Pharmacokinetics local model and its application in nuclear medicine

Ｐｈａｒｍａｃｏｋｉｎｅｔｉｃｓｌｏｃａｌｍｏｄｅｌａｎｄｉｔｓａｐｐｌｉｃａｔｉｏｎｉｎ ｎｕｃｌｅａｒｍｅｄｉｃｉｎｅＣａｏＧｕｏ－Ｘｉａｎ（曹国宪）；ＬｉＷｅｉ－Ｙｉ（李卫一）ａｎｄＹｕＨｕｉ－Ｘｉｎ（俞惠新）（ＪｉａｎｇｓｕＩｎｓｔｉｔｕｔｅ...

Solution of rate constants in pharmacokinetics local model of nuclear medicine

１ＩｎｔｒｏｄｕｃｔｉｏｎＩｔｉｓｏｂｖｉｏｕｓｔｈａｔｎｏｒｍａｌｐｈａｒｍａｃｏｋｉｎｅｔｉｃｓｍｏｄｅｌ，ｓｕｃｈａｓｔｈｅｃｏｍｐａｒｔｍｅｎｔｍｏｄｅｌ，ｃａｎｏｎｌｙｄｅｓｃｒｉｂｅｐｈａｒｍａｃｅｕｔｉｃａｌｓ’ｐｈａｒｍａｃｏｋｉｎｅ...

Application of pharmacokinetics local model to evaluaterenal function

The pharmacokinetics local model was used to evaluate renal function. Some typical kinds of renal function cases, normal or disorder, were selected to be imaged with SPECT and those data measured were treated by the pharmacokinetics local model computer program (PLM). The results indicated that parameters, including peak value, peak time, inflexion time, half-excretion time, and kinetic equation played and important role in judging renal function. The fact confirms that local model is very useful in evaluating renal function.

Mathematical Model for Electroslag Remelting Process

A mathematical model, including electromagnetic field equation, fluid flow equation, and temperature field equation, was established for the simulation of the electroslag remelting process. The distribution of temperature field was obtained by solving this model. The relationship between the local solidification time and the interdendritic spacing during the ingot solidification process was established, which has been regarded as a criterion for the evaluation of the quality of crystallization. For a crucible of 950 mm in diameter, the local solidification time is more than 1 h at the center of the ingot with the longest interdendritic spacing, whereas it is the shortest at the edge of the ingot according to the calculated results. The model can be used to understand the ESR process and to predict the ingot quality.

A Quadratic Programming Model for Blast Scheduling

A quadratic programming model is established to choose the blocks to be blasted in a given period. The length of this period depends on the production planning requirements. During the given period, the blocks' parameters are available from the geological database of the mine. The objective is to minimize the deviation of the average ore grade of blasted blocks from the standard ore grade required by the mill. Transportation ability constraint. production quantity demand constraint. minimum safety bench constraint. block size constraint and block, bench precedence constraints are considered in forming the programming model. This model has more practical objective function and reasonable constraints compared with the existing model for this kind of problems.

Mathematical Models for a Social Partitioning Problem

In this paper we develop modeling techniques for a social partitioning problem. Different social interaction regulations are imposed during pandemics to prevent the spread of diseases. We suggest partitioning a set of company employees as an effective way to curb the spread, and use integer programming techniques to model it. The goal of the model is to maximize the number of direct interactions between employees who are essential for company’s work subject to the constraint that all employees should be partitioned into components of no more than a certain size implied by the regulations. Then we further develop the basic model to take into account different restrictions and provisions. We also give heuristics for solving the problem. Our computational results include sensitivity analysis on some of the models and analysis of the heuristic performance.

