A mathematical model and computer program for adriamycin distribution and elimination

A mathematical physiological flow model is described for the distribution and elimination of adriamycin in the rat. The model includes the volume or mass of, and blood flow to the following tissues: heart, plasma, muscle, skin, kidney, bone marrow, gut, liver and bile. A compartment is also included for tight or almost irreversible binding which occurs with this drug. The program was written in FORTRAN to compute the concentration of drug in each tissue as a function of time after bolus injection or short term infusion. The computed data is printed on a line printer and recorded on disk for use in a SAS program GPLOT to obtain precision plots.     

Modeling the steady-state behavior of the Ca2+ -Mg2+ -ATPase pump of sarcoplasmic reticulum

A FORTRAN computer program capable of calculating the steady-state behavior of the Ca2+ -Mg2+-ATPase pump of skeletal sarcoplasmic reticulum under all conditions of reactant and product concentrations is described. The model describes the behavior of the enzyme in terms of occupation of three binding sites: (a) a translocator site which can bind Ca2+, K+, H+, or Mg2+, (b) an ATP/ADP binding site, and (c) a phosphorylation and phosphate binding site. The translocator site can move across the membrane in the Ca2+-laden and K+ + H+-laden form, thereby accomplishing Ca2+ for K+ + H+ countertransport. The rate constants for ion binding and the translocation reactions vary as a function of translocator orientation, ATP and ADP occupancy, phosphorylation, and phosphate binding. Rate constants for the binding and the reactant and product concentrations and association reactions and other transformations between states of the enzyme are entered and the computer program solves for the steady-state concentrations of all states of the enzyme and for the turnover number of the enzyme. The program contains a matrix of differential equations for creation and destruction of all states of the enzyme using the steady-state assumption together with the rule of conservation of the total enzyme. The matrix of equations and states is solved by Gaussian elimination. The program presents the distribution of enzyme states in histogram fashion and is capable of presenting the concentration of a particular state or the rate of turnover as a function of any of the reactant or product concentrations. Three demonstrations of the utility of the program and predictive power of the model are given.     

Could MM-GBSA be accurate enough for calculation of absolute protein/ligand binding free energies?

Implicit solvation methods such as MM-GBSA, when applied to evaluating protein/ligand binding free energies, are widely believed to be accurate only for the estimation of relative binding free energies for a congeneric series of ligands. In this work, we show that the MM-GBSA flavor of Prime 3.0, VSGB-2.0, with a variable dielectric model and a novel energy function, could be approaching the accuracy required for evaluating absolute binding free energies, albeit, through a linear regression fit. The data-set used for validation includes 106 protein–ligand complexes that were carefully selected to control for variability in the affinity data as well as error in the modeled complexes. Through systematic analysis, we also quantify the degradation in the R² of fit between experimental and calculated values with either greater variability in the affinity data or an increase in error in the modeled protein/ligand complexes. Limitations for its application in drug discovery are discussed along with the identification of areas for future development.     

Maxsim2—Real-time interactive simulations for computer-assisted teaching of pharmacokinetics and pharmacodynamics

We developed a computer program for use in undergraduate and graduate courses in pharmacology, pharmacokinetics and pharmacodynamics. This program can also be used in environmental and toxicological studies and preclinical simulation, to facilitate communication between modeling pharmacokineticists and project leaders or other decision-makers in the pharmaceutical industry. The program simulates the drug delivery and transport by means of (I) a six-compartment physiological pharmacokinetic flow model, (II) a system of traditional compartment models, or (III) a target-mediated drug disposition system. The program also can be used to simulate instantaneous equilibria between concentration and pharmacodynamic response, or as temporal delays between concentration and response. The latter is done by means of turnover models (indirect response models). Drug absorption, distribution, and elimination are represented by differential equations, which are described by organ and tissue volumes or other volumes of distribution, blood flows, clearance terms, and tissue-to-blood partition coefficients. The user can control and adjust these parameters by means of a slider in real time. By interactively changing the parameter values and simultaneously displaying the resulting concentration–time and/or response–time profiles, users can understand the major mechanisms that govern the disposition or the pharmacological response of the drug in the organism in real time. Schedule dependence is typically seen in clinical practice with a non-linear concentration–response relationship, and is difficult to communicate except via simulations. Here, we sought to illustrate the potential advantages of this approach in teaching pharmacology, pharmacokinetics, and pharmacodynamics to undergraduate pharmacy-, veterinary-, and medical students or to project teams in drug discovery/development.     

