**Purpose**:
Optical coherence tomography (OCT) has recently emerged as a source for powerful biomarkers in neurodegenerative diseases such as multiple sclerosis (MS) and neuromyelitis optica (NMO). The application of machine learning techniques to the analysis of OCT data has enabled automatic extraction of information with potential to aid the timely diagnosis of neurodegenerative diseases. These algorithms require large amounts of labeled data, but few such OCT data sets are available now.

**Methods**:
To address this challenge, here we propose a synthetic data generation method yielding a tailored augmentation of three-dimensional (3D) OCT data and preserving differences between control and disease data. A 3D active shape model is used to produce synthetic retinal layer boundaries, simulating data from healthy controls (HCs) as well as from patients with MS or NMO.

**Results**:
To evaluate the generated data, retinal thickness maps are extracted and evaluated under a broad range of quality metrics. The results show that the proposed model can generate realistic-appearing synthetic maps. Quantitatively, the image histograms of the synthetic thickness maps agree with the real thickness maps, and the cross-correlations between synthetic and real maps are also high. Finally, we use the generated data as an augmentation technique to train stronger diagnostic models than those using only the real data.

**Conclusions**:
This approach provides valuable data augmentation, which can help overcome key bottlenecks of limited data.

**Translational Relevance**:
By addressing the challenge posed by limited data, the proposed method helps apply machine learning methods to diagnose neurodegenerative diseases from retinal imaging.

^{1}

^{,}

^{2}Neuromyelitis optica (NMO) is another neurodegenerative disease that affects the eye and spinal cord and occurs when the immune system attacks healthy cells in the central nervous system.

^{3}

^{,}

^{4}This technique makes it possible to reconstruct cross-sectional structural images with an axial resolution of approximately 4 µm.

^{5}

^{6}

^{,}

^{7}Recently, diagnostic procedures have been increasingly complemented by retinal imaging with OCT, first described in MS by Parisi et al.

^{8}Further studies have shown that two features derived from OCT scans in MS and NMO—namely, the peripapillary retinal nerve fiber layer thickness as a measure of axonal health and the macular volume and ganglion cell and inner plexiform layer (GCILP) thickness as a measure of neuronal health—are linked to MRI-based measures of myelin health in the posterior visual pathway.

^{9}

^{–}

^{16}

^{17}

^{,}

^{18}The main limitation of ML in applications like discrimination of MS and NMO is the availability of large and well-annotated training data sets. Synthetic OCT data could address this issue by supplying additional training data, covering underrepresented classes to reduce bias, and avoiding the privacy issues associated with the collection of real imaging data.

^{19}

^{–}

^{22}In recent work,

^{23}

^{,}

^{24}we used an active shape model (ASM

^{25}) to construct synthetic two-dimensional (2D) and three-dimensional (3D) OCT data in the macular region. In this article, we use that model as an augmentation method to generate synthetic 3D OCT boundaries of the macular region from healthy controls (HCs) and patients with MS and NMO. The thickness maps of retinal layers (strong biomarkers of MS and NMO) are then calculated using both synthetic and real data. Three validation strategies are formulated to assess the utility and integrity of the generated data and to justify its use to augment real data in future research. The strategies include histogram comparison methods, comparison of statistical properties between original 2D maps (retinal thickness maps), and a standard classification measure to evaluate the efficacy of the synthetic data augmentation method in disease prediction. Figure 1 shows the proposed approach in a graphical abstract.

^{14}). It consists of OCT data from HCs (26 eyes) and patients with NMO (30 eyes) and MS (30 eyes). To construct the proposed model, a limited number (five OCT volumes) were randomly selected from each class to be used in the training stage and to synthesize 25 three-dimensional OCT boundaries in each category. In total, 130 OCT volumes from HCs

^{26}were used for further validation of the synthetic data (30 eyes for training and 100 eyes for further comparison with synthetic data).

^{27}with reference values presented in Kafieh et al.

^{26}The segmentation results were quality controlled and manually corrected in case of errors by an ophthalmologist using the method in Montazerin et al.

