Reconstructing foveal pit morphology from optical coherence tomography imaging
- 1Department of Cell Biology, Neurobiology, & Anatomy, Medical College of Wisconsin, Milwaukee, Wisconsin, USA
- 2Department of Ophthalmology, Medical College of Wisconsin, Milwaukee, Wisconsin, USA
- 3Department of Biophysics, Medical College of Wisconsin, Milwaukee, Wisconsin, USA
- Correspondence to Dr J Carroll, Medical College of Wisconsin, The Eye Institute, 925 N. 87th Street, Milwaukee, WI 53226, USA;
- Accepted 3 April 2009
- Published Online First 26 May 2009
Aim: The aim of this study was to describe an automated method for extracting quantitative measures of foveal morphology from optical coherence tomography (OCT) images of the human retina.
Methods: We performed a methodological study and retrospective investigation of selected cases. Sixty-five human subjects were included: 61 healthy subjects and four female carriers of blue-cone monochromacy (BCM). Thickness data from B-scans traversing the foveal pit were fitted to a mathematical model designed to capture the contour of the foveal surface. From this model, various metrics of foveal morphology were extracted (pit depth, diameter and slope).
Results: Mathematical descriptions of foveal morphology enabled quantitative and objective evaluation of foveal dimensions from archived OCT data sets. We found a large variation in all aspects of the foveal pit (depth, diameter and slope). In myopes and BCM carriers, foveal pits were slightly less deep and had a more shallow slope, although these differences were not significant.
Conclusions: Offline analysis of OCT data sets enables quantitative assessment of foveal morphology. The algorithm works on the Stratus™ and Cirrus™ macular thickness protocols, as well as the Spectralis® and Bioptigen© radial-line scan protocols, and can be objectively applied to existing data sets. These metrics will be useful in following changes associated with diseases such as retinopathy of prematurity and high myopia, as well as in studying normal postnatal development of the human fovea.
The fovea is characterised by an avascular zone, a marked increase in cone packing and an excavation of inner retinal neurons.1 While the site of the human fovea can be identified as early as 22 weeks gestation,2 foveal development is not complete until 4 to 7 years after birth.3 The fovea occupies a rather small retinal area. However, some 25% of retinal ganglion cells sample the foveal cone mosaic.4 Given the importance of central vision, characterising foveal structure in normal and diseased retina is of great interest. Previous work has revealed considerable variation in foveal characteristics of the normal retina, such as avascular zone diameter,5 peak cone density6 and rod-free zone diameter.3 The most prominent feature of the fovea is the pit itself, although little attention has been paid to describing the contour of the foveal surface. Williams (1980) used psychophysical techniques to derive an estimate of the foveal slope in four individuals, and found that the foveal slope was 43° at 150 μm eccentricity.7 Hammer et al (2008) used optical coherence tomography (OCT) to subjectively measure foveal pit depth in normal subjects and individuals with retinopathy of prematurity, and reported some variability in pit depth, although there were only five normal subjects.8 Quantitative and objective measurements of pit morphology from a large population of normal retinas would enhance our ability to use these metrics to study foveal morphology in various retinal disorders; normative data in this regard could be used to constrain models of foveal development.9 10 11
OCT provides exquisite views of foveal architecture in the living retina. Clinical OCT devices provide a variety of real-time information to the user regarding the macular region. However, there is no automated and quantitative description of foveal pit morphology currently available. We imaged 130 eyes and developed an automated algorithm to extract morphological characteristics of the foveal pit (slope, depth and diameter) from standard OCT scan data sets, both time-domain and spectral-domain.
Materials and methods
Thirty-nine emmetropic, 22 myopic and four female carriers of blue-cone monochromacy (BCM) were recruited for this study. The myopic group consisted of individuals with a refractive error of greater than –3 D. None of the eyes showed any gross signs of ocular disease, and both eyes were imaged in each individual. Subjects ranged in age from 13 to 52 years, with a mean of 26.3 years.
