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Liu S, Liu L, Ma C, Su S, Liu Y, Li B. Association between retinal vascular fractal dimensions and retinopathy of prematurity: an AI-assisted retrospective case-control study. Int Ophthalmol 2025; 45:105. [PMID: 40100468 DOI: 10.1007/s10792-025-03461-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2024] [Accepted: 02/22/2025] [Indexed: 03/20/2025]
Abstract
PURPOSE The main objective of this study was to analyze the fractal dimensions (D(f)) of retinal vasculature in premature infants with retinopathy of prematurity (ROP) and determine their correlation with ROP severity. METHODS We conducted a single-center retrospective case-control study involving 641 premature patients with ROP (641 eyes) and 684 normal preterm infants (684 eyes) matched for corrected gestational age (CGA). Computer-assisted techniques were used to quantify peripapillary retinal vascular D(f), vessel tortuosity (VT), and vessel width (VW). RESULTS Compared to the normal preterm groups, patients with ROP exhibited a significant increase in retinal vascular D(f) by 0.0061 (P = 0.0002). Subgroup analyses revealed a significant association between increasing ROP severity and increased retinal vascular D(f) (P < 0.05). Multivariable-adjusted ordered logistic regression models demonstrated that retinal vascular D(f) (aOR: 3.307, P < 0.0001) was significantly independent and associated with ROP severity. For every 0.1 increase in D(f), the probability of ROP requiring intervention increased by 33.07%. Multiple linear regression models indicated a significant positive correlation between D(f) and VT, as well as VW around the optic disc (P < 0.0001). For every 1 (104 cm-3) increase in VT, D(f) increased by 0.0010. Similarly, for every 1 (μm) increase in VW, D(f) increased by 0.0025. CONCLUSIONS Our findings suggest that increased D(f) in retinal vessels is a pathological characteristic of ROP. This increase may be attributed to the curvature and width of the retinal vasculature in infants with ROP. Quantitative measurement of retinal vascular D(f) could serve as a valuable vascular indicator for assessing the severity of ROP.
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Affiliation(s)
- Shuai Liu
- School of Information Science and Technology, University of Science and Technology of China, Hefei, 230022, China
- Eye Institute, Affiliated Hospital of Nantong University, Medical School of Nantong University, Nantong, 226006, China
| | - Lei Liu
- School of Information Science and Technology, University of Science and Technology of China, Hefei, 230022, China.
| | - Cuixia Ma
- Anhui Province Maternity and Child Health Hospital, Maternity and Child Health Hospital affiliated to Anhui Medical University, Hefei, 230001, China
| | - Shu Su
- Eye Institute, Affiliated Hospital of Nantong University, Medical School of Nantong University, Nantong, 226006, China
| | - Ying Liu
- Department of Radiology, The First Affiliated Hospital, Jiangxi Medical College, Nanchang University, Jiangxi, 330006, China.
| | - Bin Li
- School of Information Science and Technology, University of Science and Technology of China, Hefei, 230022, China
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Weber DS, Huang KT, See AP. Fractal analysis of healthy and diseased vasculature in pediatric Moyamoya disease. Interv Neuroradiol 2025; 31:101-106. [PMID: 36703285 PMCID: PMC11833850 DOI: 10.1177/15910199231152513] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2022] [Accepted: 12/23/2022] [Indexed: 01/28/2023] Open
Abstract
BACKGROUND AND PURPOSE Fractal dimension is an objective metric for the notion of structural complexity. We sought to investigate differences in structural complexity between healthy and affected territories of cerebral vasculature in moyamoya, as well as associated scalp vasculature and native transdural collaterals in patients with moyamoya by comparing their respective fractal dimensions. METHODS Our cohort consisted of 15 transdural collaterals from 12 patients with unilateral anterior circulation moyamoya. Frames of distal arterial vasculature from internal and external carotid angiograms were selected then automatically segmented and also manually annotated by a cerebrovascular surgeon. In the affected hemisphere, the region with transdural collateral supply was compared to the contralateral region. The resulting skeletonized angiograms were analyzed for their fractal dimensions. RESULTS We found the average fractal dimension (Df) of the moyamoya-side ICA was 1.82 with slightly different means for the anteroposterial (AP) and lateral views (mean = 1.82; mean = 1.81). The overall mean for healthy cerebral vasculature was also found to be 1.82 (AP: mean = 1.83; lateral: mean = 1.81). Mean Df of native transdural collaterals was found to be 1.82 (AP: mean = 1.83; lateral: mean = 1.81). The mean Df difference between autosegmented and manually segmented images was 0.013. CONCLUSION In accordance with the clinical understanding of moyamoya disease, the distal arterial structural complexity is not affected in moyamoya, and is maintained by transdural collaterals formed by vasculogenesis. Autosegmentation of cerebral vasculature is also shown to be accurate when compared to manual segmentation.
