February 2015
Volume 56, Issue 2
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Multidisciplinary Ophthalmic Imaging  |   February 2015
Automated Retinal Topographic Maps Measured With Magnetic Resonance Imaging
Author Affiliations & Notes
  • Jan-Willem M. Beenakker
    Department of Ophthalmology, Leiden University Medical Center, Leiden, The Netherlands
    Department of Radiology, C.J. Gorter Center for High-Field MRI, Leiden University Medical Center, Leiden, The Netherlands
  • Denis P. Shamonin
    Department of Radiology, Division of Image Processing, Leiden University Medical Center, Leiden, The Netherlands
  • Andrew G. Webb
    Department of Radiology, C.J. Gorter Center for High-Field MRI, Leiden University Medical Center, Leiden, The Netherlands
  • Gregorius P. M. Luyten
    Department of Ophthalmology, Leiden University Medical Center, Leiden, The Netherlands
  • Berend C. Stoel
    Department of Radiology, Division of Image Processing, Leiden University Medical Center, Leiden, The Netherlands
  • Correspondence: Jan-Willem M. Beenakker, Leiden University Medical Center, Department of Ophthalmology, PO BOX 9600, 2300RC Leiden, The Netherlands; j.w.m.beenakker@lumc.nl
Investigative Ophthalmology & Visual Science February 2015, Vol.56, 1033-1039. doi:10.1167/iovs.14-15161
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      Jan-Willem M. Beenakker, Denis P. Shamonin, Andrew G. Webb, Gregorius P. M. Luyten, Berend C. Stoel; Automated Retinal Topographic Maps Measured With Magnetic Resonance Imaging. Invest. Ophthalmol. Vis. Sci. 2015;56(2):1033-1039. doi: 10.1167/iovs.14-15161.

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      © ARVO (1962-2015); The Authors (2016-present)

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Abstract

Purpose.: Recent studies on ocular shape have raised increased interest in the peripheral characteristics of the eye, as it potentially triggers changes in the central vision. Current techniques are, however, not capable of accurately measuring the three-dimensional shape of the retina. We describe a new magnetic resonance imaging (MRI)-based method to obtain the retinal shape with high precision and use it to assess if differences in retinal shape could explain previously described trends in peripheral refraction.

Methods.: Twenty-one healthy subjects were examined using high-field ocular MRI. The resulting data were automatically segmented and processed to calculate the retinal topographic map. We validated the method against partial coherence interferometry and assessed the reproducibility for four subjects.

Results.: The retinal topographic maps describe the retinal shape with subpixel reproducibility (SD between sessions = 0.11 mm). Comparison with partial coherence interferometry showed a mean difference of 0.08 mm, 95% confidence interval −0.39 to 0.55 mm, with a standard deviation of 0.23 mm. The data give a possible geometric explanation for the previously described trend in myopic eyes toward relatively hyperopic refraction in the periphery, with full three-dimensional information. The retinal maps furthermore show small, submillimeter, irregularities that could have an important influence on the subjects' peripheral vision.

Conclusions.: The possibility to quantitatively characterize the full three-dimensional retinal shape by MRI offers new ophthalmologic possibilities, such as quantitative geometric description of staphyloma. It could in addition be used as a validation technique, independent of standard optical methods, to measure the peripheral retinal shape.

