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Original Article

The fractal geometry of proliferative diabetic retinopathy: implications for the diagnosis and the process of retinal vasculogenesis

Pages 1103-1109 | Received 22 Jul 1993, Accepted 08 Nov 1993, Published online: 02 Jul 2009

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Read on this site (9)

Knud B. Pedersen, Rebecca Broe & Jakob Grauslund. (2016) Inter-Eye Agreement in Measurement of Retinal Vascular Fractal Dimension in Patients with Type 1 Diabetes Mellitus. Ophthalmic Epidemiology 23:2, pages 131-135.
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Mads Nybo, Lauren A. B. Hodgson, Ryo Kawasaki, Tien Yin Wong & Jakob Grauslund. (2014) Hemoglobin is Associated with Retinal Vascular Fractals in Type 1 Diabetes Patients. Ophthalmic Epidemiology 21:5, pages 327-332.
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Taiji Nagaoka & Akitoshi Yoshida. (2013) Relationship Between Retinal Fractal Dimensions and Retinal Circulation in Patients with Type 2 Diabetes Mellitus. Current Eye Research 38:11, pages 1148-1152.
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Victoria Fay Cosatto, Gerald Liew, Elena Rochtchina, Alan Wainwright, YongPing Zhang, Wynne Hsu, Mong Li Lee, Qiangfeng Peter Lau, Haslina H Hamzah, Paul Mitchell, Tien Yin Wong & Jie Jin Wang. (2010) Retinal Vascular Fractal Dimension Measurement and Its Influence from Imaging Variation: Results of Two Segmentation Methods. Current Eye Research 35:9, pages 850-856.
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Audrey Karperien, Herbert F Jelinek, Jorge JG Leandro, João VB Soares, Roberto M Cesar$suffix/text()$suffix/text() & Alan Luckie. (2008) Automated detection of proliferative retinopathy in clinical practice. Clinical Ophthalmology 2:1, pages 109-122.
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Arpenik Avakian, Robert E. Kalina, E. Helene Sage, Avni H. Rambhia, Katherine E. Elliott, Elaine L. Chuang, John I. Clark, Jenq-Neng Hwang & Patricia Parsons-Wingerter. (2002) Fractal analysis of region-based vascular change in the normal and non-proliferative diabetic retina. Current Eye Research 24:4, pages 274-280.
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Yuval Gazit, James W. Baish, Nina Safabakhsh, Michael Leunig, Laurence T. Baxter & Rakesh K. Jain. (1997) Fractal Characteristics of Tumor Vascular Architecture During Tumor Growth and Regression. Microcirculation 4:4, pages 395-402.
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Albert Daxer & Armin Ettl. (1995) Corneal vascularisation and its relation to the physical properties of the tissue: a fractal analysis. Current Eye Research 14:4, pages 263-268.
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Saima Hilal, Carol Y Cheung, Tien Yin Wong, Leopold Schmetterer & Christopher Chen. (2022) Retinal parameters, cortical cerebral microinfarcts, and their interaction with cognitive impairment. International Journal of Stroke 18:1, pages 70-77.
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Xiaoling Luo, Honggang Zhang, Jingyong Su, Wai Keung Wong, Jinkai Li & Yong Xu. (2023) RV-ESA: A novel computer-aided elastic shape analysis system for retinal vessels in diabetic retinopathy. Computers in Biology and Medicine 152, pages 106406.
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Chae Hyun Song, Seok Hwan Kim & Kyoung Min Lee. (2022) Fractal Dimension of Peripapillary Vasculature in Primary Open-Angle Glaucoma. Korean Journal of Ophthalmology 36:6, pages 518-526.
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Sam Yu & Vasudevan Lakshminarayanan. (2021) Fractal Dimension and Retinal Pathology: A Meta-Analysis. Applied Sciences 11:5, pages 2376.
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Shariq Hashmi, Jennifer Lopez, Bing Chiu, Soshian Sarrafpour, Akash Gupta & Joshua Young. (2021) Fractal Dimension Analysis of OCTA Images of Diabetic Retinopathy Using Circular Mass-Radius Method. Ophthalmic Surgery, Lasers and Imaging Retina 52:3, pages 116-122.
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Sayan Das, Nilanjana Dutta Roy, Arindam Biswas & Sanjoy Kumar Saha. (2020) A novel methodology for vessel extraction from retinal fundus image and detection of neovascularization. Multimedia Tools and Applications 80:3, pages 4093-4110.
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Jianbo Mao, Yuhao Luo, Lei Liu, Jimeng Lao, Yirun Shao, Min Zhang, Caiyun Zhang, Mingzhai Sun & Lijun Shen. (2019) Automated diagnosis and quantitative analysis of plus disease in retinopathy of prematurity based on deep convolutional neural networks. Acta Ophthalmologica 98:3.
