title: Deterministic and Stochastic Study for a Microscopic Angiogenesis Model: Applications to the Lewis Lung Carcinoma.
abstract: Angiogenesis modelling is an important tool to understand the underlying mechanisms yielding tumour growth. Nevertheless, there is usually a gap between models and experimental data. We propose a model based on the intrinsic microscopic reactions defining the angiogenesis process to link experimental data with previous macroscopic models. The microscopic characterisation can describe the macroscopic behaviour of the tumour, which stability analysis reveals a set of predicted tumour states involving different morphologies. Additionally, the microscopic description also gives a framework to study the intrinsic stochasticity of the reactive system through the resulting Langevin equation. To follow the goal of the paper, we use available experimental information on the Lewis lung carcinoma to infer meaningful parameters for the model that are able to describe the different stages of the tumour growth. Finally we explore the predictive capabilities of the fitted model by showing that fluctuations are determinant for the survival of the tumour during the first week and that available treatments can give raise to new stable tumour dormant states with a reduced vascular network.
authors.affiliation: Institute of Applied Mathematics and Mechanics, Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland.
authors.forename: Marek
authors.initials: M
authors.lastname: Bodnar
authors.affiliation: Department of Mathematics, University College London, Gower Street, London WC1E 6BT, United Kingdom.
authors.forename: Pilar
authors.identifier: 0000-0002-5522-7339
authors.initials: P
authors.lastname: Guerrero
authors.affiliation: Department of Mathematics, University College London, Gower Street, London WC1E 6BT, United Kingdom.
authors.forename: Ruben
authors.identifier: 0000-0001-5348-8829
authors.initials: R
authors.lastname: Perez-Carrasco
authors.affiliation: Institute of Applied Mathematics and Mechanics, Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland.
authors.forename: Monika J
authors.initials: MJ
authors.lastname: Piotrowska
mesh_terms: D000465:Algorithms; D000818:Animals; D018827:Carcinoma, Lewis Lung / Q000473:pathology*; D003198:Computer Simulation; D006801:Humans; D008853:Microscopy / Q000379:methods; D008954:Models, Biological; D009389:Neovascularization, Pathologic / Q000378:metabolism / Q000473:pathology*; D013269:Stochastic Processes; D042461:Vascular Endothelial Growth Factor A / Q000378:metabolism
chemical_list: D042461:Vascular Endothelial Growth Factor A