Time optimal entrainment control for circadian rhythm
Autoři:
A. Agung Julius aff001; Jiawei Yin aff001; John T. Wen aff001
Působiště autorů:
Dept. Electrical, Computer, and Systems Engineering, Rensselaer Polytechnic Institute, Troy, NY, United States of America
aff001; Lighting Enabled Systems and Applications (LESA) Engineering Research Center, Rensselaer Polytechnic Institute, Troy, NY, United States of America
aff002; Dept. Industrial and Systems Engineering, Rensselaer Polytechnic Institute, Troy, NY, United States of America
aff003
Vyšlo v časopise:
PLoS ONE 14(12)
Kategorie:
Research Article
doi:
https://doi.org/10.1371/journal.pone.0225988
Souhrn
The circadian rhythm functions as a master clock that regulates many physiological processes in humans including sleep, metabolism, hormone secretion, and neurobehavioral processes. Disruption of the circadian rhythm is known to have negative impacts on health. Light is the strongest circadian stimulus that can be used to regulate the circadian phase. In this paper, we consider the mathematical problem of time-optimal circadian (re)entrainment, i.e., computing the lighting schedule to drive a misaligned circadian phase to a reference circadian phase as quickly as possible. We represent the dynamics of the circadian rhythm using the Jewett-Forger-Kronauer (JFK) model, which is a third-order nonlinear differential equation. The time-optimal circadian entrainment problem has been previously solved in settings that involve either a reduced-order JFK model or open-loop optimal solutions. In this paper, we present (1) a general solution for the time-optimal control problem of fastest entrainment that can be applied to the full order JFK model (2) an evaluation of the impacts of model reduction on the solutions of the time-optimal control problem, and (3) optimal feedback control laws for fastest entrainment for the full order Kronauer model and evaluate their robustness under some modeling errors.
Klíčová slova:
Algorithms – Body temperature – Circadian oscillators – Circadian rhythms – Graphs – Chronobiology – Nonlinear dynamics – Numerical integration
Zdroje
1. Aschoff J. Circadian rhythms in man. Science. 1965;148(3676):1427–1432. doi: 10.1126/science.148.3676.1427 14294139
2. Refinetti R. Circadian Physiology. CRC Press; 2005.
3. Rea MS, Bierman A, Figueiro MG, Bullough JD. A new approach to understanding the impact of circadian disruption on human health. J Circadian Rhythms. 2008;6(1):7. doi: 10.1186/1740-3391-6-7 18510756
4. Baggs JE, Price TS, DiTacchio L, Panda S, FitzGerald GA, Hogenesch JB. Network features of the mammalian circadian clock. PLoS Biol. 2009;7(3):563–575. doi: 10.1371/journal.pbio.1000052
5. Leloup JC, Goldbeter A. A model for circadian rhythms in Drosophila incorporating the formation of a complex between the PER and TIM proteins. J Biol Rhythms. 1998;13:70–87. doi: 10.1177/074873098128999934 9486845
6. Leloup JC, Goldbeter A. Toward a detailed computational model for the mammalian circadian clock. Proc Nati Acad Sci USA. 2003;100:7051–7056. doi: 10.1073/pnas.1132112100
7. Forger DB, Jewett ME, Kronauer RE. A simpler model of the human circadian pacemaker. J Biol Rhythms. 1999;14(6):533–538. doi: 10.1177/074873099129000867
8. Kronauer RE, Forger DB, Jewett ME. Quantifying human circadian pacemaker response to brief, extended, and repeated light stimuli over the phototopic range. J Biol Rhythms. 1999;14(6):501–516. doi: 10.1177/074873049901400609
9. Forger DB, Kronauer RE. Reconciling mathematical models of biological clocks by averaging on approximate manifolds. SIAM J Appl Math. 2002;62:1281–1296. doi: 10.1137/S0036139900373587
10. Doyle FJ III, Gunawan R, Bagheri N, Mirsky H, To TL. Circadian rhythm: A natural, robust, multi-scale control system. Comput Chem Eng. 2006;30(10-12):1700–1711. doi: 10.1016/j.compchemeng.2006.05.029
11. Abel JH, Chakrabarty A, Doyle FJ III. Controlling biological time: nonlinear model predictive control for populations of circadian oscillators. In: Tempo R, Yurkovich S, Misra P, editors. Emerging Applications of Control and Systems Theory. Lecture Notes in Control and Information Sciences. Springer; 2018. p. 123–138. doi: 10.1007/978-3-319-67068-3_9
12. Mott C, Mollicone D, van Wollen M. Modifying the human circadian pacemaker using model based predictive control. In: Proc Am Control Conf. 2003; p. 453–458.
