In diffuse gliomas, infiltration of apparently healthy tissues surrounding zones which appear as abnormal on the MRI is thought to be one of the main causes of treatment failure. Therefore, having accurate mathematical models of this phenomenon may be a key to therapeutic advances. WHO Grade II gliomas (GIIG), although ultimately lethal in most cases, are a good starting point to achieve this goal since they lack more complicated features such as neoangiogenesis, allowing one to concentrate on models with only a few parameters.
A model at the scale of the tumour (e.g. a set of PDE), which can be compared to non-invasive data such as MRI, is needed to study the outcome of the disease and of treatments. However, on one hand it is difficult to write down such a model from scratch. One often needs to start either with a model at the scale of the cells and go to the large-scale limit. On the other hand, data at the scale of the tumour is often difficult or impossible to interpret (e.g. MRI signal is not absolutely calibrated), and one needs first a calibration by comparison with data at the scale of cells (biopsy samples).
We study several examples of these changes of scales and comparison of models and data. We discuss a model of grade-II glioma (GIIG) where tumour cells migrate and proliferate, and induce the host tissue to produce ``edema’’, which we argue is the cause of the MRI signal abnormality, rather than the tumour cells themselves. The model is compared to data coming from biopsy samples of GIIG, and we use it to discuss the outcome of radiotherapy on a series of patients. Finally, we give results about the relationship of an MRI signal (ASL) and the density of microvessels in pediatric brain tumours from grade I to grade IV.