DEVELOPMENT OF A MATHEMATICAL MODEL OF LIVER FILTRATION

2021 ◽  
pp. 80-84
Author(s):  
Мария Рашитовна Ахмедзянова ◽  
Аза Валерьевна Писарева
Keyword(s):  
Mathematical Model ◽  
Lymphatic Vessels ◽  
Interstitial Space ◽  
Cellular Model ◽  
Hepatic Lobule ◽  
Flat Base ◽  
Rate Of Absorption ◽  
Metabolic Reactions ◽  
Almost All ◽  
The Mathematical Model

Клетки печени занимают центральное место в реакциях промежуточного метаболизма. Печень принимает участие в метаболизме почти всех классов веществ. Основной структурной единицей печени является печеночная долька, которая представляет собой призму размером 1,5-2 мм с плоскими основанием и вершиной. По всей дольке также распределены лимфатические сосуды, которые активно поглощают интерстициальную жидкость и выводят ее с регулируемой скоростью, однако зависимость скорости поглощения от интерстициального давления и других параметров известна не полностью. В работе представлена математическая модель для оценки кровотока в печеночной дольке. Рассмотренная клеточная модель включает в себя производство и прохождение лимфы по двум основным путям: поглощение лимфатическими сосудами и выход из печени через поверхность дольки в интерстициальное пространство. Приведены геометрические и механические допущения модели и ее недостатки. В биологической модели исследовано влияние изменений кровяного давления в печени на выработку лимфы и оценивается скорость поглощения лимфы и поток жидкости (как лимфы, так и крови) по всей поверхности печени. В математической модели показана классификация: статическая (не зависящая от времени), пространственная, детерминированная, нелинейная, непрерывная. Результаты исследования показали, что предлагаемая клеточная модель микроциркуляции печени включает в себя производство и прохождение лимфы по двум основным путям: поглощение лимфатическими сосудами и выход из печени через поверхность дольки в интерстициальное пространство. Выявлены основные недостатки разрабатываемой модели Liver cells are central to intermediate metabolic reactions. The liver is involved in the metabolism of almost all classes of substances. The main structural unit of the liver is the hepatic lobule, which is a prism 1.5-2 mm in size with a flat base and apex. Lymphatic vessels are also distributed throughout the lobule, which actively absorb interstitial fluid and remove it at a controlled rate, however, the dependence of the rate of absorption on interstitial pressure and other parameters is not fully known. The paper presents a mathematical model for assessing blood flow in the hepatic lobule. The considered cellular model includes the production and passage of lymph through two main pathways: absorption by the lymphatic vessels and exit from the liver through the surface of the lobule into the interstitial space. Geometric and mechanical assumptions of the model and its disadvantages are presented. A biological model investigates the effect of changes in liver blood pressure on lymph production and estimates the rate of lymph absorption and fluid flow (both lymph and blood) over the entire surface of the liver. The mathematical model shows the classification: static (independent of time), spatial, deterministic, nonlinear, continuous. The results of the study showed that the proposed cellular model of liver microcirculation includes the production and passage of lymph through two main pathways: absorption by the lymphatic vessels and exit from the liver through the surface of the lobule into the interstitial space. The main shortcomings of the developed model are revealed

Confronting shell morphodynamics and sclerochronology: leaving behind phenomenology to move toward integrative laws of growth

2021 ◽  
Author(s):  
Jennifer Guarini ◽  
Jean-Marc Guarini
Keyword(s):  
Mathematical Model ◽  
Environmental Changes ◽  
Growth Ring ◽  
Shell Growth ◽  
Individual Variability ◽  
Generic Model ◽  
Mathematical Framework ◽  
Unbiased Estimates ◽  
Almost All ◽  
The Mathematical Model