Computer simulation of oral fluoride clearance

The presence of fluoride in saliva and dental plaque is important for prevention of dental caries. The elimination of fluoride from the oral cavity after introduction of a fluoride containing agent is a complicated physiological process. This process was simulated with a Pascal program running under MS-DOS on IBM-compatible microcomputers. The program calculated the fluoride concentration in saliva as a function of time from several input parameters, the most important being the amount of fluoride, salivary stimulation due to the fluoride vehicle, resting salivary flow rate and volume factors. Furthermore, factors such as excretion of fluoride in the saliva following fluoride absorption in the intestinal tract were modeled. The fluoride concentration in dental plaque due to diffusion was also calculated. Output was directed to files which could be processed by a graphics interface. The results of the computations were very similar to findings in vivo.     

The C information abstraction system

A system for analyzing program structures is described. The system extracts relational information from C programs according to a conceptual model and stores the information in a database. It is shown how several interesting software tasks can be performed by using the relational views. These tasks include generation of graphical views, subsystem extraction, program layering, dead code elimination and binding analysis     

On the identification of verbs in computer programs of physiological models

The rationale for identifying verbs (actions modeled) in the source code of a mathematical model is presented, with algorithms leading to computational techniques for devising explanations of such models. Using flow graph methodology the source code of a program can be described as disjoint intervals of its directed acyclic graph. Intervals of this set containing complete loops represent the code structure conceptually equivalent to verbs modeled. In turn, such structures can be mapped uniquely as functional dependencies of the intensional form of a relational data base which is the model output. Simulation, then, can be viewed as retrieval, and the logical inferences of a model appear to be derivable via relational algebra of the data base. In these terms, a verb is a relation consisting of at least one variable defined in an interval. The relation's key attributes must include at least one variable, also defined in the interval. Verb definitions are essential if programs are to explain themselves.     

Decision procedures for term algebras with integer constraints

Term algebras can model recursive data structures which are widely used in programming languages. To verify programs we must be able to reason about these structures. However, as programming languages often involve multiple data domains, in program verification decision procedures for a single theory are usually not applicable. An important class of mixed constraints consists of combinations of data structures with integer constraints on the size of data structures. Such constraints can express memory safety properties such as absence of memory overflow and out-of-bound array access, which are crucial for program correctness. In this paper we extend the theory of term algebras with the length function which maps a term to its size, resulting in a combined theory of term algebras and Presburger arithmetic. This arithmetic extension provides a natural but tight coupling between the two theories, and hence the general purpose combination methods like Nelson-Oppen combination are not applicable. We present decision procedures for quantifier-free theories in structures with an infinite constant domain and with a finite constant domain. We also present a quantifier elimination procedure for the extended first-order theory that can remove a block of existential quantifiers in one step.     

Scalability and locality of extrapolation methods on large parallel systems

Time‐dependent processes can often be modeled by systems of ordinary differential equations (ODEs). Solving such a system for a detailed model can be highly computationally intensive. We investigate explicit extrapolation methods for solving such systems efficiently on current highly parallel supercomputer systems with shared‐or distributed‐memory architecture. We analyze and compare the scalability of several parallelization variants, some of them using multiple levels of parallelization. For a large class of ODE systems, data access costs are reduced considerably by exploiting the special structure of the ODE system. Furthermore, by employing a pipeline‐like loop structure, the locality of memory references is increased for such systems resulting in a better utilization of the cache hierarchy. Runtime experiments show that the optimized implementations can deliver a high scalability. Copyright © 2011 John Wiley & Sons, Ltd.     

