Simulation of cancer treatment using the MATLAB SimBiology application

2021 ◽  
Vol 14 (3) ◽  
pp. 90-96
Author(s):  
Anastasia Goncharova ◽  
Maria Vil'
Keyword(s):  
Mathematical Model ◽  
Cancer Treatment ◽  
Interference Competition ◽  
The Body ◽  
Continuous Treatment ◽  
Constant Concentration ◽  
Application Package ◽  
The Mathematical Model ◽  
Cancerous Cells

The paper presents the implementation of the mathematical model of cancer taking into account interference competition and the model of continuous treatment with a constant concentration of the drug in the patient's blood. The implementation was carried out using the MATLAB SimBiology application package. The principle of implementation of different stages of the course of the disease within the framework of one model is described. On the basis of the constructed models and SimBiology tools, a modification was carried out that implements the discrete administration of doses of the drug in courses and takes into account its dynamics in the body, taking into account the assumption that the drug is consumed only to suppress cancerous cells.

scholarly journals Application of Mathematical Model of Cancer Treatment by Radiotherapy

2021 ◽  
Author(s):  
Seyedeh Nasrin Hosseini Motlagh ◽  
Faeze Lari Motefaker
Keyword(s):  
Mathematical Model ◽  
Cancer Treatment ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Volterra Equations ◽  
Adomian Decomposition ◽  
Treatment Stage ◽  
Competitive Model ◽  
The Mathematical Model ◽  
Cancerous Cells

The aim of this study is achieve an analysis of the mathematical model governing radiotherapy as well as to achieve the concentration of healthy and cancerous cells to reduce the length of treatment and less damage to cancer treatment by this type of therapy. In order to obtain this, we used the latest mathematical radiotherapy model based on the Lotka-Volterra competitive equations and the Adomian decomposition method that is the one of the most advanced analytical solutions to solve differential equations to attain our goal. The calculation of the Adomian decomposition method was applied to the mathematical model governing radiotherapy, and then the concentration of healthy and cancerous cells was achieved with a very good approximation. Comparison of the behavior of healthy and cancerous cells concentrations based on experimental cases and the behavior of healthy and cancerous cells concentrations based on computations express the correctness of the work. ADM indicates the concentration of healthy and cancerous cells during the treatment stage and the no treatment stage can be effective in improving the modeling based on the competitive model of the Lotka-Volterra equations, which results in the reduction of the use of diagnostic devices, less radiation, the faster treatment process and decreasing the cost of treatment for patients and governments.

Impact of Electric Vehicle Lateral Dynamics on the Battery Pack

2014 ◽  
Vol 590 ◽  
pp. 451-457
Author(s):  
Sen Nan Song ◽  
Fa Chao Jiang ◽  
Hong Shi
Keyword(s):  
Mathematical Model ◽  
Angular Acceleration ◽  
Simulation Software ◽  
The Body ◽  
Battery Pack ◽  
Vehicle Body ◽  
Rolling Motion ◽  
Rolling Angle ◽  
On The Road ◽  
The Mathematical Model

The present work is concerned with the rolling motion of the battery pack when EV travelling on the road. First McPherson suspension system was regarded as the research object with detailed analysis of its structural features and motion characteristics. Establish the mathematical model which could apply to calculating the rolling motion of the vehicle body. Through MATLAB/Simulink simulation software, we could calculate the rolling angle on passive suspension. On this basis, assume that the battery pack mounted on the vehicle body and make it passive connection and PID connection. When the body rolls, the battery pack will produce a certain angle then. Next establish the mathematical model to summarize the relationship between the two variables. Then we set the parameters and calculate the roll angle of battery pack in both cases for comparison. Simulation results show that road irregularities will make battery rotate an angle and PID controller can effectively reduce the angle, especially angular acceleration. This paper put forward a new idea that battery is connected with body by active control on EV, and proves the superiority in reducing the rolling angle.

