Modeling of an Iterated Birth/Death Markov Process for Optimization of Radiotherapy Treatment Planning

In this work, an iterated birth/death Markov process is modeled. Recent publications show that such a process can mimic the behaviour of clonogenic tumour cells exposed to fractionated radiation treatments. The model consists of a sequence of birth/death Markov chains, separated by radiation fractions. The destruction of tumour cells during a fraction of radiation is described by the linear-quadratic cell model. The stochastic behaviour of the cell population between radiation fractions is then described by a birth/death Markov process in order to determine how many clonogenic cells are present prior to the next fraction of radiation. Numerical analysis of the model was conducted with a tumour size of 10⁹ cells. Results from the model showed it would require a schedule of 27 radiation fractions at 2Gy per fraction delivered on every business day for a total of 38 days for the clonogenic population to reach zero. An advantage to such a model is that can be used to study both constant as well as variable radiation intervals and dosages. Model construction, validation, results and its applications in optimizing radiotherapy treatment planning are discussed