Introduction
While the axial length is the center of attention when one is determining the lens strength in planned cataract surgery, over the last decade we have seen an increased interest in the determinants of peripheral vision. In 1971, Hoogerheide et al.1 examined a group of trainee pilots at different time points and concluded that a relative hypermetropic peripheral refraction may lead to an increased probability of developing myopia. Although the validity of the study by Hoogerheide et al. is being debated,2 it inspired many subsequent studies that have described the peripheral refraction in various populations and suggest a link between the shape of the retina, peripheral refraction, and myopia.310 In addition, recent studies have shown a deterioration of peripheral vision in pseudophakic eyes compared to phakic eyes.11,12 Eyes implanted with an intraocular lens, for example, present an increased myopic refraction of 2 diopters (D) at an off-axis angle of 45°. However, measuring peripheral refraction to prescribe proper refractive corrections is not an easy task. 
In order to understand differences between people and changes in peripheral refraction over time, it would be very helpful to be able to properly measure the three-dimensional (3D) shape of the complete retina. Current ocular biometry methods, such as partial coherence interferometry (PCI), result in accurate geometrical measurements along the optical axis, but are less suitable for measuring the peripheral retina. For on-axis measurements, light crosses the interfaces at a perpendicular angle and therefore does not refract. For peripheral optical measurements, however, the light crosses the optical interfaces at an angle, causing it to refract as described by Snell's law, which leads to significant systematic errors.13 
Magnetic resonance imaging (MRI) is a clinical imaging technique that can potentially measure the 3D shape of the eye noninvasively. Magnetic resonance imaging does not depend on refraction of electromagnetic energy to form the images, and its accuracy does not decrease when looking at the periphery. For this reason, MRI has been used by a number of different groups to study 3D ocular geometry.1419 Ocular MRI is, however, very susceptible to eye motion, which has severely limited its clinical application. The increased signal intensity and spatial resolution of high-field MRI may provide new options.20,21 We hypothesized that combining high-field MRI measurements using a custom-designed eye coil with a newly developed eye-blinking protocol would allow more precise imaging of the eye. This should allow us to image the complete eye with high precision. To facilitate the clinical use of this technique, software was developed that automatically reconstructs a retinal topographic map from the MRI data. We validated the complete MRI-obtained retinal image with central ocular biometry and determined its reproducibility. 
Methods
The study protocol was in accordance with the Declaration of Helsinki and was approved by the medical ethical committee of the Leiden University Medical Center. Informed consent was asked for and obtained from all participants. 
Twenty-one volunteers without ocular pathology underwent a 7 Tesla ocular MRI scan of the left eye, followed by an ophthalmologic evaluation. This evaluation consisted of an autorefraction measurement (Park 1; Oculus, Inc., Arlington, WA, USA) and ocular biometry (Lenstar LS 900; Haag-Streit AG, Koeniz, Switzerland; average of two scans). A summary of the results is shown in the Table
Table.
 
Study Population: Summary of the 21 Studied Subjects Without Ocular Pathology
Table.
 
Study Population: Summary of the 21 Studied Subjects Without Ocular Pathology
21 Left Eyes of Healthy Volunteers (5 Male, 16 Female)
Characteristics Mean Range
Age, y 26.3 19.4 to 61.0
Refraction sphere, diopters −1.2 −6.5 to +0.5
 Cylinder, diopters 0.6 −2.0 to +0.3
Best-corrected visual acuity, logMAR −0.1 −0.2 to +0.1
Axial length, mm 23.7 22.4 to 26.4
Magnetic Resonance Imaging
Magnetic resonance imaging experiments were performed on a Philips (Best, The Netherlands) Achieva 7 Tesla whole-body magnet.21 A custom-made dedicated three-channel receive eye coil was used in combination with a volume transmit coil (Nova Medical, Inc., Wilmington, MA, USA). The interface between air and tissue caused an abrupt change in magnetic susceptibility, which locally disturbed the magnetic resonance (MR) image. The imaged eye was therefore kept closed by a small piece of tape, while a piece of wetted gauze was placed on the eyelid that effectively moved the susceptibility artifacts away from the cornea to the outside of the gauze.22 A Maltese cross was presented via an MRI-compatible projector as a fixation target, which the other eye could see via a mirror integrated into the coil housing. Eye-motion artifacts were minimized by the use of a cued-blinking protocol consisting of a regular break every 3 seconds, in which the subject was visually instructed to blink and the scanner automatically paused.23 Magnetic resonance images were acquired using a 3D inversion recovery turbo gradient echo technique with an inversion time of 1280 ms, a shot interval of 3000 ms, and a turbo field echo factor of 92; the TR/TE/flip angle are 2.5 ms/4.55 ms/16°. Saturation slabs were placed around the imaging field of view to reduce the effects of aliasing in the phase encoding directions. The scan time was slightly less than 3 minutes and resulted in a spatial resolution of 0.5 × 0.5 × 1.0 mm3 and a field of view of 40 × 46 × 38 mm3. The total MRI examination took less than 15 minutes. 
Image Processing
Retinal topographic maps were constructed semiautomatically from the transverse MR images by in-house–developed software, based on the rapid-prototyping platform MevisLab (Version 2.5.1; Fraunhofer MeVis, Bremen, Germany). The analysis consisted of three steps (see Fig. 1): segmentation of the lens and vitreous body, definition of the central axis, and measurement of distances from the center of the lens and different locations on the retina. 
Figure 1
 
Schematic overview of the image analysis method. (A) Detection of the lens, based on an automatic seed point (green dot) and surface subdivision (red contours). The red arrows indicate the scan lines along which contour attraction points are allowed to move, and the yellow arrowheads indicate the detected attraction points and the direction of the attraction forces for automatically optimizing the contour. (B) Detection of the vitreous body by prefiltering, thresholding, and surface subdivision. (C) Definition of the central axis by connecting the centers of gravity of the lens and vitreous body, indicated by the white arrow. (D) Mapping the topographic information by measuring the distance between the lens and the retina (upper image) and displaying them on a projection (lower image). The crosshair in the topographic map (lower image) corresponds to the distance vector displayed in MRI data (upper image). The small black circle in the topographic map indicates the location of the blind spot, which was manually identified in the original MR images.
Figure 1
 
