Two-dimensional fractal analysis of retinal tissue of healthy and diabetic eyes with optical coherence tomography

In the ophthalmic research, the measurement of the retinal thickness is usually employed for characterizing the structural changes of the retinal tissue. However, changes in the fractal dimension (FD) may provide additional information regarding the structure of the retinal layers and their early damage in ocular diseases. In the present paper, we investigated the possibility of detecting changes in the structure of the cellular layers of the retina by applying a two-dimensional fractal analysis to optical coherence tomography (OCT) images. OCT images were obtained from diabetic patients without retinopathy (DM, n = 38 eyes) and with mild diabetic retinopathy (MDR, n = 43 eyes) as well as in healthy subjects (Controls, n = 74 eyes). The two-dimensional fractal dimension was calculated using the differentiate box counting methodology. We evaluated the usefulness of quantifying the fractal dimension of layered structures in the detection of retinal damage. Generalized estimating equations considering within-subject inter-eye relations were used to test for differences between the groups. An adjusted p-value of <0.001 was considered statistically significant. Receiver operating characteristic (ROC) curves were constructed to describe the ability of the fractal dimension to discriminate between the eyes of DM, MDR, and healthy eyes. Lower values of the fractal dimension were observed in all layers in the MDR eyes compared with controls except in the inner nuclear layer (INL). Lower values of the fractal dimension were also found in all layers in the MDR eyes compared with DM eyes. The highest area under receiver operating characteristic curve (AUROC) values estimated for the fractal dimension were observed for the outer plexiform layer (OPL) and outer segment photoreceptors (OS) when comparing MDR eyes with controls. The highest AUROC value estimated for the fractal dimension were also observed for the retinal nerve fiber layer (RNFL) and OS when comparing MDR eyes with DM eyes. Our results suggest that fractal dimension of the intraretinal layers may provide useful information to differentiate pathological from healthy eyes. Further research is warranted to determine how this approach may be used to aid diagnosis of retinal neurodegeneration at the early stage. © 2016 Journal of Biomedical Photonics & Engineering.


Introduction
Optical coherence tomography is an optical imaging modality that provides high-resolution, cross-sectional images of biological tissue in a non-invasive manner [1]. Notably, the OCT technology has been widely utilized to detect retinal diseases in Ophthalmology. By employing the OCT technique, the thickness and volume measurements of the retinal tissue can be obtained from OCT scans. Particularly, the structural alterations revealed by changes in thickness and volume of the cellular layers of the retina can be measured to characterize the neurodegeneration in patients with diabetes [2][3][4][5][6][7]. The most significant retinal pathology caused by diabetes is diabetic retinopathy (DR), which is characterized by blood vessel damage and neurodegenerative changes. The quantification of the thickness measurement of various cellular layers of the retina with OCT has helped to assess treatment efficacy and identify potential markers for monitoring the progression of DR [8][9][10][11][12]. However, in biology and medicine, the shapes of structures such as molecules, cells, tissues, and organs also play a significant role in the diagnosis of diseased retinal tissue [13][14]. Out of the various structural parameters, the fractal dimension can be capable of revealing differences and irregularities in these structures. Quantitative measurements of the fractal dimension could be an effective approach to discriminate diseased tissue from healthy tissue. Therefore, the structural changes revealed by changes in fractal dimension may provide further information regarding cellular layers and early damage in ocular diseases. The abnormal retinal tissue could be detected by performing fractal analysis for particular cellular structures visualized in OCT images. Thus, fractal analysis of OCT images could provide a useful diagnostic methodology to identify diseased tissue.
In this study, OCT images were obtained from diabetic and normal healthy subjects to investigate the possibility of OCT to detect structural changes in the retina by quantifying the two-dimensional fractal dimension of its layered structures.  The same OCT scan processed with OCTRIMA. Abbreviations: Ch, choroid; GCL+IPL, ganglion cell layer and inner plexiform layer complex; INL, inner nuclear layer; ONL+IS, combined outer nuclear layer and inner segment of photoreceptors; OS, outer segment of photoreceptors; OPL, outer plexiform layer; RNFL, retinal nerve fiber layer; RPE, retinal pigment epithelial layer; V, vitreous. Note that OCTRIMA measures the thickness of the whole retina between the inner limiting membrane and the inner boundary of the photoreceptor outer segment/RPE junction. The thickness of the combined ONL+IS structure is measured between the outer boundary of OPL and the inner boundary of the photoreceptor outer segment/RPE junction. criteria for healthy controls included best-corrected visual acuity of 20/25 or better, no history of any current ocular or systematic disease and a normalappearing macula on contact lens biomicroscopy. All eye examinations were performed at the Department of Ophthalmology, Semmelweis University, Budapest, Hungary. A total of 74 normal healthy eyes, 38 eyes with type 1 diabetes mellitus with no retinopathy and 43 eyes with mild diabetic retinopathy on biomicroscopy were included in this study (see Table 1).