^{28}To account for eye laterality, 3D OCTs from left eyes are flipped and the nasal area is located on the right side of the thickness maps.

^{29}Figure 2 shows an example of a 3D OCT image stack with extracted layers.

*n*= 18,200 points per image stack.

*i*th boundary, the

*j*th landmark point is represented by (

*x*,

_{ij}*y*,

_{ij}*z*), in coordinates where

_{ij}*x,y*corresponds to the horizontal and vertical components of each B-scan,

*z*indexes the identity of each B-scan, and

*j*runs from 1 to 91. By definition,

*z*is the same for all points in a given B-scan. The first and last landmark points are taken to be the left and right edges of the B-scan; thus, by definition,

_{ij}*x*

_{i}_{1}= 1 and

*x*

_{i}_{91}= 512 in every case, with the values

*y*

_{1}_{1}and

*y*

_{i}_{91}giving the height of the

*i*th boundary at the edges. To obtain the other landmark points, we identify the coordinates corresponding to the center of the macula in the given image stack (

*x*

_{mac}

*,y*

_{mac}

*,z*

_{mac}). For all boundaries,

*x*

_{i}_{46}is defined to be

*x*

_{mac}. The remaining points

*x*

_{i}_{2}…

*x*

_{i}_{45}and

*x*

_{i}_{47}…

*x*

_{i}_{90}are then spaced evenly between, respectively,

*x*

_{i}_{1}= 1 and

*x*

_{i}_{46}=

*x*

_{mac}, and

*x*

_{i}_{46}=

*x*

_{mac}and

*x*

_{i}_{91}= 512. Each

*y*is then the height of the

_{ij}*i*th boundary at

*x*.

_{ij}^{30}to align all image stacks to a reference image stack, and a point distribution model

^{31}is then constructed. Assuming that the variability within the population occurs along just a few directions in this space, the dimensionality is reduced to a lower space using principal component analysis (PCA). Each layer boundary in the training set can now be approximated by the mean shape plus a weighted sum of the first

*t*principal components, and we can synthesize new layer boundaries by allocating different numbers to weights of plausible principal components. Details of this procedure are elaborated in the Supplementary Material.

*, describing the locations of the 18,200 landmark points on layer boundaries of a synthetic OCT stack. We finally interpolate values linearly between the landmark points to recover the complete synthesized boundaries.*

**X**^{24}

^{32}

^{–}

^{34}They reveal information implicit in the 3D OCT volumes by providing easily interpretable maps for each retinal layer. We, therefore, calculated the thickness of each retinal layer and of the whole retina as 2D maps to be used in the validation strategies discussed below. The thickness of each retinal layer is the distance between consecutive retinal boundaries; similarly, the thickness of the entire retina is obtained as the distance between the first and the last boundaries. Accordingly, macular thickness maps are calculated for all three data classes, demonstrated in Figures 4, 5, and 6 for selected retinal layers (mRNFL, GCIPL, RPE) and the total retinal thickness. The real thickness maps and corresponding synthetic maps are shown in the first and second rows, respectively. Each thickness map has a size of 512 × 25 pixels, but the examples in Figures 4 to 6 are resized to 500 × 500 pixels for better visualization.

*H*

_{1}) and synthetic data (

*H*

_{2}), four measurements are used.

