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Dimension Fractal in Radiological Imagery for Comparison of Data Between Morphologic and Pathological Elements

Received: 11 December 2020     Accepted: 7 January 2021     Published: 16 June 2021
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Abstract

Aims: Fractal for comparison of radiological imagery between morphologic and pathological elements confirms the behavior of the experimental information through dimension itself. The irregularity of the human body is its own characteristic. However, it has traditionally been measured with Euclidean metrics, by approximating its shapes to regular lines, areas and volumes. In response to this impossibility of making reliable measurements of this class of objects, fractal geometry is developed, which allows to adequately characterize the irregular shape of the human body. Method: they use the theoretic methods: Analysis synthesis, induction deduction and abstraction concretion. Processes of understanding, explanation and interpretation. Methods, procedures and mathematical algorithms, as well as information-technology professional programs are applicable. Come true quest of information about the application of dimension fractal in the diagnostic one belonging to diseases, based in radiological imagery. The diagnostic method fractal consists in the calculation of dimension for three cellular objects defined as: the nucleus, the cytoplasm without a nucleus and the entire cell. Results: Methods and procedures to ratify diseases, where the different authors yield a mathematical model, propose which themselves fractal for the comparison of histological and pathological elements confirms the behavior of the experimental data represented in radiological imagery, by means of dimension. About fractal geometry, the fractal dimension is obtained, which is a numerical measure that represents the degree of irregularity of an object. However, it has traditionally been measured with Euclidean metrics, by approximating its shapes to regular lines, areas and volumes. In response to this impossibility of making reliable measurements of this class of objects, fractal geometry is developed, which allows to adequately characterize the irregular shape of the human body. Conclusions: A methodology of work based in radiological imagery by comparison of histological and pathological elements to determine different diseases in patients becomes established.

Published in Applied and Computational Mathematics (Volume 10, Issue 2)
DOI 10.11648/j.acm.20211002.12
Page(s) 40-45
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2021. Published by Science Publishing Group

