Optimizing the delivery of combination therapy for tumors: A mathematical model

2017 ◽  
Vol 10 (03) ◽  
pp. 1750039 ◽  
Author(s):  
Clara Rojas Rodríguez ◽  
Juan Belmonte-Beitia
Keyword(s):  
Mathematical Model ◽  
Blood Vessels ◽  
Chemotherapeutic Agent ◽  
Drug Distribution ◽  
Optimal Controls ◽  
Chemotherapy Treatment ◽  
Time Problem ◽  
Drug Doses ◽  
Angiogenic Inhibitors

We present in this paper a new mathematical model for the scheduling of angiogenic inhibitors in combination with a chemotherapeutic agent for a tumor. Our model takes into account the process of angiogenesis and the quality of the vasculature discriminating between stable blood vessels and unstable blood vessels. We characterize theoretically the optimal controls on drug distribution to minimize the number of cancer cells at the end of the treatment in a free horizon time problem with restrictions on the total amount of drug doses. Finally, we solve the optimal control problem by using numerical simulations, obtaining as a result that, despite the number of the tumor cells decrease with anti-angiogenic treatment, the best results are reached at the end of the chemotherapy treatment.

scholarly journals Chemotherapy-Induced Cachexia and Model-Informed Dosing to Preserve Lean Mass in Cancer Treatment

2021 ◽  
Author(s):  
Suzan Farhang-Sardroodi ◽  
Michael A. La Croix ◽  
Kathleen P. Wilkie
Keyword(s):  
Quality Of Life ◽  
Mathematical Model ◽  
Side Effects ◽  
Lean Mass ◽  
Dose Dependence ◽  
Muscle Loss ◽  
Chemotherapy Treatment ◽  
Linear Dose ◽  
Non Linear

AbstractAlthough chemotherapy is a standard treatment for cancer, it comes with significant side effects. In particular, certain agents can induce severe muscle loss, known as cachexia, worsening patient quality of life and treatment outcomes. 5-fluorouracil, an anti-cancer agent used to treat several cancers, has been shown to cause muscle loss. Experimental data indicates a non-linear dose-dependence for muscle loss in mice treated with daily or week-day schedules. We present a mathematical model of chemotherapy-induced muscle wasting that captures this non-linear dose-dependence. Area-under-the-curve metrics are proposed to quantify the treatment’s effects on lean mass and tumour control. Model simulations are used to explore alternate dosing schedules, aging effects, and morphine use in chemotherapy treatment with the aim of better protecting lean mass while actively targeting the tumour, ultimately leading to improved personalization of treatment planning and improved patient quality of life.Author SummaryIn this paper we present a novel mathematical model for muscle loss due to cancer chemotherapy treatment. Loss of muscle mass relates to increased drug toxicity and side-effects, and to decreased patient quality of life and survival rates. With our model, we examine the therapeutic efficacy of various dosing schedules with the aim of controlling a growing tumour while also preserving lean mass. Preservation of body composition, in addition to consideration of inflammation and immune interactions, the gut microbiome, and other systemic health measures, may lead to improved patient-specific treatment plans that improve patient quality of life.

Multifactor mathematical model of criticality of welding process of products from aluminum- magnesium alloys

2020 ◽  
pp. 12-18
Author(s):  
F.A. Urazbahtin ◽  
A.YU. Urazbahtina
Keyword(s):  
Mathematical Model ◽  
Magnesium Alloy ◽  
Magnesium Alloys ◽  
Welding Process ◽  
Welding Equipment ◽  
Equipment Operation ◽  
Aluminum Magnesium Alloys ◽  
Aluminum Magnesium Alloy ◽  
Welding Materials

A multifactor mathematical model of the welding process of products from aluminum-magnesium alloys, consisting of 71 indicators that assess the quality of the weld, the welding process, costs, equipment operation and quality of the welded material. The model can be used to control and optimize the welding process of products from aluminum-magnesium alloys. Keywords welding, products, aluminum-magnesium alloy, indicators, process parameters, welding equipment, welding materials, electrode sharpening, lining [email protected]

Network analysis models – the secret for success

2004 ◽  
Vol 4 (5-6) ◽  
pp. 383-388
Author(s):  
D.M. Rogers
Keyword(s):  
Mathematical Model ◽  
Field Data ◽  
Essential Element ◽  
Distribution Networks ◽  
Automatic Calibration ◽  
Supply And Distribution ◽  
The World ◽  
Optimum Approach ◽  
Analysis Models

Water is a fundamental necessity of life. Yet water supply and distribution networks the world over are old and lacking in adequate maintenance. Consequently they often leak as much water as they deliver and provide an unacceptable quality of service to the customer. In certain parts of the world, water is available only for a few hours of the day. The solution is to build a mathematical model to simulate the operation of the real network in all of its key elements and apply it to optimise its operation. To be of value, the results of the model must be compared with field data. This process is known as calibration and is an essential element in the construction of an accurate model. This paper outlines the optimum approach to building and calibrating a mathematical model and how it can be applied to automatic calibration systems.

