Cortical spreading depression (CSD) is an example of one of the most common abnormalities in biophysical brain functioning. Despite the fact that there are many mathematical models describing the cortical spreading depression (CSD), most of them do not take into consideration the role of redistribution of cerebral blood flow (CBF), that results in the formation of spatio-temporal patterns. The paper presents a mathematical model, which successfully explains the CBD role in the CSD process. Numerical study of this model has revealed the formation of stationary dissipative structures, visually analogous to Turing structures. However, the mechanism of their formation is not diffusion. We show these structures occur due to another type of spatial coupling, that is related to tissue perfusion rate. The proposed model predicts that at similar state of neurons the distribution of blood flow and oxygenation may by different. Currently, this effect is not taken into account when the Blood oxygen-level dependent (BOLD) contrast imaging used in functional magnetic resonance imaging (fMRI). Thus, the diagnosis on the BOLD signal can be ambiguous. We believe that our results can be used in the future for a more correct interpretation of the data obtained with fMRI, NIRS and other similar methods for research of the brain activity.