Optimal scheduling of biologically targeted radiotherapy and total body irradiation with bone marrow rescue for the treatment of systemic malignant disease.

A mathematical model analysis is used to address the question of optimal scheduling of combined treatments consisting of biologically targeted radiotherapy (BTR), total body irradiation (TBI), and bone marrow rescue. Radiation effects on normal tissue are described using an extension of the LQ model. Tumor effects are described using a simple model that allows for radiation-induced sterilization and exponential proliferation of tumor cells, a proportion of which completely escapes the effects of targeted radiotherapy. The effect on a tumor cell population of a set of treatment schedules, composed partly of targeted radiotherapy and partly of fractionated external beam irradiation, are calculated. Treatment schedules are chosen to be biologically equivalent, for a "late responding" organ, to a fractionated TBI schedule of 7 fractions of 2 Gy. The tumor effects of the treatment schedules depend on the specificity of targeting, represented by the ratio of initial dose-rate for the tumor cells to that in the dose-limiting organ, and the heterogeneity of targeting, represented by the proportion of tumor cells that escape irradiation by targeted radiotherapy. The main mechanism determining optimal combinations is an overkill of effectively targeted tumor cells. Treatment regiments consisting of targeted radiotherapy alone fail, due to the unimpeded growth of those tumor cells that escape targeted irradiation. Optimal schedules almost invariably consist of elements of both BTR and TBI. Although it is recognized that the model is simplistic in a number of respects, these findings provide support for the clinical use of integrated BTR, TBI, and bone marrow rescue for the treatment of systemic malignant disease.