Remember Me
Or use your Academic/Social account:


Or use your Academic/Social account:


You have just completed your registration at OpenAire.

Before you can login to the site, you will need to activate your account. An e-mail will be sent to you with the proper instructions.


Please note that this site is currently undergoing Beta testing.
Any new content you create is not guaranteed to be present to the final version of the site upon release.

Thank you for your patience,
OpenAire Dev Team.

Close This Message


Verify Password:
Verify E-mail:
*All Fields Are Required.
Please Verify You Are Human:
fbtwitterlinkedinvimeoflicker grey 14rssslideshare1
Kalmbach, K.; Booth, V.; Behn, C. G. Diniz (2017)
Languages: English
Types: Preprint
Subjects: Quantitative Biology - Neurons and Cognition
The structure of human sleep changes across development as it consolidates from the polyphasic sleep of infants to the single nighttime sleep period typical in adults. Across this same developmental period, time scales of the homeostatic sleep drive, the physiological drive to sleep that increases with time spent awake, also change and presumably govern the transition from polyphasic to monophasic sleep behavior. Using a physiologically-based, sleep-wake regulatory network model for human sleep, we investigated the dynamics of wake, rapid eye movement (REM) sleep, and non-REM (NREM) sleep during this transition by varying the homeostatic sleep drive time constants. Previously, we introduced an algorithm for constructing a one-dimensional circle map that represents the dynamics of the full sleep-wake network model. By tracking bifurcations in the piecewise continuous circle map as the homeostatic sleep drive time constants are varied, we establish evidence for a border collision bifurcation that results in period-adding-like behavior in the number of sleep cycles per day. Interestingly, this bifurcation is preceded by bifurcations in the number of REM bouts per sleep cycle that exhibit truncated period-adding-like behavior. The interaction of these bifurcations in numbers of sleep episodes and numbers of REM bouts per sleep episode generate non-monotonic variation in sleep cycle patterns as well as quasi-periodic patterns during the transition from polyphasic to monophasic sleep behavior. This analysis may have implications for understanding changes in sleep in early childhood when preschoolers transition from napping to non-napping behavior, and the wide interindividual variation observed during this transition.
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • [1] E. E. Abrahamson, R. K. Leak, and R. Y. Moore, The suprachiasmatic nucleus projects to posterior hypothalamic arousal systems, Neuroreport, 12 (2001), pp. 435{440.
    • [2] C. Acebo, A. Sadeh, R. Seifer, O. Tzischinsky, A. Hafer, and M. Carskadon, Sleep/wake patterns derived from activity monitoring and maternal report for healthy 1- to 5-year old children, Sleep, 28 (2005), pp. 1568{1577.
    • [3] V. Avrutin and I. Sushko, A gallery of bifurcation scenarios in piecewise smooth 1d maps, in Global Analysis of Dynamic Models in Economics and Finance, G. e. a. Bischi, ed., Springer-Verlag, 2013.
    • [4] R. Basheer, R. Strecker, M. Thakkar, and R. McCarley, Adenosine and sleep-wake regulation, Prog Neurobiol, 73 (2004), pp. 379{396.
    • [5] V. Booth and C. G. Diniz Behn, Physiologically-based modeling of sleep=wake regulatory networks, Math Biosci, 250 (2014), pp. 54{68.
    • [6] V. Booth, I. Xique, and C. G. Diniz Behn, One-dimensional map for the circadian modulation of sleep in a sleep-wake regulatory network model for human sleep, SIAM J App Dyn Systems, (In Press).
    • [7] M. Carskadon and W. Dement, Normal human sleep: an overview, in Principles and Practice of Sleep Medicine, M. Kryger, T. Roth, and W. Dement, eds., Elsevier Saunders, 2011.