Schematic overview of the image analysis method. (A) Detection of the lens, based on an automatic seed point (green dot) and surface subdivision (red contours). The red arrows indicate the scan lines along which contour attraction points are allowed to move, and the yellow arrowheads indicate the detected attraction points and the direction of the attraction forces for automatically optimizing the contour. (B) Detection of the vitreous body by prefiltering, thresholding, and surface subdivision. (C) Definition of the central axis by connecting the centers of gravity of the lens and vitreous body, indicated by the white arrow. (D) Mapping the topographic information by measuring the distance between the lens and the retina (upper image) and displaying them on a projection (lower image). The crosshair in the topographic map (lower image) corresponds to the distance vector displayed in MRI data (upper image). The small black circle in the topographic map indicates the location of the blind spot, which was manually identified in the original MR images.
The borders of the lens were detected after a seed point was positioned automatically within the lens, which appeared as a very bright region in the MR image. Subsequently, the border of the lens was detected by expanding the seed point, represented by a mesh, to iteratively fit the borders of the lens with subpixel precision.24 For detecting the borders of the vitreous body (which appeared as a dark region in the MR image), noise was first reduced, while edges were preserved by anisotropic diffusion filtering25 (see Fig. 1B); then low-intensity regions were detected by multithresholding,26 followed by morphologic erosion (using a 3 × 3 × 4 rectangular kernel) and dilation (with a 1 × 1 × 1 kernel). The borders of the vitreous body were estimated first by selecting the largest region through connected component analysis, which gave a binary image. For obtaining the final segmentation, the same procedure was followed as for the lens detection by expanding a vitreous body mesh to match the retinal border. By default, the parameters for the mesh fitting were set at the first maximum in the gradient above a threshold of 4 within a scan line 5 mm from the edge of the initially detected vitreous body. In three cases, however, these settings did not produce satisfactory results, and in these cases the gradient threshold was adjusted manually. 
The central axis, which defined the coordinate system for the topographic map, was defined by the line from the center of the lens to the center of the vitreous body. The vector connecting the two 3D points was then defined as the central axis (Fig. 1C). 
The topographic map was constructed by defining a cone of vectors from the center of the lens toward the retina, oriented around the central axis. The angle of the cone could be adjusted, and typically an angle of 30° was used. A projection plane (matrix) with a resolution of 41 × 41 pixels was defined perpendicularly to the central axis, behind the retina. For each pixel in the projection plane, a ray was defined from the center of the lens toward the pixel concerned. Subsequently, the retina was detected along each ray (Fig. 1D), if the ray was located in the predefined cone, by finding the highest gradient in the image intensities along the ray. Finally, the distance was calculated between the lens center and the retina for each ray and recorded in the projection plane. To obtain a linear scale in angles, the topographic map was corrected goniometrically. For navigation purposes, the optic disc could be indicated manually on the topographic map by aiming a vector toward the optic nerve in the 3D MR image. For verification, the user could select a point on the topographic map, and the corresponding ray was displayed automatically in the original MR images (Fig. 1D). 
Validation
The accuracy of the retinal topographic map was assessed by comparing MR measurements along the central axis to those obtained by ocular biometry (PCI, Lenstar). The axial length obtained by ocular biometry was converted to the retinal distance measure of the MRI data by RD = AL − (CT + ACD + Display FormulaImage not available LT) − RT, with RD the distance between the retina and center of the lens, AL the axial length, CT the corneal thickness, ACD the anterior chamber depth, LT the lens thickness, and RT the retinal thickness (fixed at 200 μm) as obtained by ocular biometry. The reproducibility of the complete retinal topographic mapping procedure was validated by examining four subjects who underwent the MRI protocol twice in separate sessions.  
Results
Magnetic Resonance Imaging
The cued blinking protocol results in high-quality images of the eye without visible motion artifacts (Fig. 2A). The high contrast-to-noise ratio of the inversion recovery MRI sequence yielded a well-defined boundary between the different anatomical structures of the eye. Some volunteers had small air bubbles below their eyelid, which caused small inhomogeneities in the magnetic field. The gradient echo technique used was susceptible to these inhomogeneities, which resulted in local image distortions of the anterior segment (Fig. 2B). 
Figure 2
 
