Localized travelling pulses in mirgaine
Cortical spreading depression (SD) is a massive but transient perturbation in the brain's ionic homoeostasis. It is the underlying cause of neurological symptoms during migraine. I present a mechanism by which localized SD pulse segments are formed as long-lasting but transient patterns in a subexcitable medium, in which the homogeneous steady state is a global attractor. Initial perturbed states can develop into distinct transient pulses caused by a ghost of a saddle-node bifurcation that leads to a slow passage through a bottle-neck. The location of the bottle-neck in phase space is associated with a characteristic form (shape, size) of the pulse segment that depends on the curvature of the medium, i.e., the human cortex. Similar patterns have been observed with fMRI and in patient's symptom reports. The emerging transient patterns and their classification according to size and duration offers a model-based analysis of phase-depended stimulation protocols for non-i nvasive neuromodulation devices, e.g. utilizing transcranial magnetic stimulation, to intelligently target migraine.