A quantitative model of sleep-wake dynamics based on the physiology of the brainstem ascending arousal system
Catherine
Lloyd
Bioengineering Institute, University of Auckland
Model Status
This CellML model runs in both PCEnv and COR to replicate figure 2 in the paper. The units have been checked and they are consistent.
Model Structure
Abstract: A quantitative, physiology-based model of the ascending arousal system is developed, using continuum neuronal population modeling, which involves averaging properties such as firing rates across neurons in each population. The model includes the ventrolateral preoptic area (VLPO), where circadian and homeostatic drives enter the system, the monoaminergic and cholinergic nuclei of the ascending arousal system, and their interconnections. The human sleep-wake cycle is governed by the activities of these nuclei, which modulate the behavioral state of the brain via diffuse neuromodulatory projections. The model parameters are not free since they correspond to physiological observables. Approximate parameter bounds are obtained by requiring consistency with physiological and behavioral measures, and the model replicates the human sleep-wake cycle, with physiologically reasonable voltages and firing rates. Mutual inhibition between the wake-promoting monoaminergic group and sleep-promoting VLPO causes 'flip-flop' behavior, with most time spent in 2 stable steady states corresponding to wake and sleep, with transitions between them on a timescale of a few minutes. The model predicts hysteresis in the sleep-wake cycle, with a region of bistability of the wake and sleep states. Reducing the monoaminergic-VLPO mutual inhibition results in a smaller hysteresis loop. This makes the model more prone to wake-sleep transitions in both directions and makes the states less distinguishable, as in narcolepsy. The model behavior is robust across the constrained parameter ranges, but with sufficient flexibility to describe a wide range of observed phenomena.
The original paper reference is cited below:
A quantitative model of sleep-wake dynamics based on the physiology of the brainstem ascending arousal system, A.J.K. Phillips and P.A. Robinson, 2007,
Journal of Biological Rhythms, 22, 167-179. PubMed ID: 17440218
model diagram
Schematic diagram of the Phillips and Robinson 2007 sleep model. MA is the monoaminergic group, ACh is acetylcholine, VLPO represents the ventrolateral preoptic area, and D is the drive input which consists of circadian and homeostatic components.
$\mathrm{Qv}=\frac{\mathrm{Qmax}}{1+e^{\frac{-(\mathrm{Vv}-\mathrm{theta})}{\mathrm{sigma}}}}$
$\frac{d \mathrm{Vv}}{d \mathrm{time}}=\frac{\mathrm{v\_vm}\mathrm{Qm}+D-\mathrm{Vv}}{\frac{\mathrm{tau\_v}}{3600}}$
$\mathrm{Qa}=\frac{\mathrm{Qmax}}{1+e^{\frac{-(\mathrm{Va}-\mathrm{theta})}{\mathrm{sigma}}}}$
$\mathrm{Va}=\mathrm{Vao}$
$\mathrm{Qm}=\frac{\mathrm{Qmax}}{1+e^{\frac{-(\mathrm{Vm}-\mathrm{theta})}{\mathrm{sigma}}}}$
$\frac{d \mathrm{Vm}}{d \mathrm{time}}=\frac{\mathrm{v\_maQao}+\mathrm{v\_mv}\mathrm{Qv}-\mathrm{Vm}}{\frac{\mathrm{tau\_m}}{3600}}$
$\frac{d H}{d \mathrm{time}}=\frac{\mathrm{mu}\mathrm{Qm}-H}{\mathrm{chi}}$
$D=\mathrm{v\_vc}C+\mathrm{v\_vh}H$
$C=\mathrm{c0}+\cos (\mathrm{omega}\mathrm{time})$
$\mathrm{omega}=\frac{2\pi}{24}$
Lloyd
Catherine
c.lloyd@auckland.ac.nz
Auckland Bioengineering Institute
2009-11-09
The Phillips and Robinson 2007 quantitative model of sleep-wake dynamics
This is the CellML description of the Phillips and Robinson 2007 quantitative model of sleep-wake dynamics
Catherine Lloyd
keyword
sleep
neurobiology
diurnal cycle
circadian rhythms
17440218
Phillips
A
J
K
Robinson
P
A
A quantitative model of sleep-wake dynamics based on the physiology of the brainstem ascending arousal system
2007-04
Journal of Biological Rhythms
22
167
179