<p>Sclerochronological methods are described as a means to reconstruct, from increments recorded on a shell transect (i.e. "sclerochonological growth"), the fluctuations in past environments. This was proposed by an erroneous analogy with tree-ring dendrochronology. However, shells do not grow like trees. Almost all molluscan shells grow by adding increments at the shell edge, while preserving their shape. This is called "terminal growth". The advantage of this property is that there is a generic mathematical model that can quantify the shell expansion (morphological growth). </p><p>Nonetheless, this generic model is not compatible with observed shell incrementation and accretion processes. This is because increment widths should increase geometrically in the mathematical model along a transect. We remarked that despite studying the same object, morphodynamics and sclerochronology have followed divergent paths in past decades, without incorporating advances of the other speciality. </p><p>We have now addressed this problem head-on by developing a new mathematical framework to combine incremental shell growth within shell morphodynamics. This model is designed to be able to confront a theoretical prediction of shell incrementation with a measured one. The method combines morphodynamic modelled shapes with 3D shell scans and increments measured from shell transects. </p><p>Our work in this area highlights several heretofore unrecognized fundamental problems in morphodynamics and sclerochronology which concern the way individual variability is accounted for in both areas. Regarding the reconstruction of environmental trends, we find that the arbitrary choice of one particular "best" shell transect and averaging over groups of individuals can be a source of significant bias. It is time to revise shell science methods to consider the entire incremental geometry (or growth 'ring') so that unbiased estimates of environmental changes can be provided using sclerochonological data. </p>

scholarly journals A non-linear mathematical model for the X-ray variability of the microquasar GRS 1915+105 – III. Low-frequency quasi-periodic oscillations

2020 ◽  
Vol 497 (1) ◽  
pp. 405-415
Author(s):  
E Massaro ◽  
F Capitanio ◽  
M Feroci ◽  
T Mineo
Keyword(s):  
Mathematical Model ◽  
Equilibrium Points ◽  
Low Frequency ◽  
Input Function ◽  
Power Density Spectrum ◽  
Periodic Oscillations ◽  
Density Spectrum ◽  
X Ray ◽  
Almost All ◽  
The Mathematical Model

ABSTRACT The X-ray emission from the microquasar GRS 1915+105 shows, together with a very complex variability on different time-scales, the presence of low-frequency quasi-periodic oscillations (LFQPOs) at frequencies lower than ∼30 Hz. In this paper, we demonstrate that these oscillations can be consistently and naturally obtained as solutions of a system of two ordinary differential equations, which is able to reproduce almost all variability classes of GRS 1915+105. We modified the Hindmarsh–Rose model and obtained a system with two dynamical variables x(t), y(t), where the first one represents the X-ray flux from the source, and an input function J(t), whose mean level J0 and its time evolution is responsible of the variability class. We found that for values of J0 around the boundary between the unstable and the stable interval, where the equilibrium points are of spiral type, one obtains an oscillating behaviour in the model light curve similar to the observed ones with a broad Lorentzian feature in the power density spectrum and, occasionally, with one or two harmonics. Rapid fluctuations of J(t), as those originating from turbulence, stabilize the LFQPOs, resulting in a slowly amplitude modulated pattern. To validate the model, we compared the results with real RXTE data, which resulted remarkably similar to those obtained from the mathematical model. Our results allow us to favour an intrinsic hypothesis on the origin of LFQPOs in accretion discs ultimately related to the same mechanism responsible for the spiking limit cycle.

Overview of the Methods for Service Life Prediction on Gears

2011 ◽  
Vol 488-489 ◽  
pp. 727-730
Author(s):  
Boris Aberšek ◽  
Jože Flašker
Keyword(s):  
Mathematical Model ◽  
Service Life ◽  
Crack Propagation ◽  
Life Prediction ◽  
Complex Structure ◽  
Almost All ◽  
The Mathematical Model ◽  
Multiaxial Loadings ◽  
Real Complex

For designing machines and devices the dimensioning with respect to service life is increasingly taken into account. This applies also for gearing which are still today one of very important components of almost all machines. The problem of determination of the service life of gearing is directly related to geometry of gears, multiaxial loadings, materials and appropriate models for prediction of the crack propagation. Obviously gears and gearing belong to the real complex structure, by correctly selected and carefully planned experiments we obtained results with which we can confirm and justified the mathematical model for calculating different parameters, i.e. service life.

