Stochastic Evolution of Pancreatic Cancer Metastases During Logistic Clonal Expansion

Despite recent progress in diagnostic and multimodal treatment approaches, most cancer deaths are still caused by metastatic spread and the subsequent growth of tumor cells in sites distant from the primary organ. So far, few quantitative studies are available that allow for the estimation of metastatic parameters and the evaluation of alternative treatment strategies. Most computational studies have focused on situations in which the tumor cell population expands exponentially over time; however, tumors may eventually be subject to resource and space limitations so that their growth patterns deviate from exponential growth to adhere to density-dependent growth models. In this study, we developed a stochastic evolutionary model of cancer progression that considers alterations in metastasis-related genes and intercellular growth competition leading to density effects described by logistic growth. Using this stochastic model, we derived analytical approximations for the time between the initiation of tumorigenesis and diagnosis, the expected number of metastatic sites, the total number of metastatic cells, the size of the primary tumor, and survival. Furthermore, we investigated the effects of drug administration and surgical resection on these quantities and predicted outcomes for different treatment regimens. Parameter values used in the analysis were estimated from data obtained from a pancreatic cancer rapid autopsy program. Our theoretical approach allows for flexible modeling of metastatic progression dynamics.