# Structural Derivative Model for Tissue Radiation Response

## TL;DR

This paper introduces a novel structural derivative-based model using the scale-q-derivative to describe tissue radiation response, aligning well with experimental data and extending traditional models by incorporating tumor complexity.

## Contribution

It formulates a new differential equation for radiation-induced cell death using the scale-q-derivative, providing a more comprehensive model that accounts for tumor structure complexity.

## Key findings

- Survival factor Fs aligns with maximum entropy principle.
- Model agrees with experimental data.
- Recovers linear and quadratic models as special cases.

## Abstract

By means of a recently-proposed metric or structural derivative, called scale-q-derivative approach, we formulate differential equation that models the cell death by a radiation exposure in tumor treatments. The considered independent variable here is the absorbed radiation dose D instead of usual time. The survival factor, Fs, for radiation damaged cell obtained here is in agreement with the literature on the maximum entropy principle, as it was recently shown and also exhibits an excellent agreement with the experimental data. Moreover, the well-known linear and quadratic models are obtained. With this approach, we give a step forward and suggest other expressions for survival factors that are dependent on the complex tumor structure.