title: Mathematical modelling of spatio-temporal glioma evolution.
abstract: BACKGROUND
  Gliomas are the most common types of brain cancer, well known for their aggressive proliferation and the invasive behavior leading to a high mortality rate. Several mathematical models have been developed for identifying the interactions between glioma cells and tissue microenvironment, which play an important role in the mechanism of the tumor formation and progression.
  
  
  METHODS
  Building and expanding on existing approaches, this paper develops a continuous three-dimensional model of avascular glioma spatio-temporal evolution. The proposed spherical model incorporates the interactions between the populations of four different glioma cell phenotypes (proliferative, hypoxic, hypoglychemic and necrotic) and their tissue microenvironment, in order to investigate how they affect tumor growth and invasion in an isotropic and homogeneous medium. The model includes two key variables involved in the proliferation and invasion processes of cancer cells; i.e. the extracellular matrix and the matrix-degradative enzymes concentrations inside the tumor and its surroundings. Additionally, the proposed model focuses on innovative features, such as the separate and independent impact of two vital nutrients, namely oxygen and glucose, in tumor growth, leading to the formation of cell populations with different metabolic profiles. The model implementation takes under consideration the variations of particular factors, such as the local cell proliferation rate, the variable conversion rates of cells from one category to another and the nutrient-dependent thresholds of conversion. All model variables (cell densities, ingredients concentrations) are continuous and described by reaction-diffusion equations.
  
  
  RESULTS
  Several simulations were performed using combinations of growth and invasion rates, for different evolution times. The model results were evaluated by medical experts and validated on experimental glioma models available in the literature, revealing high agreement between simulated and experimental results.
  
  
  CONCLUSIONS
  Based on the experimental validation, as well as the evaluation by clinical experts, the proposed model may provide an essential tool for the patient-specific simulation of different tumor evolution scenarios and reliable prognosis of glioma spatio-temporal progression.
authors.affiliation: Digital Image and Signal Processing Laboratory, Electronic and Computer Engineering Department, Technical University of Crete, Polytechnioupolis, Kounopidiana Campus, Chania, Crete, Greece. mpapadogiorgaki@isc.tuc.gr
authors.forename: Maria
authors.initials: M
authors.lastname: Papadogiorgaki
authors.forename: Panagiotis
authors.initials: P
authors.lastname: Koliou
authors.forename: Xenofon
authors.initials: X
authors.lastname: Kotsiakis
authors.forename: Michalis E
authors.initials: ME
authors.lastname: Zervakis
mesh_terms: D001932:Brain Neoplasms / Q000601:surgery*; D005910:Glioma / Q000601:surgery*; D006801:Humans; D008958:Models, Molecular