensland University of Technology, Brisbane, 4059 Australia 3 School of Optometry and Vision Science, Queensland University of Technology, Brisbane, 4059 Australia 4 Brien Holden Institute of Optometry and Vision Sciences, L V Prasad Eye Institute, Hyderabad 500034, India *[email protected]
Abstract: 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. 2. 3. 4. 5. 6. 7. 8. 9.
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). C. W. Pan, D. Ramamurthy, and S. M. Saw, “Worldwide prevalence and risk factors for myopia,” Ophthalmic Physiol. Opt. 32(1), 3–16 (2012). S. M. Saw, A. Shankar, S. B. Tan, H. Taylor, D. T. Tan, R. A. Stone, and T. Y. Wong, “A cohort study of incident myopia in Singaporean children,” Invest. Ophthalmol. Vis. Sci. 47(5), 1839–1844 (2006). S. M. Saw, G. Gazzard, E. C. Shih-Yen, and W. H. Chua, “Myopia and associated pathological complications,” Ophthalmic Physiol. Opt. 25(5), 381–391 (2005). Y. Timothy, “Retinal complications of high myopia,” The Hong Kong Medical Diary 12(9), 18–20 (2007). P. K. Verkicharla, K. Ohno-Matsui, and S. M. Saw, “Current and predicted demographics of high myopia and an update of its associated pathological changes,” Ophthalmic Physiol. Opt. 35(5), 465–475 (2015). A. Wilson and G. Woo, “A review of the prevalence and causes of myopia,” Singapore Med. J. 30(5), 479–484 (1989). M. Feldkämper and F. Schaeffel, “Interactions of genes and environment in myopia,” Dev. Ophthalmol. 37, 34– 49 (2003). N. Charman, “Myopia: its prevalence, origins and control,” Ophthalmic Physiol. Opt. 31(1), 3–6 (2011).
#285601 Journal © 2017
https://doi.org/10.1364/BOE.8.002386 Received 24 Jan 2017; revised 19 Mar 2017; accepted 22 Mar 2017; published 5 Apr 2017
Vol. 8, No. 5 | 1 May 2017 | BIOMEDICAL OPTICS EXPRESS 2387
10. R. A. Stone and D. I. Flitcroft, “Ocular shape and myopia,” Ann. Acad. Med. Singapore 33(1), 7–15 (2004). 11. M. C. M. Dunne, D. A. Barnes, and R. A. Clement, “A model for retinal shape changes in ametropia,” Ophthalmic Physiol. Opt. 7(2), 159–160 (1987). 12. M. C. M. Dunne, “A computing scheme for determination of retinal contour from peripheral refraction, keratometry and A-scan ultrasonography,” Ophthalmic Physiol. Opt. 15(2), 133–143 (1995). 13. N. S. Logan, B. Gilmartin, C. F. Wildsoet, and M. C. M. Dunne, “Posterior retinal contour in adult human anisomyopia,” Invest. Ophthalmol. Vis. Sci. 45(7), 2152–2162 (2004). 14. G. F. Schmid, “Axial and peripheral eye length measured with optical low coherence reflectometry,” J. Biomed. Opt. 8(4), 655–662 (2003). 15. G. F. Schmid, “Variability of retinal steepness at the posterior pole in children 7-15 years of age,” Curr. Eye Res. 27(1), 61–68 (2003). 16. G. F. Schmid, “Association between retinal steepness and central myopic shift in children,” Optom. Vis. Sci. 88(6), 684–690 (2011). 17. E. A. H. Mallen and P. Kashyap, “Technical note: Measurement of retinal contour and supine axial length using the Zeiss IOLMaster,” Ophthalmic Physiol. Opt. 27(4), 404–411 (2007). 18. D. A. Atchison and W. N. Charman, “Can partial coherence interferometry be used to determine retinal shape?” Optom. Vis. Sci. 88(5), E601–E607 (2011). 19. A. Ehsaei, C. M. Chisholm, I. E. Pacey, and E. A. H. Mallen, “Off-axis partial coherence interferometry in myopes and emmetropes,” Ophthalmic Physiol. Opt. 33(1), 26–34 (2013). 