Light-Based Circadian Rhythm Control: Entrainment and Optimization

Light is a strong synchronizer for circadian rhythm — the 24-h biological oscillation in plants, insects, and mammals. This paper considers the circadian entrainment problem for a popular circadian oscillation model (the Kronauer model) by using light intensity as the control input. This problem is commonly encountered by shift workers and international travelers — how to shift the phase of one’s circadian rhythm by a specified amount, preferably as fast as possible? We consider three approaches: 1. Periodic entrainment: use the light/dark cycle corresponding to the desired circadian rhythm as the light input. 2. Optimal entrainment: use light input to shift the circadian rhythm to the desired state in minimum time. 3. Feedback entrainment: use circadian state feedback to adjust light input. For feedback entrainment, we consider two cases: active lighting control which can inject artificial lighting on demand and subtractive lighting control which only blocks the ambient lighting. For the periodic entrainment, which is used as a baseline for comparison, we apply the harmonic balance method to assess the existence of a stable periodic solution, and verify the result by simulation. For the minimum time entrainment, we present an efficient solution to the two-point boundary value problem and show that active lighting control significantly reduces the entrainment time from the baseline. The feedback algorithm augments the periodic entrainment with a circadian state feedback to account for modeling error and noise. Results from this study provide new insight and guideline to light intensity control for circadian rhythm regulation.