Original MRI images and algorithm-derived shape of lens and vitreous body. (A) Transverse motion-suppressed MR image showing the different anatomical features of the eye. AC, anterior chamber; C, cornea; EL, eyelid; CB, ciliary body; I, iris; VB, vitreous body; R, retina and sclera; ON, optic nerve; M, ocular muscle. (B) A sagittal image shows the image distortion (arrow) caused by a small air bubble below the eyelid. (C) The algorithm accurately registers the three-dimensional shape of the lens (green) and vitreous body (blue) in the original MRI image (A).
Figure 2
 
Original MRI images and algorithm-derived shape of lens and vitreous body. (A) Transverse motion-suppressed MR image showing the different anatomical features of the eye. AC, anterior chamber; C, cornea; EL, eyelid; CB, ciliary body; I, iris; VB, vitreous body; R, retina and sclera; ON, optic nerve; M, ocular muscle. (B) A sagittal image shows the image distortion (arrow) caused by a small air bubble below the eyelid. (C) The algorithm accurately registers the three-dimensional shape of the lens (green) and vitreous body (blue) in the original MRI image (A).
Image Segmentation
The automatic segmentation successfully detected the lens and vitreous body in 18 of the 21 subjects, as illustrated in Figure 2C. In three subjects, small motion artefacts caused a slight local signal intensity increase in the vitreous body. The segmentation algorithm that was being used incorrectly detected this artefact as the boundary between the vitreous body and the retina. Although these artefacts were outside the region shown in the retinal maps, they influenced the calculation of the center of gravity of the vitreous body. This caused an inaccurate definition of the central axis, leading to a shift in the retinal map. When the gradient threshold was reduced for these three subjects, an accurate segmentation and retinal map were obtained. 
Retinal Topographic Map
As we were interested in imaging the shape and size of the midperiphery, we showed the calculated retinal shape from the central axis to 30° off-axis. Figure 3 shows these maps for three healthy volunteers with a different refraction. 
Figure 3
 
Retinal topographic maps of three subjects with different axial lengths. (A) 26-year-old female with refraction of +0.25 D/−0.25 D. (B) 20-year-old female with a refraction of −1.75 D/−1.50 D. (C) 21-year-old male with a refraction of −5.0 D/−0.25 D. As a reference, the location of the optic nerve is depicted with an x. These maps, using the same color scale, show the distance from the center of the lens to the retina from −30° to +30° in both the horizontal and vertical directions. (D, E) When an optimized color scale is used for the subjects in (A) and (B), small local irregularities in the retinal shape are visible. (F) The retinal profiles on the horizontal meridian (subject in [A], blue; subject in [B], green; subject in [C], red) show a decrease in relative peripheral lengths for longer axial lengths.
Figure 3
 
Retinal topographic maps of three subjects with different axial lengths. (A) 26-year-old female with refraction of +0.25 D/−0.25 D. (B) 20-year-old female with a refraction of −1.75 D/−1.50 D. (C) 21-year-old male with a refraction of −5.0 D/−0.25 D. As a reference, the location of the optic nerve is depicted with an x. These maps, using the same color scale, show the distance from the center of the lens to the retina from −30° to +30° in both the horizontal and vertical directions. (D, E) When an optimized color scale is used for the subjects in (A) and (B), small local irregularities in the retinal shape are visible. (F) The retinal profiles on the horizontal meridian (subject in [A], blue; subject in [B], green; subject in [C], red) show a decrease in relative peripheral lengths for longer axial lengths.
Validation
We compared the PCI measurements and the MRI-based topographic maps as shown in Figure 4, using a Bland-Altman plot of the differences in lens–retina distance as a function of the mean measurement. The mean difference was 0.08 mm, 95% confidence interval −0.39 to 0.55 mm, with a standard deviation of 0.23 mm. A significant correlation was found between the difference and mean measurement (Spearman R2 = 0.29, P = 0.01), with larger distances tending to be underestimated by MRI compared to PCI. 
Figure 4
 
Bland-Altman plot, showing the difference in central lens–retina distance, defined as the MRI measure minus the PCI (Lenstar) measure, as a function of the mean measurements. The mean difference was 0.08 mm; the 95% limits of agreement are −0.39 to 0.55 mm. The correlation between the difference and mean measurement gave a Spearman R2 = 0.29, P = 0.01.
Figure 4
 