Mathematical Modeling of a Metabolic Network to Study the Impact of Food Contaminants on Genomic Methylation and DNA Instability

Environmental contamination of food is a worldwide public health problem. Folate mediated one- carbon metabolism plays an important role in epigenetic regulation of gene expression and mutagenesis. Many contaminants in food cause cancer through epigenetic mechanisms and/or DNA instability i.e. default methylation of uracil to thymine, subsequent to the decrease of 5-methylte- trahydrofolate (5 mTHF) pool in the one-carbon metabolism network. Evaluating consequences of an exposure to food contaminants based on systems biology approaches is a promising alternative field of investigation. This report presents a dynamic mathematical modeling for the study of the alteration in the one-carbon metabolism network by environmental factors. It provides a model for predicting “the impact of arbitrary contaminants that can induce the 5 mTHF deficiency. The model allows for a given experimental condition, the analysis of DNA methylation activity and dumping methylation in the de novo pathway of DNA synthesis.

Application of Mathematical Models in the Research of Chinese Herbal Compound Prescriptions

With the interdisciplinary development of multiple disciplines,mathematical models play a role as a bridge in the research process of Chinese herbal compounds,which can make full use of the interrelationships of knowledge,making the research and use of Chinese herbal compounds from complex and cumbersome to simple.This paper reviewed the research and application of mathematical models in the production and preparation,pharmacodynamics,pharmacokinetics and other aspects of Chinese herbal compound prescriptions,providing a theoretical basis for the development of the modern Chinese medicine industry.

Predictive Mathematical and Statistical Modeling of the Dynamic Poverty Problem in Burundi: Case of an Innovative Economic Optimization System

The mathematical and statistical modeling of the problem of poverty is a major challenge given Burundi’s economic development. Innovative economic optimization systems are widely needed to face the problem of the dynamic of the poverty in Burundi. The Burundian economy shows an inflation rate of -1.5% in 2018 for the Gross Domestic Product growth real rate of 2.8% in 2016. In this research, the aim is to find a model that contributes to solving the problem of poverty in Burundi. The results of this research fill the knowledge gap in the modeling and optimization of the Burundian economic system. The aim of this model is to solve an optimization problem combining the variables of production, consumption, budget, human resources and available raw materials. Scientific modeling and optimal solving of the poverty problem show the tools for measuring poverty rate and determining various countries’ poverty levels when considering advanced knowledge. In addition, investigating the aspects of poverty will properly orient development aid to developing countries and thus, achieve their objectives of growth and the fight against poverty. This paper provides a new and innovative framework for global scientific research regarding the multiple facets of this problem. An estimate of the poverty rate allows good progress with the theory and optimization methods in measuring the poverty rate and achieving sustainable development goals. By comparing the annual food production and the required annual consumption, there is an imbalance between different types of food. Proteins, minerals and vitamins produced in Burundi are sufficient when considering their consumption as required by the entire Burundian population. This positive contribution for the latter comes from the fact that some cows, goats, fishes, ···, slaughtered in Burundi come from neighboring countries. Real production remains in deficit. The lipids, acids, calcium, fibers and carbohydrates produced in Burundi are insufficient for consumption. This negative contribution proves a Burundian food deficit. It is a decision-making indicator for the design and updating of agricultural policy and implementation programs as well as projects. Investment and economic growth are only possible when food security is mastered. The capital allocated to food investment must be revised upwards. Demographic control is also a relevant indicator to push forward Burundi among the emerging countries in 2040. Meanwhile, better understanding of the determinants of poverty by taking cultural and organizational aspects into account guides managers for poverty reduction projects and programs.

A Multiple Model Approach to Modeling Based on LPF Algorithm

Input-output data fitting methods are often used for unknown-structure nonlinear system modeling. Based on model-on-demand tactics, a multiple model approach to modeling for nonlinear systems is presented. The basic idea is to find out, from vast historical system input-output data sets, some data sets matching with the current working point, then to develop a local model using Local Polynomial Fitting (LPF) algorithm. With the change of working points, multiple local models are built, which realize the exact modeling for the global system. By comparing to other methods, the simulation results show good performance for its simple, effective and reliable estimation.

