title: A Mathematical Model Coupling Tumor Growth and Angiogenesis.
abstract: We present a mathematical model for vascular tumor growth. We use phase fields to model cellular growth and reaction-diffusion equations for the dynamics of angiogenic factors and nutrients. The model naturally predicts the shift from avascular to vascular growth at realistic scales. Our computations indicate that the negative regulation of the Delta-like ligand 4 signaling pathway slows down tumor growth by producing a larger density of non-functional capillaries. Our results show good quantitative agreement with experiments.
authors.affiliation: Applied Mathematics, University of A Coruña, A Coruña, Spain.
authors.forename: Jiangping
authors.initials: J
authors.lastname: Xu
authors.affiliation: Applied Mathematics, University of A Coruña, A Coruña, Spain.
authors.forename: Guillermo
authors.initials: G
authors.lastname: Vilanova
authors.affiliation: Applied Mathematics, University of A Coruña, A Coruña, Spain.
authors.forename: Hector
authors.initials: H
authors.lastname: Gomez
mesh_terms: D000465:Algorithms; D049109:Cell Proliferation; D003198:Computer Simulation; D006801:Humans; D047908:Intracellular Signaling Peptides and Proteins / Q000378:metabolism; D008565:Membrane Proteins / Q000378:metabolism; D008962:Models, Theoretical; D009369:Neoplasms / Q000378:metabolism / Q000473:pathology*; D009389:Neovascularization, Pathologic; D015398:Signal Transduction; D047368:Tumor Burden
chemical_list: D047908:Intracellular Signaling Peptides and Proteins; D008565:Membrane Proteins; C064045:delta protein