Radiobiological modelling of the treatment of leukaemia by total body irradiation

Total body irradiation (TBI) has been used as part of the conditioning regimen before bone marrow transplantation or stem cell re-infusion for more than 30 years. A wide variety of regimens have been used, and no single one has emerged as the best. Experimental evidence suggests a diversity of radiosensitivities of leukaemia cells in culture, which may correlate with a significant variation of leukaemic cell radiosensitivities between patients. The purpose of this project was to compute leukaemic cell killing by different schedules and determine whether a "best treatment" could be devised for individual patients.

We have developed a mathematical model for leukaemic cell killing by alternative TBI schedules, applied to a patient population with diverse leukaemic radiosensitivities. We considered 13 schedules in clinical use, and 14 theoretical schedules calculated (by the linear-quadratic model) to be iso-effective for risk of radiation pneumonitis. When each schedule of treatment is applied to the patient population, a distribution of leukaemic cell kills (log cell kill values) can be obtained for that schedule. The leukaemic kill distribution was also computed for optimized individual scheduling, each individual being treated by the schedule that was most effective for that patient. Using available data on the clinically observed dose response relationship for acute myeloid leukaemia, the model was extended to provide leukaemia cure probabilities for each of the schedules and for the individualized strategy.

The computer simulations show that each schedule, applied to the treatment of a radiobiologically diverse patient population, results in a broad distribution of leukaemic log kill values, with a mean of 3-5 for most schedules (i.e. 10(-3)-10(-5) surviving fraction of leukaemic cells), and a broad variation (1-10 log kill) amongst patients. The distributions generated by the various schedules were found to be overlapping, implying that many of the schedules would be difficult to distinguish reliably in clinical trials. Individualized optimum treatment is possible if radiobiological parameters are known for each patient and would improve the leukaemic log kill distribution by about 1 log on average, corresponding to an increase of leukaemia cure probability of several percent overall. For some individual patients, however, optimal scheduling could make a large difference to treatment outcome.

The use of many different clinical treatment schedules may be continuing because outcomes are similar when these diverse schedules are applied to unselected patient populations. The measurement of individual leukaemic cell radiosensitivity would allow individualized scheduling, which could result in modest increases in overall curability, but substantial improvements in survival or duration of remission for individual patients.