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Affiliation(s)
- Daniel S. Weber
- Department of Neurosurgery, Boston Children's Hospital, Harvard Medical School, Boston, MA, USA
| | - Kevin T. Huang
- Department of Neurosurgery, Brigham and Women's Hospital, Harvard Medical School, Boston, MA, USA
| | - Alfred P. See
- Department of Neurosurgery, Boston Children's Hospital, Harvard Medical School, Boston, MA, USA
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Rahimi M, Khameneh EA, Riazi-Esfahani H, Mahmoudi T, Khalili Pour E, Kafieh R. Application of ImageJ in Optical Coherence Tomography Angiography (OCT-A): A Literature Review. J Ophthalmol 2023; 2023:9479183. [PMID: 38033422 PMCID: PMC10686712 DOI: 10.1155/2023/9479183] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2023] [Revised: 08/23/2023] [Accepted: 11/11/2023] [Indexed: 12/02/2023] Open
Abstract
Background This study aimed to review the literature on the application of ImageJ in optical coherence tomography angiography (OCT-A) images. Methods A general search was performed in PubMed, Google Scholar, and Scopus databases. The authors evaluated each of the selected articles in order to assess the implementation of ImageJ in OCT-A images. Results ImageJ can aid in reducing artifacts, enhancing image quality to increase the accuracy of the process and analysis, processing and analyzing images, generating comparable parameters such as the parameters that assess perfusion of the layers (vessel density (VD), skeletonized density (SD), and vessel length density (VLD)) and the parameters that evaluate the structure of the layers (fractal dimension (FD), vessel density index (VDI), and lacunarity (LAC)), and the foveal avascular zone (FAZ) that are used widely in the retinal and choroidal studies), and establishing diagnostic criteria. It can help to save time when the dataset is huge with numerous plugins and options for image processing and analysis with reliable results. Diverse studies implemented distinct binarization and thresholding techniques, resulting in disparate outcomes and incomparable parameters. Uniformity in methodology is required to acquire comparable data from studies employing diverse processing and analysis techniques that yield varied outcomes. Conclusion Researchers and professionals might benefit from using ImageJ because of how quickly and correctly it processes and analyzes images. It is highly adaptable and potent software, allowing users to evaluate images in a variety of ways. There exists a diverse range of methodologies for analyzing OCTA images through the utilization of ImageJ. However, it is imperative to establish a standardized strategy to ensure the reliability and consistency of the method for research purposes.
