A compartment model for total body irradiation

Abstract

Abstract Background Total body irradiation (TBI) is a standard procedure used in radiotherapy to eliminate any remaining cancerous cells following a chemotherapy treatment. However, there is no consensus regarding which TBI regimen (dose, dose rate, and fractionation) is the most efficient and least toxic. Also, we would like to know, how the TBI regime must be updated when it was interrupted by a natural disaster or blackout. Method ology: The Jones model of radiation-induced myelopoiesis is modified by adding new compartments for mutated and cancerous cells populations. This proposed carcinogenesis model is mathematically described by five non-linear coupled differential equations. Numerical and graphical solutions are obtained for U.S. and Canadian TBI regimens. To obtain stochastic solutions, transition rates that mediate the movement of cells among all compartments are replaced with random numbers. Results The developed algorithms and computational codes allowed us to quickly update a planned TBI regime after the patient's treatment was interrupted for a length of time. It is also showed that U.S. and Canadian TBI regimens killed about the same percentage of malignant cells (80%). The stochasticity procedure shows, on average, a mortality of about 83% of the malignant cells, which is in agreement with the deterministic solutions obtained for the US and Canadian TBI regimens. A stability analysis of the deterministic equations revealed only one equilibrium point, which is globally asymptotically stable. Conclusion The proposed TBI compartmental model allows for a quick update of an interrupted TBI regimen, and a comparison among different TBI regimens.