Speaker
Description
Biologically, metastatic spread refers to the process by which a primary tumour releases cancer cells into the bloodstream that eventually colonise new organs, thereby often acquiring genetic mutations. Metastases cause about 80\% of cancer-related deaths \cite{F19}, hence, predicting when and where metastases are likely to emerge, and identifying advantageous mutations presents an urgent medical challenge. Mathematically, modelling metastatic spread is exceptionally difficult because it encompasses multiple temporal and spatial scales, is affected by both collective as well as rare events, and is governed by genetic evolution processes. Previous modelling efforts have made significant progress in each of these areas but remain mostly exclusive from one another \cite{S25, W25}.
My research aims at bridging this gap by considering a time-continuous spatial branching process tracking both the genetic genealogy of cancer cells and their spatial trajectories during dissemination from a primary tumor to metastatic sites, linking population-level spread with underlying stochastic genetic dynamics \cite{B25}. The genetic component is formulated as a dynamical system describing phenotypic switching from healthy to cancerous states, which is analyzed systematically by considering different approximations of an appropriate reduced model. Finally, extensions to more complex genetic switching networks relevant to metastatic initiation are discussed.
Bibliography
@Article{F19,
author = {Franssen, Linnea C. and Lorenzi, Tommaso and Burgess, Andrew E. F. and Chaplain, Mark A. J.},
journal = {Bulletin of Mathematical Biology},
title = {A Mathematical Framework for Modelling the Metastatic Spread of Cancer},
year = {2019},
issn = {1522-9602},
month = mar,
number = {6},
pages = {1965--2010},
volume = {81},
doi = {10.1007/s11538-019-00597-x},
publisher = {Springer Science and Business Media LLC},
}
@Article{S25,
author = {Singh, Khimeer and Jacobs, Byron A.},
journal = {Bulletin of Mathematical Biology},
title = {A Network Based Model for Predicting Spatial Progression of Metastasis},
year = {2025},
issn = {1522-9602},
month = apr,
number = {5},
volume = {87},
doi = {10.1007/s11538-025-01441-1},
publisher = {Springer Science and Business Media LLC},
}
@Article{W25,
author = {Wieland, Vincent and Hasenauer, Jan},
journal = {Journal of Mathematical Biology},
title = {A stochastic modelling framework for cancer patient trajectories: combining tumour growth, metastasis, and survival},
year = {2025},
issn = {1432-1416},
month = may,
number = {6},
volume = {90},
doi = {10.1007/s00285-025-02229-6},
publisher = {Springer Science and Business Media LLC},
}
@Misc{B25,
author = {Biočić, Ivan and Toaldo, Bruno and Zuspann, Lena},
title = {Continuous Branching Processes with Settlement in Cancer Metastasis: Stochastic Modelling and the Feller Property},
year = {2025},
copyright = {Creative Commons Attribution 4.0 International},
doi = {10.48550/ARXIV.2511.10456},
keywords = {Probability (math.PR), FOS: Mathematics, FOS: Mathematics, Primary 60J80, Secondary 60J85, 60G53},
publisher = {arXiv},
}