Sixty-four subjects were imaged using a Zeiss Stratus™ OCT3, and 21 of these subjects and one of the BCM carriers were imaged with a Zeiss Cirrus™ HD-OCT (Carl Zeiss Meditec, Dublin, California, USA). One subject was also imaged with the Bioptigen SD-OCT (Bioptigen, Durham, North Carolina, USA) and the Spectralis HRA+OCT (Heidelberg Engineering, Vista, California, USA). The fast macular thickness retinal volumetric (“fast mac”) scan was used on the Stratus. The nominal lateral scan length was 6 mm,i the standard setting for the fast mac protocol. Each fast mac scan set consists of six B-scans (at 128 A-scans/B-scan), taken at 30° intervals. Retinal thickness files (.rth) for each fast mac data set were imported into custom MatLab (Mathworks, Natick, Massachusetts, USA) analysis software using the export feature in the Zeiss software. On the Cirrus, we acquired macular volume data sets using the standard 6 mm×6 mm scan set (512 A-scans/B-scan; 128 B-scans). Retinal thickness values, from the inner limiting membrane (ILM) to the retinal pigment epithelium (RPE), were exported into MatLab, and a simulated scan set analogous to the Stratus fast mac scan set was created by extracting six radial lines separated by 30°, thus allowing a direct comparison between modalities. The data were obtained using the Cirrus Research Browser (Carl Zeiss Meditec), an off-instrument review software package. The browser allows export of calculated data that are otherwise displayed graphically or in a table with the standard instrument analysis modules. On the Bioptigen (1000 A-scans/B-scan) and Spectralis (1024 A-scans/B-scan) we also used a radial scan profile, consisting of six radial lines (B-scans) separated by 30°. Images were exported and the ILM and RPE were manually segmented using ImageJ (www.rsb.info.nih.gov/ij/) to compute retinal thickness.
Assessing pit morphology
The contour of the foveal pit is well represented by a Gaussian function.7 However, while this function approximates the shape of the foveal pit, it does not completely capture the rim contour. It is identification of the rim contour that provides access to the automated measure of pit depth and diameter. We tested several functions for their ability to fit foveal pit contour, and found that a difference of Gaussians (DoG) function (equation 1) provides the best fit to the foveal OCT scans. In this model, μ1 and μ2 serve as the means of the respective Gaussian functions, σ is the standard deviation, and x is the x-coordinate location within the scan. It is important to note that although μ1 and μ2 are not mathematically linked, in our model they are required to be equal to enable automated modelling of pit morphology and extraction of foveal pit parameters. Raw data for retinal thickness were fitted to the DoG (equation 1) using least squares analysis.
Figure 1A shows the raw thickness values for the six B-scans from a fast mac scan set for one subject, while fig 1B shows the DoG fits to the individual B-scans. One of the problems with reconstructing foveal volumes from time-domain OCT is eye movement. Even in individuals with superior fixation stability, small saccades occur that can disrupt the ability to automatically model the pit contour. Thus, aligning scans from within the fast mac data set is an important first step in reconstructing foveal morphology. Using the DoG mean (μ1 and μ2 in equation 1), we approximate the lateral shift for each scan, relative to an arbitrary centre. We then shift each scan to align to this common centre, as would be expected in the ideal observer case where there is no fixational eye movements and all scans pass through the foveal centre. This correction only accounts for lateral movement of the eye between scans in the fast mac scan set. Determining the shift of each scan allows implementation of an automated way to reject scan sets with too much eye movement, which would impair our ability to model the pit contour reliably. Thus, if any scan had a shift larger than 0.3 mm, the entire fast mac set was not used. This was an empirically derived threshold, and could be modified depending on the experiment. Figure 1C shows the result of the corrective shift applied to the six B-scans.
Extracting foveal pit parameters
In order to extract the various foveal pit metrics (diameter, depth and slope) automatically, we calculated the first derivative of the DoG fits for each of the six B-scans in each fast mac scan set. Figure 2 shows a typical B-scan from the Stratus fast mac scan set, and the exported thickness values and DoG model fit (middle panel).
To identify anatomical landmarks within the scan, we examine the first derivative F′(x) of the DoG fit (equation 2 and fig 2, bottom panel). There are five key points of interest on this curve: points A and E indicate the peak of the foveal rim, as the slope of the foveal contour is zero at these locations. Likewise, point C has a zero slope, and this marks the centre of the pit. Finally, points B and D identify the points of maximum slope on either side of the foveal centre. From these five landmarks, we can extract three prominent features of the foveal pit—diameter, depth and slope. We define diameter as the distance from rim to rim,1 13 illustrated in fig 2 as the distance between points A and E. The measured values of diameter for each eye are an average of the measured diameter of each of the six B-scans in the fast mac scan set.
