Bright solitary waves in malignant gliomas.
V.M. Pérez-García, G.F. Calvo, J. Belmonte-Beitia, D. Diego, L.A. Pérez-Romasanta
Physical Review E 84, 021921 (2011)
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.