A major goal of this project is to gain a better understanding of cortical spreading depression. This is a disorder of the brain that is the basis of migraine aura and many other diseases of the brain including stroke and epilepsy. In this disorder the ionic environment of the brain is completely disrupted and the nerve cells turn silent, with a disturbance that spreads at speeds of two to five millimeters per minute across the brain. When this happens in the visual cortex, the brain area that processes visual information, the patient will perceive an aura, a temporary visual defect that slowly travels over the field of view. Migraine sufferers often perceive an aura (migraine aura) prior to a migraine attack. Better understanding the mechanisms of cortical spreading depression will thus help in management of migraine headache and many other pathological brain conditions. This research collaboration will train graduate students who will work on various aspects of the project. Summer schools will be held at Florida International University, which is a minority serving institution. Thus this project, accompanied with existing institutional efforts, has the potential to further the goal of increasing minority representation in the sciences. Further, this collaborative effort brings together experimentalists and theorists of diverse interests and strength, and therefore provides students with an ideal opportunity for professional growth.Cortical spreading depression is a massive redistribution of ionic concentrations in the brain that results in a localized temporary loss of neuronal function. This disturbance spreads through the brain at speeds of two to five millimeters per minute and is the physiological substrate of migraine aura. Although cortical spreading depression was first described over seventy years ago, the physiological mechanisms leading to the disturbance remains elusive, most likely due to the fact that it involves many biophysical processes. In this project, a comprehensive mathematical model and computational apparatus to simulate the phenomena will be constructed and validated with experimental data obtained at high spatial resolution. An important aspect of the mathematical model is that it takes into account ionic electro-diffusion, an effect that has not been properly considered in previous studies, and may also be relevant for illucidating mechanisms in many other neurophysiological settings. In particular, the effects of electro-diffusion on extracellular recordings, electroencephalography and magneto-encephalography signals will be studied, thereby improving analysis of these measurement modalities. Overall this research may have an impact in many other brain pathologies which are linked to these underlying biophysical processes.