Abstract 5333: A mathematical model for the kinetics of metastasis formation based on SEER data

Proceedings: AACR Annual Meeting 2014; April 5-9, 2014; San Diego, CA Metastasis is responsible for most cancer mortality, yet many questions remain about how best to describe the kinetics of metastasis formation mathematically. Because the initial step of metastasis is the detachment of cells from a tumor mass, the rate of formation of new metastases is assumed to depend on the size of the original tumor mass. A power-law dependence, rather than linear proportionality, has been assumed, since access to blood vessels and lymphatics becomes more limited as tumor mass increases. Under this assumption, the cumulative distribution of fraction of patients not showing detectable metastases at diagnosis should decrease monotonically as tumor size at detection increases. Using data from the NCI's SEER (Surveillance, Epidemiology, and End Results) 1973-2010 database, it is shown here that this relation in fact shows non-monotonic behavior at larger detection sizes. A mathematical model for tumor growth and metastasis kinetics is developed to show that this implies that proliferation rates and metastatic rates are not independently distributed across the patient population, but rather, show some correlation. The model is further applied to deduce quantitative information about the size-dependence of the rate of metastasis. Kaplan-Meier curves stratified by tumor size, also computed from SEER 1973-2010 data, provide an additional data source for determining model parameters. It is found that accounting for age dependence is necessary for fitting these curves. Two possible age-related effects: a lower lethal tumor burden threshold; and an increased coefficient of metastatic rate due to declining immunity; are considered in the model, and a comparison is made of their ability to describe the observed age-dependence. In sum, the model shows how SEER data can be used to deduce information about the kinetics of metastasis formation, and is expected to have application in optimization of the treatment of metastatic tumors as well as screening schedules. Citation Format: Ardith W. El-Kareh, Timothy W. Secomb. A mathematical model for the kinetics of metastasis formation based on SEER data. [abstract]. In: Proceedings of the 105th Annual Meeting of the American Association for Cancer Research; 2014 Apr 5-9; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2014;74(19 Suppl):Abstract nr 5333. doi:10.1158/1538-7445.AM2014-5333