Modelling the radiotherapy effect in the reaction-diffusion equation.
PURPOSE
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.
['Borasi|Giovanni|G|', 'Nahum|Alan|A|']
D000465:Algorithms D001932:Brain Neoplasms D003198:Computer Simulation D004058:Diffusion D005909:Glioblastoma D006801:Humans D016014:Linear Models D009369:Neoplasms D018787:Radiation Oncology D011878:Radiotherapy D015203:Reproducibility of Results
Radiotherapy Reaction-diffusion equation Oncology Glioblastoma Fisher-Kolmogorov equation Linear-Quadratic Model