The algebra of sleepiness: investigating the interaction of homeostatic (S) and circadian (C) processes in sleepiness using linear metrics”

The present studies were conducted to contribute to the debate on the interaction between circadian (C) and homeostatic (S) processes in models of sleep regulation. The Two-Process Model of Sleep Regulation assumes a linear relationship between processes S and C. However, recent elaborations of the model, based on data from forced desynchrony studies, suggest a nonlinear interaction between both processes. Whether this interaction is due to an interaction at substantial level or an artifact from the use of nonlinear metrics remain largely unknown, partly because usual experimental procedures in sleep research do not provide the necessary means to make this distinction. In this study we apply Functional Measurement methodology to demonstrate the linearity of two subjective sleepiness scales (Karolinska Sleepiness Scale and Visual Analogue Scale for sleepiness/alertness) and subsequently use these instruments in a judgment task based on information on prior sleep and time of day. Our results show that, when using linear metrics, processes S and C are integrated according to a differential weighting averaging rule, which consequently implies that both processes are psychologically related in a nonlinear way when sleepiness judgments are performed.