Pacific Institute for the Mathematical Sciences - PIMS

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.