A stochastic model of the cell and tumor lifespans in radiotherapy

Abstract

International audienceClassical models used in radiotherapy typically assume that after treatment all surviving cells have a constant and homogeneous sensitivity during the treatment period. In (2010-Keinj), a multinomial model based on a discrete-time Markov chain able to take into account both cell repair and cell damage heterogeneity due to radiations has been proposed. In this paper, we introduce the notion of lifespan for a single cell, a tumor and a normal tissue. We also determine the cumulative distribution functions of these random variables. These results lead to original formulations of the tumor control probability (TCP) and the normal tissue complication probability (NTCP). Finally, we propose a new characteristic: the Efficiency-Complication Trade-off diagram which provides to the radiotherapeutist all the information needed to choose the most appropriate treatment plan, i.e. the suited number of dose fractions to be applied to control the tumor while preserving the adjacent normal tissue

Improvement of Markov chain processes for mathematical optimization of cancer treatment

“…Then, the number of dead cells will follow the following expression, at state m [6], Bastogne et al (2011):…”

“…For this reason, we attempt to introduce probabilities, which are used in stochastic models. Among the various stochastic models that are able to describe the biological development of cancer, we have the following stochastic static models: the Moran Model [1,2], Wright-Fisher (WF) [3], and Moolgavkar, Venzon, and Knudson (MVK) [4], and among various stochastic models that are able to describe the biological evolution of cancer cells we have the following stochastic dynamic models: Galton-Watson branching process (GWBP) [5], and the Markov chain Processes [6,7].…”