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Edited by: Xiaoying Tang, SYSU-CMU Joint Institute of Engineering, China

Reviewed by: Delia Cabrera DeBuc, University of Miami, United States; Martin Reuter, Harvard Medical School/Massachusetts General Hospital, United States

*Correspondence: Mirza Faisal Beg

This article was submitted to Brain Imaging Methods, a section of the journal Frontiers in Neuroscience

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

Optical coherence tomography provides high-resolution 3D imaging of the posterior segment of the eye. However, quantitative morphological analysis, particularly relevant in retinal degenerative diseases such as glaucoma, has been confined to simple sectorization and averaging with limited spatial sensitivity for detection of clinical markers. In this paper, we present point-wise analysis and visualization of the retinal nerve fiber layer and choroid from cross-sectional data using functional shapes (fshape) registration. The fshape framework matches two retinas, or generates a mean of multiple retinas, by jointly optimizing the surface geometry and functional signals mapped on the surface. We generated group-wise mean retinal nerve fiber layer and choroidal surfaces with the respective layer thickness mapping and showed the difference by age (normal, younger vs. older) and by disease (age-matched older, normal vs. glaucomatous) in the two layers, along with a more conventional sector-based analysis for comparison. The fshape results visualized the detailed spatial patterns of the differences between the age-matched normal and glaucomatous retinal nerve fiber layers, with the glaucomatous layers most significantly thinner in the inferior region close to Bruch's membrane opening. Between the young and older normal cases, choroid was shown to be significantly thinner in the older subjects across all regions, but particularly in the nasal and inferior regions. The results demonstrate a comprehensive and detailed analysis with visualization of morphometric patterns by multiple factors.

Volumetric optical coherence tomography (OCT) has emerged as a preferred diagnostic tool in ophthalmology for noninvasive,

Most previous studies involving registration of OCT images have averaged multiple serially acquired images for noise reduction and motion correction (Jørgensen et al.,

In this paper, we demonstrate the use of this algorithm for investigating the effect of age and glaucoma on retinal nerve fiber layer (RNFL) and choroid. Loss of RNFL in the optic nerve head (ONH) region is a well-known hallmark of glaucoma that leads to irreversible vision loss (Medeiros et al.,

In this work, we aim to (i) examine the spatial RNFL thickness patterns by age and by presence of glaucoma by comparing the reference group of older healthy eyes with younger healthy eyes and with age-matched glaucoma eyes, and (ii) study whether there is spatial relationship between age-related changes and glaucoma-related changes.

Thirty-eight eyes from five young healthy participants, five older healthy participants, and twelve older glaucoma patients were included in the study. The participant demographics are listed in Table

Participant demographics.

Young healthy | 5 | 10 | 3/2 | 29.8 ± 3.6 |

Older healthy | 5 | 10 | 2/3 | 57.0 ± 4.4 |

Older glaucoma | 12 | 18 | 6/6 | 61.7 ± 7.9 |

Images with artifacts, such as large lateral motion artifact or the ONH not being at the center of the field of view were excluded from this analysis. The image underwent axial motion correction by B-scan cross-correlation and 3D bounded-variation smoothing for reducing the effect of speckles and enhancing the visibility of anatomical structures, with no additional normalization. An example of OCT B-scan before and after processing is shown in Figures

Example OCT B-scan

The framework of functional shapes (or fshapes) provides a quantitative measure of inter-subject variability in the RNFL and choroid. In this section, we briefly summarize the algorithm which is detailed in Lee et al. (^{i}, ^{i}), where _{∗}, _{∗}), consisting of a template surface geometry _{∗} and an associated surface-indexed signal (thickness here) mapping _{∗}. Given (_{∗}, _{∗}) as the template fshape, and (^{i}, ^{i}) as the ^{i} of the template geometry _{∗} and a residual ζ^{i} to be added to the template function _{∗}, such that after transformation of the template fshape with the mapping ϕ^{i} to the ^{i}, ^{i}) for all ^{i}, ζ^{i}) consisting of a smooth deformation and a function residual are estimated such that:

The function residual added to the template function estimated by fshape matching effectively becomes the representative of the target function in the geometry of the template. By fixing a template geometry and function, a group of target fshapes can be brought into the coordinates of the template such that the residuals representing different target function values are now indexed on the same template geometry. The choice of the template is an important consideration and the mean of the observations in the database is a standard choice. A database fshape mean is hence estimated, to be used as a template, by an adaptive gradient descent algorithm that jointly optimizes a total fshape dissimilarity measure between each target fshape (^{i}, ^{i}) and the transformed template ^{i}) to compute the point-wise variability of the function values at each point on the template geometry across the database.

