It is well established that migraine is a multifactorial disorder. A deep understanding of migraine should be based upon both the underlying traits and the current states affected by different physiological, psychological, and environmental factors. At this point, there is no framework fully meeting these criteria. Here, we describe a broader view of the migraine disorder defined as a dysfunctional brain state and trait interaction. In this model, we consider events that may enhance or diminish migraine responsivity based on an individual’s trait and state. This could provide an expanded view for considering how migraine attacks are sometimes precipitated by “triggers” and sometimes not, how these factors only lead to migraine attacks in migraine patients, or how individuals with an increased risk for migraine do not show any symptoms at all. Summarizing recent studies and evidence that support the concept of migraine as a brain state–trait interaction can also contribute to improving patient care by highlighting the importance of precision medicine and applying measures that are able to capture how different traits and states work together to determine migraine.

In this paper we study a Volterra integral equation of the second kind, including two arbitrary continuous functions, in order to determine first-passage-time probability density functions through time-dependent boundaries for time-non-homogeneous one-dimensional diffusion processes with natural boundaries. These results generalize those which were obtained for time-homogeneous diffusion processes by Giorno et al. [3], and for some particular classes of time-non-homogeneous diffusion processes by Gutiérrez et al. [4], [5].