A multinomial model of tumor growth treated by radiotherapy

Abstract

A main challenge in radiotherapy is to personalize the treatment by adapting the dose fractionation scheme to the patient. One way is to model the treatment effect on the tumor growth. In this study, we propose a new multinomial model based on a discrete-time Markov chain, able to take into account both of cell repair and cell damage heterogeneity. The proposed model relies on the 'Hit' theory in Radiobiology and assumes that a cancer cell contains m targets which must be all deactivated to produce cell death. The malignant cell population is then split up into m categories to incorporate the variation of cancer cell radio-sensitivity according to their states. This work gives also a new formulation of the tumor control probability (TCP) suited to the perspective of dynamic fractionation schedules in radiotherapy.

A stochastic model of the cell and tumor lifespans in radiotherapy

“…In Keinj et al (2010), we have proposed a multinomial model of tumor growth relying on the target and hit modeling paradigm. This model is based on the following assumptions :…”

“…Unfortunately two main aspects of tumor growth are often missing in target and hit models: (i) the target reparation between two consecutive dose fractions and (ii) the heterogeneity of damages induced by radiations in the cancer cell population after each dose fraction. In Keinj et al (2010), an extension of hit models is proposed through a multinomial model that takes into account the different states of a surviving cell corresponding to the degree of DNA damage. Moreover, the proposed model is able to describe both target reparation between two consecutive dose fractions of the radiation schedule and the heterogeneity of damages induced by radiations in the cancer cell population after each dose fraction.…”

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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.

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