Generalized calculus in radiobiology: Physical implications

TL;DR

This paper introduces a generalized mathematical framework based on non-extensive statistical physics to model the survival fraction of tissues under multiple radiation doses, with potential applications in radiobiology and oncology.

Contribution

It develops a new formula for tissue survival after radiation using generalized exponential and logarithm functions, extending traditional models.

Findings

Derived a generalized survival formula for multiple radiation doses.

Provided experimental guidelines for characterizing tissue responses.

Potential to improve radiobiological modeling and treatment planning.

Abstract

Non-extensive statistical physics has allowed to generalize mathematical functions such as exponential and logarithms. The same framework is used to generalize sum and product so that the operations allow a more fluid way to work with mathematical expressions emerging from non-additive formulation of statistical physics. In this work we employ the generalization of the exponential, logarithm and product to obtain a formula for the survival fraction corresponding to the application of several radiation doses on a living tissue. Also we provide experimental recommendations to determine the universal characteristics of living tissues in interaction with radiation. These results have a potential application in radiobiology and radiation oncology.