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Tsallis entropy approach to radiotherapy treatments

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  • Sotolongo-Grau, O.
  • Rodriguez-Perez, D.
  • Sotolongo-Costa, O.
  • Antoranz, J.C.

Abstract

The biological effect of one single radiation dose on a living tissue has been described by several radiobiological models. However, the fractionated radiotherapy requires to account for a new magnitude: time. In this paper we explore the biological consequences posed by the mathematical prolongation of a previous model to fractionated treatment. Nonextensive composition rules are introduced to obtain the survival fraction and equivalent physical dose in terms of a time dependent factor describing the tissue trend towards recovering its radioresistance (a kind of repair coefficient). Interesting (known and new) behaviors are described regarding the effectiveness of the treatment which is shown to be fundamentally bound to this factor. The continuous limit, applicable to brachytherapy, is also analyzed in the framework of nonextensive calculus. Here a coefficient that rules the time behavior also arises. All the results are discussed in terms of the clinical evidence and their major implications are highlighted.

Suggested Citation

  • Sotolongo-Grau, O. & Rodriguez-Perez, D. & Sotolongo-Costa, O. & Antoranz, J.C., 2013. "Tsallis entropy approach to radiotherapy treatments," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(9), pages 2007-2015.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:9:p:2007-2015
    DOI: 10.1016/j.physa.2013.01.020
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    1. Upadhyaya, Arpita & Rieu, Jean-Paul & Glazier, James A. & Sawada, Yasuji, 2001. "Anomalous diffusion and non-Gaussian velocity distribution of Hydra cells in cellular aggregates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 293(3), pages 549-558.
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    3. Kalogeropoulos, Nikos, 2005. "Algebra and calculus for Tsallis thermo-statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 356(2), pages 408-418.
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    Cited by:

    1. Deng, Xinyang & Deng, Yong, 2014. "On the axiomatic requirement of range to measure uncertainty," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 406(C), pages 163-168.

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