Numerical Simulation on Mold Electromagnetic Eccentric Stirring and Central Segregation of Round Bloom

2013 ◽  
Vol 652-654 ◽  
pp. 2450-2454
Author(s):  
Zhi Hong Zhang ◽  
Guo Guang Cheng
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Electromagnetic Stirring ◽  
Center Line ◽  
Central Segregation

The paper describes multi-section round bloom casting using external MEMS, equipped with max section D600mm and min D280mm mold, the center line of D280mm mold not coincident with the axis of stirrer coils. it is exist eccentric electromagnetic stirring of mold which section less than max D600mm, a mathematical model of MEMS has been established, the index of central segregation of D280mm macrostructure had decreased less than 1.12 by optimized parameters of electromagnetic stirring and SEN immerse depth, in the end, the quality of round bloom had improved.

scholarly journals TMOD-07. LOCALIZATION OF ERLOTONIB RELATIVE TO MRI-BASED TUMOR EXTENT IN PDX GLIOBLASTOMA MODEL: TOWARDS A MATHEMATICAL MODEL FOR THE INTERFACE BETWEEN MRI AND DRUG DISTRIBUTION

2018 ◽  
Vol 20 (suppl_6) ◽  
pp. vi269-vi270
Author(s):  
Pamela Jackson ◽  
Sara Ranjbar ◽  
Elizabeth Randall ◽  
Michael Regan ◽  
Walid Abdelmoula ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Drug Distribution ◽  
Tumor Extent

scholarly journals A Mathematical Model of anIn VitroExperiment to Investigate Endothelial Cell Migration

2002 ◽  
Vol 4 (4) ◽  
pp. 251-270 ◽  
Author(s):  
M. J. Plank ◽  
B. D. Sleeman ◽  
P. F. Jones
Keyword(s):  
Mathematical Model ◽  
Cell Migration ◽  
Endothelial Cell ◽  
Blood Vessels ◽  
Three Dimensional ◽  
Cell Movement ◽  
Quantitative Model ◽  
Angiogenic Factors ◽  
Endothelial Cell Migration ◽  
Angiogenic Factor

Angiogenesis, the growth of new blood vessels from existing ones, is an important, yet not fully understood, process and is involved in diseases such as rheumatoid arthritis, diabetic retinopathy and solid tumour growth. Central to the process of angiogenesis are endothelial cells (EC), which line all blood vessels, and are capable of forming new capillaries by migration, proliferation and lumen formation. We construct a cell-based mathematical model of an experiment (Vernon, R.B. and Sage, E.H. (1999) “A novel, quantitative model for study of endothelial cell migration and sprout formation within three-dimensional collagen matrices”,Microvasc. Res.57, 118–133) carried out to assess the response of EC to various diffusible angiogenic factors, which is a crucial part of angiogenesis. The model for cell movement is based on the theory of reinforced random walks and includes both chemotaxis and chemokinesis. Three-dimensional simulations are run and the results correlate well with the experimental data. The experiment cannot easily distinguish between chemotactic and chemokinetic effects of the angiogenic factors. We, therefore, also run two-dimensional simulations of a hypothetical experiment, with a point source of angiogenic factor. This enables directed (gradient-driven) EC migration to be investigated independently of undirected (diffusion-driven) migration.

scholarly journals INCREASING THE COMPETITIVENESS OF INSURANCE COMPANY PRODUCTS AND SERVICES USING ECONOMIC AND MATHEMATICAL MODELING METHODS

2021 ◽  
Author(s):  
Mykhailo Demydenko ◽  
Ihor Pistunov
Keyword(s):  
Mathematical Model ◽  
Social Activity ◽  
Insurance Companies ◽  
Comprehensive System ◽  
Insurance Company ◽  
Competitive Advantages ◽  
Insurance Policy ◽  
Insurance Policies ◽  
The Impact

The competitiveness of an insurance company depends on the competitiveness of the products and services it introduces in the market. The competitive advantages of the insurance company are expressed in the attractiveness and competitiveness of insurance policies. An economic and mathematical model of increasing the competitiveness of the insurance company is proposed, which allows to calculate the integrated indicator of competitiveness of the insurance policy based on a comprehensive system of indicators characterizing the reliability of the insurance company, quality of its services, competitiveness, social activity. To analyze the impact of these indicators on the competitiveness of the insurance policy and identify areas for improving the efficiency and competitiveness of the insurance company. The competitiveness of an insurance company depends on the competitiveness of the products and services it introduces in the market. The assessment of the quality of insurance company services is compliance with the needs, requirements, and insurance interests of customers. This assessment is performed each time an individual client chooses to cooperate with an insurance company that meets his insurance interests and wishes. Therefore, the overall competitiveness of the enterprise depends on the competitiveness of products and services offered on the market. The competitive advantages of the insurance company are expressed in the attractiveness and competitiveness of insurance policies. The insurance market in recent years has shown consistently high growth, which makes it attractive for doing business. In these conditions, the task of modeling the activities of the insurance company in a highly competitive market environment becomes relevant. A mathematical model of increasing the competitiveness of the insurance company is proposed, which allows to calculate the integrated indicator of competitiveness of the insurance policy based on a comprehensive system of indicators characterizing the reliability of the insurance company, quality of its services, competitiveness, social activity. With the proposed model, insurance companies can objectively assess their weaknesses and strengths to ensure continuous growth and decent competition in a competitive market environment. The model allows you to select performance indicators and perform modeling and determine the consequences of changes in this indicator, analyze the impact of these indicators on the competitiveness of insurance policies and identify areas for improving the efficiency and competitiveness of the insurance company. By conducting such experiments, insurance companies can make more informed choices and decisions, analyze areas of competitiveness, and more efficiently allocate resources.

