  We present spatio-temporal characteristics of spreading depolarizations (SD)
in two experimental systems: retracting SD wave segments observed with
intrinsic optical signals in chicken retina, and spontaneously occurring
re-entrant SD waves that repeatedly spread across gyrencephalic feline cortex
observed by laser speckle flowmetry. A mathematical framework of
reaction-diffusion systems with augmented transmission capabilities is
developed to explain the emergence and transitions between these patterns. Our
prediction is that the observed patterns are reaction-diffusion patterns
controlled and modulated by weak nonlocal coupling. The described
spatio-temporal characteristics of SD are of important clinical relevance under
conditions of migraine and stroke. In stroke, the emergence of re-entrant SD
waves is believed to worsen outcome. In migraine, retracting SD wave segments
cause neurological symptoms and transitions to stationary SD wave patterns may
cause persistent symptoms without evidence from noninvasive imaging of
infarction.
