  Diffuse low grade gliomas are slowly growing tumors that always recur after
treatment. In this paper, we revisit the modeling of the tumor radius evolution
before and after the radiotherapy process and propose a novel model that is
simple, yet biologically motivated, and that remedies some shortcomings of
previously proposed ones. We confront it with clinical data consisting in
time-series of tumor radius for 43 patient records, using a stochastic
optimization technique and obtain very good fits in all the cases. Since our
model describes the evolution of the tumor from the very first glioma cell, it
gives access to the possible age of the tumor. Using the technique of
profile-likelihood to extract all the information from the data, we build
confidence intervals for the tumor birth age and confirm the fact that
low-grade glioma seem to appear in the late teenage years. Moreover, an
approximate analytical expression of the temporal evolution of the tumor radius
allows us to explain the correlations observed in the data.
