Transient localized wave patterns and their application to migraine

TL;DR

This study models transient cortical wave patterns using reaction-diffusion equations to support the hypothesis that spreading depression waves are causally linked to migraine headache phases, applicable to both migraine with and without aura.

Contribution

It introduces a mathematical framework connecting cortical wave dynamics to migraine subtypes, explaining clinical observations through bifurcation analysis.

Findings

Waves of cortical spreading depression are linked to migraine headache phases.

The model explains differences between migraine with aura and without aura.

Neuromodulation may influence pain pathways based on wave dynamics.

Abstract

Transient dynamics is pervasive in the human brain and poses challenging problems both in mathematical tractability and clinical observability. We investigate statistical properties of transient cortical wave patterns with characteristic forms (shape, size, duration) in a canonical reaction-diffusion model with mean field inhibition. The patterns are formed by a ghost near a saddle-node bifurcation in which a stable traveling wave (node) collides with its critical nucleation mass (saddle). Similar patterns have been observed with fMRI in migraine. Our results support the controversial idea that waves of cortical spreading depression (SD) have a causal relationship with the headache phase in migraine and therefore occur not only in migraine with aura (MA) but also 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 the statistical properties of the traveling waves' forms, according to which (i) activation of nociceptive mechanisms relevant for headache is dependent upon a sufficiently large instantaneous affected cortical area anti-correlated to both SD duration and total affected cortical area such that headache would be less severe in MA than in MO (ii) the incidence of MA is reflected in the distance to the saddle-node bifurcation, and (iii) the contested notion of MO attacks with silent aura is resolved. We briefly discuss model-based control and means by which neuromodulation techniques may affect pathways of pain formation.