Abstract
<i>Aims:</i> 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. <i>Method:</i> 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. <i>Results:</i> 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. <i>Conclusions:</i> A methodology of work based in radiological imagery by comparison of histological and pathological elements to determine different diseases in patients becomes established.
Highlights
In order to understand their use in medical sciences, we must have even a basic notion of their properties or concepts that make up this branch of mathematics, so a fractal; It is a geometric object whose basic structure, fragmented or apparently irregular, is repeated at different scales, this is one of its most important properties, the self-similarity or selfsimilarity that its structure has on a smaller scale of magnitude, starting from a mother figure or seed, to infinity. [2, 4, 5]
In 1982, with his masterpiece Fractal Geometry of Nature, he exposed a whole universe, which, not completely unknown, was loaded with a new and renewed vision of reality and the processes that develop it, and how the patterns by which Roughness and fractures are governed in nature and the chaotic behavior of many phenomena have an explanation and representation in the Fractal Dimension, not for pleasure he called this kind of mathematics the Fingerprint of God when they were reflected in everyday life
[1] From fractal geometry, the fractal dimension is obtained, which is a numerical measure that represents the degree of irregularity of an object
Summary
Mountain ranges, coasts, trees, rivers and some natural phenomena have in common with our biology, say Nervous, Cardiovascular, Neurological System plus some pathological processes that affect us as a species? All have in common the presence of patterns approximated to Fractals and their Mathematics that develops them. [1, 2, 3]In order to understand their use in medical sciences, we must have even a basic notion of their properties or concepts that make up this branch of mathematics, so a fractal; It is a geometric object whose basic structure, fragmented or apparently irregular, is repeated at different scales, this is one of its most important properties, the self-similarity or selfsimilarity that its structure has on a smaller scale of magnitude, starting from a mother figure or seed, to infinity. [2, 4, 5]This would be the ideal fractal, the classic mathematical equation that is repeated or iterated infinity of times (Figure 1) resulting in that its fractal metric dimension is a rationalErnesto Borges Batista et al.: Dimension Fractal in Radiological Imagery for Comparison of DataBetween Morphologic and Pathological Elements number greater than its topological dimension or its Hausdorff - Besicovitch dimension is strictly greater than its topological dimension, which in non-mathematical language have an infinite perimeter in a finite area. [2]That is why we say that, with respect to our biology organized by system and the natural world that surrounds us, there are well-organized structural patterns approximated to fractal forms, since by simple physics, the structural form of matter visually changes to a lesser scale and loses its selfsimilarity, which can only be observed at macroscopic scales (Figure 2). [1, 2]This does not mean that the study and development of fractal mathematics is independent of material reality, on the contrary, its birth as a theory in the second half of the 20th century had as its fundamental objective, to model, describe and analyze many natural phenomena and scientific experiments that Euclidean or classical mathematics could neither represent nor answer.Its visionary and conceptualizer Benoit Mandelbrot, a Polish mathematician nationalized in France and in the United States of America, a Jew who suffered the penalties of the Second World War, who was influenced by the work of mathematical geniuses such as Karl Theodor Wilhelm Weierstrass, Helge Von Koch, Waclaw Sierpinski, Henry Poincaré, Abram Samóilovich Bezikóvich, Pierre Fatou and Gaston Julia on the subject in question, proposed the term in 1975, which derives from the Latin fractus, which means broken or fractured.the following scientific problem is defined: How do we establish a mathematical model represented by radiological imagery?The objective of this work is to confirm the behavior of the experimental data modeled by the fractal's dimension.Julia sets represented by some of its points (in red the connected Julia sets and in blue those not related). That is why we say that, with respect to our biology organized by system and the natural world that surrounds us, there are well-organized structural patterns approximated to fractal forms, since by simple physics, the structural form of matter visually changes to a lesser scale and loses its selfsimilarity, which can only be observed at macroscopic scales (Figure 2). [1, 2] This does not mean that the study and development of fractal mathematics is independent of material reality, on the contrary, its birth as a theory in the second half of the 20th century had as its fundamental objective, to model, describe and analyze many natural phenomena and scientific experiments that Euclidean or classical mathematics could neither represent nor answer.
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