A Two-Process Model for Circadian and Sleep-dependent Modulation of Pain Sensitivity

Abstract Pain sensitivity is strongly modulated by time of day and by prior sleep behavior. These two factors, governed by the circadian rhythm and homeostatic sleep drive, respectively, likewise dictate the timing and duration of sleep. The fields of sleep and circadian research have identified much of the physiology underlying the circadian rhythm and homeostatic sleep drive with mathematical modeling playing an important role in understanding how these two processes interact to affect sleep behavior. We hypothesize that the daily rhythm of pain sensitivity and its sleep-dependent modulation reflect an interaction of the circadian rhythm and homeostatic sleep drive. To investigate this hypothesis, we adapt the formalism of a classic mathematical model for the regulation of sleep behavior by the circadian rhythm and homeostatic sleep drive, called the Two Process model, to simulate the interaction of these two processes on pain sensitivity. To construct the model, we utilize data from experimental reports on the daily rhythmicity of pain sensitivity in humans to define a “daily pain sensitivity” function. We decompose this function into two processes: a sleep-dependent process S ( t ) that follows the homeostatic sleep drive and a circadian process C ( t ) that is dictated by the circadian rhythm. By simulating different sleep schedules with the original Two Process model, we compute changes in the sleep-dependent process S ( t ) that modulates pain sensitivity. By combining S ( t ) with the circadian process C ( t ), our model predicts resultant changes in the daily pain sensitivity rhythm. We illustrate model predictions for changes in pain sensitivity due to sleep deprivation, sleep restriction and shift work schedules. We believe that this model may be a useful tool for pain management by providing predictions of the variations in pain sensitivity due to changing sleep schedules.