Bland-Altman plot, showing the difference in central lens–retina distance, defined as the MRI measure minus the PCI (Lenstar) measure, as a function of the mean measurements. The mean difference was 0.08 mm; the 95% limits of agreement are −0.39 to 0.55 mm. The correlation between the difference and mean measurement gave a Spearman R2 = 0.29, P = 0.01.
The reproducibility of the basement was determined by examining four subjects who underwent the protocol twice in two different sessions. Figure 5 shows the resulting retinal maps for both sessions. The difference between the two measurements, in the lower row, shows subpixel reproducibility of the reconstructed retinal maps for all subjects. These difference maps demonstrate a standard deviation of 0.11 mm between the two sessions, which is poorer than the reported reproducibility of PCI (SD 0.02 mm)27 but is more than sufficient to accurately describe the retinal shape. 
Figure 5
 
Retinal topographic maps of four volunteers used to test the reproducibility of the MRI method. Upper 2 rows: retinal topographic maps of the four subjects showing the reproducibility of the method. The black arrows mark some of the subpixel differences between the sessions for one of the volunteers. Bottom row: The difference between the two sessions remain below the size of one pixel (mean difference −0.001 mm; SD 0.11 mm). The MR images of the second session of subject 4 show two small irregularities on the retinal surface, seen in Supplementary Figure S1, that result in an erroneous determination of the boundary (black arrow).
Figure 5
 
Retinal topographic maps of four volunteers used to test the reproducibility of the MRI method. Upper 2 rows: retinal topographic maps of the four subjects showing the reproducibility of the method. The black arrows mark some of the subpixel differences between the sessions for one of the volunteers. Bottom row: The difference between the two sessions remain below the size of one pixel (mean difference −0.001 mm; SD 0.11 mm). The MR images of the second session of subject 4 show two small irregularities on the retinal surface, seen in Supplementary Figure S1, that result in an erroneous determination of the boundary (black arrow).
Discussion
The development of high-resolution MRI imaging should allow better imaging of the whole eye. Until recently, MRI scans of the eyes had high in-plane resolution, but the sensitivity of MRI to eye movement prevented sufficient resolution in the out-of-plane direction for a full 3D evaluation of the eye.19,28 Using a custom-made eye coil and an in-house–developed blinking control protocol, however, 3D images could be obtained. We were able to create retinal topographic maps, reconstructed from the high-resolution 3D MRI data, that accurately quantify the shape of the peripheral retina. This new technique opens up new clinical possibilities such as quantification of staphyloma and study of the impact of the retinal shape on the peripheral refraction. 
As we have studied several myopic eyes, we looked at the individual images. The retinal topographic maps of the three subjects of Figure 3 show how the distance between the lens and the retina decreases toward the periphery, a trend that was more pronounced for longer axial lengths (Fig. 3F). A group analysis of the individual horizontal retinal profiles confirms this trend and shows a decrease of more than 1.5 mm in retinal distance at 30° off-axis for the more myopic eyes (Fig. 6). This could explain the previously described trend in the periphery for the refraction of myopic eyes to be relatively more hyperopic compared to their foveal refraction.6,15,29 
Figure 6
 
Normalized horizontal retinal profiles for the all subjects. The central retinal distance for each subject is shown by the color of the curve. For all eyes, the retinal distance decreases toward the periphery, a trend that is more pronounced for the longer eyes.
Figure 6
 
Normalized horizontal retinal profiles for the all subjects. The central retinal distance for each subject is shown by the color of the curve. For all eyes, the retinal distance decreases toward the periphery, a trend that is more pronounced for the longer eyes.
We subsequently determined whether the MRI-derived values corresponded to the PCI-derived central measurements: A comparison of the retinal distance as measured by PCI and by MRI shows good agreement between the two methods over the entire range of values, with a mean difference of SD = 0.23 mm, which is lower than the resolution of the MR image (pixel size 0.5 mm). The small discrepancy is mainly the result of two assumptions in the image-processing algorithm. Firstly, the precise location of the boundary between the retina and vitreous body is currently defined as the location of the maximum pixel-to-pixel increase in signal intensity. The image spatial resolution limits this to 0.5 mm. In the future, additional modeling of ocular MRI data could potentially allow a more specific definition of the boundary between the retina and the vitreous body, which would enable a further increase in the precision of the retinal shape. 
The second assumption involves the definition of the central axis. The visual axis is defined as the line between the fixation point and the fovea. It is, however, generally known that not all the optical elements of the eye are centered on the same axis.3033 The pupil center is, for example, not centered on the visual axis, resulting in the definition of the pupillary axis as the line though the center of the pupil perpendicularly to the cornea. The difference between the visual axis and the pupillary axis is quantified by the angle kappa and is on the order of 5°.34,35 The current MRI methods do not provide a high enough spatial resolution either to detect the foveal pit, needed to define the visual axis, or to measure the center of the pupil and the perpendicular intersection with the cornea, needed to reconstruct the pupillary axis. Therefore a different axis is defined, which can be geometrically reconstructed from the MR images. This central axis definition assumes that all elements of the eye are symmetric around the pupillary axis. In this case a line through the centers of gravity of two parts of the eye would define the pupillary axis. Our data already show that this is a robust way to define a central axis, but they also show that the assumption of symmetry around the central axis is not completely valid. The retinal topographic maps are, for example, not symmetric around the center. This observation is quantified by fitting a paraboloid through the retinal map. Figure 7 shows how such a fit would determine the center of the curved retina. These fits show a systematic difference, of on average 2°, between the central axis and the apex of the retina. Furthermore, the retinal shape of a subset of subjects appears to be asymmetric around the center, as has also been observed by others.4,36 
Figure 7
 