Optimization model of truck flow at open-pit mines and standards for feasibility test

In order to increase production efficiency at open-pit mines, on the basis oflinear programming, a practical mathematical model for optimizing truck flow was developed, whichimproved the traditional fixed manual schedule method. The model has advantages from linearprogramming and objective programming, makes most handling points working at full capacity and keepsan optimized ratio between trucks and excavators. For ensuring feasibility of the model inpractical production, four standards for feasibility test were proposed. The model satisfied all thestandards. The application in a large scale open-pit iron mine indicated that the model reduced thenumber of required trucks by 10 percent compared with the fixed manual schedule method.

Mechanism Based Pharmacokinetic Pharmacodynamic Modeling of Vildagliptin as an Add-on to Metformin for Subjects with Type 2 Diabetes

Various drugs are used to maintain normoglycemia in subjects with type 2 diabetes mellitus.The combination of the drugs from different classes in one single tablet may enhance the effectiveness of the anti-diabetic drugs.To investigate the impact of combining drugs on the glucose regulation of subjects with type 2 diabetes,we propose a pharmacokinetic/pharmacodynamics(PK/PD)mathematical modeling approach for a combination of metformin and vildagliptin drugs.In the proposed modeling approach,two separate PK models representing oral administration of metformin and vildagliptin for diabetic subjects are interconnected to a PD model comprising a detailed compartmental physiological model representing the regulatory effect of insulin,incretins and glucagon hormones on glucose concentration in a human body.The impact of doses of individual drugs and their combination on the blood glucose concentration of a group of type 2 diabetic subjects is investigated.It is indicated that while administration of individual drugs reduces the blood glucose levels,since they have separate mechanisms of action,combining them synergizes lowering the blood glucose levels.

Train Students to Solve the Practical Problem by Building Mathematics Models

It focuses on that students must be developed the ability to solve the practical problem by building the mathematics models and the ability to combine the theory with the practice. It also states that students must be improved the learning interests and practical experience.

Model Study of Senior Executive Salary of Enterprises

Currently,there is a lot of discussion concerning about the salary problem of the senior managers of a business enterprise. How to determine the wage levels has already been the problem which should be urgently worked out. The establishment of the wage levels' standard should not only can attract and retain core talent,but also be able to be accepted by public thinking. Based on the considerations above,a reasonable pay system should be set up scientifically. In this paper,a point of view of the mathematical modeling has been taken in reasonable analysis of enterprises' pay system for a rational decision about the salary-level of the senior executives who according to the economic developing regulation should be made. The model founded in this paper reflects the reasonable distribution of the annual salary. On the other hand,individual contribution degree fully explains the rationality of the model.

A Review of Water Quality Optimisation Models and Techniques

This paper presents a state of the art review of water quality optimisation models and techniques from early 1970s to date in terms of the model/technique category, model/technique type, purpose and application. The models are categorised into Mathematical Programming Models and Meta-heuristic Programming Models. Similarly, the techniques are categorised into Mathematical Programming Techniques and Meta-heuristic Programming Techniques. The review is concluded by drawing attention to the rare nature of application of interior-point methods to water quality optimisation.

Estimation of CARA Preferences and Positive Mathematical Programming

The purpose of this paper is to combine the estimation of output price risk and positive mathematical programming (PMP). It reconciles the risk programming presented by Freund with a consistent estimate of the constant absolute risk aversion (CARA) coefficient. It extends the PMP approach to calibration of realized production outputs and observed input prices. The results of this specification include 1) uniqueness of the calibrating solution, 2) elimination of the tautological calibration constraints typical of the original PMP procedure, 3) equivalence between a phase I calibrating solution and a solution obtained by combining phase I and phase II of the traditional PMP procedure. In this extended PMP framework, the cost function specification involves output quantities and input prices—contrary to the myopic cost function of the traditional PMP approach. This extension allows for a phase III calibrating model that replaces the usual linear technology with relations corresponding to Shephard lemma (in the primal constraints) and the marginal cost function (in the dual constraints). An empirical example with a sample of farms producing four crops illustrates the novel procedure.

