The malignant brain tumour Glioblastoma multiforme (GBM) displays a highly invasive behaviour. Spreading of the malignant cells appears to be guided by the white matter fibre tracts within the brain. In order to understand the global growth process we introduce a lattice-gas cellular automaton model which describes the local interaction between individual malignant cells and their neighbourhood. We consider interactions between cells (brain cells and tumour cells) and between malignant cells and the fibre tracts in the brain, which are considered as a prepattern. The prepattern implies persistent individual cell motion along the fibre structure. Simulations with the model show that only the inclusion of the prepattern results in invading tumour and growing tumour islets in front of the expanding tumour bulk (i.e. the growth pattern observed in clinical practice). Our results imply that the infiltrative growth of GBMs is, in part, determined by the physical structure of the surrounding brain rather than by intrinsic properties of the tumour cells.