Automated quantification of the retinal shape. By fitting an elliptic paraboloid (z = Aθ(θθ0)2 + (φφ0)2 + L with θ and φ the horizontal and vertical angles, A a fitting constant and L the retinal distance), the apex and curvature of the retina can be quantified. The figure shows the result of this fit for the subjects of Figure 3. The blue dot shows the resulting apex of the retina (θ0,φ0), while the white lines show the isocontours of the resulting surface. This analysis furthermore quantifies radius of the retina in different directions (the inverse of Aθ and Aφ), which is directly related to the vertex curvature (which is not always equal in the horizontal and vertical meridians [e.g., left two fits]). This could relate to the earlier described differences in peripheral refraction between the horizontal and vertical meridian.4,36
Figure 7
 
Automated quantification of the retinal shape. By fitting an elliptic paraboloid (z = Aθ(θθ0)2 + (φφ0)2 + L with θ and φ the horizontal and vertical angles, A a fitting constant and L the retinal distance), the apex and curvature of the retina can be quantified. The figure shows the result of this fit for the subjects of Figure 3. The blue dot shows the resulting apex of the retina (θ0,φ0), while the white lines show the isocontours of the resulting surface. This analysis furthermore quantifies radius of the retina in different directions (the inverse of Aθ and Aφ), which is directly related to the vertex curvature (which is not always equal in the horizontal and vertical meridians [e.g., left two fits]). This could relate to the earlier described differences in peripheral refraction between the horizontal and vertical meridian.4,36
Other geometrical definitions, using, for example, the apex of the cornea and the center of the pupil, could possibly result in a better-defined axis that corresponds more accurately to the physiology of the eye. The increased spatial resolution images of the anterior segment, needed for such an axis definition, could be measured with MRI by making a separate scan of only the anterior segment of the eye with an increased resolution. Another, more promising possibility would be to combine the MR images with other anterior segment imaging modalities such as optical coherence tomography or Scheimpflug imaging. Such an improved axis definition will, however, have a minor effect on the measured axial length, since the retinal distance is relatively constant near the fovea. It will furthermore not influence the overall shape of the segmented retina but result in only a slight shift, which is clinically considered not relevant. 
Another potential source of the discrepancy between MRI and PCI could be the fact that PCI measures an optical path length. This is internally converted to an actual distance using an averaged refractive index that is, however, assumed to be same for the complete eye. 
The Bland-Altman plot shows that MRI-derived retinal topographic maps tend to underestimate the central axial length for subjects with longer eyes. A small error in the central axis definition will result in an underestimation of the central retinal distance. The size of this underestimation is directly related to the concavity of the retina, which is increased for subjects with longer eyes,6,15,29 explaining the observed trend. 
The possibility to quantitatively characterize 3D retinal shape by MRI offers new ophthalmologic possibilities. Current studies on myopia, for example, are keenly interested in the question of how refractive errors affect the peripheral shape of the retina.3739 Previous studies have already used MRI to quantify the ocular shape as a function of refraction15,18,19; but until now, the MRI methods were limited to either high-resolution two-dimensional images or low-resolution 3D image stacks, neither of which allows for a full 3D description of the ocular shape. The availability of high-resolution 3D data is of further value because of the automatic image processing, which increases the reproducibility of analysis, making it possible to three-dimensionally quantify small changes in ocular shape over time. 
This new MRI-based technique can improve the diagnosis of patients with a staphyloma. The limited field of view of current techniques, such as ultrasound, does not offer the clinician the possibility to assess the complete protrusion with respect to the rest of the retina. A retinal topographic map, however, will allow for quantitative determination of the size and location of the complete staphyloma. For these patients, these data would be a valuable addition to a visual field measurement, as they could confirm the link between the local loss of visual acuity and the retinal shape. 
Acknowledgments
The authors thank Noor Hoes and Martine Lamme for assistance with the ophthalmologic evaluation of the subjects. 
Supported in part by Agentschap NL (an agency of the Dutch Ministry of Economic Affairs) as part of the European Research Coordinating Agency/Natural Peripheral Vision (EUREKA/NPV) project. 
Disclosure: J.-W.M. Beenakker, None; D.P. Shamonin, None; A.G. Webb, None; G.P.M. Luyten, None; B.C. Stoel, None 
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Figure 1
 
