A Chaotic Model of the Cerebro-Cerebellar Migraine Generator Network

Migraine, recognized as a dynamical disease, manifests in two primary forms: Migraine with Aura (MWA) and Migraine without Aura (MWOA), distinguished by the presence or absence of pre-headache neurological symptoms. Despite the advances in dynamical theories of migraine, the mechanisms governing brain network coordination during migraine attacks — particularly in MWA — remain unclear. To address this issue, we investigate the cerebellum’s role in migraine pathophysiology by developing a biologically grounded Migraine Generator Network (MGN) model consisting of four subnetworks (fMGN) that incorporates both cerebral and cerebellar components compared to the three-subnetwork MGN (tMGN). Using bifurcation analysis, we characterize the migraine cycle’s distinct phases, revealing that the aura phase emerges as repeated transitions between chaotic and periodic states via period-doubling and period-halving bifurcations. Leveraging the Maximum Lyapunov Exponent (MLE), we quantitatively classify different phases: interictal and ictal (headache) phases correspond to small and large positive MLE values, respectively; the prodromal phase aligns with negative MLE values; and the aura phase exhibits zero-fluctuating MLE dynamics. Furthermore, two-parameter MLE analysis identifies critical physiological parameter variations necessary for fMGN modulation, offering theoretical insights for dynamical control strategies in migraine management. By integrating cerebellar dynamics into the fMGN model, this study provides a novel mechanistic explanation for aura generation and establishes a quantitative framework for analyzing migraine phases. The methodologies developed here may also extend to other disorders involving chaotic dynamics, broadening their applicability in computational neuroscience.