基于系统调用属性的程序行为监控

程序的行为轨迹常采用基于系统调用的程序行为自动机来表示.针对传统的程序行为自动机中控制流和数据流描述的程序行为轨迹准确性较低、获取系统调用上下文时间开销大、无法监控程序运行时相邻系统调用间的程序执行轨迹等问题,提出了基于系统调用属性的程序行为自动机.引入了多个系统调用属性,综合系统调用各属性的偏离程度,对系统调用序列描述的程序行为轨迹进行更准确地监控;提出了基于上下文的系统调用参数策略,检测针对系统调用控制流及数据流的行为轨迹偏离;提出了系统调用时间间距属性,使得通过系统调用及其参数无法监控的相邻系统调用间的程序行为轨迹在一定程度上得到了监控.实验表明基于系统调用属性的程序行为自动机能够更准确地刻画程序行为轨迹,较传统模型有更强的行为偏离检测能力.     

Application of a pharmacokinetic simulation program in pharmacy courses

A model which illustrates aspects of drug absorption, distribution and elimination in the body has been developed at McMaster University and St Bartholomew's Hospital Medical College over the past eight years. It is a multi-compartment model in which drug concentrations are determined by the solution of a system of non-linear differential equations with physiological and biochemical data defining the patient and drugs. The model has been used in course work for final year B.Pharm. students for examining plasma levels and distributions of several drugs following simple and multiple doses by various routes. Third year students carried out investigations using their prior knowledge of dosing regimens and pharmaco-kinetics to design suitable dosage schemes to maintain effective levels of nortryptiline, propranolol, high dose aspirin and kanamycin. In pharmacy courses, posology is taught traditionally as a series of doses to be learnt by rote, while pharmacokinetics course work consists of the interpretation of computer generated data. The model has been found to offer a more interesting and dynamic teaching method for both these subjects.     

Enhancement of the immune system in HIV dynamics by output feedback

The human immunodeficiency virus infection, that causes acquired immune deficiency syndrome, is a dynamic process that can be modeled via differential equations. In this paper we introduce an output feedback method designed for antiretroviral drug therapy to control the immune response. The purpose of the method is to steer the system to an equilibrium condition, the long-term nonprogressor, which corresponds to an infected patient who does not develop the symptoms of acquired immune deficiency syndrome. The suggested control idea guarantees that the immune state is enhanced to a certain level, which is enough for a typical patient to be driven into the long-term nonprogressor status.     

Human Age Estimation With Regression on Discriminative Aging Manifold

Recently, extensive studies on human faces in the human-computer interaction (HCI) field reveal significant potentials for designing automatic age estimation systems via face image analysis. The success of such research may bring in many innovative HCI tools used for the applications of human-centered multimedia communication. Due to the temporal property of age progression, face images with aging features may display some sequential patterns with low-dimensional distributions. In this paper, we demonstrate that such aging patterns can be effectively extracted from a discriminant subspace learning algorithm and visualized as distinct manifold structures. Through the manifold method of analysis on face images, the dimensionality redundancy of the original image space can be significantly reduced with subspace learning. A multiple linear regression procedure, especially with a quadratic model function, can be facilitated by the low dimensionality to represent the manifold space embodying the discriminative property. Such a processing has been evaluated by extensive simulations and compared with the state-of-the-art methods. Experimental results on a large size aging database demonstrate the effectiveness and robustness of our proposed framework.     

