Abstract
The human lymphatic system (HLS) is a complex network of lymphatic organs linked through the lymphatic vessels. We present a graph theory-based approach to model and analyze the human lymphatic network. Two different methods of building a graph are considered: the method using anatomical data directly and the method based on a system of rules derived from structural analysis of HLS. A simple anatomical data-based graph is converted to an oriented graph by quantifying the steady-state fluid balance in the lymphatic network with the use of the Poiseuille equation in vessels and the mass conservation at vessel junctions. A computational algorithm for the generation of the rule-based random graph is developed and implemented. Some fundamental characteristics of the two types of HLS graph models are analyzed using different metrics such as graph energy, clustering, robustness, etc.
Highlights
The human lymphatic system (HLS) is a complex network of lymphatic organs linked through the lymphatic vessels
The human lymphatic system is a complex system consisting of many components and performing several important functions related to the metabolism, fluid tissue homeostasis and the immune system [21,22]
We propose an approach based on the graph theory to modeling the human lymphatic system and analyzing the fundamental mathematical properties of the resulting graph models
Summary
The human lymphatic system (HLS) is a complex network of lymphatic organs linked through the lymphatic vessels. The graph theory provides a powerful tool to implement, visualize and analyze the characteristics of the network models It has been successfully applied for analysis of the topological properties and robustness of conduit networks in lymphatic nodes [6]. The second approach uses some general rules of lymphatic vessels network organization as discussed in [5,9]. To specify the links direction in the anatomically derived HLS graph model, the analysis of the homeostatic lymph flow through the network is performed using the Poiseuille law. The aim of the present study is to explore the fundamental mathematical properties of the lymphatic vessels network, for which the guiding organizational principles remain to be identified [2]. Conclusions and future work are discussed in the last section
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