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M4: Mathematical Models of Metastatic Malignancy
- Author / Creator
- Rhodes, Adam R
Metastasis - the spread of cancer from a primary to a distant secondary location - is implicated in over 90% of all cancer related deaths. Despite its importance in patient outcome, a full understanding of the metastatic process remains elusive, largely because of the difficulty in studying the phenomenon experimentally. In this thesis, we develop and analyze three models of metastatic cancer to shed light on the underlying mechanisms responsible for metastatic spread.
As metastasis is widely believed to be an inherently stochastic process, our first model is a spatially explicit stochastic model of cancer metastasis. The model includes the processes of primary tumor release of circulating tumor cells, circulation of these cells through the body, and metastatic colonization at a secondary site. We discover a metastatic reproduction number, R_0, which characterizes the long-term behavior of the model, and provides an explicit condition for metastatic extinction. Parameterization of the model is done using data from experimental murine models of metastasis. Simulations of the parameterized model demonstrate the suitability of our modeling framework by accurately reproducing experimental observations.
Recent experimental observations have brought the prevailing view of metastasis as a passive sequence of random events into question, with several investigators suggesting that metastasis is an actively regulated process. In particular, immune involvement in the preparation of the pre-metastatic niche has inspired the immune-mediated theory of metastasis; a theory which posits that the immune system - corrupted or `educated' by the tumor to play pro-tumor roles - actively supports metastatic dissemination and growth.
To investigate the implications of the immune-mediated theory of metastasis, our second model is an ordinary differential equation model of tumor-immune dynamics at the sites of a primary and a metastatic tumor, incorporating both anti- and pro-tumor immune populations. Model simulations using literature-derived parameter estimates suggest that the immune-mediated theory of metastasis provides explanations for the poor performance of some immunotherapies, and for the observation of metastatic spread to sites of injury. Our results also suggest new potential avenues for therapy.
Our third model is a reduction of the second, focusing on the tumor-immune dynamics at the metastatic site. Analysis of the reduced model, using methods from geometric singular perturbation theory, provides a mathematical description of metastatic phenomena such as dormancy and blow-up. A parameter sensitivity analysis is performed, and the parameterized model is used to simulate the effects of therapeutic interventions. Necessary conditions for metastatic blow-up after primary tumor resection provide hypotheses concerning the biology of metastasis.
The tumor-immune models investigated in this thesis, both based on the immune-mediated theory of metastasis, provide an explanation for many experimentally and clinically observed metastatic phenomena - including dormancy, blow-up, recurrence, and metastasis to sites of injury - under a single modelling framework; something that previous models of metastasis have been unable to do. Overall, the results of this thesis provide novel insights into the metastatic process and introduce new biological questions for future research.
- Graduation date
- Fall 2018
- Type of Item
- Master of Science
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