Non-extensive radiobiology

TL;DR

This paper derives a non-extensive radiobiological model using Tsallis entropy, providing a simple formula for survival fractions that aligns well with experimental data and can aid in radiotherapy optimization.

Contribution

It introduces a novel non-extensive framework for radiobiology based on Tsallis entropy, extending classical models and offering new insights into treatment planning.

Findings

The model fits experimental survival data well.

Provides a new interpretation of model parameters.

Suggests potential for radiotherapy optimization.

Abstract

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 has direct application in radiotherapy treatment optimization through the definition of the potential effect difference, simply calculated between the tumour and the surrounding tissue.