We are developing mathematical models to study how vascular tumors respond to specific chemotherapeutic treatment strategies. Particular attention is paid to the dynamics that result from the incorporation of a semi-resistant tumor cell type. Insight into the tumor's temporal response to therapy is gained by applying a combination of analytical and numerical techniques to the model equations. The phenomenon of tumor encapsulation is well documented. In fact, the presence of a capsule surrounding a tumor mass is a significant morphological determinant of the clinical outcome.
Encapsulated tumors are generally benign and have a favorable prognosis.
Tumors which do not form this containing capsule are generally malignant and the cells can invade the surrounding normal tissue and even enter the blood stream to relocate to other sites in the body. We are working to develop a mathematical model which describes the process of tumor encapsulation. From the model we hope to determine ways of eliciting the encapsulation of otherwise invasive cancer cells. There are two distinct stages of growth during solid tumorigenesis - the avascular stage and the vascular stage. During the avascular stage, the tumor cells obtain nutrients from surrounding tissues and can grow to a few millimeters in diameter, containing about one million cells.