Keywords

Experimental Data, Mathematical Model, Medical Applications

References
[1] Vasiljevic J, Reljin B, Sopta J, Mijucic V, Tulic G, Reljin I. Application of multifractal analysis on microscopic images in the classification of metastatic bone disease. Biomed Micro devices. 2012; 14: 541–548.
[2] Abedini M, Bowling A, Chakravorty R, Demyanov S, Garnavi R. Detection of outlier lesions based on extracted features from skin images, 2018. US Patent US 2018/0122065 A1.
[3] Hermann P; Mrkvirka T; et al. Fractal; stochastic geometry inference for breast cancer: a case study with random fractal models; Quermass-interaction process, Statistics in Medicine, vol. 34. 2015. https://doi.org/10.1002/sim.6497
[4] Pribic J; Kanjer K; et al. Fractal dimension; lacunarity of tumor microscopic images as prognostic indicators of clinical outcome in early breast cancer. Biomarkers in Medicine, vol. 9, pag. 1279–1290. 2015. https://doi.org/10.2217/bmm.15.102
[5] Shanmugavadivu P; Sivakumar V; et al. Fractal dimension-bound spatiotemporal analysis of digital mammograms. The European Physical Journal Special Topics, vol. 225, 2016, pag. 137–146.
[6] Fiz J. New diagnostic techniques for respiratory diseases. Image Analysis. March 17. 2016. Hospital Universitario Germans Trias I Pujol. Servicio de Neumología. Spain.
[7] Luzi P, Bianciardi G, Miracco C, Desanti MM, Del Vecchio MT, Alia L, et al. Fractal analysis in human pathology. Ann NY Acad Sci. 1999; 879: 255-57.
[8] Gazit Y, Baish JW, Safabaksh N. Fractal characteristics of tumor vascular architecture during tumor growth and regression. Microcirculation. 1997; 4: 395-402.
[9] Baish H, Jain R. Fractals and Cancer. Cancer research. 2000; 60: 3683-3688.
[10] Sankar D, Thomas T. A New Fast Fractal Modeling Approach for the Detection of Microcalcifications in Mammograms. Journal of Digital Imaging. 2010; 23 (5): 538-546.
[11] Rodríguez J. Fractales: Ayuda diagnóstica para células preneoplásicas y cancerígenas del epitelio escamoso cervical confirmación de aplicabilidad clínica. Revista 24 (1): 79-88, 2016.
[12] Rodríguez J, Prieto S, Correa C, Posso H, Bernal P, ViteryS, et al. Generalización fractal de células preneoplásicas y cancerígenas del epitelio escamoso cervical de aplicaciónclínica. Rev Med. 2010; 18 (2): 173-181.
[13] West J. Fractal physiology and chaos in medicine. Singapore: World Scientific; 1990.
[14] Dobrescu R; Ichim L; et al. Benignand malignant breast tumors: Diagnosis using fractal measures. In 2014 18th International Conference on System Theory, Control; Computing, ICSTCC 2014, Faculty of Automatic Control; Computers, Politehnica University of Bucharest, pag. 82–86.
[15] Ascencio A, Zapata J. Nevus classification by calculating the fractal dimension and the harmonic analysis of the contour extracted from multispectral images. Revista INGENIERÍA UC, vol. 25, núm. 2, 2018 Universidad de Carabobo.
[16] Liang Y, Sun L, Ser W, Lin F, Tien S, Chen O, Lin Z. Classification of non-tumorous skin pigmentation disorders using voting based probabilistic linear discriminant analysis. Computers in Biology and Medicine, 2018.
[17] Fernandez S, Rngel F. Comparativo de los Algoritmos de Dimensión Fractal Higuchi, Katz y Multiresolución de Conteo de Cajas en Señales EEG Basadas en Potenciales Relacionados por Eventos. September 2017. Revista EIA 14 (27): 7317.
[18] Mandelbrot B. Introducción. En: Mandelbrot B. Los Objetos Fractales. Barcelona. Tusquets Eds. S. A.; 2000. p. 13-26. US 2018/0122065 A1.
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    Ernesto Borges Batista, Luis Alberto Escalona Fernandez, Kirelis Napoles Dominguez, Yamila Ochoa Sarmiento, Claudia del Carmen Pupo Marrero. (2021). Dimension Fractal in Radiological Imagery for Comparison of Data Between Morphologic and Pathological Elements. Applied and Computational Mathematics, 10(2), 40-45. https://doi.org/10.11648/j.acm.20211002.12

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    Ernesto Borges Batista; Luis Alberto Escalona Fernandez; Kirelis Napoles Dominguez; Yamila Ochoa Sarmiento; Claudia del Carmen Pupo Marrero. Dimension Fractal in Radiological Imagery for Comparison of Data Between Morphologic and Pathological Elements. Appl. Comput. Math. 2021, 10(2), 40-45. doi: 10.11648/j.acm.20211002.12

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    AMA Style

    Ernesto Borges Batista, Luis Alberto Escalona Fernandez, Kirelis Napoles Dominguez, Yamila Ochoa Sarmiento, Claudia del Carmen Pupo Marrero. Dimension Fractal in Radiological Imagery for Comparison of Data Between Morphologic and Pathological Elements. Appl Comput Math. 2021;10(2):40-45. doi: 10.11648/j.acm.20211002.12

