1. Introduction

Non-invasive retinal imaging with Optical Coherence Tomography (OCT) is of increasing interest to vision scientists investigating rodent models of ophthalmic diseases. OCT provides micron scale resolution images of the retinal layers non-invasively, which can be used for visualization and measurement of changes to the thickness of the retinal layers in time course studies. Changes to the thickness of the Outer Nuclear Layer (ONL) in OCT images have been correlated with degeneration of photoreceptor rods and cones in histology [1], and thinning of the combined Nerve Fiber Layer, Ganglion Cell Layer, and Inner Plexiform Layer (NGI) in OCT images have been correlated with optic neuropathic degeneration [2].

To date, the non-invasive measurements of retinal thinning in rodents have largely concentrated only on individual B-scan depth profiles. For correct quantification in longitudinal studies, the B-scans must be topologically fixed with respect to a reference landmark. In the rat, the thickness of the combined NGI layer is radially symmetric relative to the Optic Nerve Head (ONH), gradually decreasing toward the retinal periphery. For this reason, only a limited number of points are generally quantified in a raster scanned OCT volume, and a significant amount of information is acquired but never used because the vast amounts of data collected are too large to be efficiently analyzed manually. Quantitative measurement of a large area of the retinal surface is imperative for developing and validating new treatments for disease. Automated techniques are required to measure the thickness of retinal layers from volumetric FD OCT data and to analyze longitudinal changes.

Significant effort has been invested on the development of computation tools for segmentation of human retinal images [3–9]. Conversely, customization of segmentation algorithms for rodent retina are only just emerging [10–14]. Automated segmentation of rodent retinal layers is complicated by the comparatively lower quality of images relative to human. This is due to the highly curved surfaces of the rat eye which cause significant aberrations [15] and have overall worse imaging performance relative to human eyes.

The purpose of this report is to investigate the quantitative measurement of longitudinal retinal thickness in rat retinal degeneration using a semi-automatic segmentation algorithm, used in combination with a three dimensional thickness measurement adapted from brain cortical measurement [16]. Section 2 summarizes the methods and Section 3 presents the results and discussion. We conclude the paper and discuss future work in Section 4.

2. Methods

Optic nerve axotomy

A complete optic nerve transection microsurgery was performed on the right eye of a rat. Referred to as axotomy, the microsurgery causes an acute injury that induces degeneration over the whole retina, which is well characterized and highly reproducible [2,17]. Following the axotomy, the death of the ganglion cells and nerve fibers results in thickness changes in the corresponding retinal layers. The contralateral eye was maintained as a control in which the retinal layer thickness was anticipated to be constant. The microsurgery was performed under anesthesia using a ketamine, xylazine, and acepromazine mixture (50:5:1 mg/kg body weight) injected intraperitoneally. All animal procedures adhered to the Institutional Animal Care and Use Committee (IACUC) recommendations for use of animals in research.

Optical Coherence Tomography imaging

Volumetric SD OCT imaging of both eyes was performed over 14 days post-axotomy. The OCT system operated at line rate of 20 kHz, and utilized a superluminescent diode (SLD) source with a center wavelength of 826nm and a full width half maximum bandwidth of 72nm. Spectrally resolved detection was performed using a semi-customized spectrometer from Bioptigen (Research Triangle Park, NC, USA), and processing of the interferometric signal to a real time image was performed using custom software developed at Simon Fraser University.

The rat was anesthetised for imaging, and both eyes were imaged in a single session. Imaging was performed on Days 3, 7, 10, and 14 after the axotomy to allow sufficient time between anesthetisations. The OCT sample arm was mounted on a customized slit lamp stage to facilitate alignment, and the head was gently oriented manually such that the eye was aligned to the optical beam. The pupils were dilated using a topical solution (Atropine sulphate 1%, Alcon). A converging beam was used for imaging with refraction at the cornea cancelled using a flat coverslip coated with a generic artificial tear gel. Alignment of the optical system to the rat retina required a few minutes to get to the ONH which was used as a landmark. Since the OCT system only provided a two dimensional depth profile of the retina in real time, alignment of the OCT system to the same point on the retina in a longitudinal study was challenging. Alignment of the OCT scan area to the ONH was performed based on the fly-through images observed in real time during volumetric acquisition. Further exacerbating the realignment issues was that the orientation of the eye was different between imaging sessions. Unlike human OCT imaging, in which the subject is awake and able to follow a fixation target, the rats rolled their eyes when anesthetized, and needed a longer time for alignment.

