A three process approach for insomnia-like awakenings

Mathematical modelling of sleep is a growing field, with an increasing number of applications to sleep disorders. However, despite its high prevalence and under-diagnosis worldwide, insomnia has not been among these disorders. We chart the development of sleep models and investigate the hypothesis that they can be simply modified to model insomnia, ultimately introducing a new model focusing on nocturnal awakenings as a starting point of insomnia-like behaviour, based on a three process approach. We find that several of these models can make promising steps towards producing nighttime awakenings characteristic of many types of insomnia with minor modifications, but that none can fully reproduce every key criterion with only minor adaptations. In particular, we find that the stability of the sleeping state is an important factor in more complex contemporary neuronal population models’ abilities to incorporate awakenings, with both permanently stable and permanently non-stable sleep proving to be obstacles. Instead, we base our new model on the simpler foundational two process model, incorporating an original, quantitative wakefulness drive. We further analyse the sensitivity of its new parameters and the statistical properties of the nighttime awakening phenomena it produces. This new drive includes both physiology-based arousal impulses and environmental and psychological disturbances, and provides the foundation of a new approach to future quantitative modelling of insomnia phenotypes.