13. Bagheri N, Stelling J, Doyle FJ III. Circadian phase entrainment via nonlinear model predictive control. Int J Robust Nonlin. 2007;17(17):1555–1571. doi: 10.1002/rnc.1209
14. Bagheri N, Stelling J, Doyle FJ. Circadian phase resetting via single and multiple control targets. PLoS Comput Biol. 2008;4(7):e1000104. doi: 10.1371/journal.pcbi.1000104 18795146
15. Abel JH, Doyle FJ. A systems theoretic approach to analysis and control of mammalian circadian dynamics. Chem Eng Res Des. 2016;116:48–60. doi: 10.1016/j.cherd.2016.09.033 28496287
16. Forger DB. Biological clocks, rhythms, and oscillations: The theory of biological timekeeping. MIT Press; 2017.
17. Zhang JX, Wen JT, Julius AA. Optimal circadian rhythm control with light input for rapid entrainment and improved vigilance. In: Proc IEEE Conf Decis Control; 2012. p. 3007–3012.
18. Zhang JX, Wen JT, Julius AA. Optimal and feedback control for light-based circadian entrainment. In: Proc IEEE Conf Decis Control; 2013. p. 2677–2682.
19. Zhang JX, Qiao W, Wen JT, Julius AA. Light-based circadian rhythm control: Entrainment and optimization. Automatica. 2016;68:44–55. doi: 10.1016/j.automatica.2016.01.052
20. Qiao W, Wen JT, Julius AA. Entrainment control of phase dynamics. IEEE Trans Autom Control. 2017;62(1):445–450. doi: 10.1109/TAC.2016.2555885
21. Julius AA, Yin J, Wen JT. Time-optimal control for circadian entrainment for a model with circadian and sleep dynamics. In: Proc IEEE Conf Decis Control. Melbourne, Australia; 2017. p. 4709–4714.
22. Serkh K, Forger DB. Optimal schedules of light exposure for rapidly correcting circadian misalignment. PLOS Comput Biol. 2014;10(4):e1003523. doi: 10.1371/journal.pcbi.1003523 24722195
23. Khalsa SBS, Jewett ME, Cajochen C, Czeisler CA. A phase response curve to single bright light pulses in human subjects. J Physiol. 2003;549:945–952. doi: 10.1113/jphysiol.2003.040477 12717008
24. Taylor SR, Gunawan R, Petzold LR, Doyle FJ III. Sensitivity measures for oscillating systems: application to mammalian circadian gene network. IEEE Trans Autom Control. 2008;53:177–188. doi: 10.1109/TAC.2007.911364
25. Moeck M, Yoon YJ. Green buildings and potential electric light energy savings. J Archit Eng. 2004;10(4):143–159. doi: 10.1061/(ASCE)1076-0431(2004)10:4(143)
26. Bryson AE, Ho YC. Applied optimal control. Taylor & Francis; 1975.
27. Liberzon D. Calculus of variations and optimal control theory. Princeton University Press; 2012.
28. Diekman CO, Bose A. Reentrainment of the circadian pacemaker during jet lag: East-west asymmetry and the effects of north-south travel. J Theor Biol. 2018;437:261–285. doi: 10.1016/j.jtbi.2017.10.002 28987464
29. Jewett ME, Kronauer RE, Czeisler CA. Light-induced suppression of endogenous circadian amplitude in humans. Nature. 1991;350:59–62. doi: 10.1038/350059a0 2002845
30. Yin J, Julius AA, Wen JT. Rapid circadian entrainment in models of circadian genes regulation. In: Proc IEEE Conf Decis Control. 2019.
31. Baehr EK, Revelle W, Eastman CI. Individual differences in the phase and amplitude of the human circadian temperature rhythm: with an emphasis on morningness-eveningness. J Sleep Res. 2000;9:117–127. doi: 10.1046/j.1365-2869.2000.00196.x 10849238
32. Kräuchi K, Wirz-Justice A. Circadian clues to sleep onset mechanisms. Neuropsychopharmacology. 2001;25:S92–S96. doi: 10.1016/S0893-133X(01)00315-3 11682282
33. Pell R.’Earable’ sensor monitors core body temp; 2017. Available from: https://www.eenewseurope.com/news/earable-sensor-monitors-core-body-temp.
Článek vyšel v časopise
PLOS One
2019 Číslo 12
- Pomohou nám s detekcí karcinomu plic i včely?
- Duševní onemocnění se u teenagerů přenáší v rámci školní třídy
- Od kostiček k lidské kůži. Jak si postavit 3D biotiskárnu?
- Řekněte mi, co jíte, a já vám řeknu, jaká je úroveň vaší kognice
- Umělá inteligence v mozkovém implantátu pomáhá muži po mrtvici s dvojjazyčnou konverzací
Nejčtenější v tomto čísle
- Methylsulfonylmethane increases osteogenesis and regulates the mineralization of the matrix by transglutaminase 2 in SHED cells
- Oregano powder reduces Streptococcus and increases SCFA concentration in a mixed bacterial culture assay
- The characteristic of patulous eustachian tube patients diagnosed by the JOS diagnostic criteria
- Parametric CAD modeling for open source scientific hardware: Comparing OpenSCAD and FreeCAD Python scripts
Zvyšte si kvalifikaci online z pohodlí domova
Všechny kurzy