Rapid Prototype Development Approach for Genetic Programming

Genetic Programming (GP) is an important approach to deal with complex problem analysis and modeling, and has been applied in a wide range of areas. The development of GP involves various aspects, including design of genetic operators, evolutionary controls and implementations of heuristic strategy, evaluations and other mechanisms. When designing genetic operators, it is necessary to consider the possible limitations of encoding methods of individuals. And when selecting evolutionary control strategies, it is also necessary to balance search efficiency and diversity based on representation characteristics as well as the problem itself. More importantly, all of these matters, among others, have to be implemented through tedious coding work. Therefore, GP development is both complex and time-consuming. To overcome some of these difficulties that hinder the enhancement of GP development efficiency, we explore the feasibility of mutual assistance among GP variants, and then propose a rapid GP prototyping development method based on πGrammatical Evolution (πGE). It is demonstrated through regression analysis experiments that not only is this method beneficial for the GP developers to get rid of some tedious implementations, but also enables them to concentrate on the essence of the referred problem, such as individual representation, decoding means and evaluation. Additionally, it provides new insights into the roles of individual delineations in phenotypes and semantic research of individuals.

Strain localization of Mohr-Coulomb soils with non-associated plasticity based on micropolar continuum theory

To address the problems of strain localization, the exact Mohr-Coulomb (MC) model is used based on second-order cone programming (mpcFEM-SOCP) in the framework of micropolar continuum finite element method. Using the uniaxial compression test, we focused on the earth pressure problem of rigid wall segment involving non-associated plasticity. The numerical results reveal that when mpcFEM-SOCP is applied, the problems of mesh dependency can be effectively addressed. For geotechnical strain localization analysis involving non-associated MC plasticity, mpcFEM-SOCP in conjunction with the pseudo-time discrete scheme can improve the numerical stability and avoid the unreasonable softening issue in the pressure-displacement curves, which may be encountered in the conventional FEM. It also shows that the pressure-displacement responses calculated by mpcFEM-SOCP with the pseudo-time discrete scheme are higher than those calculated by mpcFEM-SOCP with the Davis scheme. The inclination angle of shear band predicted by mpcFEM-SOCP with the pseudo-time discrete scheme agrees well with the theoretical solution of non-associated MC plasticity.

GURTIN-TYPE VARIATIONAL PRINCIPLES FOR DYNAMICS OF A NON-LOCAL THERMAL EQUILIBRIUM SATURATED POROUS MEDIUM

Based on the porous media theory and by taking into account the efects of the pore fuid viscidity, energy exchanges due to the additional thermal conduction and convection between solid and fuid phases, a mathematical model for the dynamic-thermo-hydro-mechanical coupling of a non-local thermal equilibrium fuid-saturated porous medium, in which the two constituents are assumed to be incompressible and immiscible, is established under the assumption of small de- formation of the solid phase, small velocity of the fuid phase and small temperature changes of the two constituents. The mathematical model of a local thermal equilibrium fuid-saturated porous medium can be obtained directly from the above one. Several Gurtin-type variational principles, especially Hu-Washizu type variational principles, for the initial boundary value problems of dy- namic and quasi-static responses are presented. It should be pointed out that these variational principles can be degenerated easily into the case of isothermal incompressible fuid-saturated elastic porous media, which have been discussed previously.

A MATHEMATICAL MODEL OF PHARMACOKINETICS FOR INTRAMUSCULAR INJECTION

A new mathematical model of pharmacokinetics was presented for intramuscular injection. In view of the effect of initial pressure which is formed with the injection of the concentration of drug, we obtained an analytical solution of concentration distribution of drug as a function of time and position.