Schematic overview of the image analysis method. (A) Detection of the lens, based on an automatic seed point (green dot) and surface subdivision (red contours). The red arrows indicate the scan lines along which contour attraction points are allowed to move, and the yellow arrowheads indicate the detected attraction points and the direction of the attraction forces for automatically optimizing the contour. (B) Detection of the vitreous body by prefiltering, thresholding, and surface subdivision. (C) Definition of the central axis by connecting the centers of gravity of the lens and vitreous body, indicated by the white arrow. (D) Mapping the topographic information by measuring the distance between the lens and the retina (upper image) and displaying them on a projection (lower image). The crosshair in the topographic map (lower image) corresponds to the distance vector displayed in MRI data (upper image). The small black circle in the topographic map indicates the location of the blind spot, which was manually identified in the original MR images.
Figure 1
 
Schematic overview of the image analysis method. (A) Detection of the lens, based on an automatic seed point (green dot) and surface subdivision (red contours). The red arrows indicate the scan lines along which contour attraction points are allowed to move, and the yellow arrowheads indicate the detected attraction points and the direction of the attraction forces for automatically optimizing the contour. (B) Detection of the vitreous body by prefiltering, thresholding, and surface subdivision. (C) Definition of the central axis by connecting the centers of gravity of the lens and vitreous body, indicated by the white arrow. (D) Mapping the topographic information by measuring the distance between the lens and the retina (upper image) and displaying them on a projection (lower image). The crosshair in the topographic map (lower image) corresponds to the distance vector displayed in MRI data (upper image). The small black circle in the topographic map indicates the location of the blind spot, which was manually identified in the original MR images.
Figure 2
 
Original MRI images and algorithm-derived shape of lens and vitreous body. (A) Transverse motion-suppressed MR image showing the different anatomical features of the eye. AC, anterior chamber; C, cornea; EL, eyelid; CB, ciliary body; I, iris; VB, vitreous body; R, retina and sclera; ON, optic nerve; M, ocular muscle. (B) A sagittal image shows the image distortion (arrow) caused by a small air bubble below the eyelid. (C) The algorithm accurately registers the three-dimensional shape of the lens (green) and vitreous body (blue) in the original MRI image (A).
Figure 2
 
Original MRI images and algorithm-derived shape of lens and vitreous body. (A) Transverse motion-suppressed MR image showing the different anatomical features of the eye. AC, anterior chamber; C, cornea; EL, eyelid; CB, ciliary body; I, iris; VB, vitreous body; R, retina and sclera; ON, optic nerve; M, ocular muscle. (B) A sagittal image shows the image distortion (arrow) caused by a small air bubble below the eyelid. (C) The algorithm accurately registers the three-dimensional shape of the lens (green) and vitreous body (blue) in the original MRI image (A).
Figure 3
 
Retinal topographic maps of three subjects with different axial lengths. (A) 26-year-old female with refraction of +0.25 D/−0.25 D. (B) 20-year-old female with a refraction of −1.75 D/−1.50 D. (C) 21-year-old male with a refraction of −5.0 D/−0.25 D. As a reference, the location of the optic nerve is depicted with an x. These maps, using the same color scale, show the distance from the center of the lens to the retina from −30° to +30° in both the horizontal and vertical directions. (D, E) When an optimized color scale is used for the subjects in (A) and (B), small local irregularities in the retinal shape are visible. (F) The retinal profiles on the horizontal meridian (subject in [A], blue; subject in [B], green; subject in [C], red) show a decrease in relative peripheral lengths for longer axial lengths.
Figure 3
 
Retinal topographic maps of three subjects with different axial lengths. (A) 26-year-old female with refraction of +0.25 D/−0.25 D. (B) 20-year-old female with a refraction of −1.75 D/−1.50 D. (C) 21-year-old male with a refraction of −5.0 D/−0.25 D. As a reference, the location of the optic nerve is depicted with an x. These maps, using the same color scale, show the distance from the center of the lens to the retina from −30° to +30° in both the horizontal and vertical directions. (D, E) When an optimized color scale is used for the subjects in (A) and (B), small local irregularities in the retinal shape are visible. (F) The retinal profiles on the horizontal meridian (subject in [A], blue; subject in [B], green; subject in [C], red) show a decrease in relative peripheral lengths for longer axial lengths.
Figure 4
 