scholarly journals ANALISIS KONDISI RESERVOIR PANAS BUMI DENGAN MENGGUNAKAN DATA GEOKIMIA DAN MONITORING PRODUKSI SUMUR ELS-02 LAPANGAN ELSA

PETRO ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 194
Author(s):  
Nabilla Elsaphira Putri ◽  
Onnie Ridaliani ◽  
Widia Yanti
Keyword(s):  
Chloride Concentration ◽  
Reservoir Management ◽  
Calcium Sulphate ◽  
Geothermal Field ◽  
Carbonate Concentration ◽  
Enthalpy Changes ◽  
Geothermal Fluids ◽  
Time Problem ◽  
Concentration Changes

<p><em>A</em><em> good reservoir management is needed </em><em>to maintain</em><em> the </em><em>availability and </em><em>quality of geothermal production fluid. When producing geothermal fluids, there are some changes in reservoir parameters such as declining of reservoir pressure and temperature, chemical composition of geothermal fluids, </em><em>and </em><em>states of fluid that would affect the quality of reservoir by mixing, boiling, or cooling processes that may be happened </em><em>because of</em><em> those changes. </em><em>It is</em><em> becoming a concern on reservoir management. In this case, chemical </em><em>concentrations </em><em>of fluid</em><em>s</em><em> monitoring is one of methods that can perform to reach a well reservoir management of geothermal field. With </em><em>chemical </em><em>monitoring process, current reservoir condition and processes </em><em>that </em><em>occurred during exploitation can be defined</em><em>. In ELS-02 by monitoring and analyzing its enthalpy changes, chloride concentration changes, and NCG concentration changes and supported by its calcium, sulphate, and carbonate concentration profile, two processes could be defined:</em><em> </em><em>mixing with </em><em>surface </em><em>cooler water and reinjection breakthrough.</em><em> </em><em>Other than that, casing leak that causing surface water enter the well could be detected.  </em><em>These become a sign to reservoir engineer to prepare for problems that may occur in near time </em><em>term </em><em>relating to well problem </em><em>such as scaling </em><em>and long time problem like massive cooling or drying of reservoir. After all, further development scenario of Elsa field can be made to improve its performance in producing fluids and heats. </em></p><p> </p>

scholarly journals The Applied model of grinding a spherical solid particle with a direct impact on a non-deformable flat surface

2020 ◽  
pp. 32-42
Author(s):  
G A Guryanov ◽  
B M Abdeev
Keyword(s):  
Mathematical Model ◽  
Flat Surface ◽  
Spherical Shape ◽  
Grinding Process ◽  
Direct Impact ◽  
Applied Model ◽  
Technical Theory ◽  
Force Contact ◽  
Breakage Mechanism

A grinding process using a free impact breakage mechanism is used in industries. In order to make calculations, predict grinding results, and evaluate mills functioning, it is necessary to assess the parameters of the grinding process and interrelations between the process parameters, mills parameters and materials properties, i.e. it is necessary to use an adequate mechanical-mathematical model of the process. However it is difficult to model due to some phenomena occurring in this process. Nowadays, various researchers have established the basis for the structure of the grinding process, but the application of the existing hypotheses and methods to evaluate the grinding process is quite difficult. This paper solves the problem of a spherical shape particle impacting an absolutely rigid half-space. It proposes a refined mechanical and mathematical model describing the process of destruction of the particle using the free direct impact breakage mechanism on an absolutely rigid, stationary, and flat surface. By using the Hertz-Staerman's classical analytical dependencies on the force contact interaction of the spherical bodies and the technical theory of the longitudinal waves’ propagation in the elastic continuous medium, we obtained a new refined solution of the applied dynamic problem related to a direct impact of a ball simulating a particle of a feeding material (an absolutely rigid surface simulating the working body of the mill) taking into account local physically linear deformations, the time parameter and radial particle size. The improved theoretical model of the spherical particle destruction was brought to applicable analytical calculations, tested and illustrated by a numerical example. It made it possible to describe the fracture of the material particles, predict the result and calculate the grinding process depending on its parameters providing the required quality of grinding by regulating and selecting characteristics, designing and selecting the grinding equipment, and modeling the grinding process using the free impact breakage mechanism.

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