REM sleep complicates period adding bifurcations from monophasic to polyphasic sleep behavior in a sleep-wake regulatory network model for human sleep

Preprint English OPEN
Kalmbach, K. ; Booth, V. ; Behn, C. G. Diniz (2017)
  • Subject: 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.
  • References (51)
    51 references, page 1 of 6

    [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.

  • Related Research Results (4)
  • Metrics
    No metrics available