Bland-Altman plot, showing the difference in central lens–retina distance, defined as the MRI measure minus the PCI (Lenstar) measure, as a function of the mean measurements. The mean difference was 0.08 mm; the 95% limits of agreement are −0.39 to 0.55 mm. The correlation between the difference and mean measurement gave a Spearman R2 = 0.29, P = 0.01.
Figure 4
 
Bland-Altman plot, showing the difference in central lens–retina distance, defined as the MRI measure minus the PCI (Lenstar) measure, as a function of the mean measurements. The mean difference was 0.08 mm; the 95% limits of agreement are −0.39 to 0.55 mm. The correlation between the difference and mean measurement gave a Spearman R2 = 0.29, P = 0.01.
Figure 5
 
Retinal topographic maps of four volunteers used to test the reproducibility of the MRI method. Upper 2 rows: retinal topographic maps of the four subjects showing the reproducibility of the method. The black arrows mark some of the subpixel differences between the sessions for one of the volunteers. Bottom row: The difference between the two sessions remain below the size of one pixel (mean difference −0.001 mm; SD 0.11 mm). The MR images of the second session of subject 4 show two small irregularities on the retinal surface, seen in Supplementary Figure S1, that result in an erroneous determination of the boundary (black arrow).
Figure 5
 
Retinal topographic maps of four volunteers used to test the reproducibility of the MRI method. Upper 2 rows: retinal topographic maps of the four subjects showing the reproducibility of the method. The black arrows mark some of the subpixel differences between the sessions for one of the volunteers. Bottom row: The difference between the two sessions remain below the size of one pixel (mean difference −0.001 mm; SD 0.11 mm). The MR images of the second session of subject 4 show two small irregularities on the retinal surface, seen in Supplementary Figure S1, that result in an erroneous determination of the boundary (black arrow).
Figure 6
 
Normalized horizontal retinal profiles for the all subjects. The central retinal distance for each subject is shown by the color of the curve. For all eyes, the retinal distance decreases toward the periphery, a trend that is more pronounced for the longer eyes.
Figure 6
 
Normalized horizontal retinal profiles for the all subjects. The central retinal distance for each subject is shown by the color of the curve. For all eyes, the retinal distance decreases toward the periphery, a trend that is more pronounced for the longer eyes.
Figure 7
 
Automated quantification of the retinal shape. By fitting an elliptic paraboloid (z = Aθ(θθ0)2 + (φφ0)2 + L with θ and φ the horizontal and vertical angles, A a fitting constant and L the retinal distance), the apex and curvature of the retina can be quantified. The figure shows the result of this fit for the subjects of Figure 3. The blue dot shows the resulting apex of the retina (θ0,φ0), while the white lines show the isocontours of the resulting surface. This analysis furthermore quantifies radius of the retina in different directions (the inverse of Aθ and Aφ), which is directly related to the vertex curvature (which is not always equal in the horizontal and vertical meridians [e.g., left two fits]). This could relate to the earlier described differences in peripheral refraction between the horizontal and vertical meridian.4,36
Figure 7
 
Automated quantification of the retinal shape. By fitting an elliptic paraboloid (z = Aθ(θθ0)2 + (φφ0)2 + L with θ and φ the horizontal and vertical angles, A a fitting constant and L the retinal distance), the apex and curvature of the retina can be quantified. The figure shows the result of this fit for the subjects of Figure 3. The blue dot shows the resulting apex of the retina (θ0,φ0), while the white lines show the isocontours of the resulting surface. This analysis furthermore quantifies radius of the retina in different directions (the inverse of Aθ and Aφ), which is directly related to the vertex curvature (which is not always equal in the horizontal and vertical meridians [e.g., left two fits]). This could relate to the earlier described differences in peripheral refraction between the horizontal and vertical meridian.4,36
Table.
 
Study Population: Summary of the 21 Studied Subjects Without Ocular Pathology
Table.
 
Study Population: Summary of the 21 Studied Subjects Without Ocular Pathology
21 Left Eyes of Healthy Volunteers (5 Male, 16 Female)
Characteristics Mean Range
Age, y 26.3 19.4 to 61.0
Refraction sphere, diopters −1.2 −6.5 to +0.5
 Cylinder, diopters 0.6 −2.0 to +0.3
Best-corrected visual acuity, logMAR −0.1 −0.2 to +0.1
Axial length, mm 23.7 22.4 to 26.4
Supplementary Figure S1
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