Alertness Optimization for Shift Workers Using a Physiology-based Mathematical Model

Abstract

Sleep is vital for maintaining cognitive function, facilitating metabolic waste removal, and supporting memory consolidation. However, modern societal demands, particularly shift work, often disrupt natural sleep patterns. This can induce excessive sleepiness among shift workers in critical sectors such as healthcare and transportation and increase the risk of accidents. The primary contributors to this issue are misalignments of circadian rhythms and enforced sleep-wake schedules. Regulating circadian rhythms that are tied to alertness can be regarded as a control problem with control inputs in the form of light and sleep schedules. In this paper, we address the problem of optimizing alertness by optimizing light and sleep schedules to improve the cognitive performance of shift workers. A key tool in our approach is a mathematical model that relates the control input variables (sleep and lighting schedules) to the dynamics of the circadian clock and sleep. In the sleep and circadian modeling literature, the newer physiology-based model shows better accuracy in predicting the alertness of shift workers than the phenomenology-based model, but the dynamics of physiological-based model have differential equations with different time scales, which pose challenges in optimization. To overcome the challenge, we propose a hybrid version of the PR model by applying singular perturbation techniques to reduce the system to a non-stiff, differentiable hybrid system. This reformulation facilitates the application of the calculus of variation and the gradient descent method to find the optimal light and sleep schedules that maximize the subjective alertness of shift worker. Our approach is validated through numerical simulations, and the simulation results demonstrate improved alertness compared to other existing schedules.