McCullough M, Small M, Iu H H C, Stemler T
School of Mathematics and Statistics, The University of Western Australia, Crawley, Western Australia 6009, Australia
School of Mathematics and Statistics, The University of Western Australia, Crawley, Western Australia 6009, Australia.
Philos Trans A Math Phys Eng Sci. 2017 Jun 28;375(2096). doi: 10.1098/rsta.2016.0292.
In this study, we propose a new information theoretic measure to quantify the complexity of biological systems based on time-series data. We demonstrate the potential of our method using two distinct applications to human cardiac dynamics. Firstly, we show that the method clearly discriminates between segments of electrocardiogram records characterized by normal sinus rhythm, ventricular tachycardia and ventricular fibrillation. Secondly, we investigate the multiscale complexity of cardiac dynamics with respect to age in healthy individuals using interbeat interval time series and compare our findings with a previous study which established a link between age and fractal-like long-range correlations. The method we use is an extension of the symbolic mapping procedure originally proposed for permutation entropy. We build a Markov chain of the dynamics based on order patterns in the time series which we call an ordinal network, and from this model compute an intuitive entropic measure of transitional complexity. A discussion of the model parameter space in terms of traditional time delay embedding provides a theoretical basis for our multiscale approach. As an ancillary discussion, we address the practical issue of node aliasing and how this effects ordinal network models of continuous systems from discrete time sampled data, such as interbeat interval time series.This article is part of the themed issue 'Mathematical methods in medicine: neuroscience, cardiology and pathology'.
在本研究中，我们提出了一种基于时间序列数据来量化生物系统复杂性的新信息论度量方法。我们通过将该方法应用于人类心脏动力学的两个不同方面，展示了其潜力。首先，我们表明该方法能够清晰地区分以正常窦性心律、室性心动过速和心室颤动为特征的心电图记录片段。其次，我们使用心跳间期时间序列研究健康个体心脏动力学随年龄变化的多尺度复杂性，并将我们的研究结果与之前一项建立了年龄与分形样长程相关性之间联系的研究进行比较。我们使用的方法是最初为排列熵提出的符号映射过程的扩展。我们基于时间序列中的顺序模式构建一个动力学马尔可夫链，我们将其称为序数网络，并从该模型计算出一个直观的过渡复杂性熵度量。从传统时间延迟嵌入的角度对模型参数空间进行的讨论为我们的多尺度方法提供了理论基础。作为一个辅助讨论，我们探讨了节点混叠的实际问题以及它如何影响从离散时间采样数据（如心跳间期时间序列）构建的连续系统的序数网络模型。本文是主题为“医学中的数学方法：神经科学、心脏病学和病理学”的特刊的一部分。
