Study of the mathematical model of an organism’s immune response to the intrusion of an infection using methods of pattern recognition

2009 ◽  
Vol 19 (1) ◽  
pp. 181-185 ◽  
Author(s):  
Yu. I. Neimark ◽  
I. V. Kotel’nikov ◽  
L. G. Teklina
Keyword(s):  
Mathematical Model ◽  
Immune Response ◽  
Pattern Recognition ◽  
The Mathematical Model

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.

scholarly journals Assessment of the Efficient Strategies for Applying Antitumor Viral Vaccine Therapy Based On Mathematical Modeling

2019 ◽  
Vol 14 (1) ◽  
pp. 34-53 ◽  
Author(s):  
N.A. Babushkina ◽  
E.A. Kuzina ◽  
A.A. Loos ◽  
E.V. Belyaeva
Keyword(s):  
Mathematical Model ◽  
Immune Response ◽  
Tumor Cells ◽  
Tumor Size ◽  
Single Shot ◽  
Complete Elimination ◽  
Antitumor Therapy ◽  
Viral Vaccine ◽  
Two Stages ◽  
The Mathematical Model

The paper presents the mathematical description of the two stages of tumor cells’ death as a result of immune response after antitumor viral vaccine introduction. This mathematical description is presented by the system of nonlinear equations implemented in the MatLab-Simulink system. As a result of the computing experiment, two strategies for effective application of the antitumor viral vaccine were identified. The first strategy leads to complete elimination of the tumor cells after a single-shot administration of the vaccine. The second strategy makes it possible to stabilize tumor size through the recurrent introductions of the vaccine. Using the mathematical model of antitumor therapy, appropriate dosages were identified based on the number of tumor cells that die at the two stages of immune response. Dynamics of tumor growth for the two strategies of the viral vaccine application was forecasted based on the mathematical model of antitumor therapy with discontinuous trajectories of tumor growth. The computing experiments made it possible to identify initial tumor size at the start of the therapy and the dosages that allow complete elimination of the tumor cells after the single-shot introduction. For the second strategy, dosages and intervals between recurrent vaccine introductions required to stabilize tumor size at the initial level were also identified. The proposed approach to exploring the effectiveness of vaccine therapy may be applied to different types of experimental tumors and antitumor vaccines.

Numerical analysis of fractional-order tumor model

2015 ◽  
Vol 08 (05) ◽  
pp. 1550069 ◽  
Author(s):  
Ayesha Sohail ◽  
Sadia Arshad ◽  
Sana Javed ◽  
Khadija Maqbool
Keyword(s):  
Mathematical Model ◽  
Immune Response ◽  
Fractional Order ◽  
Interleukin 2 ◽  
Tumor Model ◽  
Graphical Analysis ◽  
System A ◽  
The Stability ◽  
The Mathematical Model ◽  
Limiting Values

In this paper, the tumor-immune dynamics are simulated by solving a nonlinear system of differential equations. The fractional-order mathematical model incorporated with three Michaelis–Menten terms to indicate the saturated effect of immune response, the limited immune response to the tumor and to account the self-limiting production of cytokine interleukin-2. Two types of treatments were considered in the mathematical model to demonstrate the importance of immunotherapy. The limiting values of these treatments were considered, satisfying the stability criteria for fractional differential system. A graphical analysis is made to highlight the effects of antigenicity of the tumor and the fractional-order derivative on the tumor mass.

A CONTROL THEORY APPROACH TO CANCER REMISSION AIDED BY AN OPTIMAL THERAPY

2010 ◽  
Vol 18 (01) ◽  
pp. 75-91 ◽  
Author(s):  
SIDDHARTHA P. CHAKRABARTY ◽  
SANDIP BANERJEE
Keyword(s):  
Mathematical Model ◽  
Immune Response ◽  
Control Theory ◽  
Malignant Tumors ◽  
Interleukin 2 ◽  
Cellular Immunotherapy ◽  
Theory Approach ◽  
Optimal Therapy ◽  
Cancer Remission ◽  
The Mathematical Model

The mathematical model depicting cancer remission as presented by Banerjee and Sarkar1is reinvestigated here. Mathematical tools from control theory have been used to analyze and determine how an optimal external treatment of Adaptive Cellular Immunotherapy and interleukin-2 can result in more effective remission of malignant tumors while minimizing any adverse affect on the immune response.

scholarly journals MATHEMATICAL MODELLING OF IMMUNE PROCESSES AND ITS APPLICATION

2020 ◽  
Vol 13 (5) ◽  
pp. 5-18
Author(s):  
N. I. ARALOVA ◽  
Keyword(s):  
Mathematical Model ◽  
Immune Response ◽  
Blood Flow ◽  
Blood Circulation ◽  
Moving Objects ◽  
Scientific School ◽  
Blood Flows ◽  
Theory Of Optimal Control ◽  
Complex Mathematical Model ◽  
The Mathematical Model

The aim of the study was to develop a mathematical model to research hypoxic states in case of simulation of an organism infectious lesions. The model is based on the methods of mathematical modeling and the theory of optimal control of moving objects. The processes of organism damage are simulated with the mathematical model of immune response developed by G.I. Marchuk and the members of his scientific school, adapted to current conditions. This model is based on Burnet’s clone selection theory of the determining role of antigen. Simulation results using the model are presented. The dependencies of infectious courses on the volumetric velocity of systemic blood flow is analyzed on the complex mathematical model of immune response, respiratory and blood circulation systems. The immune system is shown to be rather sensitive to the changes in blood flow via capillaries. Thus, the organ blood flows can be used as parameters for the model by which the respiratory, immune response, and blood circulation systems interact and interplay.

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

Sign in / Sign up

Export Citation Format

Share Document