title: Modelling the radiotherapy effect in the reaction-diffusion equation.
abstract: OBJECTIVE
  In recent years, the reaction-diffusion (Fisher-Kolmogorov) equation has received much attention from the oncology research community due to its ability to describe the infiltrating nature of glioblastoma multiforme and its extraordinary resistance to any type of therapy. However, in a number of previous papers in the literature on applications of this equation, the term (R) expressing the 'External Radiotherapy effect' was incorrectly derived. In this note we derive an analytical expression for this term in the correct form to be included in the reaction-diffusion equation.
  
  
  METHODS
  The R term has been derived starting from the Linear-Quadratic theory of cell killing by ionizing radiation. The correct definition of R was adopted and the basic principles of differential calculus applied.
  
  
  RESULTS
  The compatibility of the R term derived here with the reaction-diffusion equation was demonstrated. Referring to a typical glioblastoma tumour, we have compared the results obtained using our expression for the R term with the 'incorrect' expression proposed by other authors.
authors: University of Milano Bicocca, Milano, Italy. Electronic address: giovanni.borasi@gmail.com.
authors: Giovanni
authors: G
authors: Borasi
authors: Physics Dept., Liverpool University, Liverpool, UK.
authors: Alan
authors: A
authors: Nahum
mesh_terms: D000465:Algorithms; D001932:Brain Neoplasms / Q000532:radiotherapy*; D003198:Computer Simulation; D004058:Diffusion; D005909:Glioblastoma / Q000532:radiotherapy*; D006801:Humans; D016014:Linear Models; D009369:Neoplasms / Q000532:radiotherapy*; D018787:Radiation Oncology / Q000379:methods; D011878:Radiotherapy / Q000379:methods*; D015203:Reproducibility of Results
keywords: Fisher-Kolmogorov equation; Glioblastoma; Linear-Quadratic Model; Oncology; Radiotherapy; Reaction-diffusion equation