The FD OCT volumes consisted of 400 frames and data acquisition lasted ~10 seconds. A representative rat retina volume rendering is presented in Fig. 1(A) . Changes to the thickness of the combined NGI layers due to axotomy have been previously compared with the loss of retinal ganglion cells in histology [2]. A representative comparison of the NGI thinning due to axotomy is presented in Fig. 1(B) and 1(C).

 

Fig. 1 (A) Representative FDOCT rat retina volume. Thickness changes to the NGI can be observed between (B) a control eye and (C) an eye 14 days after axotomy.

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Semi-automatic segmentation of rat retina data

The rat retina volumes were pre-processed for axial motion correction, and cropped to exclude the ONH and the edges of the volume. The retinal layer images were segmented in each cross sectional B-scan using an active contour without edges algorithm [13,14]. The algorithm segmented five intra-retinal layers, but only the NGI thickness was retained for this study. The active contour approach requires user initialization, and for segmentation of a volume, points were placed manually on every third frame. Representative segmentation results are shown in Fig. 2 on one of the FDOCT B-scans. The initial contours fit to these points were circular shapes with a common center but a unique radius, modeling the retinal layer boundaries. The volume segmentations defined surfaces bounding the NGI in 3D space.

 

Fig. 2 (A) The original FD OCT B-scan of a rat retina and manual initialization points (green). (B) The segmentation for the NGI layers only using the active contour algorithm [13,14].

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Thickness measurement and visualization

We measured the thickness of the rat retina layers in 3D using Laplace’s equation from mathematical physics; we denote this as the Laplacian Streamline Correspondence Thickness (LSCT) method. Laplace’s equation is a well known second-order partial difference equation that is used to model many natural phenomenon in flows of gravity, charge, heat and fluids, to name a few. As an example, in electrostatics, Laplace’s equation is used to model the distribution of the streamlines of potential between two surfaces held at different electrostatic potential. In the case of the retina, we will model the inner and outer retinal surfaces enclosing the retinal layer , a volumetric domain whose thickness is to be measured, as charged surfaces with a potential 1 on the inside surface and 0 on the outside surface. Using Laplace’s equation, the scalar potential , at all points in the enclosed retinal layer volume, is given by . The resulting potential function makes a smooth transition from the potential of the inner surface to that of the outer surface giving a family of nested non-intersecting surfaces of iso-potential in the enclosed volume that depend only on the geometry of the enclosed retinal layer volume and not on it’s orientation in 3D space. The gradient field of this potential function, given by is a unit vector field that, starting from one surface and terminating on the other, is perpendicular to the iso-potential surface at each point in the volume. For each point on one surface, the path along the gradient field to the other surface is found by integration to yield the “streamline” of flow from one surface to another giving a smooth one-to-one correspondence between the two surfaces. The Euclidean distance between the corresponding points is the 3D retinal layer thickness defined at that point, analogous to the 3D cortical thickness between the inner and outer surfaces of cortical mantle for which this method was initially proposed in [16].

