Activity driven sleep dynamics: A conceptual modeling study

The sleep state is traditionally defined as global, involving the entire body. Accordingly, a two-process mathematical model of the switch between sleep and wakefulness was proposed by Borbely more than 30 years ago and successfully used in deep modeling studies. However, in recent decades, new data have been obtained that call for a more complex understanding of sleep, both in spatial and temporal aspects. In particular, this concerns such phenomena as local sleep and short sleep episodes (naps). Here, we propose a mathematical model that gives the space for both local sleep phenomena and short sleep episodes. In doing so, we rely on the concept of a "sleep unit" and propose a phenomenological rate model of its activity. We also use a concept of a psycho-sensory drive to simulate various scenarios induced by external or internal stimuli. An essential element of our model is the representation of the background neural activity as a random signal, which reflects the real situation of overlapping multiple internal and external stimuli. The corresponding simulation runs confirm that the model reproduces both phenomena: local sleep and short nap episodes. As a particular but illustrative result, we demonstrate an example of involuntary global falling asleep under conditions of an overload of a separate sleep unit. In conclusion, we discuss the potential of our model and ways of its further quantitative parameterization.