BioMed Research International
Volume 2015 (2015), Article ID 801057, 1 page
http://dx.doi.org/10.1155/2015/801057

Letter to the Editor

Comment on “Simulating Radiotherapy Effect in High-Grade Glioma by Using Diffusive Modeling and Brain Atlases”

Giovanni Borasi¹ and Alan E. Nahum²

¹The Italian National Research Council (CNR), Institute of Bioimaging and Molecular Physiology (IBFM), Edificio LITA, Via F.lli Cervi 93, Segrate, 20090 Milan, Italy
²Clatterbridge Cancer Centre, Bebington CH63 4JY, UK

Received 3 September 2015; Accepted 26 October 2015

Academic Editor: L. Michel Espinoza-Fonseca

Copyright © 2015 Giovanni Borasi and Alan E. Nahum. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

The paper by Roniotis et al. [1] contains a serious error. The problematic term is representing the effect of radiotherapy on the tumor (equation (11) page 4). This term is inserted in the reaction-diffusion (Fisher-Kolmogorov) equation (3), describing the expansion-infiltration of brain tumors. As is well known, in a mathematical expression, adding (or subtracting) two terms with different dimensions is invalid (e.g., what would be the result obtained by adding a length with an area?). That is exactly what has been done in equation (11), first line, that we rewrite here, adding square brackets for greater clarity:

The term included in the curved brackets is a simple number (i.e., dimensionless), but has the dimensions of 1/time and represents the tumor expansion rate. Therefore one cannot subtract the (1 – exponential) term from . It is probable that all the subsequent results are erroneous (in particular Figure ).

The “dimensional” control of an equation is so important in physics that it is included in the program of undergraduate courses. In the present case, the error may have serious consequences in the context of applications of physics to medicine, particularly, regarding the treatment of brain tumors.

Conflict of Interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

References

A. Roniotis, K. Marias, V. Sakkalis, G. C. Manikis, and M. Zervakis, “Simulating radiotherapy effect in high-grade glioma by using diffusive modeling and brain atlases,” Journal of Biomedicine and Biotechnology, vol. 2012, Article ID 715812, 9 pages, 2012.