Statistical inference on interacting particle systems with applications to cancer biology
Doktorsavhandling, 2023
Interacting particle is a mathematical framework which allows for condensed and elegant modelling of complex phenomena undergoing both deterministic and random dynamics. While there are several ways to formulate an interacting particle system, this thesis focuses on modelling such dynamics using stochastic differential equations. The application in mind is describing the in vitro population dynamics of cancer cells.
The introductory portion of the thesis presents the necessary mathematical and biological context, and formulate a model that is subsequently studied in the appended research papers. In the first of three papers, we introduce a novel method of inferring the diffusive properties in such systems based on a higher order numerical approximation of the underlying stochastic differential equations. In the second paper, we model the effect of cell-to-cell interactions, and conduct inference on this model using microscopy data. The third and last paper concerns modelling how the spatial distribution of the cell population effect the division rate, and apply our theoretical results to microscopy data.
Put together, the three papers present a cohesive package on modelling and inference strategies one can use when tackling some of the most challenging problems in mathematical biology.
The introductory portion of the thesis presents the necessary mathematical and biological context, and formulate a model that is subsequently studied in the appended research papers. In the first of three papers, we introduce a novel method of inferring the diffusive properties in such systems based on a higher order numerical approximation of the underlying stochastic differential equations. In the second paper, we model the effect of cell-to-cell interactions, and conduct inference on this model using microscopy data. The third and last paper concerns modelling how the spatial distribution of the cell population effect the division rate, and apply our theoretical results to microscopy data.
Put together, the three papers present a cohesive package on modelling and inference strategies one can use when tackling some of the most challenging problems in mathematical biology.
reaction-diffusion equations
bayesian inference
mathematical biology
gent based modelling
stochastic differential equations
Pascal
Opponent: Professor Jan Hasenauer, Bonn University, Germany
Författare
Gustav Lindwall
Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik
Lindwall, G., Gerlee, P. (2023). Inference on an interacting diffusion system with application to in vitro glioblastoma migration
Lindwall, G., Gerlee, P. (2023). Bayesian inference on the Allee effect in cancer cell populations using time-lapse microscopy images.
Fast and precise inference on diffusivity in interacting particle systems
Journal of Mathematical Biology,;Vol. 86(2023)
Artikel i vetenskaplig tidskrift
This is a thesis on the topic of inference methods in mathematical biology. Although mathematical and statistical reasoning has long been the cornerstone in all of the natural sciences, biology and medicine has until the 20th century been thought of and taught without an agreed upon mathematical mode of analysis. However, in the last couple of decades, there has been a burgeoning surge of research into mathematical biology, establishing it as a field of its own. Thus, biology and medicine in the 21st century has served as a driver for innovative research in applied mathematics.
Oncology is the branch of medicine that deal with the study, treatment, diagnosis and prevention of cancerous tumours. In this thesis, we will focus on modelling of tumours, formulate models of in vitro cancer cell migration, and use statistical tools to infer what parameters govern the behaviour detected in experimental data.
Oncology is the branch of medicine that deal with the study, treatment, diagnosis and prevention of cancerous tumours. In this thesis, we will focus on modelling of tumours, formulate models of in vitro cancer cell migration, and use statistical tools to infer what parameters govern the behaviour detected in experimental data.
Ämneskategorier
Sannolikhetsteori och statistik
ISBN
978-91-7905-899-9
Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie: 5365
Utgivare
Chalmers
Pascal
Opponent: Professor Jan Hasenauer, Bonn University, Germany