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Anastasia Korolj, Hau-Tieng Wu & Milica Radisic. (2019) A healthy dose of chaos: Using fractal frameworks for engineering higher-fidelity biomedical systems. Biomaterials 219, pages 119363.
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Pablo Chamoso, Sara Rodríguez, Fernando de la Prieta & Javier Bajo. (2018) Classification of retinal vessels using a collaborative agent-based architecture. AI Communications 31:5, pages 427-444.
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Orhan E. Arslan. 2018. Drug Delivery for the Retina and Posterior Segment Disease. Drug Delivery for the Retina and Posterior Segment Disease 3 33 .
José Ignacio Orlando, Karel van Keer, João Barbosa Breda, Hugo Luis Manterola, Matthew B. Blaschko & Alejandro Clausse. (2017) Proliferative diabetic retinopathy characterization based on fractal features: Evaluation on a publicly available dataset. Medical Physics 44:12, pages 6425-6434.
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Pablo Chamoso, Sara Rodríguez, Fernando De La Prieta, Juan F. De Paz, Javier Bajo Pérez, Juan Manuel Corchado Rodríguez & Luis García-Ortiz. 2017. Multi-Agent Systems and Agreement Technologies. Multi-Agent Systems and Agreement Technologies 509 523 .
Diego F. G. Coelho, Rangaraj M. Rangayyan & Vassil S. Dimitrov. (2016) Detection of neovascularization near the optic disk due to diabetic retinopathy. Detection of neovascularization near the optic disk due to diabetic retinopathy.
Sathvika Mudigonda, Faraz Oloumi, Kalyana M. Katta & Rangaraj M. Rangayyan. (2015) Fractal analysis of neovascularization due to diabetic retinopathy in retinal fundus images. Fractal analysis of neovascularization due to diabetic retinopathy in retinal fundus images.
Fan Lin, Pengli Zhu, Feng Huang, Qiaowei Li, Yin Yuan, Zhonghai Gao, Peng Yu, Jing Lin & Falin Chen. (2015) Aortic stiffness is associated with the central retinal arteriolar equivalent and retinal vascular fractal dimension in a population along the southeastern coast of China. Hypertension Research 38:5, pages 342-348.
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Rebecca Broe. (2015) Early risk stratification in paediatric type 1 diabetes. Acta Ophthalmologica 93, pages 1-19.
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Alun D. Hughes. (2015) Optimality, cost minimization and the design of arterial networks. Artery Research 10:C, pages 1.
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Gábor Márk Somfai, Erika Tátrai, Lenke Laurik, Boglárka E Varga, Vera Ölvedy, William E Smiddy, Robert Tchitnga, Anikó Somogyi & Delia Cabrera DeBuc. (2014) Fractal-based analysis of optical coherence tomography data to quantify retinal tissue damage. BMC Bioinformatics 15:1.
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Rebecca Broe, Malin L. Rasmussen, Ulrik Frydkjaer-Olsen, Birthe S. Olsen, Henrik B. Mortensen, Tunde Peto & Jakob Grauslund. (2014) Retinal vascular fractals predict long-term microvascular complications in type 1 diabetes mellitus: the Danish Cohort of Pediatric Diabetes 1987 (DCPD1987). Diabetologia 57:10, pages 2215-2221.
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M.Z. Che Azemin, F. Ab Hamid, A. Aminuddin, J.J. Wang, R. Kawasaki & D.K. Kumar. (2013) Age-related rarefaction in retinal vasculature is not linear. Experimental Eye Research 116, pages 355-358.
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Albert Daxer. (2011) Retinal Vascular Fractals. Ophthalmology 118:5, pages 1013-1014.
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Jakob Grauslund, Anne Katrin Sjølie & Ryo Kawasaki. (2011) Author reply. Ophthalmology 118:5, pages 1014.
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Jakob Grauslund. (2011) Eye Complications and Markers of Morbidity and Mortality in Long-term Type 1 Diabetes. Acta Ophthalmologica 89:thesis1, pages 1-19.
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Göran Darius Hildebrand & Alistair R. Fielder. 2011. Pediatric Retina. Pediatric Retina 39 65 .
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J. W. Y. Yau, R. Kawasaki, F. M. A. Islam, J. Shaw, P. Zimmet, J. J. Wang & T. Y. Wong. (2010) Retinal fractal dimension is increased in persons with diabetes but not impaired glucose metabolism: the Australian Diabetes, Obesity and Lifestyle (AusDiab) study. Diabetologia 53:9, pages 2042-2045.
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Jakob Grauslund, Anders Green, Ryo Kawasaki, Lauren Hodgson, Anne Katrin Sjølie & Tien Y. Wong. (2010) Retinal Vascular Fractals and Microvascular and Macrovascular Complications in Type 1 Diabetes. Ophthalmology 117:7, pages 1400-1405.
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