A Theoretical Investigation into Phase Change Clothing Benefits for Firefighters under Extreme Conditions

2009 ◽  
Vol 4 (3) ◽  
Author(s):  
Geoffry N. Mercer ◽  
Harvinder S Sidhu
Keyword(s):  
Mathematical Model ◽  
Thermal Properties ◽  
Phase Change ◽  
Protective Clothing ◽  
The Body ◽  
Extreme Conditions ◽  
Heat Absorption ◽  
Fire Exposure ◽  
Subcutaneous Layer ◽  
The Mathematical Model

We investigate the thermal performance of protective clothing that has an embedded phase change layer. Heat absorption due to phase change within the material is used to limit the thermal penetration of heat into the material and hence to the firefighter. The distribution of temperature within the fabric and skin during the exposure to an extreme firefighting situation is determined. To determine the protective nature of the clothing, we also include a model of the skin as three layers with differing thermal properties namely the epidermis, dermis and the subcutaneous layer. In our model, we have also incorporated the air gap between the garment and the body. The mathematical model is used to predict the duration of fire exposure during which the garment is able to protect the firefighter from getting first and second degree burns.

scholarly journals Estimation of Full Strap-down Rotating Bomb Guidance Information Based on Unscented Kalman Filter

2020 ◽  
Vol 38 (3) ◽  
pp. 604-609
Author(s):  
Wei Gao ◽  
Benbing Gao ◽  
Hongsong Fang ◽  
Xin Lu
Keyword(s):  
Mathematical Model ◽  
Kalman Filter ◽  
Unscented Kalman Filter ◽  
Angular Rate ◽  
The Body ◽  
Filter Method ◽  
Measurement Information ◽  
Kalman Filter Method ◽  
The Mathematical Model ◽  
Navigation Information

In this paper, the full strap-down seeker of rotating bomb is taken as the research object, and the method of extracting the LOS (line-of-sight) angle and angular rate of the full strap-down seeker of the rotating bomb is studied. The structure of the full strap-down seeker is quite different from that of the conventional rate gyro seeker. The measurement system of full strap-down seeker is fixed to the missile, the seeker can only obtain the measurement information in the projectile coordinate system, and the measurement information is coupled with the body posture information, so it cannot be directly used for the control guidance of the rotating projectile. First, based on the conversion relationship between coordinate systems, the mathematical model of the inertial LOS angle of the rotating bomb is established, and the mathematical model of the extraction of the inertial LOS angle and angular rate of the rotating bomb is further established. Then, the Kalman filter is designed by using the unscented Kalman filter method (UKF), and the extracted LOS angle containing noise information is filtered. Finally, the mathematical simulation is carried out to verify the validity of the mathematical model of LOS angle and angular rate extraction. Compared with the Extended Kalman filter method (EKF), the UKF has a higher accuracy for estimating the navigation information of the full strap-down rotating projectile.

scholarly journals МАТЕМАТИЧЕСКАЯ МОДЕЛЬ И МЕТОД РАСЧЕТА ДИНАМИКИ СУШКИ И ТЕРМОДЕСТРУКЦИИ БИОМАССЫ

2018 ◽  
Vol 82 (1) ◽  
Author(s):  
Наталья Николаевна Сороковая ◽  
Дмитрий Николаевич Коринчук
Keyword(s):  
Mathematical Model ◽  
Mass Transfer ◽  
Thermal Decomposition ◽  
Numerical Method ◽  
Heat And Mass Transfer ◽  
The Body ◽  
Physical Factors ◽  
Deformation Equation ◽  
The Mathematical Model ◽  
Kinetics Of

