Tsallis entropy approach to radiotherapy treatments

TL;DR

This paper applies Tsallis entropy and nonextensive calculus to model the biological effects of fractionated radiotherapy, introducing a time-dependent factor that influences treatment effectiveness and tissue recovery.

Contribution

It extends radiobiological models to include time dependence using Tsallis entropy, providing new insights into treatment effectiveness and tissue recovery dynamics.

Findings

Treatment effectiveness depends on a tissue recovery factor.

The model describes both fractionated and brachytherapy treatments.

New behaviors in tissue response are identified through nonextensive calculus.

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 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. Also here a coefficient arises that rules the time behavior. All the results are discussed in terms of the clinical evidence and their major implications are highlighted.