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Affiliation(s)
- Masoud Rahimi
- Retina Ward, Farabi Eye Hospital, Tehran University of Medical Sciences, Tehran, Iran
| | | | - Hamid Riazi-Esfahani
- Retina Ward, Farabi Eye Hospital, Tehran University of Medical Sciences, Tehran, Iran
| | - Tahereh Mahmoudi
- Department of Medical Physics and Biomedical Engineering, School of Medicine, Shiraz University of Medical Sciences, Shiraz, Iran
| | - Elias Khalili Pour
- Retina Ward, Farabi Eye Hospital, Tehran University of Medical Sciences, Tehran, Iran
| | - Rahele Kafieh
- Department of Engineering, Durham University, South Road, Durham DH1 3LE, UK
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Li P, Pan Q, Jiang S, Kuebler WM, Pries AR, Ning G. Visualizing the spatiotemporal pattern of yolk sac membrane vascular network by enhanced local fractal analysis. Microcirculation 2022; 29:e12746. [PMID: 34897901 DOI: 10.1111/micc.12746] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2021] [Revised: 11/09/2021] [Accepted: 12/07/2021] [Indexed: 12/30/2022]
Abstract
OBJECTIVE To establish methods for providing a comprehensive and detailed description of the spatial distribution of the vascular networks, and to reveal the spatiotemporal pattern of the yolk sac membrane vascular network during the angiogenic procedure. METHODS Addressing the limitations in the conventional local fractal analysis, an improved approach, named scanning average local fractal dimension, was proposed. This method was conducted on 6 high-resolution vascular images of the yolk sac membrane for 3 eggs at two stages (E3 and E4) to characterize the spatial distribution of the complexity of the vascular network. RESULTS With the proposed method, the spatial distribution of the complexity of the yolk sac membrane vascular network was visualized. From E3 to E4, the local fractal dimension increased in 3 eggs, 1.80 ± 0.02 vs. 1.85 ± 0.02, 1.72 ± 0.03 vs. 1.83 ± 0.02, and 1.77 ± 0.03 vs. 1.82 ± 0.02, respectively. The mean local fractal dimension in the most distal area from the embryo proper was the lowest at E3 while the highest at E4. At E3, the most peaks of the local fractal dimension were located in the vein territories and shifted to artery territories at E4. CONCLUSIONS The spatial distribution of the complexity of the yolk sac membrane vascular network exhibited diverse patterns at different stages. In addition from E3 to E4, the increment of complexity at the intersection areas between arteries and sinus terminalis was with the most advance. This is consistent with the physiologic evidence. The present work provides a potential approach for investigating the spatiotemporal pattern of the angiogenic process.
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Affiliation(s)
- Peilun Li
- Department of Biomedical Engineering, Zhejiang University, Hangzhou, China
| | - Qing Pan
- College of Information Engineering, Zhejiang University of Technology, Hangzhou, China
| | - Sheng Jiang
- Department of Biomedical Engineering, Zhejiang University, Hangzhou, China
| | - Wolfgang M Kuebler
- Institute of Physiology, Charité Universitätsmedizin Berlin, Berlin, Germany
| | - Axel R Pries
- Institute of Physiology, Charité Universitätsmedizin Berlin, Berlin, Germany
| | - Gangmin Ning
- Department of Biomedical Engineering, Zhejiang University, Hangzhou, China
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Popovic N, Vujosevic S, Radunović M, Radunović M, Popovic T. TREND database: Retinal images of healthy young subjects visualized by a portable digital non-mydriatic fundus camera. PLoS One 2021; 16:e0254918. [PMID: 34297749 PMCID: PMC8301647 DOI: 10.1371/journal.pone.0254918] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/13/2021] [Accepted: 07/06/2021] [Indexed: 01/22/2023] Open
Abstract
Topological characterization of the Retinal microvascular nEtwork visualized by portable fuNDus camera (TREND) is a database comprising of 72 color digital retinal images collected from the students of the Faculty of Medicine at the University of Montenegro, in the period from February 18th to March 11th 2020. The database also includes binarized images of manually segmented microvascular networks associated with each raw image. The participant demographic characteristics, health status, and social habits information such as age, sex, body mass index, smoking history, alcohol use, as well as previous medical history was collected. As proof of the concept, a smaller set of 10 color digital fundus images from healthy older participants is also included. Comparison of the microvascular parameters of these two sets of images demonstrate that digital fundus images recorded with a hand-held portable camera are able to capture the changes in patterns of microvascular network associated with aging. The raw images from the TREND database provide a standard that defines normal retinal anatomy and microvascular network geometry in young healthy people in Montenegro as it is seen with the digital hand-held portable non-mydriatic MiiS HORUS Scope DEC 200.This knowledge could facilitate the application of this technology at the primary level of health care for large scale telematic screening for complications of chronic diseases, such as hypertensive and diabetic retinopathy. In addition, it could aid in the development of new methods for early detection of age-related changes in the retina, systemic chronic diseases, as well as eye-specific diseases. The associated manually segmented images of the microvascular networks provide the standard that can be used for development of automatic software for image quality assessment, segmentation of microvascular network, and for computer-aided detection of pathological changes in retina. The TREND database is freely available at https://doi.org/10.5281/zenodo.4521043.
