Non-extensive radiobiology

• Published in: AIP conference proceedings Vol. 1305; no. 1
• Main Authors: Sotolongo-Grau, O., Rodriguez-Perez, D., Antoranz, J. C., UH, Catedra de Sistemas Complejos Henri Poincare, Sotolongo-Costa, O.
• Format: Journal Article
• Language: English
• Published: United States 01.01.2010
• Subjects: ANIMAL CELLS; BIOLOGICAL EFFECTS; BIOLOGICAL RADIATION EFFECTS; BIOLOGY; CALCULATION METHODS; DISEASES; DOSES; ENTROPY; HYPOTHESIS; IONIZATION; MEDICINE; NEOPLASMS; NUCLEAR MEDICINE; OPTIMIZATION; PHYSICAL PROPERTIES; PROBABILISTIC ESTIMATION; PROBABILITY; RADIATION DOSES; RADIATION EFFECTS; RADIATION, THERMAL, AND OTHER ENVIRONMENTAL POLLUTANT EFFECTS ON LIVING ORGANISMS AND BIOLOGICAL MATERIALS; RADIOBIOLOGY; RADIOLOGY; RADIOTHERAPY; SURVIVAL CURVES; THERAPY; THERMODYNAMIC PROPERTIES
• ISSN: 0094-243X; 1551-7616
• DOI: 10.1063/1.3573620

The expression of survival factors for radiation damaged cells is based on probabilistic assumptions and experimentally fitted for each tumor, radiation and conditions. Here we show how the simplest of these radiobiological models can be derived from the maximum entropy principle of the classical Boltzmann-Gibbs expression. We extend this derivation using the Tsallis entropy and a cutoff hypothesis, motivated by clinical observations. A generalization of the exponential, the logarithm and the product to a non-extensive framework, provides a simple formula for the survival fraction corresponding to the application of several radiation doses on a living tissue. The obtained expression shows a remarkable agreement with the experimental data found in the literature, also providing a new interpretation of some of the parameters introduced anew. It is also shown how the presented formalism may have direct application in radiotherapy treatment optimization through the definition of the potential effect difference, simply calculated between the tumour and the surrounding tissue.