Oncologic mathematics: evolution of a new specialty

Mathematical methods and their derivatives have practical applications to oncology. They can be used to describe fundamental aspects of tumor behavior, such as loss of genetic stability, tumor growth, immunologic identity, genesis of diversity, and methods of prognosticating cancer.

Descriptive models and published literature in the fields of oncology and applied mathematics.

Cancer does not conform to simple mathematical principles. Its irregular mode of carcinogenesis, erratic tumor growth, variable response to tumoricidal agents, and poorly understood metastatic patterns constitute highly variable clinical behavior. Defining this process requires an accurate understanding of the interactions between tumor cells and host tissues and ultimately determines prognosis. Applying time-tested and evolving mathematical methods to oncology may provide new tools with inherent advantages for the description of tumor behavior, selection of therapeutic modes, prediction of metastatic patterns, and providing an inclusive basis for prognostication. We term this combined field of research "oncologic mathematics." As surgeons, we have the unique opportunity to be active participants and assume leadership in research that affects selection of the optimal anticancer treatment for our patients. Mathematicians describe equations that define tumor growth and behavior, whereas surgeons actively deal with biological processes. Oncologic mathematics applies these principles to clinical settings.

Experimentally testable, oncologic mathematics may provide a framework to determine clinical outcome on a patient-specific basis and increase the growing awareness that mathematical models help simplify seemingly complex and random tumor behavior.