Graph Theory for Modeling and Analysis of the Human Lymphatic System

Savinkov, Rostislav; Grebennikov, Dmitry; Puchkova, Darya; Chereshnev, V. А.; Sazonov, Igor; Bocharov, Gennady

doi:10.3390/math8122236

Cited by 14 publications

(10 citation statements)

References 26 publications

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“…The lymphatic system serves an important transport function in the human body and the body's immune system [32]. The mathematical models of the LS developed so far describe various aspects of the system topology [8][9][10] and the lymph flow through lymphatic vessels [8,37,45]. The filtering function of the LNs has been much less explored [46] with some studies addressing the flow through the macroscopic structures [30,31] and the microscopic components, such as the conduit system [29,47].…”

Section: Discussionmentioning

confidence: 99%

“…Central to modeling of the whole LS is the development of an appropriate graph model of the system. There are only three studies which analyze and describe the topology of the LS [6,[8][9][10]. They range from a simple network model suggested by Reddy [6] with 29 nodes and 28 edges to a comprehensive anatomical databased graph of the human LS with 996 vertices and 1117 edges [10].…”

Section: Introductionmentioning

confidence: 99%

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Mathematical Modeling of Lymph Node Drainage Function by Neural Network

et al. 2021

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The lymph node (LN) represents a key structural component of the lymphatic system network responsible for the fluid balance in tissues and the immune system functioning. Playing an important role in providing the immune defense of the host organism, LNs can also contribute to the progression of pathological processes, e.g., the spreading of cancer cells. To gain a deeper understanding of the transport function of LNs, experimental approaches are used. Mathematical modeling of the fluid transport through the LN represents a complementary tool for studying the LN functioning under broadly varying physiological conditions. We developed an artificial neural network (NN) model to describe the lymph node drainage function. The NN model predicts the flow characteristics through the LN, including the exchange with the blood vascular systems in relation to the boundary and lymphodynamic conditions, such as the afferent lymph flow, Darcy’s law constants and Starling’s equation parameters. The model is formulated as a feedforward NN with one hidden layer. The NN complements the computational physics-based model of a stationary fluid flow through the LN and the fluid transport across the blood vessel system of the LN. The physical model is specified as a system of boundary integral equations (IEs) equivalent to the original partial differential equations (PDEs; Darcy’s Law and Starling’s equation) formulations. The IE model has been used to generate the training dataset for identifying the NN model architecture and parameters. The computation of the output LN drainage function characteristics (the fluid flow parameters and the exchange with blood) with the trained NN model required about 1000-fold less central processing unit (CPU) time than computationally tracing the flow characteristics of interest with the physics-based IE model. The use of the presented computational models will allow for a more realistic description and prediction of the immune cell circulation, cytokine distribution and drug pharmacokinetics in humans under various health and disease states as well as assisting in the development of artificial LN-on-a-chip technologies.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Mathematical Modeling of Lymph Node Drainage Function by Neural Network

et al. 2021

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“…Following our previous study of the human LS [7], we characterize the topological properties of the murine LS graph model using some fundamental metrics. Let G = (n, m) be the graph with n nodes and m edges, respectively.…”

Section: Topological Properties Of the Ls Graphmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…The application of graph theory methods to describe the spatial organization of the human LS has been addressed in a number of recent studies (see for a review [7]). In [7], we developed a computational algorithm for representing the anatomy-based and rule-based graphs of the LS in humans. The graph models enabled the analysis of different metrics of complexity of human LS such as spectral radius, clustering coefficient, average path length, number of separators.…”

Section: Introductionmentioning

confidence: 99%

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Network Modelling of Murine Lymphatic System

Grebennikov¹,

Savinkov²,

Zelenova³

et al. 2023

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Animal models of diseases in particular, the mice, are considered to be the cornerstone for translational research in immunology. The aim of the present study is to model the geometry and analyze the network structure of murine lymphatic system (LS). The algorithm for building the graph model of the LS makes use of anatomical data. To identify the edge directions of the graph model, a mass balance approach to lymph dynamics based on Hagen-Poiseuille equation is applied. It is the first study in which a geometric model of the murine LS has been developed and characterized in terms of its structural organization and the lymph transfer function. Our study meets the demand for quantitative mechanistic approaches in the growing field of immunoengineering to utilize or exploit the lymphatic system for immunotherapy.

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