Booth Victoria, Diniz Behn Cecilia G
Departments of Mathematics and Anesthesiology, University of Michigan, 530 Church Street, Ann Arbor, MI 48109-1043, United States.
Department of Applied Mathematics and Statistics, Colorado School of Mines, 1015 14th Street, Golden, CO 80401, United States.
Math Biosci. 2014 Apr;250:54-68. doi: 10.1016/j.mbs.2014.01.012. Epub 2014 Feb 11.
Mathematical modeling has played a significant role in building our understanding of sleep-wake and circadian behavior. Over the past 40 years, phenomenological models, including the two-process model and oscillator models, helped frame experimental results and guide progress in understanding the interaction of homeostatic and circadian influences on sleep and understanding the generation of rapid eye movement sleep cycling. Recent advances in the clarification of the neural anatomy and physiology involved in the regulation of sleep and circadian rhythms have motivated the development of more detailed and physiologically-based mathematical models that extend the approach introduced by the classical reciprocal-interaction model. Using mathematical formalisms developed in the field of computational neuroscience to model neuronal population activity, these models investigate the dynamics of proposed conceptual models of sleep-wake regulatory networks with a focus on generating appropriate sleep and wake state transition patterns as well as simulating disease states and experimental protocols. In this review, we discuss several recent physiologically-based mathematical models of sleep-wake regulatory networks. We identify common features among these models in their network structures, model dynamics and approaches for model validation. We describe how the model analysis technique of fast-slow decomposition, which exploits the naturally occurring multiple timescales of sleep-wake behavior, can be applied to understand model dynamics in these networks. Our purpose in identifying commonalities among these models is to propel understanding of both the mathematical models and their underlying conceptual models, and focus directions for future experimental and theoretical work.
数学建模在增进我们对睡眠-觉醒和昼夜节律行为的理解方面发挥了重要作用。在过去40年里，现象学模型，包括双过程模型和振荡器模型，有助于梳理实验结果，并指导在理解稳态和昼夜节律对睡眠的相互作用以及理解快速眼动睡眠周期的产生方面取得进展。最近在阐明参与睡眠和昼夜节律调节的神经解剖学和生理学方面的进展，推动了更详细的、基于生理学的数学模型的发展，这些模型扩展了经典相互作用模型所引入的方法。利用计算神经科学领域开发的数学形式来模拟神经元群体活动，这些模型研究了睡眠-觉醒调节网络的概念模型的动态，重点是生成适当的睡眠和觉醒状态转换模式以及模拟疾病状态和实验方案。在这篇综述中，我们讨论了几种最近的基于生理学的睡眠-觉醒调节网络数学模型。我们确定了这些模型在网络结构、模型动态和模型验证方法方面的共同特征。我们描述了快速-慢速分解的模型分析技术，该技术利用睡眠-觉醒行为自然存在的多个时间尺度，如何能够应用于理解这些网络中的模型动态。我们识别这些模型之间共性的目的是推动对数学模型及其潜在概念模型的理解，并为未来的实验和理论工作指明方向。
