title: Mathematical modelling of angiogenesis using continuous cell-based models.
abstract: In this work, we develop a mathematical formalism based on a 3D in vitro model that is used to simulate the early stages of angiogenesis. The model treats cells as individual entities that are migrating as a result of chemotaxis and durotaxis. The phenotypes used here are endothelial cells that can be distinguished into stalk and tip (leading) cells. The model takes into account the dynamic interaction and interchange between both phenotypes. Next to the cells, the model takes into account several proteins such as vascular endothelial growth factor, delta-like ligand 4, urokinase plasminogen activator and matrix metalloproteinase, which are computed through the solution of a system of reaction-diffusion equations. The method used in the present study is classified into the hybrid approaches. The present study, implemented in three spatial dimensions, demonstrates the feasibility of the approach that is qualitatively confirmed by experimental results.
authors.affiliation: Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands.
authors.forename: F D
authors.initials: FD
authors.lastname: Bookholt
authors.affiliation: Department of Dermatology (VUmc), VU University Medical Center, MOVE Research Institute Amsterdam, Amsterdam, The Netherlands.
authors.forename: H N
authors.initials: HN
authors.lastname: Monsuur
authors.affiliation: Department of Dermatology (VUmc), VU University Medical Center, MOVE Research Institute Amsterdam, Amsterdam, The Netherlands.|Department of Oral Cell Biology, Academic Centre for Dentistry Amsterdam (ACTA), University of Amsterdam and VU University Amsterdam, MOVE Research Institute Amsterdam, Amsterdam, The Netherlands.
authors.forename: S
authors.initials: S
authors.lastname: Gibbs
authors.affiliation: Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands. F.J.Vermolen@tudelft.nl.
authors.forename: F J
authors.initials: FJ
authors.lastname: Vermolen
mesh_terms: D001696:Biomechanical Phenomena; D003198:Computer Simulation; D020405:Dermis / Q000166:cytology; D042783:Endothelial Cells / Q000166:cytology / Q000378:metabolism; D005337:Fibrin / Q000378:metabolism; D020342:Finite Element Analysis; D006801:Humans; D020782:Matrix Metalloproteinases / Q000378:metabolism; D008954:Models, Biological; D018919:Neovascularization, Physiologic; D014568:Urokinase-Type Plasminogen Activator / Q000378:metabolism; D042461:Vascular Endothelial Growth Factor A / Q000378:metabolism
chemical_list: D042461:Vascular Endothelial Growth Factor A; D005337:Fibrin; D014568:Urokinase-Type Plasminogen Activator; D020782:Matrix Metalloproteinases
keywords: Angiogenesis; Cell-based model; Endothelial cells; Finite-element method; In vitro experiments; Stalk cells; Tip cells