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Affiliation(s)
- Natasa Popovic
- Faculty of Medicine, University of Montenegro, Podgorica, Montenegro
- * E-mail:
| | | | | | - Miodrag Radunović
- Faculty of Medicine, University of Montenegro, Podgorica, Montenegro
| | - Tomo Popovic
- Faculty for Information Systems and Technologies, University of Donja Gorica, Podgorica, Montenegro
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Li M, Wang G, Xia H, Feng Z, Xiao P, Yuan J. Retinal vascular geometry detection as a biomarker in diabetes mellitus. Eur J Ophthalmol 2021; 32:1710-1719. [PMID: 34284606 DOI: 10.1177/11206721211033488] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
OBJECTIVE To compare the vessel geometry characteristics of color fundus photographs in normal control and diabetes mellitus (DM) patients and to find potential biomarkers for early diabetic retinopathy (DR) based on a neural network vessel segmentation system and automated vascular geometry parameter analysis software. METHODS A total of 102 consecutive patients with type 2 DM (T2DM) and 132 healthy controls were recruited. All participants underwent general ophthalmic examinations, and retinal fundus photographs were taken with a digital fundus camera without mydriasis. Color fundus photographs were input into a dense-block generative adversarial network (D-GAN)-assisted retinal vascular segmentation system (http://www.gdcerc.cn:8081/#/login) to obtain binary images. These images were then analyzed by customized software (ocular microvascular analysis system V2.9.1) for automatic processing of vessel geometry parameters, including the monofractal dimension (Dbox), multifractal dimension (D0), vessel area ratio (R), max vessel diameter (dmax), average vessel diameter (dave), arc-chord ratio (A/C), and tortuosity (τn). Geometric differences between the healthy subjects and DM patients were analyzed. Then, regression analysis and receiver operating characteristic (ROC) curve analysis were performed to evaluate the diagnostic efficiency of the vascular geometry parameters. RESULTS No significant differences were observed between the baseline characteristics of each group. DM patients had lower Dbox and D0 values (1.330 ± 0.041; 1.347 ± 0.038) than healthy subjects (1.343 ± 0.048, p < 0.05; 1.362 ± 0.042, p < 0.05) and showed increasing values of dmax, dave, A/C, and τn compared with normal controls, although only the differences in dave and τn between the groups were statistically significant. In the regression analysis, dave and τn showed a good correlation with diabetes (dave, OR 1.765, 95% CI 1.319-2.362, p < 0.001; τn, OR 9.323, 95% CI 1.492-58.262, p < 0.05). CONCLUSIONS We demonstrated the relationship between retinal vascular geometry and the process in DM patients, showing that Dbox, D0, dave, and τn may be indicators of morphological changes in retinal vessels in DM patients and can be early biomarkers of DR.