- i. The correlation coefficient is used to determine the type (direct or inverse) and degree of the relationship between two discretized probability distributions, approximating the similarity of the histograms. This coefficient ranges between 1 and –1 (zero if no correlation exists): where \(\overline {{H_i}} ,\ i = [ {1,2} ]\) is the mean value of each histogram over the total number of histogram bins, and\begin{eqnarray}&&C\left( {{H_1},{H_2}} \right) \nonumber\\ &&= \frac{{\mathop \sum \nolimits_I ({H_1}\left( I \right) - \overline {{H_1}} {\rm{\ }})({H_2}\left( I \right) - \overline {{H_2}} {\rm{\ }})}}{{\sqrt {\mathop \sum \nolimits_I {{({H_1}\left( I \right) - \overline {{H_1}} {\rm{\ }})}^2}\mathop \sum \nolimits_I {{({H_2}\left( I \right) - \overline {{H_2}} {\rm{\ }})}^2}} }}\end{eqnarray}(1)
*I*denotes the bin number. - ii. The chi-square distance calculates the normalized square difference between two histograms, and for identical histograms, this distance equals zero: \begin{equation}{\chi ^2}\left( {{H_1},{H_2}} \right) = \mathop \sum \nolimits_I \frac{{{{({H_1}\left( I \right) - {H_2}\left( I \right)\ )}^2}}}{{{H_1}\left( I \right)}}\end{equation}(2)
- iii. The histogram intersection calculates the similarity of two discretized probability distributions (histograms), with possible values of the intersection lying between 0 (no overlap) and 1 (identical distributions).
^{35}\begin{equation}I\left( {{H_1},{H_2}} \right) = \mathop \sum \nolimits_I \min ({H_1}\left( I \right),{H_2}\left( I \right)\ )\end{equation}(3) - iv. The Hellinger distance is related to the Bhattacharyya coefficient
*BC*(*H*_{1},*H*_{2}) and is used to quantify the similarity between two probability distributions.^{36}The maximum Hellinger distance is 1, and in the case of best match with a Bhattacharyya coefficient of 1, the Hellinger distance is 0.\begin{equation}BC\left( {{H_1},{H_2}} \right) = \ \mathop \sum \nolimits_I \sqrt {{H_1}\left( I \right)\ {H_2}\left( I \right)} \ \end{equation}(4)\begin{equation}H\left( {{H_1},{H_2}} \right) = \sqrt {1 - BC\left( {{H_1},{H_2}} \right)} \end{equation}(5)

^{9}

^{–}

^{16}Each of these three thickness maps has a size of 512 × 25 pixels, and we used PCA to reduce the dimension of each map to 5. Overall, we construct a 15

*D*space as input features for classification models. We train two types of binary classifiers, one to discriminate HC from MS and one for classifying HC from NMO, using a support vector machine (SVM) with radial basis kernel functions in both cases. A stratified fivefold cross-validation was used to evaluate the predictive performance of these models with a nested cross-validation for hyperparameter tuning (C and gamma) based on grid search. The partition into folds was done using the real data only, and in cross-validation iterations when a fold was used for training, we enhanced it with our synthetic data for the experiments with augmentation. This ensured that all test predictions were done on the real data and that the experiments with or without augmentation used the same partitions.

*H*

_{1}) and synthetic data (

*H*

_{2}).

*t*-test. The

*P*values reported in Table 1 show that real and synthetic data are not significantly different for any layer.

^{37}instead of synthesizing full 3D OCT data and then generating thickness maps to extract the final feature vector for the classification model, we directly resampled from the thickness map of the annotated training set to generate additional sample points for training in Figure 9. For this purpose, we use SMOTE to produce the synthetic points, generating a number of synthetic points equal to that of our method in order to have a fair comparison. Accuracy and F1 score are compared, and the results indicate that using SMOTE in this way also effectively enhances the training set, and the samples generated by our method lead to better performance in all scenarios. The rationale behind this result is that the oversampling technique assumes that the feature space behaves as a Euclidean space with equal relevance for each axis, so that distances are meaningful.

^{38}The thickness maps may not fully fulfill this assumption.

^{9}

^{–}

^{16}that indicate the greatest effect of disease on those parameters.

^{39}The method could be expanded to produce synthetic OCT image data with different features ranging from age, ethnicity, and severity (e.g., for use in tele-education platforms).

^{40}Thus, the ASM model has potential for aiding future education of neuro-ophthalmology trainees.

**H. Danesh**, None;

**D.H. Steel**, None;

**J. Hogg**, None;

**F. Ashtari**, None;

**W. Innes**, None;

**J. Bacardit**, None;

**A. Hurlbert**, None;

**J.C.A. Read**, None;

**R. Kafieh**, None

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