Cryodestruction of tissue is influenced by cooling and thawing rates, absolute tissue temperature, number of freeze-thaw cycles, and type of tissue. However, under clinical conditions a MRT visualization of the temperature distribution during cryo-procedures is not possible. Thus, the extent of necrotic areas within the cryo-influenced regions are not precisely predictable. This limitation is particularly relevant for the application of cryoablation in the brain. The present paper proposes the concept of a local, cryo-induced ischemic necrosis. The basic concept is that the MRT-observable and surgically well-manageable frozen region is ischemic. This cryo-induced ischemia causes a necrosis. The extent of the necrotic region is exclusively determined by the ischemia tolerance of the tissue. The effectiveness of this method is demonstrated on sheep brain in vivo. Compared to the freeze-thaw method, histological examinations show a sharper demarcation between regions of necrosis and healthy tissue. In conclusion, the method of MR-controlled local, cryo-induced ischemia enables an exact definition of the region of necrosis in the brain.