title: Effects of Surgery and Chemotherapy on Metastatic Progression of Prostate Cancer: Evidence from the Natural History of the Disease Reconstructed through Mathematical Modeling.
abstract: This article brings mathematical modeling to bear on the reconstruction of the natural history of prostate cancer and assessment of the effects of treatment on metastatic progression. We present a comprehensive, entirely mechanistic mathematical model of cancer progression accounting for primary tumor latency, shedding of metastases, their dormancy and growth at secondary sites. Parameters of the model were estimated from the following data collected from 12 prostate cancer patients: (1) age and volume of the primary tumor at presentation; and (2) volumes of detectable bone metastases surveyed at a later time. This allowed us to estimate, for each patient, the age at cancer onset and inception of the first metastasis, the expected metastasis latency time and the rates of growth of the primary tumor and metastases before and after the start of treatment. We found that for all patients: (1) inception of the first metastasis occurred when the primary tumor was undetectable; (2) inception of all or most of the surveyed metastases occurred before the start of treatment; (3) the rate of metastasis shedding is essentially constant in time regardless of the size of the primary tumor and so it is only marginally affected by treatment; and most importantly, (4) surgery, chemotherapy and possibly radiation bring about a dramatic increase (by dozens or hundred times for most patients) in the average rate of growth of metastases. Our analysis supports the notion of metastasis dormancy and the existence of prostate cancer stem cells. The model is applicable to all metastatic solid cancers, and our conclusions agree well with the results of a similar analysis based on a simpler model applied to a case of metastatic breast cancer.
authors.affiliation: Department of Mathematics, Idaho State University, 921 S. 8th Avenue, Stop 8085, Pocatello, ID 83209, USA. hanin@isu.edu.
authors.forename: Leonid
authors.initials: L
authors.lastname: Hanin
authors.forename: Marco
authors.initials: M
authors.lastname: Zaider