scholarly journals Exact and Numerical Solutions of a Spatially-Distributed Mathematical Model for Fluid and Solute Transport in Peritoneal Dialysis

Symmetry ◽  
2016 ◽  
Vol 8 (6) ◽  
pp. 50 ◽  
Author(s):  
Roman Cherniha ◽  
Kateryna Gozak ◽  
Jacek Waniewski
2014 ◽  
Vol 986-987 ◽  
pp. 1418-1421
Author(s):  
Jun Shan Li

In this paper, we propose a meshless method for solving the mathematical model concerning the leakage problem when the pressure is tested in the gas pipeline. The method of radial basis function (RBF) can be used for solving partial differential equation by writing the solution in the form of linear combination of radius basis functions, that is, when integrating the definite conditions, one can find the combination coefficients and then the numerical solution. The leak problem is a kind of inverse problem that is focused by many engineers or mathematical researchers. The strength of the leak can find easily by the additional conditions and the numerical solutions.


Author(s):  
İREM ÇAY ◽  
SERDAL PAMUK

In this work, we obtain the numerical solutions of a 2D mathematical model of tumor angiogenesis originally presented in [Pamuk S, ÇAY İ, Sazci A, A 2D mathematical model for tumor angiogenesis: The roles of certain cells in the extra cellular matrix, Math Biosci 306:32–48, 2018] to numerically prove that the certain cells, the endothelials (EC), pericytes (PC) and macrophages (MC) follow the trails of the diffusions of some chemicals in the extracellular matrix (ECM) which is, in fact, inhomogeneous. This leads to branching, the sprouting of a new neovessel from an existing vessel. Therefore, anastomosis occurs between these sprouts. In our figures we do see these branching and anastomosis, which show the fact that the cells diffuse according to the structure of the ECM. As a result, one sees that our results are in good agreement with the biological facts about the movements of certain cells in the Matrix.


2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Pratchaya Chanprasopchai ◽  
I. Ming Tang ◽  
Puntani Pongsumpun

The dengue disease is caused by dengue virus, and there is no specific treatment. The medical care by experienced physicians and nurses will save life and will lower the mortality rate. A dengue vaccine to control the disease is available in Thailand since late 2016. A mathematical model would be an important way to analyze the effects of the vaccination on the transmission of the disease. We have formulated an SIR (susceptible-infected-recovered) model of the transmission of the disease which includes the effect of vaccination and used standard dynamical modelling methods to analyze the effects. The equilibrium states and their stabilities are investigated. The trajectories of the numerical solutions plotted into the 2D planes and 3D spaces are presented. The main contribution is determining the role of dengue vaccination in the model. From the analysis, we find that there is a significant reduction in the total hospitalization time needed to treat the illness.


Author(s):  
Najma Ahmed ◽  
Dumitru Vieru ◽  
Fiazud Din Zaman

A generalized mathematical model of the breast and ovarian cancer is developed by considering the fractional differential equations with Caputo time-fractional derivatives. The use of the fractional model shows that the time-evolution of the proliferating cell mass, the quiescent cell mass, and the proliferative function are significantly influenced by their history. Even if the classical model, based on the derivative of integer order has been studied in many papers, its analytical solutions are presented in order to make the comparison between the classical model and the fractional model. Using the finite difference method, numerical schemes to the Caputo derivative operator and Riemann-Liouville fractional integral operator are obtained. Numerical solutions to the fractional differential equations of the generalized mathematical model are determined for the chemotherapy scheme based on the function of "on-off" type. Numerical results, obtained with the Mathcad software, are discussed and presented in graphical illustrations. The presence of the fractional order of the time-derivative as a parameter of solutions gives important information regarding the proliferative function, therefore, could give the possible rules for more efficient chemotherapy.


