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

Wei Gao, Delia Cabrera DeBuc, Valery P. Zakharov, Erika Tatrai, Gabor M. Somfai, Oleg O. Myakinin, Ivan A. Bratchenko, Dmitry N. Artemyev, Dmitry V. Kornilin


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.


Optical Coherence Tomography; Retina; Diabetic Retinopathy; Fractal Analysi;Differentiate Box Counting

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