title: Soliton driven angiogenesis.
abstract: Angiogenesis is a multiscale process by which blood vessels grow from existing ones and carry oxygen to distant organs. Angiogenesis is essential for normal organ growth and wounded tissue repair but it may also be induced by tumours to amplify their own growth. Mathematical and computational models contribute to understanding angiogenesis and developing anti-angiogenic drugs, but most work only involves numerical simulations and analysis has lagged. A recent stochastic model of tumour-induced angiogenesis including blood vessel branching, elongation, and anastomosis captures some of its intrinsic multiscale structures, yet allows one to extract a deterministic integropartial differential description of the vessel tip density. Here we find that the latter advances chemotactically towards the tumour driven by a soliton (similar to the famous Korteweg-de Vries soliton) whose shape and velocity change slowly. Analysing these collective coordinates paves the way for controlling angiogenesis through the soliton, the engine that drives this process.
authors: Gregorio Millán Institute for Fluid Dynamics, Nanoscience and Industrial Mathematics and Department of Materials Science &Engineering, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganés, Spain.
authors: L L
authors: LL
authors: Bonilla
authors: Gregorio Millán Institute for Fluid Dynamics, Nanoscience and Industrial Mathematics and Department of Materials Science &Engineering, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganés, Spain.
authors: M
authors: M
authors: Carretero
authors: Gregorio Millán Institute for Fluid Dynamics, Nanoscience and Industrial Mathematics and Department of Materials Science &Engineering, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganés, Spain.
authors: F
authors: F
authors: Terragni
authors: Center for Complex and Nonlinear Science and Department of Mathematics, University of California at Santa Barbara, USA.
authors: B
authors: B
authors: Birnir
mesh_terms: D020533:Angiogenesis Inhibitors / Q000494:pharmacology*; D000818:Animals; D002320:Cardiovascular Physiological Phenomena; D002633:Chemotaxis; D006801:Humans; D008955:Models, Cardiovascular; D009369:Neoplasms / Q000188:drug therapy; D009389:Neovascularization, Pathologic; D012984:Software; D013269:Stochastic Processes
chemical_list: D020533:Angiogenesis Inhibitors