Modeling a Radiotherapy Clinical Procedure: Total Body Irradiation

Abstract

Leukemia, non-Hodgkin’s lymphoma, and neuroblastoma patients prior to bone marrow transplants may be subject to a clinical radiotherapy procedure called total body irradiation (TBI). To mimic a TBI procedure, we modified the Jones model of bone marrow radiation cell kinetics by adding mutant and cancerous cell compartments. The modified Jones model is mathematically described by a set of n + 4 differential equations, where n is the number of mutations before a normal cell becomes a cancerous cell. Assuming a standard TBI radiotherapy treatment with a total dose of 1320 cGy fractionated over four days, two cases were considered. In the first, repopulation and sub-lethal repair in the different cell populations were not taken into account (model I). In this case, the proposed modified Jones model could be solved in a closed form. In the second, repopulation and sub-lethal repair were considered, and thus, we found that the modified Jones model could only be solved numerically (model II). After a numerical and graphical analysis, we concluded that the expected results of TBI treatment can be mimicked using model I. Model II can also be used, provided the cancer repopulation factor is less than the normal cell repopulation factor. However, model I has fewer free parameters compared to model II. In either case, our results are in agreement that the standard dose fractionated over four days, with two irradiations each day, provides the needed conditioning treatment prior to bone marrow transplant.Partial support for this research was supplied by the NIH-RISE program, the LSAMP-Puerto Rico program, and the University of Puerto Rico-Humacao.