A Markovian approach to prostate cell survival under fractionated radiotherapy

In this work, the survival of clonogenic PC-3 and DU-145 prostate cell lines exposed to conventional fractionated radiotherapy are modeled using an iterated birth-death Markov process. The model consists of a birth-death Markov process where the states in the chain represent the number of surviving clonogenic cells, and are separated by radiation fractions in which the survival of tumor cells immediately following a fraction is described by the linear-quadratic model. The stochastic behavior of the cell population between fractions is described by a birth-death Markov process, which determines the number of cells present for the subsequent fraction. Results show that for an initial clonogen population of 109 cells to reach zero at 2 Gy/fraction, 44 fractions must be delivered to DU-145 prostate cells, and 19 fractions to PC-3 prostate cells. At 2.75 Gy/fraction, 27 fractions must be delivered to DU-145 prostate cells and 13 fractions to PC-3 prostate cells for treatment termination. An advantage of the proposed model is that it can be used to simulate constant as well as variable radiation intervals and dosages. Model construction, validation, results, and applications are discussed.