title: A mathematical model of tumour angiogenesis: growth, regression and regrowth.
abstract: Cancerous tumours have the ability to recruit new blood vessels through a process called angiogenesis. By stimulating vascular growth, tumours get connected to the circulatory system, receive nutrients and open a way to colonize distant organs. Tumour-induced vascular networks become unstable in the absence of tumour angiogenic factors (TAFs). They may undergo alternating stages of growth, regression and regrowth. Following a phase-field methodology, we propose a model of tumour angiogenesis that reproduces the aforementioned features and highlights the importance of vascular regression and regrowth. In contrast with previous theories which focus on vessel remodelling due to the absence of flow, we model an alternative regression mechanism based on the dependency of tumour-induced vascular networks on TAFs. The model captures capillaries at full scale, the plastic dynamics of tumour-induced vessel networks at long time scales, and shows the key role played by filopodia during angiogenesis. The predictions of our model are in agreement with in vivo experiments and may prove useful for the design of antiangiogenic therapies.
authors.affiliation: Departamento de Métodos Matemáticos e de Representación, Grupo de Métodos Numéricos en Ingeniería-Universidade da Coruña, Campus de Elviña, 15071 A Coruña, Spain gvilanovac@udc.es.
authors.forename: Guillermo
authors.identifier: 0000-0002-9650-0602
authors.initials: G
authors.lastname: Vilanova
authors.affiliation: Departamento de Métodos Matemáticos e de Representación, Grupo de Métodos Numéricos en Ingeniería-Universidade da Coruña, Campus de Elviña, 15071 A Coruña, Spain.
authors.forename: Ignasi
authors.identifier: 0000-0002-9005-1375
authors.initials: I
authors.lastname: Colominas
authors.affiliation: School of Mechanical Engineering, Purdue University, 585 Purdue Mall, West Lafayette, IN 47907, USA.
authors.forename: Hector
authors.identifier: 0000-0002-2553-9091
authors.initials: H
authors.lastname: Gomez
mesh_terms: D043925:Angiogenesis Inducing Agents / Q000378:metabolism*; D000818:Animals; D006801:Humans; D008954:Models, Biological; D009363:Neoplasm Proteins / Q000378:metabolism*; D009369:Neoplasms / Q000098:blood supply / Q000378:metabolism / Q000473:pathology; D009389:Neovascularization, Pathologic / Q000378:metabolism / Q000473:pathology / Q000503:physiopathology
chemical_list: D043925:Angiogenesis Inducing Agents; D009363:Neoplasm Proteins
keywords: angiogenesis; capillary regression and regrowth; mathematical modelling