MATHEMATICAL MODELING OF IMMUNE-INFLAMMATORY REACTION IN ACUTE PNEUMONIA

1995 ◽  
Vol 03 (02) ◽  
pp. 429-439 ◽  
Author(s):  
S. G. RUDNEV ◽  
A. A. ROMANYUKHA
Keyword(s):  
Mathematical Modeling ◽  
Experimental Data ◽  
Mathematical Model ◽  
Immune Response ◽  
Sensitivity Analysis ◽  
Inflammatory Reaction ◽  
Humoral Immune ◽  
Disease Characteristics ◽  
Acute Pneumonia ◽  
Lung Resistance

Using ordinary differential equations, we propose a mathematical model describing an “averaged” dynamics of variables involved in which some parameters are shown to be important characteristics of lung resistance. The model consists of modified D.A. Lauffenburger’s mathematical model for inflammatory reaction in lungs, and the model of humoral immune response (G. I. Marchuk). Coefficients are identified against clinical and experimental data. We attempt to elucidate some disease characteristics in terms of sensitivity analysis of model solutions with respect to parameters variations.

scholarly journals Mathematical modelling of trastuzumab-induced immune response in an in vivo murine model of HER2+ breast cancer

2018 ◽  
Vol 36 (3) ◽  
pp. 381-410 ◽  
Author(s):  
Angela M Jarrett ◽  
Meghan J Bloom ◽  
Wesley Godfrey ◽  
Anum K Syed ◽  
David A Ekrut ◽  
...  
Keyword(s):  
Breast Cancer ◽  
Experimental Data ◽  
Mathematical Model ◽  
Immune Response ◽  
Immune System ◽  
Murine Model ◽  
Tumour Growth ◽  
Experimental Approach ◽  
Her2 Breast Cancer ◽  
The Mathematical Model

Abstract The goal of this study is to develop an integrated, mathematical–experimental approach for understanding the interactions between the immune system and the effects of trastuzumab on breast cancer that overexpresses the human epidermal growth factor receptor 2 (HER2+). A system of coupled, ordinary differential equations was constructed to describe the temporal changes in tumour growth, along with intratumoural changes in the immune response, vascularity, necrosis and hypoxia. The mathematical model is calibrated with serially acquired experimental data of tumour volume, vascularity, necrosis and hypoxia obtained from either imaging or histology from a murine model of HER2+ breast cancer. Sensitivity analysis shows that model components are sensitive for 12 of 13 parameters, but accounting for uncertainty in the parameter values, model simulations still agree with the experimental data. Given theinitial conditions, the mathematical model predicts an increase in the immune infiltrates over time in the treated animals. Immunofluorescent staining results are presented that validate this prediction by showing an increased co-staining of CD11c and F4/80 (proteins expressed by dendritic cells and/or macrophages) in the total tissue for the treated tumours compared to the controls ($p < 0.03$). We posit that the proposed mathematical–experimental approach can be used to elucidate driving interactions between the trastuzumab-induced responses in the tumour and the immune system that drive the stabilization of vasculature while simultaneously decreasing tumour growth—conclusions revealed by the mathematical model that were not deducible from the experimental data alone.

Mathematical Modeling of Capillary Pumping Within Micron Sized Channels

2013 ◽  
Author(s):  
Yuelei Yang ◽  
Dan Zhang
Keyword(s):  
Mathematical Modeling ◽  
Experimental Data ◽  
Mathematical Model ◽  
Capillary Pressure ◽  
Heat Engine ◽  
Velocity Profiles ◽  
Vof Method ◽  
Numerical Results ◽  
Micro Heat Engine ◽  
Volume Of Fluids

This paper introduces a mathematical model which can be used to simulate the capillary pumping process of a micro heat engine. The micro heat engine has micron sized channels where the capillary pumping occurs. The classic Volume of Fluids (VOF) method is applied to obtain the velocity profiles of the fluids and to track the motions of the liquid-gas interfaces. The numerical results based this model have been compared with the experimental data and the initial retard of the pumping has been found and this phenomenon can be explained by the initial capillary pressure build-ups across the liquid-gas interfaces.

Mathematical Modeling and Experimental Study on Electrochemical Deburring of Miniature Holes

2013 ◽  
Vol 721 ◽  
pp. 382-386 ◽  
Author(s):  
Ze Fei Wei ◽  
Xing Hua Zheng ◽  
Zi Yuan Yu
Keyword(s):  
Mathematical Modeling ◽  
Experimental Data ◽  
Mathematical Model ◽  
Finite Element Analysis ◽  
Experimental Study ◽  
Finite Element ◽  
Electrochemical Machining ◽  
Current Density Distribution ◽  
Element Analysis ◽  
The Finite Element Analysis

The paper mainly focused on burr removal of the miniature hole drilled on aluminum plate by electrochemical machining. A mathematical model for the electrochemical deburring of miniature holes (M-ECD) was established based on the finite element analysis to the current density distribution. Both theoretical analysis and experimental study were held on the effects of many factors to the deburring results. The results proved that predictions based on our mathematical model were agreed with the experimental data comparatively.

scholarly journals Comparative Analysis of Methods for Mathematical Modeling of Specific Electrical Conductivity of Plasma in the Channel of an Electric Discharge in Water

