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Transient dynamics is pervasive in the human brain and poses challengingproblems both in mathematical tractability and clinical observability. Weinvestigate statistical properties of transient cortical wave patterns withcharacteristic forms (shape, size, duration) in a canonical reaction-diffusionmodel with mean field inhibition. The patterns are formed by a ghost near asaddle-node bifurcation in which a stable traveling wave (node) collides withits critical nucleation mass (saddle). Similar patterns have been observed withfMRI in migraine. Our results support the controversial idea that waves ofcortical spreading depression (SD) have a causal relationship with the headachephase in migraine and therefore occur not only in migraine with aura (MA) butalso in migraine without aura (MO), i.e., in the two major migraine subforms.We suggest a congruence between the prevalence of MO and MA with thestatistical properties of the traveling waves' forms, according to which (i)activation of nociceptive mechanisms relevant for headache is dependent upon asufficiently large instantaneous affected cortical area anti-correlated to bothSD duration and total affected cortical area such that headache would be lesssevere in MA than in MO (ii) the incidence of MA is reflected in the distanceto the saddle-node bifurcation, and (iii) the contested notion of MO attackswith silent aura is resolved. We briefly discuss model-based control and meansby which neuromodulation techniques may affect pathways of pain formation.

Transient localized wave patterns and their application to migraine