A stochastic model of the cell and tumor lifespans in radiotherapy

Thierry Bastogne (1, 2) , Roukaya Keinj (1, 3) , Pierre Vallois (1, 3)

1 BIGS - Biology, genetics and statistics
2 CRAN - Centre de Recherche en Automatique de Nancy
3 IECN - Institut Élie Cartan de Nancy

Classical 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.

Mots clés: cell lifespan; multinomial distribution; stochastic models; dynamic models; cancer; target theory

Domaines: Bio-Informatique, Biologie Systémique [q-bio.QM]; Bio-informatique [q-bio.QM]

Thierry Bastogne, Roukaya Keinj, Pierre Vallois. A stochastic model of the cell and tumor lifespans in radiotherapy. 18th IFAC World Congress, IFAC WC'2011, Aug 2011, Milan, Italy. pp.CDROM, ⟨10.3182/20110828-6-IT-1002.02073⟩. ⟨hal-00645164⟩