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Affiliation(s)
- Meng Li
- State Key Laboratory of Ophthalmology, Zhongshan Ophthalmic Center, Sun Yat-sen University, Guangzhou, People's Republic of China
| | - Gengyuan Wang
- State Key Laboratory of Ophthalmology, Zhongshan Ophthalmic Center, Sun Yat-sen University, Guangzhou, People's Republic of China
| | - Honghui Xia
- Department of Ophthalmology, Zhaoqing Gaoyao People's Hospital, Zhaoqing, People's Republic of China
| | - Ziqing Feng
- State Key Laboratory of Ophthalmology, Zhongshan Ophthalmic Center, Sun Yat-sen University, Guangzhou, People's Republic of China
| | - Peng Xiao
- State Key Laboratory of Ophthalmology, Zhongshan Ophthalmic Center, Sun Yat-sen University, Guangzhou, People's Republic of China
| | - Jin Yuan
- State Key Laboratory of Ophthalmology, Zhongshan Ophthalmic Center, Sun Yat-sen University, Guangzhou, People's Republic of China
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Abdelsalam MM, Zahran MA. A Novel Approach of Diabetic Retinopathy Early Detection Based on Multifractal Geometry Analysis for OCTA Macular Images Using Support Vector Machine. IEEE ACCESS 2021; 9:22844-22858. [DOI: 10.1109/access.2021.3054743] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 08/30/2023]
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El Damrawi G, Zahran MA, Amin E, Abdelsalam MM. Enforcing artificial neural network in the early detection of diabetic retinopathy OCTA images analysed by multifractal geometry. JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE 2020. [DOI: 10.1080/16583655.2020.1796244] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- G. El Damrawi
- Glass Research Group, Physics Department, Faculty of Science, Mansoura University, Mansoura, Egypt
| | - M. A. Zahran
- Theoretical Physics Group, Physics Department, Faculty of Science, Mansoura University, Mansoura, Egypt
| | - ElShaimaa Amin
- Physics Department (Biophysics), Faculty of Science, Mansoura University, Mansoura, Egypt
| | - Mohamed M. Abdelsalam
- Computers and Systems Department, Faculty of Engineering, Mansoura University, Mansoura, Egypt
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Wu HQ, Shan YX, Wu H, Zhu DR, Tao HM, Wei HG, Shen XY, Sang AM, Dong JC. Computer aided diabetic retinopathy detection based on ophthalmic photography: a systematic review and Meta-analysis. Int J Ophthalmol 2019; 12:1908-1916. [PMID: 31850177 DOI: 10.18240/ijo.2019.12.14] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/25/2019] [Accepted: 06/10/2019] [Indexed: 12/17/2022] Open
Abstract
AIM To ensure the diagnostic value of computer aided techniques in diabetic retinopathy (DR) detection based on ophthalmic photography (OP). METHODS PubMed, EMBASE, Ei village, IEEE Xplore and Cochrane Library database were searched systematically for literatures about computer aided detection (CAD) in DR detection. The methodological quality of included studies was appraised by the Quality Assessment Tool for Diagnostic Accuracy Studies (QUADAS-2). Meta-DiSc was utilized and a random effects model was plotted to summarize data from those included studies. Summary receiver operating characteristic curves were selected to estimate the overall test performance. Subgroup analysis was used to identify the efficiency of CAD in detecting DR, exudates (EXs), microaneurysms (MAs) as well as hemorrhages (HMs), and neovascularizations (NVs). Publication bias was analyzed using STATA. RESULTS Fourteen articles were finally included in this Meta-analysis after literature review. Pooled sensitivity and specificity were 90% (95%CI, 85%-94%) and 90% (95%CI, 80%-96%) respectively for CAD in DR detection. With regard to CAD in EXs detecting, pooled sensitivity, specificity were 89% (95%CI, 88%-90%) and 99% (95%CI, 99%-99%) respectively. In aspect of MAs and HMs detection, pooled sensitivity and specificity of CAD were 42% (95%CI, 41%-44%) and 93% (95%CI, 93%-93%) respectively. Besides, pooled sensitivity and specificity were 94% (95%CI, 89%-97%) and 87% (95%CI, 83%-90%) respectively for CAD in NVs detection. No potential publication bias was observed. CONCLUSION CAD demonstrates overall high diagnostic accuracy for detecting DR and pathological lesions based on OP. Further prospective clinical trials are needed to prove such effect.
