title: Bright solitary waves in malignant gliomas.
abstract: We put forward a nonlinear wave model describing the fundamental dynamical features of an aggressive type of brain tumors. Our model accounts for the invasion of normal tissue by a proliferating and propagating rim of active glioma cancer cells in the tumor boundary and the subsequent formation of a necrotic core. By resorting to numerical simulations, phase space analysis, and exact solutions we prove that bright solitary tumor waves develop in such systems. Possible implications of our model as a tool to extract relevant patient specific tumor parameters in combination with standard preoperative clinical imaging are also discussed.
authors.affiliation: Departamento de Matemáticas, E. T. S. I. Industriales and Instituto de Matemática Aplicada a la Ciencia y la Ingeniería, Universidad de Castilla-La Mancha, E-13071 Ciudad Real, Spain.
authors.forename: Víctor M
authors.initials: VM
authors.lastname: Pérez-García
authors.forename: Gabriel F
authors.initials: GF
authors.lastname: Calvo
authors.forename: Juan
authors.initials: J
authors.lastname: Belmonte-Beitia
authors.forename: David
authors.initials: D
authors.lastname: Diego
authors.forename: Luis
authors.initials: L
authors.lastname: Pérez-Romasanta
mesh_terms: D001932:Brain Neoplasms / Q000473:pathology*; D005909:Glioblastoma / Q000473:pathology*; D008279:Magnetic Resonance Imaging; D008954:Models, Biological; D009361:Neoplasm Invasiveness; D017711:Nonlinear Dynamics