DETERMINATION OF PERFORMANCE INDICATORS OF THE TRUCK KrAZ-6510TE

2020 ◽  
pp. 19-26
Author(s):  
Olexandr Pavlenko ◽  
Serhii Dun ◽  
Maksym Skliar
Keyword(s):  
Mathematical Model ◽  
Surface Friction ◽  
Building Structures ◽  
Maximum Torque ◽  
Military Equipment ◽  
Military Vehicles ◽  
Force Magnitude ◽  
Vehicle Mobility ◽  
The Mathematical Model

In any economy there is a need for the bulky goods transportation which cannot be divided into smaller parts. Such cargoes include building structures, elements of industrial equipment, tracked or wheeled construction and agricultural machinery, heavy armored military vehicles. In any case, tractor-semitrailer should provide fast delivery of goods with minimal fuel consumption. In order to guarantee the goods delivery, tractor-semitrailers must be able to overcome the existing roads broken grade and be capable to tow a semi-trailer in off-road conditions. These properties are especially important for military equipment transportation. The important factor that determines a tractor-semitrailer mobility is its gradeability. The purpose of this work is to improve a tractor-semitrailer mobility with tractor units manufactured at PJSC “AutoKrAZ” by increasing the tractor-semitrailer gradeability. The customer requirements for a new tractor are determined by the maximizing the grade to 18°. The analysis of the characteristics of modern tractor-semitrailers for heavy haulage has shown that the highest rate of this grade is 16.7°. The factors determining the limiting gradeability value were analyzed, based on the tractor-semitrailer with a KrAZ-6510TE tractor and a semi-trailer with a full weight of 80 t. It has been developed a mathematical model to investigate the tractor and semi-trailer axles vertical reactions distribution on the tractor-semitrailer friction performances. The mathematical model has allowed to calculate the gradeability value that the tractor-semitrailer can overcome in case of wheels and road surface friction value and the tractive force magnitude from the engine. The mathematical model adequacy was confirmed by comparing the calculations results with the data of factory tests. The analysis showed that on a dry road the KrAZ-6510TE tractor with a 80 t gross weight semitrailer is capable to climb a gradient of 14,35 ° with its coupling mass full use condition. The engine's maximum torque allows the tractor-semitrailer to overcome a gradient of 10.45° It has been determined the ways to improve the design of the KrAZ-6510TE tractor to increase its gradeability. Keywords: tractor, tractor-semitrailer vehicle mobility, tractor-semitrailer vehicle gradeability.

EXPERIMENTAL STUDIES OF CAR PROPERTIES ON A PHYSICAL MODEL

2019 ◽  
pp. 10-16
Author(s):  
Oleksii Timkov ◽  
Dmytro Yashchenko ◽  
Volodymyr Bosenko
Keyword(s):  
Mathematical Model ◽  
Remote Control ◽  
Physical Model ◽  
Model Experiment ◽  
Experimental Studies ◽  
Electrical Energy ◽  
Short Term ◽  
Motor Current ◽  
Memory Card ◽  
The Mathematical Model

The article deals with the development of a physical model of a car equipped with measuring, recording and remote control equipment for experimental study of car properties. A detailed description of the design of the physical model and of the electronic modules used is given, links to application libraries and the code of the first part of the program for remote control of the model are given. Atmega microcontroller on the Arduino Uno platform was used to manage the model and register the parameters. When moving the car on the memory card saved such parameters as speed, voltage on the motor, current on the motor, the angle of the steered wheel, acceleration along three coordinate axes are recorded. Use of more powerful microcontrollers will allow to expand the list of the registered parameters of movement of the car. It is possible to measure the forces acting on the elements of the car and other parameters. In the future, it is planned to develop a mathematical model of motion of the car and check its adequacy in conducting experimental studies on maneuverability on the physical model. In addition, it is possible to conduct studies of stability and consumption of electrical energy. The physical model allows to quickly change geometric dimensions and mass parameters. In the study of highway trains, this approach will allow to investigate the various layout schemes of highway trains in the short term. It is possible to make two-axle road trains and saddle towed trains, three-way hitched trains of different layout. The results obtained will allow us to improve not only the mathematical model, but also the experimental physical model, and move on to further study the properties of hybrid road trains with an active trailer link. This approach allows to reduce material and time costs when researching the properties of cars and road trains. Keywords: car, physical model, experiment, road trains, sensor, remote control, maneuverability, stability.

