Glioblastoma is a rapidly evolving high-grade astrocytoma that is distinguished pathologically from lower grade gliomas by the presence of necrosis and microvascular hyperplasia. Necrotic areas are typically surrounded by hypercellular regions known as “pseudopalisades” originated by local tumor vessel occlusions that induce collective cellular migration events. This leads to the formation of waves of tumor cells actively migrating away from central hypoxia. We present a mathematical model that incorporates the interplay among two tumor cell phenotypes, a necrotic core and the oxygen distribution. Our simulations reveal the formation of a traveling wave of tumor cells that reproduces the observed histologic patterns of pseudopalisades. Additional simulations of the model equations show that preventing the collapse of tumor microvessels leads to slower glioma invasion, a fact that might be exploited for therapeutic purposes.

This paper shows the potential of microfluidic devices as advanced artificial systems capable of modeling in vivo nutrient and oxygen gradients during tumor evolution.

Low-grade gliomas (LGGs) are a group of primary brain tumours usually encountered in young patient populations. These tumours represent a difficult challenge because many patients survive a decade or more and may be at a higher risk for treatment-related complications. Specifically, radiation therapy is known to have a relevant effect on survival but in many cases it can be deferred to avoid side effects while maintaining its beneficial effect. However, a subset of LGGs manifests more aggressive clinical behaviour and requires earlier intervention. Moreover, the effectiveness of radiotherapy depends on the tumour characteristics. Recently Pallud et al. (2012. Neuro-Oncology, 14: , 1-10) studied patients with LGGs treated with radiation therapy as a first-line therapy and obtained the counterintuitive result that tumours with a fast response to the therapy had a worse prognosis than those responding late. In this paper, we construct a mathematical model describing the basic facts of glioma progression and response to radiotherapy. The model provides also an explanation to the observations of Pallud et al. Using the model, we propose radiation fractionation schemes that might be therapeutically useful by helping to evaluate tumour malignancy while at the same time reducing the toxicity associated to the treatment.

We propose a mathematical model of tumor cell nutrient uptake governed by the presence of two key biomolecular fuels: glucose and lactate. The model allows us to describe, in a remarkably simple way, different in vitro scenarios previously reported in experiments of tumor cell metabolism using distinct energy sources. The predictions of our model show good agreement with all the examined tumor cell lines (cervix, colon, and glioma) and provide a first step toward the development of more comprehensive frameworks accounting for in vivo cancer dynamics under complex spatial heterogeneities.

• Three-dimensional segmentation on magnetic resonance images allows the study of geometric measures. • Patients with small width of contrast enhancing areas have better prognosis. • The irregularity of contrast enhancing areas predicts survival in glioblastoma patients.