Timing and Dosage of Anti-Cancer Drug Therapies: An Optimal Control Approach

A systematic study of cancer treatment requires that we take into account not only the cancerous cells and their growth, but also various aspects of the tumor microenvironment. Its elemets include various types of cancer cells, sensitive and resistant to the treatment, healthy cells, tumor vasculature, immune system and more.  We shell discuss mathematical models that describe the dynamics of tumor growth in relation to its supproting vasculature under reciprocal angiogenic signaling. For such models, in addition to standard direct treatments that kill cancer cells, one can introduce the second indirect treatment by means of angiogenic inhibitors that target the tumor vasculature. A second indirect approach is to consider the interactions between the tumor and the immune system, inclusing tumor surveillance. Here a classical, minimally parametrized model of tumor-immune interactions will be discussed in connection with optimizing the treatment that combined traditional chemotherapy with   a stimulatory effect of the immune system. We will also outline some future work on a more complex model wich encompasses more elements of the microenvironment  and multi-target therapies. This will naturally lead to the topic of metronomic chemotherapy, a new direction in cancer treatment where the various aspects of the tumor microenvironment being targeted by one cytotoxic drug applied accord to a properly chosen "metronomic" protocol which involves between 20% and 80% MTD. It has been observed in experimental studies that such treatment has lower toxicity, lowe drug resistance and in addition exhibits anti-agiogenic and immune system stimulatory effects. The challenges concerning the modeling and mathematical analysis for metronomic chemotherapy will be addressed.