RESEARCH OF INDICATORS OF A VEHICLE WITH A DIESEL WORKING ON DIESEL AND DIESEL GAS CYCLES USING THE MATHEMATICAL MODEL

2020 ◽  
pp. 14-19
Author(s):  
Serhii Kovbasenko ◽  
Andriy Holyk ◽  
Serhii Hutarevych
Keyword(s):  
Mathematical Model ◽  
Diesel Engine ◽  
Environmental Performance ◽  
Energy Performance ◽  
Dual Fuel ◽  
Fuel System ◽  
Compressed Natural Gas ◽  
Diesel Vehicles ◽  
Diesel Cycle ◽  
The Mathematical Model

The features of an advanced mathematical model of motion of a truck with a diesel engine operating on the diesel and diesel gas cycles are presented in the article. As a result of calculations using the mathematical model, a decrease in total mass emissions as a result of carbon monoxide emissions is observed due to a decrease in emissions of nitrogen oxides and emissions of soot in the diesel gas cycle compared to the diesel cycle. The mathematical model of a motion of a truck on a city driving cycle according to GOST 20306-90 allows to study the fuel-economic, environmental and energy indicators of a diesel and diesel gas vehicle. The results of the calculations on the mathematical model will make it possible to conclude on the feasibility of converting diesel vehicles to using compressed natural gas. Object of the study – the fuel-economic, environmental and energy performance diesel engine that runs on dual fuel system using CNG. Purpose of the study – study of changes in fuel, economic, environmental and energy performance of vehicles with diesel engines operating on diesel and diesel gas cycles, according to urban driving cycle modes. Method of the study – calculations on a mathematical model and comparison of results with road tests. Bench and road tests, results of calculations on the mathematical model of motion of a truck with diesel, working on diesel and diesel gas cycles, show the improvement of environmental performance of diesel vehicles during the converting to compressed natural gas in operation. Improvement of environmental performance is obtained mainly through the reduction of soot emissions and nitrogen oxides emissions from diesel gas cycle operations compared to diesel cycle operations. The results of the article can be used to further develop dual fuel system using CNG. Keywords: diesel engine, diesel gas engine, CNG

Glycemia monitoring

1998 ◽  
Vol 2 ◽  
pp. 23-30
Author(s):  
Igor Basov ◽  
Donatas Švitra
Keyword(s):  
Diabetes Mellitus ◽  
Mathematical Model ◽  
Numerical Methods ◽  
Differential Equations ◽  
Blood Sugar ◽  
Self Regulation ◽  
Physiological System ◽  
Non Linear ◽  
The Mathematical Model

Here a system of two non-linear difference-differential equations, which is mathematical model of self-regulation of the sugar level in blood, is investigated. The analysis carried out by qualitative and numerical methods allows us to conclude that the mathematical model explains the functioning of the physiological system "insulin-blood sugar" in both normal and pathological cases, i.e. diabetes mellitus and hyperinsulinism.

Mathematical Models of Papermaking

2001 ◽  
Vol 6 (1) ◽  
pp. 9-19 ◽  
Author(s):  
A. Buikis ◽  
J. Cepitis ◽  
H. Kalis ◽  
A. Reinfelds ◽  
A. Ancitis ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Initial Value Problems ◽  
Moisture Transfer ◽  
Bound Water ◽  
Drying Process ◽  
Initial Value ◽  
First Order ◽  
Heat And Moisture ◽  
The Mathematical Model ◽  
The Web

The mathematical model of wood drying based on detailed transport phenomena considering both heat and moisture transfer have been offered in article. The adjustment of this model to the drying process of papermaking is carried out for the range of moisture content corresponding to the period of drying in which vapour movement and bound water diffusion in the web are possible. By averaging as the desired models are obtained sequence of the initial value problems for systems of two nonlinear first order ordinary differential equations. 

The mathematical modelling of corrosion in hot dip galvanized steel reinforced concrete

2011 ◽  
Vol 2 (1) ◽  
pp. 1-12
Author(s):  
A. Hegyi ◽  
H. Vermeşan ◽  
V. Rus
Keyword(s):  
Mathematical Model ◽  
Reinforced Concrete ◽  
Numerical Model ◽  
Equation System ◽  
Galvanized Steel ◽  
Steel Reinforced Concrete ◽  
Numeric Model ◽  
Physical And Mathematical Models ◽  
Physical Phenomena ◽  
The Mathematical Model

Abstract In this paper we wish to present the numerical model elaborated in order to simulate some physical phenomena that influence the general deterioration of steel, whether hot dip galvanized or not, in reinforced concrete. We describe the physical and mathematical models, establishing the corresponding equation system, the initial and boundary conditions. We have also presented the numeric model associated to the mathematical model and the numeric methods of discretization and solution of the differential equations system that describes the mathematical model.

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