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  • @article{10.11648/j.acm.20211002.12,
      author = {Ernesto Borges Batista and Luis Alberto Escalona Fernandez and Kirelis Napoles Dominguez and Yamila Ochoa Sarmiento and Claudia del Carmen Pupo Marrero},
      title = {Dimension Fractal in Radiological Imagery for Comparison of Data Between Morphologic and Pathological Elements},
      journal = {Applied and Computational Mathematics},
      volume = {10},
      number = {2},
      pages = {40-45},
      doi = {10.11648/j.acm.20211002.12},
      url = {https://doi.org/10.11648/j.acm.20211002.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20211002.12},
      abstract = {Aims: Fractal for comparison of radiological imagery between morphologic and pathological elements confirms the behavior of the experimental information through dimension itself. The irregularity of the human body is its own characteristic. However, it has traditionally been measured with Euclidean metrics, by approximating its shapes to regular lines, areas and volumes. In response to this impossibility of making reliable measurements of this class of objects, fractal geometry is developed, which allows to adequately characterize the irregular shape of the human body. Method: they use the theoretic methods: Analysis synthesis, induction deduction and abstraction concretion. Processes of understanding, explanation and interpretation. Methods, procedures and mathematical algorithms, as well as information-technology professional programs are applicable. Come true quest of information about the application of dimension fractal in the diagnostic one belonging to diseases, based in radiological imagery. The diagnostic method fractal consists in the calculation of dimension for three cellular objects defined as: the nucleus, the cytoplasm without a nucleus and the entire cell. Results: Methods and procedures to ratify diseases, where the different authors yield a mathematical model, propose which themselves fractal for the comparison of histological and pathological elements confirms the behavior of the experimental data represented in radiological imagery, by means of dimension. About fractal geometry, the fractal dimension is obtained, which is a numerical measure that represents the degree of irregularity of an object. However, it has traditionally been measured with Euclidean metrics, by approximating its shapes to regular lines, areas and volumes. In response to this impossibility of making reliable measurements of this class of objects, fractal geometry is developed, which allows to adequately characterize the irregular shape of the human body. Conclusions: A methodology of work based in radiological imagery by comparison of histological and pathological elements to determine different diseases in patients becomes established.},
     year = {2021}
    }
    

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  • TY  - JOUR
    T1  - Dimension Fractal in Radiological Imagery for Comparison of Data Between Morphologic and Pathological Elements
    AU  - Ernesto Borges Batista
    AU  - Luis Alberto Escalona Fernandez
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    AB  - Aims: Fractal for comparison of radiological imagery between morphologic and pathological elements confirms the behavior of the experimental information through dimension itself. The irregularity of the human body is its own characteristic. However, it has traditionally been measured with Euclidean metrics, by approximating its shapes to regular lines, areas and volumes. In response to this impossibility of making reliable measurements of this class of objects, fractal geometry is developed, which allows to adequately characterize the irregular shape of the human body. Method: they use the theoretic methods: Analysis synthesis, induction deduction and abstraction concretion. Processes of understanding, explanation and interpretation. Methods, procedures and mathematical algorithms, as well as information-technology professional programs are applicable. Come true quest of information about the application of dimension fractal in the diagnostic one belonging to diseases, based in radiological imagery. The diagnostic method fractal consists in the calculation of dimension for three cellular objects defined as: the nucleus, the cytoplasm without a nucleus and the entire cell. Results: Methods and procedures to ratify diseases, where the different authors yield a mathematical model, propose which themselves fractal for the comparison of histological and pathological elements confirms the behavior of the experimental data represented in radiological imagery, by means of dimension. About fractal geometry, the fractal dimension is obtained, which is a numerical measure that represents the degree of irregularity of an object. However, it has traditionally been measured with Euclidean metrics, by approximating its shapes to regular lines, areas and volumes. In response to this impossibility of making reliable measurements of this class of objects, fractal geometry is developed, which allows to adequately characterize the irregular shape of the human body. Conclusions: A methodology of work based in radiological imagery by comparison of histological and pathological elements to determine different diseases in patients becomes established.
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Author Information
  • Department of Basic Biomedical Sciences, Holguin University of Medical Sciences, Holguin, Cuba

  • Department of Medical Information Technology, Faculty of Medical Sciences, Holguin University of Medical Sciences, Holguin, Cuba

  • Department of Basic Biomedical Sciences, Holguin University of Medical Sciences, Holguin, Cuba

  • Department of Basic Biomedical Sciences, Holguin University of Medical Sciences, Holguin, Cuba

  • Department of Basic Biomedical Sciences, Holguin University of Medical Sciences, Holguin, Cuba

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