Computation of fshape mean template.

In order to compare the fshape analysis with more conventional “intrinsic” analysis where an individual-specific coordinate system is placed on each geometry separately such as using sectoral analysis, the peri-papillary retinal layers were divided into regional sectors (Lee et al.,

Sectorization of the layer surface with reference to the Bruch's Membrane Opening (BMO) as reference.

Two analyses were conducted (1) the fshape analysis of computing the mean fshape geometry and function and the residual function for each subject indexed on the common mean template, enabling point-wise comparison across the subjects in the database and (2) sectoral averages within each subject that enable comparison across subjects by the sectors defined over the subject's layer geometry.

The database consisted of members from three groups: young normal (Group A), older normal (Group B), and older glaucomatous (Group C) individuals. These groups enable analyses of two main questions (1) the effect of age on RNFL and choroid layer thicknesses in healthy young and older individuals (Group A and B comparison) and, (2) the effect of glaucoma between age-matched individuals (Group B and Group C comparison). These two questions were analyzed by point-wise (fshape) and sector-wise group mean thickness difference maps and two-sample

The effect of age and glaucoma on RNFL and choroidal thicknesses was additionally examined by point-wise and sector-wise linear regression to quantify trend, on Group A and B for the effect of age, and Group B and C for the effect of glaucoma. Each layer thickness (RNFL or choroid) values from Group A and B were fitted to ^{*}^{*}

To visualize the measurements across the database highlighting the variability and trends, the fshape measures for each subject on the common template were normalized by using a z-score computed by subtracting the mean of a reference group and dividing by the standard deviation of the measures in the reference group. The z-score was calculated point-wise as _{k} is the thickness at k^{th} point for, ^{th} point, and ^{th} point. The reference groups were chosen to be Group A for age comparison and Group B for glaucoma comparison such that the average measures of the young normal (Group A) or older healthy (Group B) subjects are removed to visualize the residual effects of age and glaucoma, respectively. To present a compact visualization, measurement of each subject was unraveled into a column format by subdividing the mean template surface into sectors, and subdividing each sector into smaller sub-sectors, and arranging the z-score values by their sectors in a column format consistent across the database while preserving spatial adjacencies.

This section will present the results of point-wise (using fshape) and sectoral analysis of RNFL and choroid thickness across the three cohorts chosen for this study. All figures are right-eye oriented, with the left side temporal and the right side nasal. Group averages of RNFL thickness are visualized in Figure

Retinal nerve fiber layer (RNFL) thickness using fshapes point-wise registration

The group averages of choroidal thickness by fshape (top row) and sectoral averaging (bottom row) is shown in Figure

Choroid thickness using fshapes

The effect of age and glaucoma in RNFL thickness is shown by difference of group averages in Figure

Effect of age (top row) and glaucoma (bottom row) on RNFL thickness. The point- and sector-wise subtraction of mean RNFL thickness between older normal (Group B) and young normal (Group A) is shown in the top left panel, and the

Similar group difference visualization for choroid is shown in Figure

Effect of age (top row) and glaucoma (bottom row) on choroidal thickness. The point- and sector-wise subtraction of mean choroidal thickness across older normal (Group B) and young normal (Group A) is shown in the top left panel, and the

The relationship of RNFL thickness to aging and severity of glaucoma was examined by point- and sector-wise linear regression in Figure ^{2}. The estimated slope or the rate of change associated with visual field loss (mm/dB) in the cross-sectional age-matched subjects was plotted in the bottom row along with the goodness of fit by ^{2}. Aging did not show consistent, significant trend with RNFL thickness, whereas increasing glaucoma severity (more negative VFMD) was correlated to decreasing RNFL thickness. Similar spatial patterns are observed as seen in the group difference maps shown in Figure

