Victoria Booth, Departments of Mathematics and Anesthesiology, Univ. of Michigan
Megan Hastings Hagenauer, Molecular and Behavioral Neuroscience Institute, Univ. of Michigan
Sleep and circadian rhythms have been increasingly recognized as significant influences on human health and disease. A critical aspect of disease and healing from clinical interventions for disease is patient pain and its management. Studies in both humans and animals have identified strong correlations between poor sleep quality and pain sensitivity (reviewed in ). Pain intensity has also been shown to display a circadian (~24 h) rhythm, with different types of pain showing different phases of the day at which intensity is highest or lowest (reviewed in ). As pain is a complex phenomenon arising from myriad sources and most likely processed through multiple neural pathways, the physiological mechanisms relating pain, sleep regulation and circadian rhythms are not completely understood. However, numerous studies of the modulation of pain by sleep behavior and circadian rhythms have identified inter-relationships that can provide the foundations for the construction of a mathematical model. Such a model can provide a cohesive framework to investigate physiological mechanisms that may be governing the observed inter-relationships between these 3 important processes.
As the physiology underlying the neural regulation of sleep and circadian rhythms is much better understood, numerous mathematical models of these processes have been developed . A classic, though phenomenological, model for the circadian modulation of sleep propensity is the two-process model . More recently developed models are based on physiological hypotheses for networks of brainstem and hypothalamic neuronal populations governing sleep regulation . Math modeling of circadian rhythms, governed by the master circadian clock in the suprachiasmatic nucleus (SCN), has a long history with models developed on different resolutions, from phenomenological models based on Van der Pol oscillators  to large, complex models of the intracellular gene transcription and translation loops that govern rhythms at the cellular level . This rich repertoire of mathematical models for sleep regulation and circadian rhythms will provide the framework for extensions to include measures of pain threshold and sensitivity.
The goal of this project is to develop a mathematical model of the interactions between sleep, circadian rhythms and pain sensitivity. A hypothesis for this interaction has been proposed by Foo and Mason  who have identified subpopulations of neurons in the raphe magnus that display pain ON and pain OFF firing activity. Populations of neurons in the same area are well-known to participate in the maintenance of waking and display wake ON firing activity, with firing activity ceasing during sleep states. Both of these areas are involved in serotonin regulation in the brain which is one of the primary wake-promoting neuromodulators. The group will explore this hypothesis and its consequence for other observations of the inter-relationships between sleep and pain. Experimental results for the model to address include the reciprocal relationship, or “vicious cycle”, between sleep disturbance and pain intensity/sensitivity, the interaction of circadian modulation of pain with sleep fragmentation and disturbance, and effects of different circadian phasing of pain sensitivity on its dependency on sleep quality.
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