Mathematical Study of Brain Tumor Therapies

Glioma is the most serious malignant brain tumor. In order to improve the efficacy of therapies, it is important to understand its progression with therapies and its genesis. In this talk, I will first present our effort in understanding of glioma progression with different therapies in terms of mathematical models. The first model is about virotherapy of glioma, which is a free boundary problem with five nonlinear partial differential equations. Virotherapy is a promising treatment for malignant solid tumors, and it is now in animal experimental stage. In order to treat human glioma by virotherapy, it is critical to understand all factors involved in the therapy. Our model finds an important factor burst size of virus, and the effect of immunosuppression drug cyclophosphamide in animal experiments. The model prediction has been verified by experimental results. The second model is about radiotherapy plus chemotherapy after surgical resection, which is a two-component free boundary problem. After surgery, the tumor progression depends on the degree of resection and radiation, and a particular drug. We use human data to estimate parameter values, and the model can predict the mean survival times of patients who undergo different protocols of treatments.