Multinomial model-based formulations of TCP and NTCP for radiotherapy treatment planning

Abstract

Hit and target models of tumor growth, typically assume that all surviving cells have a constant and homogeneous sensitivity during the radiotherapy period. In this study, we propose a new multinomial model based on a discrete-time Markov chain, able to take into account cell repair, cell damage heterogeneity and cell proliferation. The proposed model relies on the 'Hit paradigm' and 'Target' theory in radiobiology and assumes that a cancer cell contains m targets which must be all deactivated to produce cell death. The surviving cell population is then split up into m categories to introduce the variation of cancer cell radio-sensitivity according to their damage states. New expressions of the Tumor Control Probability (TCP) and Normal Tissue Complication Probability (NTCP) are provided. Moreover, we show that hit and target models may be regarded as particular cases of the multinomial model. Numerical results should permit to keep the efficiency of treatment with a lower total radiation dose then that given by the typical hit models, which allow to decrease side effects.

Tumor growth modeling based on cell and tumor lifespans

“…In Keinj et al (2011), a multinomial model of tumor growth relying on the target and hit modeling paradigm and based on a discrete-time Markov chain has been proposed. We keep the same modeling assumptions stated in Keinj et al (2011).…”

“…In a previous study (Keinj et al, 2011), we proposed a multinomial model of tumor response based on a discrete-time Markov chain. This model is derived from the Target Theory and assumes that there exists a number of radio-sensitive sites within the cell, called targets.…”

“…The cell death is finally caused by the deactivation of those targets by radiation particles. We showed in Keinj et al (2011) that the multinomial model is a generalization of typical target models (Chapman, 2007;Pollard et al, 1955), able to account for the heterogeneity of cell damage caused by the treatment. However, like the majority of models used to measure the tumor response to treatment, the multinomial model examines the number of surviving cells in the tumor and not the tumor lifespan.…”

“…We start by considering the lifespan of a single cancer cell that behaves as described in Keinj et al (2011). It is important to emphasize that the cell lifespan is the minimal random number of radiation dose fractions to be applied to kill the cell.…”

“…This paper is structured as follows: in Section 2 we give a reminder of the individual cell behavior (cf. Keinj et al, 2011). In Section 3, we study the cancer cell lifespan T as a random variable, determining its mean, variance and confidence intervals and a related set of numerical results is given.…”