20. M. Faria-Ribeiro, A. Queirós, D. Lopes-Ferreira, J. Jorge, and J. M. González-Méijome, “Peripheral refraction and retinal contour in stable and progressive myopia,” Optom. Vis. Sci. 90(1), 9–15 (2013). 21. X. Ding, D. Wang, Q. Huang, J. Zhang, J. Chang, and M. He, “Distribution and heritability of peripheral eye length in Chinese children and adolescents: the Guangzhou Twin Eye Study,” Invest. Ophthalmol. Vis. Sci. 54(2), 1048–1053 (2013). 22. P. K. Verkicharla, M. Suheimat, J. M. Pope, F. Sepehrband, A. Mathur, K. L. Schmid, and D. A. Atchison, “Validation of a partial coherence interferometry method for estimating retinal shape,” Biomed. Opt. Express 6(9), 3235–3247 (2015). 23. P. K. Verkicharla, M. Suheimat, K. L. Schmid, and D. A. Atchison, “Peripheral refraction, peripheral eye length and retinal shape in myopia,” Optom. Vis. Sci. 93(9), 1072–1078 (2016). 24. P. K. Verkicharla, M. Suheimat, K. L. Schmid, and D. A. Atchison, “Differences in retinal shape between East Asian and Caucasian eyes,” Ophthalmic Physiol. Opt., doi:10.1111/opo.12359. 25. A. N. Kuo, R. P. McNabb, S. J. Chiu, M. A. El-Dairi, S. Farsiu, C. A. Toth, and J. A. Izatt, “Correction of ocular shape in retinal optical coherence tomography and effect on current clinical measures,” Am. J. Ophthalmol. 156(2), 304–311 (2013). 26. A. N. Kuo, P. K. Verkicharla, R. P. McNabb, C. Y. Cheung, S. Hilal, S. Farsiu, C. Chen, T. Y. Wong, M. K. Ikram, C. Y. Cheng, T. L. Young, S. M. Saw, and J. A. Izatt, “Posterior eye shape measurement with retinal OCT compared to MRI,” Invest. Ophthalmol. Vis. Sci. 57(9), OCT196 (2016). 27. J. F. Chen, A. E. Elsner, S. A. Burns, R. M. Hansen, P. L. Lou, K. K. Kwong, and A. B. Fulton, “The effect of eye shape on retinal responses,” Clin. Vis. Sci. 7(6), 521–530 (1992). 28. D. A. Atchison, N. Pritchard, K. L. Schmid, D. H. Scott, C. E. Jones, and J. M. Pope, “Shape of the retinal surface in emmetropia and myopia,” Invest. Ophthalmol. Vis. Sci. 46(8), 2698–2707 (2005). 29. B. Gilmartin, M. Nagra, and N. S. Logan, “Shape of the posterior vitreous chamber in human emmetropia and myopia,” Invest. Ophthalmol. Vis. Sci. 54(12), 7240–7251 (2013). 30. S. Kasthurirangan, E. L. Markwell, D. A. Atchison, and J. M. Pope, “In vivo study of changes in refractive index distribution in the human crystalline lens with age and accommodation,” Invest. Ophthalmol. Vis. Sci. 49(6), 2531–2540 (2008). 31. P. K. Verkicharla, A. Mathur, E. A. H. Mallen, J. M. Pope, and D. A. Atchison, “Eye shape and retinal shape, and their relation to peripheral refraction,” Ophthalmic Physiol. Opt. 32(3), 184–199 (2012). 32. D. A. Atchison, “Optical models for human myopic eyes,” Vision Res. 46(14), 2236–2250 (2006). 33. D. A. Atchison, C. E. Jones, K. L. Schmid, N. Pritchard, J. M. Pope, W. E. Strugnell, and R. A. Riley, “Eye shape in emmetropia and myopia,” Invest. Ophthalmol. Vis. Sci. 45(10), 3380–3386 (2004). 34. D. A. Atchison, N. Pritchard, and K. L. Schmid, “Peripheral refraction along the horizontal and vertical visual fields in myopia,” Vision Res. 46(8-9), 1450–1458 (2006). 35. D. A. Berntsen, D. O. Mutti, and K. Zadnik, “Study of theories about myopia progression (STAMP) design and baseline data,” Optom. Vis. Sci. 87(11), 823–832 (2010).