2021 ◽  
Author(s):  
Jan De Rydt ◽  
Ronja Reese ◽  
Fernando Paolo ◽  
G Hilmar Gudmundsson

<p>Pine Island Glacier in West Antarctica is among the fastest changing glaciers worldwide. Much of its fast-flowing central trunk is thinning and accelerating, a process thought to have been triggered by ocean-induced changes in ice-shelf buttressing. The measured acceleration in response to perturbations in ice thickness is a non-trivial manifestation of several poorly-understood physical processes, including the transmission of stresses between the ice and underlying bed. To enable robust projections of future ice flow, it is imperative that numerical models include an accurate representation of these processes. Here we combine the latest data with analytical and numerical solutions of SSA ice flow to show that the recent increase in flow speed of Pine Island Glacier is only compatible with observed patterns of thinning if a spatially distributed, predominantly plastic bed underlies large parts of the central glacier and its upstream tributaries.</p>


Author(s):  
Georgy Kolesnik

High competition in the markets of goods and services makes it urgent to improve the efficiencyof the use of production assets by the enterprises. One of the possible ways to solve the problem is joint use of the assets by different subjects. The use of this mechanism in the various branches grows rapidly in the last decade due to the opportunities for aggregation of supply and demand and automated contracting provided by the modern digital technologies. The basis for production asset management systems based on sharing is a mathematical model that allows determining the optimal modes of asset use in terms of their utilization, reducing the total cost of ownership and obtaining additional operating profit. This article considers a mathematical model of a multi-product spatially distributed production system that reflects the features of the activities of machine-building enterprises and assumes the possibility of joint use of their fixed assets. Economic and social criteria for the efficiency of fixed assets sharing are formulated in terms of maximizing the profit of enterprises, minimizing logistics and downtime costs. The optimal modes of joint use of the fixed assets concerning these criteria are investigated. It is shown that the joint use of fixed assets under the certain conditions can significantly improve the efficiency of the operating activities of enterprises.


2001 ◽  
Vol 21 (2) ◽  
pp. 225-232 ◽  
Author(s):  
Simon J. Davies

Objective Peritoneal membrane function influences dialysis prescription and clinical outcome and may change with time on treatment. Increasingly sophisticated tools, ranging from the peritoneal equilibration test (PET) to the standard permeability analysis (SPA) and personal dialysis capacity (PDC) test, are available to the clinician and clinical researcher. These tests allow assessment of a number of aspects of membrane function, including solute transport rates, ultrafiltration capacity, effective reabsorption, transcellular water transport, and permeability to macromolecules. In considering which tests are of greatest value in monitoring long-term membrane function, two criteria were set: those that result in clinically relevant interpatient differences in achieved ultrafiltration or solute clearances, and those that change with time in treatment. Study Selection Clinical validation studies of the PET, SPA, and PDC tests. Studies reporting membrane function using these methods in either long-term (5 years) peritoneal dialysis patients or longitudinal observations (> 2 years). Data Extraction Directly from published data. Additional, previously unpublished analysis of data from the Stoke PD Study. Results Solute transport is the most important parameter. In addition to predicting patient and technique survival at baseline, there is strong evidence that it can increase with time on treatment. Whereas patients with initially high solute transport drop out early from treatment, those with low transport remain longer on treatment, although, over 5 years, a proportion develop increasing transport rates. Ultrafiltration capacity, while being a composite measure of membrane function, is a useful guide for the clinician. Using the PET (2.27% glucose), a net ultrafiltration capacity of < 200 mL is associated with a 50% chance of achieving less than 1 L daily ultrafiltration at the expense of 1.8 hypertonic (3.86%) exchanges in anuric patients. Using a SPA (3.86% glucose), a net ultrafiltration capacity of < 400 mL indicates ultrafiltration failure. While there is circumstantial evidence that, with time on peritoneal dialysis, loss of transcellular water transport might contribute to ultrafiltration failure, none of the current tests is able to demonstrate this unequivocally. Of the other membrane parameters, evidence that interpatient differences are clinically relevant (permeability to macro-molecules), or that they change significantly with time on treatment (effective reabsorption), is lacking. Conclusion A strong case can be made for the regular assessment by clinicians of solute transport and ultrafiltration capacity, a task made simple to achieve using any of the three tools available.


2005 ◽  
Vol 25 (1) ◽  
pp. 16-24 ◽  
Author(s):  
Siska Mortier ◽  
Norbert H. Lameire ◽  
An S. De Vriese

The development of an adequate animal model for peritoneal research remains an object of concern. In vivo peritoneal dialysis (PD) research is hampered by the large variety of available models that make interpretation of results and comparison of studies very difficult. Species and strain of experimental animals, method of peritoneal access, study duration, measures of solute transport and ultrafiltration, and sampling for histology differ substantially among the various research groups. A collective effort to discuss the shortcomings and merits of the different experimental models may lead to a consensus on a standardized animal model of PD.


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