The depth of the foveal pit is defined as the difference between retinal thickness at the rim and the pit centre. This is illustrated in fig 2 as the difference between retinal thickness at plane A–E (rim height) and point C. The measured values of depth for each eye are an average of the measured depth for each of the six B-scans in the fast mac scan set. Other investigators have used a manual method to measure foveal pit depth, based on the distance between the temporal rim and the pit floor.11
The slope of the foveal pit is not constant. Here, we define foveal slope as the maximum slope of the foveal contour (points B and D in fig 2). Once the x-coordinate location of the minimum and maximum points were derived from F′(x), the function F′(x) was solved at these x-coordinates. The arc tangent was then taken to produce a slope value in degrees, and the absolute values were averaged. Measured values of slope for each eye are an average of the average slope for each of the six B-scans.
Three-dimensional model reconstruction
Custom Matlab programs were used to create a three-dimensional (3D) rendering of the retinal volume. Using the surf function, the six B-scans from a fast mac data set were combined to produce a 3D map of the fovea. To represent this foveal reconstruction, the shifted raw data sets were fitted to a two-dimensional (2D) DoG function (equation 3). These fits provided a qualitative picture of the fovea, though all foveal metrics were derived from the DoG fits to the individual B-scans, as DoG provides a better overall fit to the data than the 2D DoG. MatLab code for deriving foveal metrics/creating 3D renderings from .txt formatted thickness values is available upon request.
Assessing model fit
The DoG (equation 1) fits the foveal contour extremely well (average root mean square (rms) error per B-scan = 141.22 (SD 23.24) μm; average error per A-scan is about 1 μm). For comparison, average rms error using a single Gaussian is about 300 μm per B-scan. However, some foveae have a slightly higher rim on the nasal side13 due to the location of the papillomacular bundle heading from the fovea to the optic disc (located 4 mm nasal to the fovea1). Since the means of the two Gaussians are constrained to be equal, this difference will not be captured. Observations made in the data showed that the eye movements, defined by the position of the central point of the foveal pit, varied laterally about the mean at most by six A-scans (256 μm), and the average variation was 110 μm (just over two A-scans).
Measured pit characteristics
Measured parameters are given in table 1. We found significant inter-subject variability in all foveal metrics (depth, diameter and slope) in our sample; however, a high degree of individual interocular symmetry was observed (Pearson r = 0.9185, 0.8735, 0.8621 for depth, diameter and slope, respectively; p<0.0001). Previous reports show that while on average there is symmetry in retinal thickness, there is potential for significant asymmetry in normal individuals.14
The average pit depth for the emmetropes was 122 (SD 20.2) μm. Pit depth was not statistically different between emmetropes and myopes (t(59) = 1.502, p = 0.1384; two-tail t test) or between emmetropes and BCM carriers (t(41) = 1.103, p = 0.2763; two-tail t test). The average pit diameter for the emmetropes subjects was 1.97 (SD 0.177) mm. Pit diameter was not statistically different between emmetropes and myopes (t(59) = 0.5751, p = 0.5674; two-tail t test). The BCM carriers had broader pits than the emmetropes, although this was not significant (t(41) = 1.157, p = 0.2538; two-tail t test). Pit slope was not statistically different between myopes and emmetropes (t(59) = 1.478, p = 0.1447; two-tail t test), nor between emmetropes and BCM carriers (t (41) = 1.759, p = 0.0861; two-tail t test). Previous reports in affected BCM men found significant thinning of the fovea,15 although BCM carriers are generally unaffected, except for a possible reduction in cone-driven electroretinogram (ERG) amplitudes.16
Comparison with other OCT devices
Twenty-one subjects were imaged with both Zeiss OCT systems. Previous results have shown that Zeiss Stratus and Cirrus have a difference of 60 μm in total retinal thickness,17 18 as a result of an improvement in the assignment of the RPE layer within the outer hyper-reflective complex. This thickness difference would not be expected to affect our foveal metrics, as the difference in thickness between the two devices should be uniform across the retina and our measurements depend on relative, not absolute, differences in thickness.
