Gregory Gavin G, Cabeza Rafael
Department of Mathematical Sciences, The University of Texas at El Paso, El Paso, Texas 79968, USA.
J Neurophysiol. 2002 Nov;88(5):2589-97. doi: 10.1152/jn.00861.2001.
Rapid eye movement (REM) sleep is a recurring state throughout the sleeping period. Based on the examination of 45 sleep records of 3-mo-old male rats during the middle of the light phase, a stochastic model is proposed for the sequence X(1),Y(2), X(2),Y(2),. of REM sleep durations X and inter-REM sleep waiting times Y experienced by a rat during a sleeping period. In our model the probability distribution of any variable in the sequence, given the past, is allowed to depend on only the immediately previous variable. The conditional distributions f(y(i) | x(i)) and g(x(i+1) | y(i)) do not depend on the index i. It is shown that the marginal distributions tend to stationarity. Aggregations of the data on a discrete time scale suggest that the conditional distributions be formulated as two-component mixtures. These component distributions are modeled as Poisson and their means are called the means of short and long waiting time and the means of short and long REM sleep duration. Associated with each mean is a probability weight. Parametric forms are given to the means and probability weights. The model estimated by maximum likelihood shows a good fit to data of the 3-mo-old rats. The model fit to a smaller data set obtained from rats aged 15-22 mo shows a significant shortening of the means for both short and long REM sleep bout durations compared with the means of the 3-mo-old rats. Neuronal correlates for the behavior of the model are discussed in the context of the reciprocal interaction model of REM sleep regulation.
快速眼动（REM）睡眠是整个睡眠期间反复出现的一种状态。基于对3月龄雄性大鼠在光照期中期的45份睡眠记录的检查，针对大鼠在一个睡眠周期中经历的快速眼动睡眠时间X和快速眼动睡眠间隔等待时间Y的序列X(1),Y(2), X(2),Y(2),...提出了一个随机模型。在我们的模型中，给定过去的情况下，序列中任何变量的概率分布仅允许依赖于紧接在前的变量。条件分布f(y(i) | x(i))和g(x(i + 1) | y(i))不依赖于索引i。结果表明，边际分布趋于平稳。在离散时间尺度上对数据的汇总表明，条件分布应被表述为双组分混合分布。这些组分分布被建模为泊松分布，其均值被称为短等待时间和长等待时间的均值以及短快速眼动睡眠时间和长快速眼动睡眠时间的均值。与每个均值相关联的是一个概率权重。给出了均值和概率权重的参数形式。通过最大似然估计的模型对3月龄大鼠的数据拟合良好。对从15 - 22月龄大鼠获得的较小数据集进行模型拟合，结果显示与3月龄大鼠的均值相比，短快速眼动睡眠发作持续时间和长快速眼动睡眠发作持续时间的均值均显著缩短。在快速眼动睡眠调节的相互作用模型的背景下讨论了该模型行为的神经元相关性。