    • [8] C. A. Czeisler and O. M. Buxton, The human circadian timing system and sleep=wake regulation, in Principles and Practice of Sleep Medicine, M. Kryger, T. Roth, and W. Dement, eds., Elsevier Saunders, 2011.
    • [9] P. Dayan and L. Abbott, Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems, The MIT Press, 2001.
    • [10] T. Deboer, V. M., L. Detarii, and J. Meijer, Sleep states alter activity of suprachiasmatic nucleus neurons, Nat Neurosci, 6 (2003), pp. 1086{1090.
    • [11] G. Deco, V. K. Jirsa, P. A. Robinson, M. Breakspear, and K. Friston, The dynamic brain: from spiking neurons to neural masses and cortical elds, PLoS Comput Biol, 4 (2008), p. e1000092.
    • [12] M. di Bernardo, C. Budd, A. Champneys, and P. Kowalczyk, Piecewise-smooth Dynamical Systems: Theory and Applications, Springer, 2008.
    • [13] C. Diniz Behn, A. Ananthasubramaniam, and V. Booth, Contrasting existence and robustness of REM/NREM cycling in physiologically based models of REM sleep regulatory networks, SIAM J on App Dyn Systems, 12 (2013), pp. 279{314.
    • [14] C. Diniz Behn and V. Booth, A fast-slow analysis of the dynamics of REM sleep, SIAM J on App Dyn Systems, 11 (2012), pp. 212{242.
    • [15] D. Edgar, W. Dement, and C. Fuller, E ect of SCN lesions on sleep in squirrel monkeys: evidence for opponent processes in sleep-wake regulation, J Neurosci, 13 (1993), pp. 1065{1079.
    • [16] G. B. Ermentrout, Neural networks as spatio-temporal pattern-forming systems, Rep. Prog. Phys., 61 (1998), pp. 353{430.
    • [17] G. B. Ermentrout, Simulating, analyzing, and animating dynamical systems: a guide to XPPAUT for researchers and students, Society for Industrial and Applied Mathematics, Philadelphia, 2002.
    • [18] I. Feinberg and T. Floyd, Systematic trends across the night in human sleep cycles, Psychophysiology, 16 (1979), pp. 283{291.
    • [19] M. Fleshner, V. Booth, D. Forger, and C. Diniz Behn, Circadian regulation of sleep-wake behavior in nocturnal rats requires multiple signals from suprachiasmatic nucleus, Phil. Trans. R. Soc. A, 369 (2011), pp. 3855{3883.
    • [20] D. B. Forger, M. E. Jewett, and R. E. Kronauer, A simpler model of the human circadian pacemaker, J Biol Rhythms, 14 (1999), pp. 532{537.
    • [21] H. Gaudreau, J. Carrier, and J. Montplaisir, Age-related modi cations of NREM sleep EEG: from childhood to middle age, J Sleep Res, 10 (2001), pp. 165{172.
    • [22] R. D. Gleit, C. Diniz Behn, and V. Booth, Modeling interindividual di erences in spontaneous internal desynchrony patterns, J Biol Rhythms, 28 (2013), pp. 339{355.
    • [23] A. Granados, L. Alseda, and M. Krupa, The period adding and incrementing bifurcations: from rotation theory to applications, SIAM Review, 59 (2017), pp. 225{292.
    • [24] Z. Huang, Y. Urade, and O. Hayaishi, Prostaglandins and adenosine in the regulation of sleep and wakefulness, Curr Opin Pharmacol, 7 (2007), pp. 33{38.
    • [25] I. Iglowstein, O. Jenni, L. Molinari, and R. Largo, Sleep duration from infancy to adolescence: reference values and generational trends, Pediatrics, 111 (2003), pp. 302{307.
    • [26] O. Jenni, P. Achermann, and M. Carskadon, Homeostatic sleep regulation in adolescents, SLEEP, 28 (2005), pp. 1446{1454.
    • [27] O. Jenni and M. LeBourgeois, Understanding sleepwake behavior and sleep disorders in children: the value of a model, Curr Opin Psychiatry, 19 (2006), pp. 282{287.
    • [28] D. Kaplan and L. Glass, Understanding Nonlinear Dynamics, Springer Science Business Media, 2012.
    • [29] R. E. Kronauer, D. B. Forger, and M. E. Jewett, Errata: Quantifying human circadian pacemaker response to brief, extended, and repeated light stimuli over the photopic range, J Biol Rhythms, 15 (2000), pp. 184{186.
    • [30] R. Kumar, A. Bose, and B. Mallick, A mathematical model towards understanding the mechanism of neuronal regulation of wake-NREMS-REMS states, PLoS One, 7 (2012), p. e2059.