Разработана математическая модель и численный метод расчета динамики тепломассопереноса, фазовых превращений и усадки при сушке коллоидных капиллярно-пористых тел цилиндрической формы в условиях равномерного обдува теплоносителем. Математическая модель строилась на базе дифференциального уравнения переноса субстанции (энергии, массы, импульса) в деформируемых системах. Проведены экспериментальные исследования кинетики обезвоживания частиц энергетической вербы в потоке воздуха с целью верификации математической модели. Обоснована возможность ее использования для расчета совместных процессов сушки и начального этапа термического разложения биомассы. С использованием ранее полученных данных по значениям энергии активации Аэф(Т) для различных видов биомассы проведено математическое моделирование динамики и кинетики высокотемпературной сушки в потоке дымовых газов энергетической вербы, которая сопровождается термодеструкцией гемиоцеллюлозы. Результаты численных экспериментов свидетельствуют об адекватности предложенного подхода, эффективности математической модели и метода ее реализации. На их основе возможно проводить исследование динамики тепломассопереноса при сушке частиц различных видов измельченной биомассы; определение температуры начала и окончания первой стадии термического разложения; момента достижения равновесного влагосодержания в зависимости от свойств материала и сушильного агента. Эти данные позволяют выбирать оптимальные с точки зрения сохранения энергии и качества высушиваемого продукта  режимные параметры процесса.         A mathematical model and a numerical method for calculating the dynamics of heat and mass transfer, phase transformations and shrinkage during the drying of colloidal capillary-porous cylindrical bodies under conditions of equitable winding by a coolant are developed. The mathematical model was based on the differential equation of substance (energy, mass, impulse) transfer in deformable systems. It includes the equations diffusion-filtration transfer of energy for the system as a whole, and the mass transfer of the liquid, vapor and air phases in the pores of the body. Expressions for the intensity of evaporation of a liquid, capillary pressure, and the diffusion coefficients are presented. The relative volume strain was found by means of an analytical solution of the thermoconcentration deformation equation. Based on the explicit three-layer counting difference scheme and the procedure splitting of algorithm  by physical factors, a numerical method for realizing this mathematical model is developed.Experimental studies of the kinetics of dehydration of energy willow particles in the airflow were carried out to verify the mathematical model. Its applicability for calculating combined processes of drying and of the initial stage of thermal decomposition of biomass is substantiated. Using the previously obtained data on the activation energy values for various types of biomass, a mathematical simulation of the dynamics and kinetics of high-temperature drying in the flue gas flow of energy willow was carried out, which is accompanied by thermal destruction of hemiocellulose. The results of numerical experiments indicate the adequacy of the proposed approach, the effectiveness of the mathematical model and the method of its implementation. On their basis, it is possible to study the dynamics of heat and mass transfer when drying particles of different types of ground biomass; determination of the temperature of the beginning and ending of the first stage of thermal decomposition; the moment when the equilibrium moisture content is reached, depending on the properties of the material and the drying agent. These data allow choosing the process parameters that are optimal in terms of energy saving and quality of the dried product.

Mathematical Relationship Between Palpation Forces and Displacement Associated With Restriction

2019 ◽  
Vol 3 (1) ◽  
Author(s):  
Anneke Hoyer ◽  
Brian F. Degenhardt ◽  
Todd Hammond Palumbo ◽  
Steven J. Webb ◽  
Roger C. Fales
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Goodness Of Fit ◽  
The Body ◽  
Low Back ◽  
Human Volunteers ◽  
Tissue Compliance ◽  
Key Variables ◽  
The Mathematical Model ◽  
Force Displacement

Abstract Based on the clinical data, a mathematical model was developed that characterized the palpation forces and the associated deformation/displacement of the surface of the body when osteopathic clinicians examine the low back or lumbar spine region. The purpose of this work was to better understand the haptic perception of clinicians who use palpation to assist in their assessment of patients with low back pain. Clinicians use palpation to identify areas of reduced tissue compliance thought to be associated with restriction of segmental vertebral motion. Using existing experimental data generated by multiple clinicians examining human volunteers, palpation forces and associated displacements were modeled by using three key variables: stiffness, damping, and inertia of the system. Of the total number of force application cycles analyzed, 92% had a goodness of fit, R2, that was better than 95% (R2≥ 0.95). When comparing the experimental data to the response of the three-parameter force/displacement mathematical model, the mathematical model delivered an accurate representation of palpation forces and displacements. A normalized stiffness difference (NSD) was generated to compare to clinician assessments. Recommendations for design specifications of a palpation-training device were suggested.

Flight mechanics of a free-wing tilt-body aircraft

2008 ◽  
Vol 112 (1137) ◽  
pp. 625-640
Author(s):  
K. Ro ◽  
J. W. Kamman ◽  
J. B. Barlow
Keyword(s):  
Mathematical Model ◽  
Incidence Angle ◽  
Equations Of Motion ◽  
Dynamic Modelling ◽  
Flight Simulation ◽  
The Body ◽  
Flight Mechanics ◽  
Short Takeoff And Landing ◽  
And Control ◽  
The Mathematical Model

Abstract The free-wing tilt-body aircraft refers to a vehicle configuration in which the wing, fuselage, and empennage are in a longitudinally articulated connection. This allows the main wing to freely rotate relative to the body, while the empennage, which is in the form of a long twin boom connected to the rear of the body, changes its incidence angle relative to the body in response to external commands. The principal advantages claimed for the configuration are short takeoff and landing capability, and reduced gust sensitivity. The aerodynamics of the free-wing tilt-body configuration has been previously studied, but analysis of its flight mechanics is limited. In this paper we present derivations of the flight dynamic equations of motion using multi-body dynamic modelling techniques, and combine the resulting equations of motion with experimental aerodynamic data to achieve a nonlinear mathematical model for flight simulation of a generic free-wing tilt-body vehicle. The mathematical model is suitable for the study of detailed dynamic characteristics as well as for model based control law synthesis. Key flight performance, and stability and control characteristics of a generic configuration are obtained from the mathematical model.