OCT System and Measurements
The OCT system (Stratus OCT, Carl Zeiss Meditec, Dublin, California) used in this study employs a broadband light source, delivering an output power of 1 mW at the central wavelength of 820 nm with a bandwidth of 25 nm. It has a scanning speed of 400 A-scans per second with a resolution of 10 µm in tissue that determines the imaging axial resolution of the system. A cross-sectional image is achieved by the axial reflectance while the sample is scanned laterally. All Stratus OCT study cases were obtained using the macular thickness map protocol. This protocol consists of six radial scan lines centered on the fovea, each having a 6 mm transverse length. To obtain the best image quality, focusing and optimization settings were controlled, and scans were accepted only if the signal strength was above 6 (preferably 9-10) [15]. Scans with J of Biomedical Photonics & Eng 2(4) 040302-5 31 Dec 2016 © JBPE foveal decentration (i.e., with center point thickness SD >10%) were repeated.

OCT image processing
OCT signals were collected and exported from the OCT device in the form of 16-bit grayscale images. To use OCT to quantitatively evaluate structural changes of the cellular layers of the retina caused by some severe eye diseases, a segmentation of these layers is required. We used a computer-aided grading methodology for OCT retinal image analysis (OCTRIMA) that is an interactive, user-friendly stand-alone application for analyzing Stratus OCT retinal images [16]. This method integrates a denoising and edge enhancement technique along with a segmentation algorithm previously developed by Cabrera et al [17]. The denoising and edge enhancement techniques are part of a novel preprocessing step that facilitates better automatic segmentation results (see Figure 1). Also, the semiautomatic segmentation correction tool minimizes segmentation errors generated during the automatic segmentation process, significantly reducing the need for manual error corrections. It also gives quantitative information about intraretinal structures and facilitates the analysis of other retinal features that may be of diagnostic and prognostic value, such as morphology and reflectivity.

Fractal Analysis
In the analysis of OCT images, fractal analysis has been used to investigate the structural change of biological tissue. For example, Fluearu et al. used the box counting method to calculate the fractal dimension to characterize porcine arterial tissue [18]. Sullivan et al. utilized the box counting method to calculate the fractal dimension to classify the breast carcinoma [19]. The power spectrum method has been used to perform the fractal analysis on the layered retinal tissue for investigating the diseased tissue in diabetic patients and healthy subjects [5][6][7]17,20]. In those studies, the fractal analysis was performed on each A-scan within each region of interest (ROI). Therefore, only the irregularity or roughness along the direction of A-scans was considered in the one-dimensional fractal analysis, while the irregularity or unevenness in all other directions was ignored. Therefore, to extend the fractal analysis in all directions in OCT images and to improve the accuracy of the fractal analysis, the two-dimensional fractal analysis for intraretinal layers of OCT images is necessary.
To determine the fractal dimension of 2D OCT images, several definitions of fractal dimension have been used [21]. One straightforward and understandable methodology for calculating the 2D fractal dimension is the differentiate box counting method [22]. The method of differentiate box counting method is described below.
Consider a grayscale image in a Cartesian coordinate (x,y,z), the coordinates (x,y) denote the 2D position on the image plane, and the coordinate (z) represents the intensity value. In the 2D differentiate box-counting method, the image plane is covered by the nonoverlapping grids. Assume the grayscale image's size is × and the non-overlapping grid's size is × , and need to meet the requirement as /2 ≥ ≥ 2. Assume the is the total number of gray level, the value ′ can be derived from the following equation: ′ = / . Thus, the size of the box that is used to cover the 3D spatial surface is × × ′ as showed in Figure 2. Here, assume that the minimum and maximum gray level in the ( , ) grid were in the box number and , respectively, the number of the boxes covering the surface in the grid ( , ) is:

