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A Mathematical Model for the Energy Allocation Function of Sleep

Swang, Theodore W, II
http://rave.ohiolink.edu/etdc/view?acc_num=osu1483392711778623

Abstract Details

2017, Doctor of Philosophy, Ohio State University, Mathematics.
The function of sleep remains one of the greatest unsolved questions in biology. Schmidt has proposed the unifying Energy Allocation Function of sleep, which posits that the ultimate function of sleep is effective energy allocation in the service of state-dependent division of labor, or repartitioning of metabolic operations. We present a mathematical model based on Schmidt's Energy Allocation model. The fundamental quantity we model is called biological debt (BD). We define biological requirements (BR) as the summation of maintenance obligations generated by all metabolic operations, biological investment (BI) as the summation of completed functions servicing this requirements, and BD as the difference (BD = BR - BI). We model BD as a discontinuous non-autonomous ordinary differential equation. We analyze bifurcations as well as existence and nonexistence of limit cycles. In order to apply the theory of averaging, we construct a smooth approximation to the equation for BD, and show this approximation undergoes a saddle-node bifurcation of limit cycles. We compare and contrast our model with the Borbely's two-process model of sleep and with empirical data of human neurobehavioural performance. We define a division of labor parameter (DOL) and use BD to develop an algorithm to compute the energy saved by sleep-wake cycling compared to continuous wakefulness. We quantify the contributions to energy savings from DOL and from metabolic rate reduction during sleep. We numerically compute energy savings with this method, finding substantially greater savings than previous estimates. Some implications of the energy savings model include predictions that biological debt may govern sleep homeostasis; that short sleepers may increased metabolic rate in sleep compared to long sleepers, for whom energy savings may be primarily derived from metabolic rate reduction; and that dampening circadian amplitude during periods of sleep deprivation may be an adaptive feature. We present an alternative energy savings calculation based on averaging theory and compare it to our original energy savings computation. Finally, we develop a Markov Decision Process with a reward of net energy intake in order to find an optimal sleep-wake policy under a variety of conditions. We use this Markov Decision Process to optimize a policy under three different sets of conditions.
Janet Best (Advisor)
Ian Hamilton (Committee Member)
Chuan Xue (Committee Member)
126 p.
Mathematics
Sleep; mathematical biology; differential equations; Markov decision process

Recommended Citations

Citations

  • Swang, II, T. W. (2017). A Mathematical Model for the Energy Allocation Function of Sleep [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1483392711778623

    APA Style (7th edition)

  • Swang, II, Theodore. A Mathematical Model for the Energy Allocation Function of Sleep. 2017. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1483392711778623.

    MLA Style (8th edition)

  • Swang, II, Theodore. "A Mathematical Model for the Energy Allocation Function of Sleep." Doctoral dissertation, Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1483392711778623

    Chicago Manual of Style (17th edition)

osu1483392711778623
488
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This open access ETD is published by The Ohio State University and OhioLINK.