Linear regression plots of RNFL thickness v. age (top row) and v. visual field mean deviation (VFMD). The slope in RNFL thickness = a^{*}Age + b is plotted point- and sector-wise in the top left panel, along with the goodness of fit (^{2}) in the top right panel. The slope of RNFL thickness = a^{*}VFMD + b is plotted point- and sector-wise in the bottom left panel, along with the goodness of fit (^{2}) on the bottom right panel. As with the group difference, RNFL thickness is negatively correlated with VFMD. The point-wise maps reveal that the rate of change has distinct spatial pattern with greater thinning along the regions where RNFL is generally thicker in healthy subjects. All images are in the right-eye orientation.

The relationship of choroidal thickness to aging and severity of glaucoma was also examined by point- and sector-wise linear regression in Figure ^{2}. The estimated slope or the rate of change associated with visual field loss (mm/dB) in the cross-sectional age-matched subjects was plotted in the bottom row along with the goodness of fit by ^{2}. Again, compared to the RNFL thickness, change in the choroidal thickness was associated more with aging than glaucoma. Aging was correlated to globally decreasing choroidal thickness, most significantly in the nasal and inferior regions. In the most severely affected regions, the average choroidal thickness change per year was ~3–4 μm.

Linear regression plots of choroidal thickness v. age (top row) and v. visual field mean deviation (VMFD). The slope in Choroidal thickness = a^{*}Age + b is plotted point- and sector-wise in the top left panel, along with the goodness of fit (^{2}) in the top right panel. The slope of Choroidal thickness = a^{*}VFMD + b is plotted point- and sector-wise in the bottom left panel, along with the goodness of fit (^{2}) on the bottom right panel. As with the group difference, choroidal thickness is negatively correlated with age. The point-wise maps show the steepest change in the nasal and inferior regions. All images are in the right-eye orientation.

The point-wise nature of fshape metrics can be utilized by simultaneous visualization of all data points from multiple subjects. Figure _{i} ≈ f_{∗} + ζ_{i}) at each point. Horizontally, the eyes are ordered by VFMD, plotted below the thickness plot in grayscale. Vertically, the points are ordered by sectors from Nasal (N) and counter-clockwise to Inferior Nasal (IN). Within each sector, the points are ordered by the distance from BMO center, from the closest to the farthest. This visualization allows one to compare all eyes at each spatial location. There is observed an overall group-wise difference between Healthy older subjects, Early Glaucoma, and Moderate to Severe Glaucoma subjects. Comparing vertically from the top to the bottom, the healthy eyes show the thickness pattern that follows the mean template for Group B in Figure

The bottom panel of Figure

Multi-subjects RNFL thickness by visual field mean deviation (VFMD). By mapping to the common template space, all subjects have estimated thickness values (t_{i} ≈ f_{∗} + ζ_{i}) at the same corresponding spatial points, visualized in the top panel. Vertically, the points are ordered by regions, from Nasal (N) to Inferior Nasal (IN). Within each region, the points are ordered by their distance from BMO center, from the closest to the farthest. Horizontally, the eyes are ordered by VFMD, plotted in grayscale below the thickness plot. In the bottom panel, the same data is visualized z-scores, which normalizes the values by the mean and standard deviation of the reference group (Group A, young healthy) and highlights the trend across regions and increasing VFMD magnitude.

Figure

Multi-subjects choroidal thickness by age. By mapping to the common template space, all subjects have estimated thickness values (t_{i} ≈ f_{∗} + ζ_{i}) at the same corresponding spatial points, visualized in the top panel. Vertically, the points are ordered by regions, from Nasal (N) to Inferior Nasal (IN). Within each region, the points are ordered by their distance from BMO center, from the closest to the farthest. Horizontally, the eyes are ordered by age, plotted in grayscale below the thickness plot. In the bottom panel, the same data is visualized in z-scores, which normalizes the values by the mean and standard deviation of the reference group (Group A, young healthy), and highlights the trend across regions and increasing age.

