Chalmers Conferences, 9th European Conference on Mathematical and Theoretical Biology

An edema‐ based model for diffuse low‐grade gliomas under radiotherapy
M. Badoual

Last modified: 2014-06-09


Diffuse low‐grade gliomas are rare and initially slowly growing tumours. Treatments consist in the first
place in surgery when possible, followed by chemotherapy or radiotherapy. However, despite
technical progress in imaging techniques and therapeutic management, they remain incurable. The
major obstacle to cure these tumors surgically lays in the fact that tumor cells migrate well beyond
the tumor limits detected by imaging techniques, precluding to remove all tumor cells. Hence the
tumor always recurs and an anaplastic transformation eventually occurs: angiogenesis is triggered
and the tumor becomes more aggressive, quickly leading to the patients demise. Optimizing
treatments, for example with modeling, could help to delay the tumor regrowth and the anaplastic
transformation. We present here a model for the effect of radiotherapy on diffuse low‐grade gliomas.
We complemented a migration‐proliferation equation by an equation describing the appearance and
draining of edema, and we argue that the latter effect accounts for the long decrease of the tumour’s
radius (sometimes even years) after the end of the radiotherapy. Using our four‐parameter model, we
are able to fit the data of the evolution of the tumor radius along time, of 28 patients [1]. The model
predicts a strong correlation between a high proliferation coefficient and a low progression‐free gain
of lifetime among the patients, in agreement with clinical studies [1]. Moreover, by measuring or
fixing the values of the parameters, we show that it is possible to predict, at the time of the
radiotherapy, the duration of the tumour’s radius decrease.
[1] Pallud J. et al. Dynamic imaging response following radiation therapy predicts long‐term outcomes
for diffuse low‐grade gliomas. Neuro Oncol. 2012;14:1‐10.