# A novel microdosimetry-based formalism for cell survival modelling applicable to hypofractionated radiotherapy

## TL;DR

This paper introduces a new model for predicting cell survival in high-dose radiotherapy by combining microdosimetry with a non-linear cell damage approach.

## Contribution

A novel microdosimetry-based formalism that determines sensitive volume size through optimization and improves cell survival modeling for hypofractionated radiotherapy.

## Key findings

- The model successfully matched 24 proton survival curves across various LET ranges and irradiation conditions.
- The sensitive volume size varies with linear energy transfer (LET) and fluence spectrum, unlike standard microdosimetry.
- The approach simplifies multi-particle microdosimetric spectra calculations and eliminates arbitrary assumptions about sensitive volume size.

## Abstract

Hypofractionated radiotherapy requires reliable cell survival models for doses much higher than the standard 2 Gy, for which the linear-quadratic (LQ) model is not applicable. We developed an alternative approach applicable to both low doses and high doses used in hypofractionated treatments and radiobiological experiments.

We combined a standard microdosimetric technique with a recently introduced non-LQ cell survival model. Our formulation accounts for cell damage by multi-track events involving any number of particles. This is necessary for modelling cell survival at therapeutic doses. We characterise each cell type by the size R of the sensitive volume (SV) and biological response function B(q), where q is the total energy deposited in the SV after a given dose is delivered. q is a random quantity characterised by a probability density (microdosimetric spectrum) calculate with Geant4. We determine R and B(q) through an optimisation procedure that minimises differences between model predictions and cell survival measurements that cover an appropriate linear energy transfer (LET) range.

Our method eliminated a serious flaw of the standard microdosimetric approach—arbitrary SV size. We determine SV size by solving the above optimisation problem. Furthermore, our method drastically simplifies calculations of multi-particle microdosimetric spectra. We applied our approach to 24 proton survival curves for three cell lines with various irradiation conditions and LET range of 0.589-19.6keVμm-1 with good agreement between all these measurements and the model. R for a given cell type depended on fluence spectrum and increased with increasing LET owing to variations in the development and spatial spread of damage triggered by initial physical impact. This differ from the standard microdosimetry where SV size is constant.

Our model is relatively simple and suitable for implementation in a treatment planning system potentially improving treatment plan optimisation, calculation of RBEs and biologically equivalent doses.