Statistical Analysis
The differences in fractal dimension between study groups were tested using an ANOVA followed by Newman-Keuls posthoc analysis and the student's t-test. Because of the number of comparisons, ≤ 0.001 was considered statistically significant. Receiver operating characteristic analysis was also performed on the fractal dimension between study groups to determine the ability of fractal dimension to differentiate diabetic eyes with and without MDR from healthy eyes. AUROC was used to compare diagnostic power. This area summarizes the sensitivity and specificity of diagnosis over the total range of valid diagnostic thresholds. An AUROC of 1.0 indicated perfect discrimination. An AUROC of 0.5 indicated no discrimination. The AUROC calculations and statistical analyses were performed using the software package SPSS version 16 (SPSS Inc., Chicago, Illinois).

Results and Discussion
OCT is usually employed for the measurement of retinal thickness. However, the fractal analysis may provide further information regarding cellular layers and early damage in ocular diseases. In this study, the fractal dimension showed the most powerful diagnostic utility for detecting early changes in the diabetic retina.
Significantly smaller values of fractal dimension were observed in all layers in the MDR eyes compared with controls (except INL, see Table 2). Specifically, the fractal dimension was 2.0% smaller in the OPL as compared to healthy eyes. When comparing MDR with DM eyes, the fractal dimension had a significantly less value in all intraretinal layers. Specifically, the fractal dimension was 1.7% smaller in the RNFL. Our results suggest that the RNFL, OPL, ONL+IS, and OS are more susceptible to initial damage when comparing MDR with control eyes. Mainly, the trend observed for the fractal dimension of the RNFL in MDR eyes might be associated with pathological metabolic changes in the retina and may reflect neurodegenerative changes in the diabetic retina. These findings also have possible implications for the early detection of macular damage in diabetes. Because the macular region is rich in retinal ganglion cells, it could be suggested that diabetic damage of this central area might occur early in the disease process. In fact, animal models of DR have shown significant loss of macular ganglion cells [24][25][26][27][28]. Moreover, the fractal dimension of the OPL and OS in MDR eyes was significantly smaller than similar measures in normal healthy eyes. Previous studies have shown that not only retinal pericytes and endothelial cells are susceptible to hyperglycemia, but neuroglial elements of the retinal are also involved in the retinal damage caused by diabetes. Interestingly, in the onedimensional fractal analysis performed using the same OCT data, the fractal dimension of the OPL in MDR eyes showed significantly higher values compared to healthy eyes [20]. The opposite conclusion might be due to Henle fiber layer artifacts that the thickness and the reflectance information might have been changed as the scanning is performed at oblique angles [29][30].
The ROC analysis was performed for the fractal dimension measures of each intraretinal layer. The AUROC values are shown in Table 3 by study groups.  There are some potential shortcomings of our study. Time domain OCT technology has some limitations compared to the more advanced OCT technology. Also, current OCT devices include different segmentation algorithms and methods for speckle noise removal. Therefore, data analysis is influenced by particular assumptions and technological specifications that are in place for each OCT device. Moreover, the box-counting method to calculate the fractal dimension has been reported as not the best technique to estimate fractal dimension when the image intensity surface is smooth [22,32]. Therefore, a modified differentiate box counting method should be considered to avoid the underestimation of fractal dimension. In the modified differentiate box-counting method, a random shift is added to the column in the vertical or horizontal direction when counting the number of the boxes for the 3D spatial surface. Though the random shifting in each column needs some additional computation time, the modified differentiate box counting method could generate the exact fractal dimension in smoothly textured images.   Also, fractal analysis using the power spectrum technique, which is generalizable and potentially more precise, should be compared with the modified differentiate box counting method results to investigate which one produce better estimates in OCT imaging [34-35].

Conclusion
The early results presented have shown this methodology could have the potential to differentiate diabetic eyes with early retinopathy from normal healthy eyes. Particularly, this result is in agreement with previous reports showing a significant reduction of the fractal dimension during induced apoptosis throughout early apoptotic phases in breast cancer cells. This observation could be an early indication of visual function degeneration and could be used to improve early sign of diabetic retinal damage and disease progression. Future studies are needed to determine the accuracy, repeatability and full capability of this methodology with more OCT scans and advanced technology. A possibility of error exists due to the quantization nature of the approach, especially when the image intensity surface is smooth.