Citation:Ţălu &,Stach S,Călugăru DM,Lupaşcu CA,Nicoară SD.Analysis of normal human retinal vascular network architecture using multifractal geometry.Int J Ophthalmol 2017;10(3):434-438,doi:10.18240/ijo.2017.03.17
Analysis of normal human retinal vascular network architecture using multifractal geometry
Received:December 16, 2015  Revised:August 18, 2016
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DOI:10.18240/ijo.2017.03.17
Key Words:generalized dimensions; multifractal; retinal vessel segmentation; retinal image analysis; retinal microvasculature; standard box-counting method
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Ştefan Ţălu Discipline of Descriptive Geometry and Engineering Graphics, Department of AET, Faculty of Mechanical Engineering, Technical University of Cluj-Napoca, 103-105 B-dul Muncii St., Cluj-Napoca , Cluj, Romania
Sebastian Stach Department of Biomedical Computer Systems, Institute of Informatics, Faculty of Computer Science and Materials Science, University of Silesia, B?dzińska 39, 41-205 Sosnowiec, Poland
Dan Mihai Călugăru Discipline of Ophthalmology, Department of Surgical Specialties and Medical Imaging, Faculty of Medicine, “Iuliu Ha?ieganu” University of Medicine and Pharmacy Cluj-Napoca, 8 Victor Babe? St., Cluj-Napoca , Cluj, Romania
Carmen Alina Lupaşcu Department of Mathematics and Informatics, University of Palermo, Via Archirafi 34, Palermo 90123, Italy
Simona Delia Nicoară Discipline of Ophthalmology, Department of Surgical Specialties and Medical Imaging, Faculty of Medicine, “Iuliu Ha?ieganu” University of Medicine and Pharmacy Cluj-Napoca, 8 Victor Babe? St., Cluj-Napoca , Cluj, Romania
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Abstract:
      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 box-counting method. Statistical analyses were performed using the GraphPad InStat software.

    RESULTS: The architecture of normal human retinal microvascular network was able to be described using the multifractal geometry. The average of generalized dimensions (Dq) for q=0, 1, 2, the width of the multifractal spectrum (Δα=αmax - αmin) and the spectrum arms’ heights difference (│Δf│) of the normal images were expressed as mean±standard deviation (SD): for segmented versions, D0=1.7014±0.0057; D1=1.6507±0.0058; D2=1.5772±0.0059; Δα=0.92441±0.0085; │Δf│= 0.1453±0.0051; for skeletonised versions, D0=1.6303±0.0051; D1=1.6012±0.0059; D2=1.5531±0.0058; Δα=0.65032±0.0162; │Δf│= 0.0238±0.0161. The average of generalized dimensions (Dq) 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.

PMC FullText Html:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5360780/
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