This method of defining thickness is well suited for the retinal layers over the existing methods of defining retinal layer thickness. First, it is a fully 3D method that takes into account of the full retinal layer geometry in 3D and does not make 2D measurements in B-scans or a 1D measurement along an A-scan. Since the solution of Laplace’s equation is invariant to the orientation of the enclosing volume in 3D, the same thickness values are found that depend only on the geometry of the enclosed volume irrespective of orientation in 3D space. This property is very important for retinal layer thickness measurement as it renders it insensitive to the orientation of the eye with respect to the imaging apparatus, the possible differing orientations of the resulting A-scans and the B-scans with respect to the retinal geometry or possible differences in orientation that can result via manual measurements. Second, the definition of the thickness via streamlines that are non-intersecting, flow smoothly between the inner and outer surfaces and emanate and terminate perpendicular to both the inner and outer surface is more in concordance with properties that are associated with the definition of thickness than single, point to point, manual measurements between a sparse number of points taken in the 3D volumetric image space.

In our implementation of the LSCT, Laplace’s PDE was solved using the Laplace-Beltrami operator on a tetrahedral mesh finite element approximation of the enclosed retinal layer segmentation region following a method adapted from computer graphics [18]. The Euclidean distance between the corresponding surface points from solving Laplace’s equation on this domain gave the retinal layer thickness. The thickness measurements were overlaid on the vertices of the outermost surface of the tetrahedral mesh which lay within 20 μm of a segmented voxel, and whose corresponding point also lay within 20 μm of a segmented voxel. These results are presented in Fig. 3 .

 

Fig. 3 The thickness measurement between the two segmented surfaces of the retina.

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3. Results and discussion

The 2D colour coded rat retina thickness maps from Days 3,7, 10, and14 post-axotomy are shown in Fig. 4 superimposed on their corresponding reconstructed fundus image. Figure 4 shows the results for Days 3, 7, 10 and 14 post-axotomy. In the thickness map for an individual day, a general trend of NGI thinning can be observed from the ONH outward. Comparing the thickness maps from Day 3 post axotomy to Day 14, a progressive thinning of the NGI at similar distances from the ONH can be observed.

 

Fig. 4 False colour 2D thickness maps of the NGI overlaid on the reconstructed fundus images.

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The change in thickness of the NGI as a function of distance from the optic nerve head and time can be extracted from the thickness maps in Fig. 4. The thickness of the NGI in a control eye is plotted in Fig. 5 , indicating general decrease from 86 μm near the optic nerve head to a thickness of 71 μm at a distance of nominally 2.5 mm. The error bars represent the standard deviation of the NGI thickness in the region (between two consecutive circles and falling within the radial strip shown in Fig. 4) used to determine the line profile. The thickness plots from the axotomy eye show a decreasing trend in NGI thickness in successive days and increasing distance from the optic nerve head.

 

Fig. 5 Average thickness of the NGI as a function of distance from the optic nerve head. OS: left eye, control; OD: right eye with optic nerve transection.

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4. Conclusion

Volumetric imaging with OCT in small animals is important for investigating large areas on the back of the retina, in order to observe spatial trends within an animal. Quantitative analysis of structural changes over a large area of the rodent retina is required for evaluation of the effects of localized treatments (for example, retinal injections) in the investigation of therapy for retinal degeneration. Using the same rat over time minimizes the variability the measurements in addition to reducing the number of rats used in a longitudinal study.

In this report, we demonstrated quantitative measurement of the longitudinal thinning of the combined NGI in a rat that had undergone optic nerve transection. Quantitative results were obtained through a combination of semi-automatic segmentation of the retinal layers using an active contour algorithm [13,14], followed by thickness measurement using Laplacian streamlines [16]. Unlike 2D thickness measurement, the 3D thickness measurement methods are insensitive to orientation which is important for accurate measurement of thickness and additionally helps to reduce noise in the measurements. Furthermore, this step is automated, avoiding manual inter-rater variability, and intra-rater variability over time. The combination of semi-automatic segmentation algorithms and fully automated three dimensional thickness measurements of the retinal cell layers from FD OCT volumes is a powerful computational anatomical tool for vision scientists. Although demonstrated here for the NGI layers in a model of acute retinal injury only, the computational pipeline presented can be readily extended investigate rodent models of retinal degenerative diseases affecting other retinal cell layers, such as the Outer Nuclear Layer (ONL).