Microdosimetric characterisation of radiation fields for modelling tissue response in radiotherapy

Purpose: Our overall goal is the development of an approach to model tissue response to radiotherapy in which a tissue is viewed as a statistical ensemble of interacting cells. This involves characterisation of radiation fields on the spatial scale of subcellular structures. On this scale, the spatial distribution of radiation energy imparted to tissue is highly non-uniform and should be characterised in statistical terms. Microdosimetry provides a formalism developed for that purpose. This study addresses limitations of the standard microdosimetric approach to modelling tissue response by introducing two new characteristics that include additional information in a form convenient for this application. Methods: The standard microdosimetric approach is based on the concept of a sensitive volume (SV) representing a target volume in the cell. It is considered in isolation from other SVs, implying that energy depositions in different SVs are statistically independent and that individual cells respond to radiation independent of each other. In this study, we examined the latter approximation through analysis of correlation functions. All calculations were performed with Geant4-DNA Monte Carlo code. Results: We found that for some realistic scenarios, spatial correlations of deposited energy can be significant. Two new characteristics of radiation fields are proposed. The first is the specific energy-volume histogram (zVH), which is a microscopic analogue of the dose-volume histogram. The second describes the probability distribution of deposited energies in two SVs without assuming statistical independence between the SVs. Numerical examples for protons and carbon ions of therapeutic energies are presented and discussed. Conclusion: We extended the microdosimetric approach to modelling tissue response by including additional important characteristics and presented them in a more conventional radiotherapy format.