Liu Runsang, Yang Hui
Complex System Monitoring, Modeling, and Control Laboratory, The Pennsylvania State University, University Park, Pennsylvania 16802, USA.
Chaos. 2024 Dec 1;34(12). doi: 10.1063/5.0243391.
Network represents adjacent relationships, connections, and interactions among constituent elements in complex systems but often loses critical information about spatial configurations. However, structure-function relationships in biological systems, e.g., the human heart, are highly dependent on both connectivity relationships and geometric details. Therefore, this paper presents a new self-organizing approach to derive the geometric structure from a network representation of the heart. We propose to simulate the network as a physical system, where nodes are treated as charged particles and edges as springs and then let these nodes self-organize to reconstruct geometric details. Despite random initiations, this network evolves into a steady topology when its energy is minimized. This study addresses the open question, i.e., "whether a network representation can effectively resemble spatial geometry of a biological system," thereby paving a stepstone to leverage network theory to investigate disease-altered biological functions.
网络表示复杂系统中组成元素之间的相邻关系、连接和相互作用，但往往会丢失有关空间配置的关键信息。然而，生物系统中的结构-功能关系，例如人类心脏，高度依赖于连接关系和几何细节。因此，本文提出了一种新的自组织方法，从心脏的网络表示中推导几何结构。我们建议将网络模拟为一个物理系统，其中节点被视为带电粒子，边被视为弹簧，然后让这些节点自组织以重建几何细节。尽管初始状态是随机的，但当网络能量最小时，它会演变成一个稳定的拓扑结构。本研究解决了一个开放性问题，即“网络表示是否能有效地模拟生物系统的空间几何形状”，从而为利用网络理论研究疾病改变的生物功能奠定了一块基石。
