Abstract
The theory of fractals, proposed by the mathematician Mandelbrot (1975), has been applied to many fields in Biology, mainly due to the property of self-similarity observed in the natural world, such as in the DNA molecule and chromatin structure. Many researches have proven the applicability of this mathematical analysis for the identification of cells containing mutations, in the case of cancers, or due to exposures to chemicals and ultraviolet radiation, but until the present moment, no work was done with ionizing radiation. The aim of the present study was to investigate the use of fractal analysis for the identification of irradiated cells, and to discuss its potential use as an indicator of human exposures to ionizing radiation. For this, 200 cells were digitalized, where 100 were from a blood sample irradiated with an absorbed dose of 3 Gy of gamma radiation, and 100cells were non-irradiated. Fractal dimensions (FD) were calculated by the method of Box-Counting. It was possible to notice an increase in FDs of chromatin after exposure to ionizing radiation, and an overdispersion of the values of FD only in irradiated sample. Also, when the data was reorganized in crescent order, it was possible to clearly distinct the irradiated sample from the non-irradiated one. With this, we present an efficient method for the identification of irradiated human blood samples, in a fast and most simplified way, what can be of valuable importance in cases where there is a need of quick responses to human exposures to ionizing radiation.
Highlights
The theory of fractals, proposed by the mathematician Mandelbrot (1975), has been applied to many fields in Biology, mainly due to the property of self-similarity observed in the natural world, such as in the DNA molecule and chromatin structure
We present an efficient method for the identification of irradiated human blood samples, in a fast and most simplified way, what can be of valuable importance in cases where there is a need of quick responses to human exposures to ionizing radiation
When the variance is compared (Figure 2, A and B), it is possible to notice that the irradiated sample presented a higher dispersion
Summary
The theory of fractals, proposed by the mathematician Mandelbrot (1975), has been applied to many fields in Biology, mainly due to the property of self-similarity observed in the natural world, such as in the DNA molecule and chromatin structure. The theory of fractals, introduced by the mathematician Benoit Mandelbrot in 1975, has shown to be useful to understand many of the structures and processes in many fields of science, for describing geometry closer to natural objects, which present irregular forms [1] These objects, so-called non-linear, are found in many of the physiological processes, such as heart beating, vascular system, brain signals, and the organization of genes [2,3,4]. One of the possible morphometric parameters is the measurement of changes in fractal properties of biological tissues, such as self-similarity and fractal dimension (FD) [3,4] This geometric pattern is found, for example, in the shape and organization of the chromatin (into the nucleus of euchariotic cells). This will interfere in genetic activity (DNA transcription) and in the condensation-decondensation transition during cell cycle, without the formation of knots
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