Mathematical Modeling of Lymph Node Drainage Function by Neural Network

Rufina Tretiakova, Alexey Setukha, Rostislav Savinkov, Dmitry Grebennikov and Gennady Bocharov
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Rufina Tretiakova: Marchuk Institute of Numerical Mathematics of the RAS, 119333 Moscow, Russia
Alexey Setukha: Marchuk Institute of Numerical Mathematics of the RAS, 119333 Moscow, Russia
Rostislav Savinkov: Marchuk Institute of Numerical Mathematics of the RAS, 119333 Moscow, Russia
Dmitry Grebennikov: Marchuk Institute of Numerical Mathematics of the RAS, 119333 Moscow, Russia
Gennady Bocharov: Marchuk Institute of Numerical Mathematics of the RAS, 119333 Moscow, Russia

Mathematics, 2021, vol. 9, issue 23, 1-18

Abstract: 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.

Keywords: lymph node; lymph filtration; porous medium; boundary integral equations; Darcy’s law; Starling’s equation; neural network model; linear regression (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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