Mathematical Modeling of Lymph Node Drainage Function by Neural Network

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.

The Human Meniscus Behaves as a Functionally Graded Fractional Porous Medium under Confined Compression Conditions

In this study, we observe that the poromechanical parameters in human meniscus vary spatially throughout the tissue. The response is anisotropic and the porosity is functionally graded. To draw these conclusions, we measured the anisotropic permeability and the “aggregate modulus” of the tissue, i.e., the stiffness of the material at equilibrium, after the interstitial fluid has ceased flowing. We estimated those parameters within the central portion of the meniscus in three directions (i.e., vertical, radial and circumferential) by fitting an enhanced model on stress relation confined compression tests. We noticed that a classical biphasic model was not sufficient to reproduce the observed experimental behaviour. We propose a poroelastic model based on the assumption that the fluid flow inside the human meniscus is described by a fractional porous medium equation analogous to Darcy’s law, which involves fractional operators. The fluid flux is then time-dependent for a constant applied pressure gradient (in contrast with the classical Darcy’s law, which describes a time independent fluid flux relation). We show that a fractional poroelastic model is well-suited to describe the flow within the meniscus and to identify the associated parameters (i.e., the order of the time derivative and the permeability). The results indicate that mean values of λβ,β in the central body are λβ=5.5443×10−10m4Ns1−β, β=0.0434, while, in the posterior and anterior regions, are λβ=2.851×10−10m4Ns1−β, β=0.0326 and λβ=1.2636×10−10m4Ns1−β, β=0.0232, respectively. Furthermore, numerical simulations show that the fluid flux diffusion is facilitated in the central part of the meniscus and hindered in the posterior and anterior regions.

Comparison between different infiltration models to describe the infiltration of permeable brick pavement system via lab-scale experiment

Permeable brick pavement system (PBPs) is one of a widely used low impact development (LID) measures to alleviate runoff volume and pollution caused by urbanization. The performance of PBPs on decreasing runoff volume is decided by its permeability, and it was general described by hydraulic conductivity based on Darcy's law. But there is large error when using hydraulic conductivity to describe the infiltration of PBPs, and which infiltration process is not following to the Darcy's law, so it is important to found a more accurate infiltration models to describe the infiltration of PBPs. The Horton, Philip, Green-Ampt, and Kostiakov infiltration models were selected to found an optimal model to investigate infiltration performance of PBPs via lab-scale experiment, and the maximum absolute error (MAE), Bias, and coefficient of determination (R2) were selected to evaluate the models' errors via fitting with experiment data. The results showed that the fitting accuracy of Kostiakov, Philip, and Green-Ampt models was significantly affected by the monitoring area and hydraulic gradients. Meanwhile, Horton model is fitting well (MAE = 0.25–0.32 cm/h, Bias = 0.07–0.11 cm/h, and R2 = 0.98–0.99) with the experiment data, and the parameters of Horton model often can be achieved by monitoring, such as the maximum infiltration rate and the stable infiltration rate. Therefore, the Horton model is an optimal model to describe the infiltration performance of PBPs, which can also be adopt to evaluate hydrological characterization of PBPs.

Use of filtration and electricity analogy in simulation of underflooding protection in urban construction

Introduction. The fight against underflooding remains an urgent problem. The application of the analogy between water filtration and electric current has the goal of protecting the environment, built-up areas and, in particular, highways in cities from underflooding. Writing Ohm’s law similarly to Darcy’s filtration law, we achieve a better match to their analogy. This, in turn, makes it possible to develop new technologies for protection against underflooding in urban construction, for example, electroosmotic dewatering and its modeling. Such technologies make it possible to drain clayey soils.Methods and materials. Darcy’s law, Ohm’s law and the law of electroosmotic filtration are considered together. A methodology for modelling construction dewatering is given, taking into account the combined effect of the two physical laws of water filtration and electroosmosis, optimally combining the high-altitude geometric arrangement of drainage bases and contact electrodes. The options for draining clay soil under the action of an electric field are presented. With the combined use of gravitational forces and electric direct current forces in the drained soil, the total filtration rate is the sum of the Darcy’s law component and another component of the water velocity – electroosmotic filtration. An additional feature of joint modelling in a porous medium of water filtration and electroosmosis is that the mass of the water-resistant part of the soil and its part related to the dielectric may not coincide. This complexity of the model is overcome by dividing it into modules, which can then be combined in compliance with the balance principle, stitching modules along the boundaries. To continue the scientific discussion, a short but informative overview of international publications on the topic under consideration is given.Discussion. The methodology for complex calculation and modelling of the joint processes of water filtration in soils, the flow of electric current and electroosmotic filtration can find useful application in the development of effective protection against underflooding in urban construction. a sequence of algorithmic modelling steps is recommended. initially, it is recommended to run rough spreadsheet simulations on personal computers and mobile phones. next, a different modelling approach should be applied. based on the initial rough models of the previous step, it is necessary to write the algorithms in the programming language. the compiled model of the investigated filtration and electroosmosis processes will significantly increase the reliability of the design of protection against underflooding.conclusion. a comparison is made of the joint use of construction dewatering means of different physical essence, with simultaneous processes of gravitational filtration of underground water and passing a direct electric current through the drained soil, which causes an additional effect of electroosmosis. it is proposed to apply in a new way the analogy of water filtration and electric current in order to achieve more effective results of engineering activities by modeling protection against underflooding of building areas, ensuring the safety of urban construction when the level of groundwater rises.

Groundwater Flow Algorithm: A Novel Hydro-geology based Optimization Algorithm

A novel meta-heuristic nature-inspired optimization algorithm known as Groundwater Flow Algorithm (GWFA) is proposed in this paper. GWFA is inspired from the movement of groundwater from recharge areas to discharge areas. It follows a position update procedure guided by Darcy's law which provides a mathematical framework of groundwater flow. The proposed optimization algorithm has been evaluated on 23 benchmark functions. The significance of the results is statistically validated using Wilcoxon rank-sum, Friedman and Kruskal Walis tests. To prove the robustness of the algorithm, it has been further applied on several standard engineering problems. From these exhaustive experiments, it has been observed that the proposed GWFA can outperform many state-of-the-art optimization algorithms.

Laws of Gas Diffusion in Coal Particles: A Study Based on Experiment and Numerical Simulation

In order to research on the law of methane released through the pore in coal particles, the methane desorption experiments were conducted, respectively, on four types of particle size of coal samples under three different initial adsorption pressures. The cumulative methane desorption quantity (CMDQ) with time increasing was obtained to show that the reciprocal of CMDQ was in linear relation with the reciprocal of the square root of time, and the correlation coefficients were all above 0.99, on basis of which an empirical formula of CMDQ was established. Then, according to Fick diffusion law and Darcy percolation law, the mathematical models of methane emission from the spherical coal particles were created, respectively, and the corresponding calculating software was programmed by the finite difference method to obtain the simulated CMDQ of each sample under different conditions. The methane emission rate functions (MERF) of the simulation and the experiment were also calculated, respectively. Comparative analysis between the numerically simulated outcomes and the assay results reveals that the simulation outcomes as per Darcy’s law match the experimental data better, while the simulated results by Fick’s law deviate greatly, which indicates that the methane flowing through coal particles is more in accordance with Darcy’s law.