In order to compare the data from the two devices, we analysed the simulated fast mac scan sets we created from the Cirrus volumetric scan set. As for the Stratus data, the DoG (equation 1) fits the Cirrus data extremely well (average rms error per B-scan = 141.49 (SD 38.57) μm). In comparing foveal metrics derived from the two systems, we found a significant correlation between measurements obtained using the two systems (table 2). Any systematic difference between the systems could be due to the fact that our correction for lateral shifts between scans does not account for eye movements during a single scan. In either case, the good correlation between metrics derived from the two systems indicates that it is possible to convert metrics derived from either system reliably.
In order to demonstrate that our algorithm can be applied to any OCT data set, we imaged one retina using the Bioptigen and Spectralis SD-OCT systems as well. Figure 3 shows topographical maps of the same retina obtained with four instruments. Foveal metrics were similar (within about 6%); for example, the pit diameters were 1.91, 1.85, 1.96 and 1.94 mm for the Stratus, Cirrus, Bioptigen and Spectralis data sets, respectively.
We developed an offline analytical technique to increase the utility of time-domain OCT. This can be used on existing OCT data sets, and could easily be modified for real-time analysis. One of the advantages of this analytical technique is that it is platform-independent and could be applied to any OCT data set (including SD-OCT), as long as one has access to retinal thickness data (or raw images from which thickness could be calculated or the difference between the ILM/RPE contours plotted). While SD-OCT technology has superior axial resolution and speed compared with time-domain systems,19 both modalities capture foveal morphology equally well.
Time-domain OCT devices have permeated the ophthalmology and vision research communities and there is tremendous interest in the development of post-processing methods to expand the utility of these devices. For example, averaging multiple Stratus line scans from the same retinal location can be used to increase the signal to noise ratio. The resultant image quality is significantly improved, and these images can reveal subtle alterations of intraretinal architecture where individual scans cannot.20 In addition, these high signal to noise time-domain images enable assessment of retinal lamination.21 Bernardes et al (2008) modified existing scan protocols on the Stratus to improve the spatial resolution of retinal thickness maps by reducing the interpolation.22 These studies, together with ours, illustrate how the clinical utility of time-domain devices (Stratus) could be improved through offline image processing. There is no doubt that SD-OCT offers superior image quality and resolution. However, given the abundance of time-domain systems and the significant cost associated with upgrading to SD-OCT, for some clinics the implementation of similar image processing techniques may prove to be a valuable, if not necessary, intermediate step.
We observed remarkable variation in foveal morphology across clinically normal individuals. It is somewhat difficult to make direct comparisons between the values presented here and those from previous studies. One of the main reasons is that we relied on automated data acquisition based on objective definitions of the various morphological features. For example, the diameters presented here represent the upper bound of typical measurements, which are often based on other features of the fovea, such as the avascular zone or rod-free region. A recent study by Hammer et al (2008) defined depth arbitrarily as the distance from base of the pit to the point where the radius is 0.728 μm.8 Making the same measurement on our data we found no difference between the data sets, supporting the idea that any differences between our data and those of others rests solely on the definition of the foveal metrics used. Peak cone density in normal subjects can vary by a factor of three,6 so future work will examine whether this variation is correlated with variation in gross foveal morphology, and how pit morphology compares with other anatomical landmarks, such as the rod-free region or the foveal avascular zone. Finally, normative data such as these should prove useful in quantitatively characterising clinically foveal hypoplasia/fovea plana.23
The authors thank J Rha, and J Kuchenbecker for helpful insights on mathematical modelling, T Connor Jr for valuable discussion, and A Gegios, N Ayub and J Beringer for assistance with imaging.
Funding The authors acknowledge grant support from the National Institutes of Health (EY001931 and EY017607) and from the Posner Foundation, Fight for Sight, The E. Matilda Ziegler Foundation for the Blind, the RD & Linda Peters Foundation, and an unrestricted grant from Research to Prevent Blindness. J C is the recipient of a Career Development Award from Research to Prevent Blindness.
Competing interests None declared.
Provenance and Peer review Not commissioned; externally peer reviewed.
Ethics approval The study followed the tenets of the Declaration of Helsinki and was approved by the Medical College of Wisconsin Institutional Review Board.
Patient consent Obtained.
↵i Scans for each subject were corrected for inter-individual differences in axial length based on Leung et al (2007).12 Axial length in our subjects ranged from 21.44 to 27.5 mm; thus, actual scan lengths ranged from 5.26 to 6.75 mm.