ABSTRACT
The objective of mathematical pathology is to mathematically model and explain the structural and functional mechanistic changes happening within the body as a result of the onset of disease. This chapter describes the functional changes in the body brought on by the evolution of cancer can be explained mathematically. It identifies the justification for mathematical pathology as a necessary and useful step in the diagnosis of cancer, using the example brought by our recent collaborative work with Dr. Mary Edgerton (MD Anderson Cancer Center) on ductal carcinoma in situ (DCIS), the most common form of noninvasive breast cancer, which often precedes invasive ductal carcinoma (IDC). DCIS is an early form of breast cancer in which the tumor originates within and is confined to the breast duct. The chapter investigates how modeling can contribute to patient-specific treatment plans, as it includes predictions of how diffusion barriers might impact drug diffusion.
