Migraine is a prevailing disease in present day population. Cortical spreading depression (CSD) - a depolarisation wave that originates in the visual region and propagates across the cortex to the peripheral areas - has been deemed, by several studies, a correlate of visual aura, a neurological phenomenon preceding migraine and causing perceptual disturbance. As of today, little is known about the mechanisms that can trigger or stop such phenomenon. However, the complex and highly individual characteristics of the brain cortex suggest that the geometry might have a significant impact in supporting or contrasting the propagation of CSD. Accurate patient-specific computational models are thus fundamental to cope with the high variability in cortical geometries among individuals, but also with the anisotropies induced in a given cortex by the complex neuronal organisation in the grey matter. One of the most accepted assumption to explain CSD propagation is that of a progressive wave of extracellular potassium, which is presumed to follow ordinary diffusion law. Following this assumption, we present a distributed model for the extracellular potassium propagation, coupled with patient-specific conductivity tensors derived locally from Diffusion Tensor Imaging (DTI) data. We also discuss our simulation results highlighting significant differences in the propagation traveling patterns of CSD, both intra and inter-hemispherically, as well as some preliminary application to clinical case studies. This is a joint work with JM Kroos and I. Marinelli from BCAM (Bilbao), JM Cortes and I. Diez from BioCruces Health Research Institute (Bilbao), and S. Stramaglia from University of Bari.