1. 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 [4–6]. Myopia is associated with axial elongation of the eye, but although causes and treatment of myopia have been debated for decades, the
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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 [11–13], partial coherence interferometry [14–24] 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) [27–29]. 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. 2. Methods 2.1 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 SRW5000 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. Table 1. Participant characteristics (right eyes) Gender/Race Female/East Asian Female/Caucasian Female/South Asian Male/East Asian Male/Caucasian Male/South Asian
Number 21 16 1 9 7 4
Mean refraction ± SD –2.81 ± 2.52 –1.30 ± 1.93 –0.75 –1.57 ± 2.04 –1.00 ± 1.75 + 0.19 ± 0.18
Range (D) + 0.31 to –8.15 + 0.75 to –4.18 N/A + 0.37 to –5.75 + 0.56 to –3.52 + 0.44 to + 0.01
2.2 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
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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]. 2.3 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 F ( % ) = 100[1 – cos(θ / 2)] / 2
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 C X 2 X 2 + C Y 2 Y 2 + C Z 2 Z 2 – 2C Z Z = 0
Solving for Z gives Z=
CX 2 X 2 + CY 2Y 2 CZ 1 ± 1 − CX 2 X 2 − CY 2Y 2
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where CX = 1/RX, CY = 1/RY and CZ = 1/RZ and with RX, RY and RZ being the principal radii of ellipsoids. The data were also fitted with the axially symmetric equation X 2 + Y 2 + (1 + Q ) Z 2 – 2ZRv = 0
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
RXv = RX 2 / RZ , RYv = RY 2 / RZ are the vertex radii of curvatures in the XZ and YZ planes respectively, with corresponding asphericities [31] QX = CZ 2 / Cx 2 – 1, QY = CZ 2 / CY 2 – 1
Fig. 1. Eye length and width measurements from 3D HASTE image data (0.5 mm isotropic resolution).
2.4 Statistics
Multiple linear regressions using the backward variant (IBM SPSS Statistics, version 21, Armonk, NY) were conducted for length, width, height, RX, RY and RZ, Rv, RXv, RYv, Q, QX and QY, 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. 3. Results
Table 2 shows the simple linear regression results for spherical equivalent refraction (henceforth referred to as refraction), including slopes and corresponding R2 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. 3.1 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 (0.30 mm/D) than eye width and height (0.14mm/D and 0.10mm/D, respectively). The height/width ratio was constant at ≈1.02.
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Table 2. Simple linear regressions with spherical refraction for all participants. Fraction (%)
variable
constant
slope
R2
P
75 75 75 75 75 75 75 75 75
Length Width height Height/width Height/length Width/length Rz Rx Ry Rxv Ryv Qx Qy Rv Q
24.16 23.56 24.14 1.025 1.000 0.975 10.87 11.86 11.74 12.98 12.72 + 0.199 + 0.174 12.90 0.193
–0.297 –0.138 –0.099 + 0.0018 + 0.0076 + 0.0059 –0.19 –0.04 –0.07 + 0.12 + 0.06 + 0.030 + 0.024 + 0.08 + 0.025
0.44 0.11 0.06 0.01 0.24 0.17 0.37 0.05 0.12 0.07 0.02 0.22 0.19 0.05 0.18
< 0.001 0.01 0.06 0.46 < 0.001 0.001