    • [31] R. W. McCarley and J. A. Hobson, Neuronal excitability modulation over the sleep cycle: a structural and mathematical model, Science, 189 (1975), pp. 58{60.
    • [32] R. W. McCarley and S. G. Massaquoi, A limit-cycle mathematical-model of the REM-sleep oscillator system, Am J Physiol, 251 (1986), pp. R1011{R1029.
    • [33] R. E. Mistlberger, Circadian regulation of sleep in mammals: role of the suprachiasmatic nucleus, Brain Res Rev, 49 (2005), pp. 429{454.
    • [34] M. Nakao, H. Sakai, and M. Yamamoto, An interpretation of the internal desynchronizations based on dynamics of the two-process model, Meth Inform Med, 36 (1997), pp. 282{285.
    • [35] M. Ohayon, M. Carskadon, C. Guilleminault, and M. Vitiello, Meta-analysis of quantiative sleep parameters from childhood to old age in healthy individuals: developing normative sleep values across the human lifespan, SLEEP, 27 (2004), pp. 1255{1273.
    • [36] A. J. K. Phillips, B. D. Fulcher, P. A. Robinson, and E. B. Klerman, Mammalian rest/activity patterns explained by physiologically based modeling, PLoS Comput Biol, 9 (2013), https://doi.org/ 10.1371/journal.pcbi.1003213.
    • [37] A. J. K. Phillips and P. A. Robinson, A quantitative model of sleep-wake dynamics based on the physiology of the brainstem ascending arousal system, J Biol Rhythms, 22 (2007), pp. 167{179.
    • [38] M. Rempe, J. Best, and D. Terman, A mathematical model of the sleepwake cycle, J Math Biol, 60 (2010), pp. 615{644.
    • [39] T. Rusterholz, R. Durr, and P. Achermann, Inter-individual di erences in the dynamics of sleep homeostasis, SLEEP, 33 (2010), pp. 491{498.
    • [40] C. B. Saper, T. C. Chou, and T. E. Scammell, The sleep switch: hypothalamic control of sleep and wakefulness, Trends Neurosci, 24 (2001), pp. 726{731.
    • [41] C. B. Saper, T. E. Scammell, and J. Lu, Hypothalamic regulation of sleep and circadian rhythms, Nature, 437 (2005), pp. 1257{1263.
    • [42] K. Serkh and D. B. Forger, Optimal schedules of light exposure for rapidly correcting circadian misalignment, PLoS Comput Biol, 10 (2014), p. e1003523.
    • [43] J. Siegel, REM sleep, in Principles and Practice of Sleep Medicine, M. Kryger, T. Roth, and W. Dement, eds., Elsevier Saunders, 2011.
    • [44] A. Skeldon, D.-J. Dijk, and G. Derks, Mathematical models for sleep-wake dynamics: Comparison of the two-process model and a mutual inhibition neuronal model, PLoS One, 9 (2014), p. e103877.
    • [45] S. Strogatz, R. E. Kronauer, and C. A. Czeisler, Circadian pacemaker interferes with sleep onset and speci c times each day: role in insomnia, Am J Physiol - Reg, Int, and Comp Physiol, 253 (1987), pp. R172{R178.
    • [46] Y. Tamakawa, A. Karashima, Y. Koyama, N. Katayama, and M. Nakao, A quartet neural system model orchestrating sleep and wakefulness mechanisms, Journal of Neurophysiology, epub (2006), pp. 2055{2069.
    • [47] I. Tobler, Is sleep fundamentally di erent between mammalian species?, Behavioral Brain Research, 69 (1995), pp. 35{41.
    • [48] I. Tobler, P. Franken, L. Trachsel, and A. Borbely, Models of sleep regulation in mammals, Journal of Sleep Research, 1 (1992), pp. 125{127.
    • [49] T. A. Wehr, In short photoperiods, human sleep is biphasic, J Sleep Res, 1 (1992), pp. 103{107.
    • [50] H. R. Wilson and J. D. Cowan, Excitatory and inhibitory interactions in localized populations of model neurons, Biophys J, 12 (1972), pp. 1{24.
    • [51] Y. Zhang, A. Bose, and F. Nadim, The in uence of the a-current on the dynamics of an oscillatorfollower inhibitory network, SIAM J Applied Dynamical Systems, 8 (2009), pp. 1564{1590.
  • No similar publications.

Share - Bookmark

Funded by projects

  • NSF | Collaborative research: Mul...
  • NSF | Collaborative Research: Mul...

Cite this article

Collected from