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The equation (2) is dimensionally uncorrect

Posted by 1236 on 08 Sep 2015 at 08:21 GMT

The paper in question contains a serious error. The problematic term is the third term in eq. 2, pag.3

“-R(x,t,d_i)∙c∙(1-c/k_t ) “ (1)

representing the effect of Radiotherapy on the tumor. This term is inserted in the reaction-diffusion (Fisher-Kolmogorov) equation 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. (For example, what would be the result obtained by adding a length with a time?). That is exactly what has been done in Eq. (2), where the term on the left and the first two term on the right of the equal sign have the dimensions of a cell concentration per unit time. In the quoted term (1),” -R(x,t,d_i) “ is dimensionless (a number), as can be verified by observing eq. (3), “ c “ has the dimension of a cell concentration and “ (1-c/k_t ) “ is dimensionless (a number). So the whole term (1)“ -R(x,t,d_i)∙c∙(1-c/k_t ) “ has the dimension of a cell concentration and not a cell concentration per unit time, as would be required.

All the subsequent results should considered potentially erroneous (in particular Fig.2).

We suggest that authors prepare an extended “Errata Corrige”, with the corrected mathematical expressions and the results that follow from these expressions.
Further we find it disturbing that the referees did not pick up a dimensional error that is one of the first things that should be controlled in an equation.

No competing interests declared.