The network representation is becoming increasingly popular for the description of cardiovascular interactions based on the analysis of multiple simultaneously collected variables. However, the traditional methods to assess network links based on pairwise interaction measures cannot reveal high-order effects involving more than two nodes, and are not appropriate to infer the underlying network topology. To address these limitations, here we introduce a framework which combines the assessment of high-order interactions with statistical inference for the characterization of the functional links sustaining physiological networks. The framework develops information-theoretic measures quantifying how two nodes interact in a redundant or synergistic way with the rest of the network, and employs these measures for reconstructing the functional structure of the network. The measures are implemented for both static and dynamic networks mapped respectively by random variables and random processes using plug-in and model-based entropy estimators. The validation on theoretical and numerical simulated networks documents the ability of the framework to represent high-order interactions as networks and to detect statistical structures associated to cascade, common drive and common target effects. The application to cardiovascular networks mapped by the beat-to-beat variability of heart rate, respiration, arterial pressure, cardiac output and vascular resistance allowed noninvasive characterization of several mechanisms of cardiovascular control operating in resting state and during orthostatic stress. Our approach brings to new comprehensive assessment of physiological interactions and complements existing strategies for the classification of pathophysiological states.

翻译：网络表示法基于对多个同步采集变量进行分析，在描述心血管相互作用中日益普及。然而，传统基于成对交互测度评估网络连接的方法无法揭示涉及两个以上节点的高阶效应，也不适用于推断潜在网络拓扑结构。针对这些局限性，本文提出一个框架，将高阶交互评估与统计推断相结合，用于表征维持生理网络的功能连接。该框架开发了信息论测度，量化两个节点如何以冗余或协同方式与网络其余部分交互，并利用这些测度重构网络的功能结构。这些测度分别针对随机变量和随机过程映射的静态与动态网络，采用插件式与基于模型的熵估计器实现。在理论及数值模拟网络上的验证表明，该框架能够将高阶交互表示为网络，并检测与级联、共同驱动及共同目标效应相关的统计结构。将其应用于心跳间隔、呼吸、动脉压、心输出量及血管阻力的逐搏变异映射的心血管网络，实现了静息状态及直立应激下多种心血管调节机制的非侵入性表征。本研究方法带来了对生理交互的全新综合评估，并补充了现有病理生理状态分类策略。