Calculating normal tissue complication probabilities and probabilities of complication-free tumour control from stochastic models of population dynamics

TL;DR

This paper develops stochastic models to estimate the probability of normal tissue complications and complication-free tumor control during radiotherapy, incorporating cell interactions and intrinsic noise effects.

Contribution

It introduces new stochastic approximation methods for calculating NTCP and tumor control probabilities using birth-death models with nonlinear interactions.

Findings

Approximate NTCP using Kramers-Moyal expansion techniques.

Modeling of normal and damaged cell populations.

Estimation of complication-free tumor control probabilities.

Abstract

We use a stochastic birth-death model for a population of cells to estimate the normal tissue complication probability (NTCP) under a particular radiotherapy protocol. We specifically allow for interaction between cells, via a nonlinear logistic growth model. To capture some of the effects of intrinsic noise in the population we develop several approximations of NTCP, using Kramers-Moyal expansion techniques. These approaches provide an approximation to the first and second moments of a general first-passage time problem in the limit of large, but finite populations. We use this method to study NTCP in a simple model of normal cells and in a model of normal and damaged cells. We also study a combined model of normal tissue cells and tumour cells. Based on existing methods to calculate tumour control probabilities, and our procedure to approximate NTCP, we estimate the probability of complication free tumour control.