Indirect Effect Model with Surge-Function for Describing Melatonin Circadian Rhythm: Quantitative Comparison and Application Between Normal Sleepers and Patients with Delayed Sleep-Wake Phase Disorder

Introduction: This study investigates the circadian rhythm of melatonin in normal sleepers and delayed sleep-wake phase disorder (DSWPD) patients using quantitative pharmacology methods to better understand sleep disorders and their underlying mechanisms. Methods: We developed an indirect effect model incorporating a surge function using data from 10 normal sleepers and 26 DSWPD patients. Model accuracy and stability were evaluated using diagnostic plots, visual predictive check (VPC) and bootstrapping. Monte Carlo simulations (n=1000) quantitatively compared melatonin circadian rhythm characteristics between normal sleepers and DSWPD patients. Finally, Bayesian estimation utilizing external data from 3 normal sleepers and 3 DSWPD patients predicted melatonin concentration at different time points and the dim light melatonin onset (DLMO). Results: An indirect effect model incorporating a surge function effectively described the circadian rhythm of endogenous melatonin. The model estimates a population typical value (relative standard error%) of: amplitude (AMP), 7.95 (15.47%); peak time (T0), 23:59 (4.13%); peak width (WID), 4.12 (5.78%); elimination rate constant (Kout), 1.23 h-1 (21.82%); baseline melatonin concentration (Baseline), 3.21 pg/ml (23.27%). Monte Carlo simulation revealed that DSWPD patients exhibited approximately 7-hour delay in DLMO, similar melatonin elimination rate constants, and a significantly lower melatonin production rate constants compared to normal sleepers. Bayesian estimation of the melatonin circadian characteristics and DLMO in DSWPD patients closely matched actual data, with model-estimated DLMO exhibiting an error margin within ±10%. Conclusion: Compared to normal sleepers, DSWPD patients exhibited a reduced rate of melatonin production, similar rate of melatonin elimination, and delayed DLMO, highlighting notable circadian melatonin profile alterations. The final model employed Bayesian feedback to estimate melatonin circadian rhythm characteristics and DLMO in DSWPD patients using sparsely sampled data.