title: Brain glioma growth model using reaction-diffusion equation with viscous stress tensor on brain MR images.
abstract: In this paper, a new reaction-diffusion model with viscous stress tensor is proposed for modeling the diffusion and invasion of brain glioma cells, which is based on the model in Yuan J.J., Liu L., Hu Q.M. Mathematical modeling of brain glioma growth using modified reaction-diffusion equation on brain MR images. Comput Biol Med 2013;43:2007-2013. The corresponding parameters are computed. The viscous stress tensor is introduced into reaction-diffusion equation, and can describe more accurately the adhesion of gliomas and normal cells. The experimental results demonstrate the effectiveness and accuracy of the proposed reaction-diffusion equation with viscous stress tensor for real brain glioma MR images.
authors.affiliation: School of Mathematics and Statistics, Southwest University, Chongqing, 400715, PR China. Electronic address: jianjuny@sina.com.
authors.forename: Jianjun
authors.initials: J
authors.lastname: Yuan
authors.affiliation: College of mathematics and statistics, Chongqing University of Arts and Sciences, Chongqing, 402160, PR China.
authors.forename: Lipei
authors.initials: L
authors.lastname: Liu
mesh_terms: D001932:Brain Neoplasms / Q000473:pathology* / Q000503:physiopathology*; D003198:Computer Simulation; D005910:Glioma / Q000473:pathology* / Q000503:physiopathology*; D006801:Humans; D007090:Image Interpretation, Computer-Assisted / Q000379:methods; D008279:Magnetic Resonance Imaging / Q000379:methods*; D008954:Models, Biological; D009361:Neoplasm Invasiveness; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D014783:Viscosity
keywords: Anisotropic reaction-diffusion; Glioma cells; Glioma growth; Viscous stress tensor