The 3D OCT images reveal the structure of the ocular posterior segment in great detail so as to enable visualization and quantification of the retinal layer morphometry. Individual measurements of layer thicknesses can be pooled into population-wide assessments of normative layer thicknesses and any changes that may occur as a function of age and disease. These allow insights into whether age and disease have a stereotypical pattern of influence in the retina, with common shape features and localizations, as well as variability across individuals and deviation of a particular subject from a reference population. In this paper, we presented the effect of age and glaucoma on retina nerve fiber layer (RNFL) and choroid using our novel f-shapes approach, which enables a point-wise assessment of retinal morphometrics across individuals via a registration approach. The fshape registration estimates a residual function that is added to the template thickness such that the template geometry after transformation matches the subject geometry, and the template thickness plus the residual function after transformation matches the subject thickness. This maps an individual's layer thicknesses onto the common coordinate system of the template geometry via the specific residual function estimated for that individual. At each location on the template surface, subsequent statistical analysis across the database can reveal trends and features that are common across individuals as a function of age and disease. A more conventional approach utilizes sectorization of the layer surface by calculating the average of all thickness measurements within each sector for each individual eye. Assuming that the sectors are defined with consistent anatomical and spatial correspondence across individuals, within-sector average provides a single scalar summary measure for a given sector that can be statistically analyzed for cross-sectional data taken from the same sector across the individual eyes. However, such approach is limited in spatial sensitivity due to averaging of values in a region. We examined the effect of age and glaucoma in RNFL and choroidal thickness in both of these approaches with four quantitative visualizations: (i) group rages (Figures

With age, RNFL showed relatively little difference between the young and older healthy subjects, with regression estimating no strong relationship between age and RNFL thickness. In previous studies using OCT measurements, RNFL thickness has been negatively associated with age (Budenz et al.,

Glaucoma, as expected, was observed to be associated with significant thinning of RNFL. The pattern of loss visualized in the point-wise maps forms the hourglass crescent-shaped ridge, particularly in the inferior arm, highest toward the middle of the ridge, decreasing further away from the ridge center. The same hourglass-like pattern is observed in young normal subjects. The results of our study are consistent with known patterns of RNFL loss in glaucoma, but more importantly, it shows that the glaucomatous RNFL loss occur in a specific, uneven pattern that follows the initial RNFL thickness, suggesting that the time of onset and significance of the RNFL loss may be proportional to the initial RNFL thickness in the region. The loss significance was also higher in the region closer to BMO. The fshape RNFL loss map elucidates the results of previous studies that found the highest diagnostic ability of the RNFL loss in the inferior and temporal-inferior sectors (Sehi et al.,

Figures

The patterns of change shown in the point-wise and sector-wise approaches were overall consistent. The point-wise registration was able to show localized features in higher resolution compared to the sectorization, revealing detailed regional patterns and potentially furthering our understanding of the disease mechanism. This approach may be useful for characterizing the focal localized patterns that are often seen in glaucoma, both in RNFL and in other subsurface structures such as lamina cribrosa and peripapillary tissues. In this work, we also examined multiple factors (age, glaucoma) in multiple layers (RNFL, choroid) concurrently for a more complete picture in understanding our data. The results showed glaucomatous thinning of RNFL, and age-related thinning of choroid and how the spatial patterns of the tissue loss in the two layers were localized and distinct. Limitations of this work include relatively small sample size, inclusion of fellow eyes, and light beam angle-related uncertainty in retinal layer thickness measurement, although given the relatively small size of the field of view in the images in this study, this effect is likely limited. Our future work will include expanding the analyses presented here to other retinal layers and to the macular region to build a comprehensive presentation of the retinal morphometrics, and incorporating retinal vessels and capillary density measures from SV-OCT as metrics along with layer thickness.

The study followed the tenets of the Declaration of Helsinki, and informed and written consents were obtained from the participants. Ethics review for the study was approved by Simon Fraser University (SFU) and University of British Columbia (UBC).

Designed research: SL, KP, NC, BC, AT, PJM, MVS, and MFB. Analyzed and interpreted data: SL and MFB. Wrote manuscript: SL, MLH, MVS, and MFB. Reviewed and approved manuscript: KP, NC, BC, AT, PJM, MVS, and MFB.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

This work is based on our conference presentation (Lee S. et al.,