Mathematical Models and Methods in Applied Sciences c © World Scientific Publishing Company Mathematical Modelling of Glioblastoma Tumour Development: A Review

Communicated by (xxxxxxxxxx) During the past several years mathematical models have been applied to various as-pects of cancer dynamics, in particular avascular and vascular tumour growth, invasion, angiogenesis, and metastasis. The present paper focuses on the most common and ma-lignant brain tumour, glioblastoma, and surveys the growing number of studies dealing with mathematical modelling of this tumour. We attempt to classify these studies by their biomedical relevance and critically analyse their results. The aim of this review is to provide a meaningful reference, to both biomedical and mathematical researchers, of the current state of the art of glioma tumour modelling. The discussion attempts to identify current open problems as well as new research perspectives in the mathematical modelling of glioblastoma growth