Giovanni Borasi1, Alan Nahum2. 1. University of Milano Bicocca, Milano, Italy. Electronic address: giovanni.borasi@gmail.com. 2. Physics Dept., Liverpool University, Liverpool, UK.
Abstract
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.
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.
Authors: E A B F Lima; J T Oden; B Wohlmuth; A Shahmoradi; D A Hormuth; T E Yankeelov; L Scarabosio; T Horger Journal: Comput Methods Appl Mech Eng Date: 2017-08-18 Impact factor: 6.756
Authors: J C L Alfonso; K Talkenberger; M Seifert; B Klink; A Hawkins-Daarud; K R Swanson; H Hatzikirou; A Deutsch Journal: J R Soc Interface Date: 2017-11 Impact factor: 4.118
Authors: Giovanni Borasi; Alan Nahum; Margarethus M Paulides; Gibin Powathil; Giorgio Russo; Laura Fariselli; Debora Lamia; Roberta Cirincione; Giusi Irma Forte; Cristian Borrazzo; Barbara Caccia; Elisabetta di Castro; Silvia Pozzi; Maria Carla Gilardi Journal: J Ther Ultrasound Date: 2016-12-08