The concept of migraine with aura (MwA) is a widespread condition that can affect up to 30% of migraine patients and manifests itself as a temporary visual illusion followed by a prolonged headache. It was initially pitched as a neurological disease, and observed that the spread of accompanying electrophysiological waves as part of the condition, which came to be known as cortical spreading depression (CSD). A strong theoretical basis for a link between MwA and CSD has eventually led to knowledge of the dynamics between the pair. In addition to experiment-based observations, mathematical models make an important contribution towards a numerical means of expressing codependent neural-scale manifestations. This provides alternate means of understanding and observing the phenomena while helping to visualize the links between the variables and their magnitude in contributing towards the emanation and dynamic pulsing of the condition. A number of biophysical mechanisms are believed to contribute to the MwA-CSD, spanning ion diffusion, ionic currents of membranes, osmosis, spatial buffering, neurotransmission, gap junctions, metabolic pumping, and synapse connections. As part of this review study, the various mathematical models for the description of the condition are expressed, reviewed, and contrasted, all of which vary in their depth, perspective, and level of information presented. Subsequent to this, the review looked into links between electrophysiological data-driven manifestations from measurements such as EEG and fMRI. While concluding remarks forged a structured pathway in the area on sub-themes that need to be investigated in order to strengthen and robustify the existing models, they include an accounting for inter-personal variability in models, sex and hormonal factors, and age groups, i.e., pediatrics vs. adults.
Keywords: cortical spreading depression; epidemic; mathematical medicine; mathematical psychiatry; mathematical psychology; migraine with aura; migraines.