Implications of immune-mediated metastatic growth on metastatic dormancy, blow-up, early detection, and treatment
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Mathematical Biology
Implications of immune-mediated metastatic growth on metastatic dormancy, blow-up, early detection, and treatment Adam Rhodes1
· Thomas Hillen1
Received: 21 October 2019 / Revised: 1 May 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Metastatic seeding of distant organs can occur in the very early stages of primary tumor development. Once seeded, these micrometastases may enter a dormant phase that can last decades. Curiously, the surgical removal of the primary tumor can stimulate the accelerated growth of distant metastases, a phenomenon known as metastatic blow-up. Recent clinical evidence has shown that the immune response can have strong tumor promoting effects. In this work, we investigate if the pro-tumor effects of the immune response can have a significant contribution to metastatic dormancy and metastatic blow-up. We develop an ordinary differential equation model of the immune-mediated theory of metastasis. We include both anti- and pro-tumor immune effects, in addition to the experimentally observed phenomenon of tumor-induced immune cell phenotypic plasticity. Using geometric singular perturbation analysis, we derive a rather simple model that captures the main processes and, at the same time, can be fully analyzed. Literature-derived parameter estimates are obtained, and model robustness is demonstrated through a time dependent sensitivity analysis. We determine conditions under which the parameterized model can successfully explain both metastatic dormancy and blow-up. The results confirm the significant active role of the immune system in the metastatic process. Numerical simulations suggest a novel measure to predict the occurrence of future metastatic blow-up in addition to new potential avenues for treatment of clinically undetectable micrometastases. Keywords Mathematical oncology · Cancer modeling · Metastasis · Dormancy · Geometric singular perturbation analysis · Ordinary differential equations Mathematics Subject Classification 92C32 · 92C50
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Adam Rhodes [email protected] Thomas Hillen [email protected]
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Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, Canada
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A. Rhodes, T. Hillen
1 Introduction Metastasis has long been viewed as the inevitable final step in cancer progression—the growth of a primary tumor leads to local invasion into the surrounding tissue where the tumor eventually encounters (or recruits) blood vessels, which provide it with a method for distant dissemination, which occurs stochastically downstream from the primary tumor (Valastyan and Weinberg 2011). From this point of view it is reasonable to assume that treatment of a primary tumor at a sufficiently early time may have a good chance of preventing metastatic spread. However, recent evidence across multiple cancers has suggested that metastases can be seeded during early stages of primary tumor development, well before the primary tumor is clinically detectable (Friberg and Nystrom 2015; Hanin and Rose 2018). Ea
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