Narrow Results

This paper deals with a procedure for cancer radiovirotherapy which requires not only injection of replication-competent viruses but also administration of radioiodide. The viruses infect tumor cells, replicate inside them and eventually cause their death. As infected cells die, the viruses inside them are released and then proceed to infect adjacent tumor cells. Radioiodide is in a continuous state of flux between the tumor and the remaining part. Iodide undergoes beta particle decay and the emitted beta particles have a significant effect on tumor cells. The combination of virotherapy with radiotherapy has recently been shown to be significantly more effective than treatment with virotherapy alone. Cancer radiovirotherapy can be described by a free boundary problem for a nonlinear system of partial differential equations, where the free boundary is the surface of a tumor. Global existence and uniqueness of solutions to this free boundary problem is proved, and a new explicit parameter condition corresponding to the success of therapy is also found. Furthermore, numerical simulations are given to show that there is an optimal timing for radio-iodine administration, and that there is an optimal dose for the radioactive iodide.