2021 ◽  
Vol 57 (4) ◽  
pp. 24-34
Author(s):  
V.M. Kosenkov ◽  
Keyword(s):  
Mathematical Modeling ◽  
Experimental Data ◽  
Mathematical Model ◽  
Electrical Conductivity ◽  
Comparative Analysis ◽  
Electric Discharge ◽  
Specific Electrical Conductivity ◽  
Empirical Function ◽  
Electric Discharge In Water

In the present work, a comparative analysis of three methods for determining the specific electrical conductivity of the plasma formed in the channel of an electric discharge in water is carried out for its mathematical modeling. The parameters of the empirical function are determined, at which the results of mathematical modeling are consistent with the experimental data. The necessity of using empirical functions in calculating the specific electrical conductivity of plasma has been substantiated. The obtained ratios made it possible to significantly increase the adequacy of the previously developed mathematical model of the physical discharge processes in water and to expand the range of parameters in which it can be used.

scholarly journals Construction of a mathematical model of the film absorber for sulfating two-component mixtures of organic substances

2021 ◽  
Vol 6 (6 (114)) ◽  
Author(s):  
Oleksandr Dzevochko ◽  
Mykhaylo Podustov ◽  
Alona Dzevochko ◽  
Vladimir Panasenko
Keyword(s):  
Mathematical Modeling ◽  
Experimental Data ◽  
Mathematical Model ◽  
Sulfur Trioxide ◽  
Coconut Oil ◽  
Molar Ratio ◽  
Organic Substances ◽  
Two Component ◽  
Gaseous Sulfur ◽  
The Mathematical Model

The processes that occur in film absorbers during the sulfation of two-component mixtures of organic substances are quite complex and require mathematical modeling. This paper reports the construction of a mathematical model that makes it possible to adequately describe the process of sulfation involving gaseous sulfur trioxide in the production of surfactants. Based on the model, it became possible to investigate this process for higher alcohols of fractions С12–С14 and monoethanolamides of higher fatty acids of coconut oil. The data are given on the comparison of mathematical modeling results based on the mathematical model built with known experimental data and results of alternative mathematical modeling for different ratios of the length of the reaction pipe to its diameter (l/d). It is shown that the error in comparing the experimental data was 4.8–9.6 % at l l/d=29; 1.1–8.7 % at l/d=70; 3.9–12.3 % at l/d=144. The error in comparing known results of alternative mathematical modeling was, respectively, 6.3–7.2 %, 0.1–6.5 %, 0–1.0 %. These results were obtained for the molar ratio in the range of 1.0–1.15 and the SO3 concentration in the stream of 4.0–6.0 %. Such findings suggest that the established dependences of the basic parameters for the sulfation process are adequate in terms of the absorber length and its radial direction. Therefore, the mathematical model built does hold within the considered ranges of input variables. Consequently, it could be used in the theoretical study of the process of sulfation of two-component mixtures of organic substances by gaseous sulfur trioxide in a film absorber with a downward flow of phases. The results obtained could be used in practice, in particular in the manufacture of high-quality products for the cosmetic industry.

scholarly journals Experimental studies of the method of mutual load of induction motors

2020 ◽  
pp. 44-49
Author(s):  
V. V. Kharlamov ◽  
◽  
D. I. Popov ◽  
P. S. Sokolov ◽  
L. E. Serkova ◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Experimental Data ◽  
Mathematical Model ◽  
Induction Motors ◽  
Experimental Studies ◽  
Electromechanical System ◽  
Experimental Equipment ◽  
Frequency Converters ◽  
Parameter Values ◽  
The Mathematical Model

The article presents the results of comparison of experimental studies and mathematical modeling of the stand for testing induction motors by the method of mutual load. A detailed description of the composition of the experimental equipment, which is based on a pair of frequency converters and connected to them a pair of engines of the АИС71В4 type with a nominal power of 0,75 kW, the shafts of which are rigidly connected by a coupling. The mathematical model of the electromechanical system used in the calculations is presented, and its main assumptions are listed. A table of parameter values and graphs obtained from calculated and experimental data are presented. The analysis of the obtained data shows the possibility of using the considered mathematical model with the existing assumptions in the design of electrical complexes intended for testing induction motors by the method of mutual load

Mathematical Model of the Cell Growth for Methane-Oxidizing Bacteria

2015 ◽  
Vol 731 ◽  
pp. 345-348
Author(s):  
Jing Dong ◽  
He Teng Wang ◽  
Ying Xin Zhang
Keyword(s):  
Mathematical Modeling ◽  
Experimental Data ◽  
Mathematical Model ◽  
Cell Growth ◽  
Living Cell ◽  
Fermentation Process ◽  
Logistic Curve ◽  
Cell Content ◽  
Methane Oxidizing Bacteria

The dynamic trends of living cell content of methane-oxidizing bacteria during its fermentation process were analyzed. According to the experimental data, mathematical modeling of methane-oxidizing bacteria cell growth was simulated. The results showed that the logistic curve could be used to describe the mathematical modeling of methane-oxidizing bacteria cell growth well. The establishment of the model is the theoretic basis in optimizing the fermentable parameters and analyzing the fermented metabolites.

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