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Affiliation(s)
- Hui-Qun Wu
- Department of Medical Informatics, Medical School of Nantong University, Nantong 226001, Jiangsu Province, China
| | - Yan-Xing Shan
- Department of Medical Informatics, Medical School of Nantong University, Nantong 226001, Jiangsu Province, China
| | - Huan Wu
- Department of Medical Informatics, Medical School of Nantong University, Nantong 226001, Jiangsu Province, China
| | - Di-Ru Zhu
- Department of Medical Informatics, Medical School of Nantong University, Nantong 226001, Jiangsu Province, China
| | - Hui-Min Tao
- Department of Medical Informatics, Medical School of Nantong University, Nantong 226001, Jiangsu Province, China
| | - Hua-Gen Wei
- Department of Medical Informatics, Medical School of Nantong University, Nantong 226001, Jiangsu Province, China
| | - Xiao-Yan Shen
- School of Information Science and Technology, Nantong University, Nantong 226001, Jiangsu Province, China
| | - Ai-Min Sang
- Department of Ophthalmology, Affiliated Hospital of Nantong University, Nantong 226001, Jiangsu Province, China
| | - Jian-Cheng Dong
- Department of Medical Informatics, Medical School of Nantong University, Nantong 226001, Jiangsu Province, China
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Popovic N, Vujosevic S, Popovic T. Regional Patterns in Retinal Microvascular Network Geometry in Health and Disease. Sci Rep 2019; 9:16340. [PMID: 31705046 PMCID: PMC6841983 DOI: 10.1038/s41598-019-52659-8] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/19/2019] [Accepted: 10/21/2019] [Indexed: 01/04/2023] Open
Abstract
The study explores the regional differences in microvascular geometry between the optic disc (O) and the macular area (M) in health and disease. Skeletonized manually segmented vascular networks from 15 healthy, 15 retinas with diabetic retinopathy (DR), and 15 retinas with glaucoma from publicly available High-Resolution Fundus (HRF) image database were used. When visualized by a digital fundus camera, O has a substantial proportion of small arteries and larger arterioles, while M contains smaller arterioles at the periphery and avascular zone in the center. We hypothesized that in pathological conditions the vascular network remodelling patterns in these two regions may be different. The analysis of box-counting fractal dimension (Db), lacunarity (Λ), and microvascular density showed that in healthy retinas, Λ and vessel density were lower in the M compared to the O, while the Db did not change. In retinas with DR, the Db was the lowest in the M, which was different from all other groups. The vessel density followed this trend. Lacunarity was the highest in the O of DR group compared to all other groups. The results show that in DR various regions of retinal microvascular network remodel in a different manner and to different extent.
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Affiliation(s)
- Natasa Popovic
- Faculty of Medicine, University of Montenegro, Kruševac bb, Podgorica, Montenegro.
| | - Stela Vujosevic
- Eye Clinic, University Hospital "Maggiore della Caritá", Novara, Italy
| | - Tomo Popovic
- Faculty for Information Systems and Technologies, University of Donja Gorica, Oktoih 1, Podgorica, Montenegro
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Metze K, Adam R, Florindo JB. The fractal dimension of chromatin - a potential molecular marker for carcinogenesis, tumor progression and prognosis. Expert Rev Mol Diagn 2019; 19:299-312. [DOI: 10.1080/14737159.2019.1597707] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Affiliation(s)
- Konradin Metze
- Department of Pathology, Faculty of Medical Sciences, State University of Campinas (UNICAMP), Campinas, Brazil
| | - Randall Adam
- Department of Pathology, Faculty of Medical Sciences, State University of Campinas (UNICAMP), Campinas, Brazil
| | - João Batista Florindo
- Department of Applied Mathematics, Institute of Mathematics, Statistics and Scientific Computing, State University of Campinas, Campinas, Brazil
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