A mathematical modelling approach to the prediction of circadian phase under conditions of entrainment

夹带条件下昼夜节律相位预测的数学建模方法

• 批准号: 2141809
• 金额: --
• 依托单位: University of Surrey
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2018
• 资助国家: 英国
• 起止时间: 2018 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2141809
• 关键词: mathematical; modelling; approach; prediction; circadian

The circadian rhythm in humans is a cycle of physiological and behavioural changes in the body that takes place over the course of the day. Medical interventions may be more effective if they are delivered at particular phases of the circadian cycle but in order to time the interventions correctly we require a convenient method of estimating circadian phase. Dim-light melatonin onset (DLMO) is an accurate physiological marker of circadian phase but the procedure to measure DLMO is costly and impractical for use in a clinical setting. Mathematical models of the circadian rhythm provide a non-invasive method to predict circadian phase but the existing models have only been validated in the laboratory setting and it is not known if the models produce accurate predictions in real world conditions. The thesis will review key properties of the circadian rhythm such as endogenous periodicity and sensitivity to light, and explore how they can be modelled mathematically using one-dimensional or two-dimensional oscillators. The Jewett-Forger-Kronauer (JFK) model is a popular model of the human circadian system based on a two-dimensional limit cycle oscillator, and it was designed to try and reproduce the effects of bright light stimuli on the phase and amplitude of the circadian system in laboratory conditions. The JFK model was not specifically designed to predict the phase of entrainment in subjects entrained in real world conditions. The model will be reviewed in detail with a view to understanding how the oscillator entrains to a periodic light stimulus. The predictions of the model will be tested using light data from subjects wearing monitoring devices in real world conditions. The model's predictions of phase will be compared with measurements of phase in these subjects by DLMO. The JFK model has two principal parts: (i) Process C, which is a mathematical oscillator, and (ii) Process L, whereby a light signal is transduced to a forcing term that acts on the oscillator. These two parts of the model will be considered separately. In many circumstances the angular dynamics of the oscillator part of the JFK model can be well-approximated by a one-dimensional 'phase only' model. Phase only models can facilitate a better understanding of how oscillators entrain to periodic light stimuli under different conditions. A simple phase only clock model can be written down which has analytic solutions. This provides a good starting point to improve our understanding of entrainment. The thesis will investigate the dynamical behaviour of the simple clock model including the effects of perturbations. Process L in the JFK model was developed in the late 1990s but there has been no significant development of this part of the model since its inception. Meanwhile in that time there have been a number of important discoveries about the effect of light on the circadian system, for example we know that it is mediated by intrinsically-photosensitive retinal ganglion cells in the retina which have a different spectral responsivity compared to rods and cones. In particular it is clear that measuring the light intensity in photopic lux (as in the JFK model) is not an appropriate measure of the intensity of the signal received by the circadian system. The thesis will review the latest understanding of the processing and transmission of light information to the circadian system, and try and incorporate this knowledge in a new model of the transduction of a light signal.

人体的昼夜节律是一天中发生的身体生理和行为变化的周期。如果在昼夜节律周期的特定阶段进行医疗干预，可能会更有效，但为了正确地进行干预，我们需要一种方便的方法来估计昼夜节律阶段。昏暗光褪黑激素起始（DLMO）是昼夜节律相位的准确生理标记，但是测量DLMO的程序对于在临床环境中使用是昂贵且不切实际的。昼夜节律的数学模型提供了一种非侵入性方法来预测昼夜相位，但现有的模型仅在实验室环境中得到验证，并且不知道该模型是否在真实的世界条件下产生准确的预测。本论文将回顾昼夜节律的关键特性，如内源性周期性和对光的敏感性，并探讨如何使用一维或二维振荡器对它们进行数学建模。Jewett-Forger-Kronauer（JFK）模型是基于二维极限环振荡器的人类昼夜节律系统的流行模型，其被设计用于在实验室条件下尝试和再现强光刺激对昼夜节律系统的相位和振幅的影响。JFK模型不是专门设计来预测在真实的世界条件下夹带的受试者的夹带阶段。该模型将详细审查，以期了解振荡器如何夹带到一个周期性的光刺激。该模型的预测将使用来自真实的世界条件下佩戴监测设备的受试者的光数据进行测试。该模型的相位预测将与DLMO测量这些受试者的相位进行比较。JFK模型有两个主要部分：（i）过程C，这是一个数学振荡器，和（ii）过程L，其中光信号被转换为作用于振荡器的强迫项。模型的这两个部分将分别考虑。在许多情况下，JFK模型的振荡器部分的角动力学可以很好地近似于一维“仅相位”模型。纯相位模型有助于更好地理解振荡器在不同条件下如何夹带周期性光刺激。可以写出具有解析解的简单的仅相位时钟模型。这提供了一个很好的起点，以提高我们对夹带的理解。本论文将研究简单时钟模型的动力学行为，包括微扰的影响。肯尼迪模型中的过程L是在20世纪90年代后期开发的，但自其成立以来，模型的这一部分没有重大发展。与此同时，在这段时间里，有许多关于光对昼夜节律系统的影响的重要发现，例如，我们知道它是由视网膜中的内在光敏视网膜神经节细胞介导的，与视杆细胞和视锥细胞相比，视网膜神经节细胞具有不同的光谱响应。特别是，很明显，测量明视勒克斯（如在JFK模型中）的光强度不是昼夜节律系统接收的信号强度的适当测量。本论文将回顾光信息在昼夜节律系统中的处理和传输的最新认识，并尝试将这些知识结合到光信号转导的新模型中。