A stochastic model of the cell and tumor lifespans in radiotherapy

Classical models used in radiotherapy typically assume that after treatment all surviving cells have a constant and homogeneous sensitivity during the treatment period. In Keinj et al. (2010), 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. ∗ ∗ Proc of the 18th IFAC World Congress. Invited session ’Modeling and Identification in Systems Biology: Advances and Challenges’, Milano, Italy, Aug. 28 Sep. 2, 2011