scholarly journals Mathematical Model Applied to Monitoring the Glucose-Insulin Interaction inside the Body of Diabetes Patients

2020 ◽  
Vol 40 (1) ◽  
pp. 1-12
Author(s):  
Sonia Akter ◽  
Md Sirajul Islam ◽  
Md Haider Ali Biswas ◽  
Sajib Mandal
Keyword(s):  
Mathematical Model ◽  
Numerical Approximation ◽  
Regulatory System ◽  
The Body ◽  
Normal Person ◽  
Complex Situation ◽  
Critical Situation ◽  
The World ◽  
The Mathematical Model ◽  
Diabetes Patients

The incidence and prevalence of diabetes are increasing all over the world and complication of diabetes constitutes a burden for the individuals and whole society. In this paper, we propose a mathematical model for monitoring glucose-insulin regulatory system in the human body. The non-linear cases are considered, and the model is analysed by using Lyapunov’s method. The mathematical model, discussed the critical situation of the diabetes patients as well as for normal person are analysed for stability. The numerical approximation is used to verify the analytical results and the obtained solutions represent the complex situation of diabetes patients. GANIT J. Bangladesh Math. Soc.Vol. 40 (2020) 1-12

scholarly journals Different strategies in the liver regeneration processes. Numerical experiments on the mathematical model

2020 ◽  
Keyword(s):  
Mathematical Model ◽  
Liver Regeneration ◽  
Mixed Strategy ◽  
The Body ◽  
Competitive Dynamics ◽  
Biological Processes ◽  
Volterra Type ◽  
Toxic Factors ◽  
The Mathematical Model ◽  
Homogeneous Approximation

It is considered the generalized mathematical model which describes the processes of maintaining / restoring dynamic homeostasis (regeneration) of the liver and obviously depends on the control parameters. The model is a system of discrete controlled equations of the Lotka – Volterra type with transitions. These equations describe the controlled competitive dynamics of liver cell populations’ (hepatic lobules) various types in their various states and controlled competitive transitions between types and states. To develop this model there were accepted such assumptions: homogeneous approximation; independence of biological processes; small toxic factors. In the mathematical model the process of the liver regeneration occurs due to hyperplasia processes, replication, polyplodia and division of binuclear hepatocytes into mononuclear and controlled apoptosis. All these processes are necessary for adequate modeling of the liver regeneration. For example, single and constant toxic functions show that the above processes are not able to cope with the toxic factors that are accumulated in the body. The process of restoring the body’s functional state requires the non-trivial strategy of the liver regeneration. Numerical calculations revealed that the mathematical model corresponds to biological processes for different strategies of the liver regeneration. Based on the calculations in the case of partial hapatectomy it is concluded that the mixed strategy of regeneration should be used for the regeneration process. Henceforward it is planned to extend the mathematical model in the case of the liver regeneration, which occurs under the influence of strong toxins, that is, using the stem cells and fibrosis. It is also supposed to justify the principles and criteria for optimal regulation of the processes of maintaining / restoring liver’s dynamic homeostasis.

scholarly journals Mathematical Model of Cervical Cancer Treatment Using Chemotherapy Drug

2019 ◽  
Vol 8 (1) ◽  
pp. 11-15 ◽  
Author(s):  
Murtono Murtono ◽  
Meksianis Zadrak Ndii ◽  
Sugiyanto Sugiyanto
Keyword(s):  
Mathematical Model ◽  
Cervical Cancer ◽  
Cancer Treatment ◽  
Cancer Cells ◽  
Surrounding Tissue ◽  
Chemotherapy Drugs ◽  
Cervical Cancer Cells ◽  
Abnormal Cells ◽  
Infected Cells ◽  
The Mathematical Model

Cervical cancer is a malignant disease that causes problems in women's health, especially in developing countries such as Indonesia. Cervical cancer cells will develop quickly, uncontrollably, and will continue to divide and then infiltrate the surrounding tissue and continue to spread to connective tissue, blood, and attack important organs and spinal nerves. The aim of the research is to study the mathematical model of cervical cancer by chemotherapy treatment. The results of this study are that cervical cancer treatment using chemotherapy is effective enough to kill abnormal cells such as infected cells, pre-cancerous cells and cancer cells, although there are side effects, namely the killing of normal cells due to chemotherapy drugs.

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