Mathematical Models of Cell Survival After Ionizing Radiation

Abstract

The work described here represents an attempt to use mathematical models of single-cell survival for radiotherapy planning. The aim of the study is to develop a procedure in which the distribution of the effects achieved by optimizing physical radiation dose is implemented by taking into account radiobiological terms. An algorithmic model has been developed to evaluate the probability of tumor control and of excessive damage to normal tissue on the basis of the linear-quadratic model of cell survival. In its present preliminary form, the procedure can be used to predict differential isoeffect distributions obtained by varying the total dose and the fraction size of multifraction radiotherapy courses. This approach can also be used to extract from historical clinical results, by maximum-likelihood methods, parameters related to the cellular response to radiation (for instance, alpha and beta of the linear-quadratic model).