title: Hybrid mathematical model of glioma progression.
abstract: OBJECTIVE
  Gliomas are an important form of brain cancer, with high mortality rate. Mathematical models are often used to understand and predict their behaviour. However, using current modeling techniques one must choose between simulating individual cell behaviour and modeling tumours of clinically significant size.
  
  
  METHODS
  We propose a hybrid compartment-continuum-discrete model to simulate glioma growth and malignant cell invasion. The discrete portion of the model is capable of capturing intercellular interactions, including cell migration, intercellular communication, spatial cell population heterogeneity, phenotype differentiation, epigenetic events, proliferation, and apoptosis. Combining this with a compartment and continuum model allows clinically significant tumour sizes to be evaluated.
  
  
  CONCLUSIONS
  This model is used to perform multiple simulations to determine sensitivity to changes in important model parameters, specifically, the fundamental length parameter, necrotic cell degradation rate, rate of cell migration, and rate of phenotype transformation. Using these values, the model is able to simulate tumour growth and invasion behaviour, observed clinically. This mathematical model provides a means to simulate various tumour development scenarios, which may lead to a better understanding of how altering fundamental parameters can influence neoplastic progression.
authors.affiliation: Department of Orthopaedic Surgery, Wake Forest University, Winston-Salem, North Carolina, USA.
authors.forename: M L
authors.initials: ML
authors.lastname: Tanaka
authors.forename: W
authors.initials: W
authors.lastname: Debinski
authors.forename: I K
authors.initials: IK
authors.lastname: Puri
mesh_terms: D001932:Brain Neoplasms / Q000473:pathology* / Q000503:physiopathology; D002450:Cell Communication / Q000502:physiology; D002454:Cell Differentiation / Q000502:physiology; D002455:Cell Division / Q000502:physiology; D002465:Cell Movement / Q000502:physiology; D003198:Computer Simulation; D005910:Glioma / Q000473:pathology* / Q000503:physiopathology; D006801:Humans; D008954:Models, Biological; D009336:Necrosis; D009361:Neoplasm Invasiveness / Q000473:pathology* / Q000503:physiopathology; D009389:Neovascularization, Pathologic / Q000473:pathology / Q000503:physiopathology; D013269:Stochastic Processes