Analysis of normal human retinal vascular network architecture using multifractal geometry

AIM：To apply the multifractal analysis method as a quantitative approach to a comprehensive description of the microvascular network architecture of the normal human retina.METHODS：Fifty volunteers were enrolled in this study in the Ophthalmological Clinic of Cluj-Napoca,Romania,between January 2012 and January 2014. A set of 100 segmented and skeletonised human retinal images,corresponding to normal states of the retina were studied. An automatic unsupervised method for retinal vessel segmentation was applied before multifractal analysis. The multifractal analysis of digital retinal images was made with computer algorithms,applying the standard boxcounting method. Statistical analyses were performed using the Graph Pad In Stat software.RESULTS：The architecture of normal human retinal microvascular network was able to be described using the multifractal geometry. The average of generalized dimensions（D_q）for q=0,1,2,the width of the multifractal spectrum（Δα=α_（max）-α_（min））and the spectrum arms＇ heights difference（│Δf│）of the normal images were expressed as mean±standard deviation（SD）：for segmented versions,D_0=1.7014±0.0057; D_1=1.6507±0.0058; D_2=1.5772±0.0059; Δα=0.92441±0.0085; │Δf│= 0.1453±0.0051; for skeletonised versions,D_0=1.6303±0.0051; D_1=1.6012±0.0059; D_2=1.5531± 0.0058; Δα=0.65032±0.0162; │Δf│= 0.0238±0.0161. The average of generalized dimensions（D_q）for q=0,1,2,the width of the multifractal spectrum（Δα）and the spectrum arms＇ heights difference（│Δf│）of the segmented versions was slightly greater than the skeletonised versions.CONCLUSION：The multifractal analysis of fundus photographs may be used as a quantitative parameter for the evaluation of the complex three-dimensional structure of the retinal microvasculature as a potential marker for early detection of topological changes associated with retinal diseases.

Characterisation of human non-proliferative diabetic retinopathy using the fractal analysis

· AIM: To investigate and quantify changes in the branching patterns of the retina vascular network in diabetes using the fractal analysis method.·METHODS: This was a clinic-based prospective study of 172 participants managed at the Ophthalmological Clinic of Cluj-Napoca, Romania, between January 2012 and December 2013. A set of 172 segmented and skeletonized human retinal images, corresponding to both normal(24 images) and pathological(148 images)states of the retina were examined. An automatic unsupervised method for retinal vessel segmentation was applied before fractal analysis. The fractal analyses of the retinal digital images were performed using the fractal analysis software Image J. Statistical analyses were performed for these groups using Microsoft Office Excel2003 and Graph Pad In Stat software.·RESULTS: It was found that subtle changes in the vascular network geometry of the human retina are influenced by diabetic retinopathy(DR) and can be estimated using the fractal geometry. The average of fractal dimensions D for the normal images(segmented and skeletonized versions) is slightly lower than the corresponding values of mild non-proliferative DR(NPDR) images(segmented and skeletonized versions).The average of fractal dimensions D for the normal images(segmented and skeletonized versions) is higher than the corresponding values of moderate NPDR images(segmented and skeletonized versions). The lowestvalues were found for the corresponding values of severe NPDR images(segmented and skeletonized versions).· CONCLUSION: The fractal analysis of fundus photographs may be used for a more complete understanding of the early and basic pathophysiological mechanisms of diabetes. The architecture of the retinal microvasculature in diabetes can be quantitative quantified by means of the fractal dimension.Microvascular abnormalities on retinal imaging may elucidate early mechanistic pathways for microvascular complications and distinguish patients with DR from healthy individuals.