Activation of Immune Response in Disease Dynamics via Controlled Drug Scheduling

The human immunodeficiency virus (HIV) infection, that causes acquired immune deficiency syndrome (AIDS), is a dynamic process that can be modeled via differential equations. The primary goal of this paper is to introduce a control philosophy to boost the response of the immune system by means of drug scheduling. The control purpose is to steer the system to an equilibrium condition known as long-term nonprogressor, which corresponds to an infected patient that does not develop the symptoms of AIDS. The feasibility of the control methodology is illustrated via simulations on two HIV dynamic models and on a general disease model.     

基于多模型的非线性系统自适应最小方差控制

对于一类典型的离散时间非线性系统, 提出了一种基于多模型的自适应最小方差控制方法. 通过在平衡点附近建立线性模型, 用径向基函数神经元网络来补偿建模误差和未建模动态, 形成了非线性系统的多模型表示. 采用了具有积分性质的切换指标函数作为切换法则和最小方差的控制方法构成了多模型自适应控制器. 仿真实验的结果表明了这种方法的有效性.     

在线性模型中确定化学实验参数

物理化学的因变量与函数式中各待定参数之间若是线性关系,此时必须求解线性方程组。以Visual Basic 6.0为开发工具,采用高斯主元素消去法拟合待定系数,以丙酮碘化反应的速率方程为例,阐述利用VB编程求解线性模型的方法,从而得到准确、科学的实验结果。     

A location–inventory supply chain problem: Reformulation and piecewise linearization

In this paper, we study a two-echelon inventory management problem with multiple warehouses and retailers. The problem is a natural extension to the well-known one-warehouse multi-retailer inventory problem. The problem is formulated as a mixed integer non-linear program such that its continuous relaxation is non-convex. We propose an equivalent formulation with fewer non-linear terms in the objective function so that the continuous relaxation of the new model is a convex optimization problem. We use piecewise linearization to transform the resulting MINLP to a mixed integer program and we solve it using CPLEX. Through numerical experiments, we compare the solutions obtained by solving the new formulation using CPLEX with two previously published Lagrangian relaxation based heuristics to solve the original mixed integer non-linear program. We demonstrate that the new approach is capable of providing almost the same solutions without the need of using specialized algorithms. This important contribution further implies that additional variants of the problem, such as multiple products, capacitated warehouses and routing, can be added to result in a problem that will again be solvable by commercial optimization software, while the respective Lagrangian heuristics will fail to solve such variants or extended problems.     

Kinetic modelling of the role of the aldehyde dehydrogenase enzyme and the breast cancer resistance protein in drug resistance and transport

A compartmental model for the in vitro uptake kinetics of the anti-cancer agent topotecan (TPT) has been extended from a previously published model. The extended model describes the drug activity and delivery of the pharmacologically active form to the DNA target as well as the catalysis of the aldehyde dehydrogenase (ALDH) enzyme and the elimination of drug from the cytoplasm via the efflux pump. Verification of the proposed model is achieved using scanning-laser microscopy data from live human breast cancer cells. Before estimating the unknown model parameters from the experimental in vitro data it is essential to determine parameter uniqueness (or otherwise) from this imposed output structure. This is formally performed as a structural identifiability analysis, which demonstrates that all of the unknown model parameters are uniquely determined by the output structure corresponding to the experiment.     

Use-definition chains with applications

Methods of compile-time program analysis for automatic code optimization usually include control flow analysis, in which possible execution flow paths are modeled, and data flow analysis, in which data relatiohsips are modeled. One representation of data relations in a program, via use-definition chains, is examined in the light of a particular example problem—the global elimination of “useless” computation. Two elimination algorithms which use differently organized use-definition chains are presented and compared for space complexity on two pathologically different families of flow graphs. Algorithms to compute chains of both varieties are also developed.     

A mathematical theory of the value of information

An algorithm is given for finding where the variables of a program are active or live. While the algorithm is modeled after that of Kennedy, it is based on the flow graph straightening procedure of Earnest, Balke, and Anderson, rather than on Cocke-Allen intervals. Thus it can be applied to any program, without appeal to any additional mechanism such as node splitting.