抗血管生成治疗抑制实体肿瘤细胞生长的数值模拟:应用血管生成与肿瘤生长的耦合数学模型

为研究抗血管生成因子angiostatin和抗血管生成药物endostatin对肿瘤血管生成和肿瘤细胞的抑制作用,建立耦合肿瘤血管生长、肿瘤生长和血液灌注的数学模型．模拟结果显示抗血管生成因子angiostatin和抗血管生成药物endostatin可明显抑制血管生成和减少肿瘤细胞数量,从而起到改善肿瘤组织内部异常微环境的作用．模型可作为肿瘤抗血管生成治疗的一种理论研究．     

A coupled column generation,mixed integer approach to optimal planning of intensity modulated radiation therapy for cancer

Approximately 40% of all U.S. cancer cases are treated with radiation therapy. In Intensity-Modulated Radiation Therapy (IMRT) the treatment planning problem is to choose external beam angles and their corresponding intensity maps (showing how the intensity varies across a given beam) to maximize tumor dose subject to the tolerances of surrounding healthy tissues. Dose, like temperature, is a quantity defined at each point in the body, and the distribution of dose is determined by the choice of treatment parameters available to the planner. In addition to absolute dose limits in healthy tissues, some tissues have at least one dose-volume restriction that requires a fraction of its volume to not exceed a specified tighter threshold level for damage. There may also be a homogeneity limit for the tumor that restricts the allowed spread of dose across its volume. We formulate this planning problem as a mixed integer program over a coupled pair of column generation processes -- one designed to produce intensity maps, and a second specifying protected area choices for tissues under dose-volume restrictions. The combined procedure is shown to strike a balance between computing an approximately optimal solution and bounding its maximum possible suboptimality that we believe holds promise for implementations able to offer the power and flexibility of mixed-integer linear programming models on instances of practical scale.A portion of the work of Dr. Langer, Mr. Thai and Dr. Preciado-Walters was supported by National Science Foundation grant ECS-0120145 and National Cancer Institute 1R41CA91688-01. Dr. Rardin is participated while on rotation as Program Director for Operations Research and Service Enterprise Engineering at the National Science Foundation.     

Simulations of the electrostatic field,temperature, and tissue damage generated by multiple electrodes for electrochemical treatment

Integrated analysis of the spatial distributions of the electric potential, electric field, temperature, and tissue damage generated by multiple arrays of straight needle electrodes inserted into tumors is highly significant for improving the effectiveness of electrochemical treatment. In this study, we simulated the spatial profiles generated by multiple electrodes inserted individually into a tumor and multiple pairs of straight needle electrodes inserted in a tumor surrounded by healthy tissue. Poisson nonlinear and Laplace equations were used to calculate the electric potential in the tumor and the surrounding healthy tissue, respectively. The stationary bioheat transfer equation of Pennes was used to calculate the temperature in both tissues. The percentage tissue damage was computed in each biological medium for each electrode array shape. Numerical simulations showed that the non-homogeneous spatial distributions of the temperature (above 40°C) generated by different types of multiple pairs of straight needle electrodes covered the whole tumor volume. Spatial profiles of this physical magnitude were generated by multiple straight needle electrodes, which were individually inserted into the tumor and partially covered by its volume. In addition, the simulations showed that multiple pairs of electrodes led to tumor damage percentages above 80%. By contrast, multiple electrodes inserted individually in the tumor induced damage percentages below 25%. We conclude that multiple pairs of straight needle electrodes may be applied to deep-seated solid tumors in treatment with electrochemical therapy considering their theoretically calculated high tumor damage percentages.     

Optimal Control for a Mathematical Model of Glioma Treatment with Oncolytic Therapy and TNF-$$\alpha $$ Inhibitors

A mathematical model for combination therapy of glioma with oncolytic therapy and TNF-\(\alpha \) inhibitors is analyzed as an optimal control problem. In the objective, a weighted average between the tumor volume and the total amount of viruses given is minimized. It is shown that optimal controls representing the virus administration are generically of the bang-bang type, i.e., the virus should be applied at maximal allowed dose with possible rest periods. On the other hand, optimal controls representing the dosage of TNF-\(\alpha \) inhibitors follow a continuous regimen of concatenations between pieces that lie on the boundary and in the interior of the control set.     

Meso-Macro Modelling of Coated Forming Tools under Thermal Shock Conditions

In hybrid-forming processes workpieces are heated up before forming in order to reduce the forming forces. They are innovative methods for the production of components with graded properties, particularly with regard to tailored material properties and geometrical shape. During service life the forming tools are subjected to cyclic thermal shock loading conditions which can result into damage and failure. For improvement of the tool durability in the hybrid-forming process coated forming tools with multilayered coating systems are considered to be applied in future. This contribution shows the actual state of work for the development of a twoscale FE model for the simulation of the multilayered coated forming tool. Within this model the three-dimensional model of the forming tool builds the macromodel. On the macrolevel the multilayered coating is discretized with one element over the coating thickness. The mesomodel of the coating considers the actual layer design with metallic and ceramic layers. The macro-meso transition is realized with a Taylor-assumption. As the microscale is not considered in our model, the constitutive equations are formulated on the mesoscale. The meso-macro transition is done using volume averaging procedures. Furthermore, a damage model is included for particular layers. The scalar damage variable is used in a thermo-mechanical coupled model for simulation of a reduced heat transfer through a partially damaged layer. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A continuous approach to combinatorial optimization: application of water system pump operations

In this paper, we have suggested a penalty method to modify the combinatorial optimization problem with the linear constraints to a global optimization problem with linear constraints. It also deals with a topic of vital significance of pump operation optimization in a water system. In this connection we have done a lot of work to formulate a model based on a simplified flow volume balance to resolve the problem of optimal pump operation settings of switching “ON” and “OFF” with the reduced gradient method. This global solution approach incorporates some benefits for practical application to a real system as is shown in the case study.     

The nonrelativistic limit in radiation hydrodynamics: I. Weak entropy solutions for a model problem

This paper is concerned with a model system for radiation hydrodynamics in multiple space dimensions. The system depends singularly on the light speed c and consists of a scalar nonlinear balance law coupled via an integral-type source term to a family of radiation transport equations. We first show existence of entropy solutions to Cauchy problems of the model system in the framework of functions of bounded variation. This is done by using difference schemes and discrete ordinates. Then we establish strong convergence of the entropy solutions, indexed with c, as c goes to infinity. The limit function satisfies a scalar integro-differential equation.     

微波诱导生物热传导方程的最优控制问题

用一组方程式描述均匀平板状生物组织的热传导,分析其分布式的最优控制问题,研究该生物组织在肿瘤局部特殊点上达到所必需的温度,通过控制微波,使微波辐射的诱导作用,在手术进程的总时间内,该肿瘤点达到过高热．研究在手术过程不同时间点上生物组织温度与其长度间的依赖关系,使肿瘤达到期望的温度值．     

An adaptive solar radiation numerical model

A numerical model for the evaluation of solar radiation in different locations is presented. The solar radiation model is implemented taking into account the terrain surface using two-dimensional adaptive meshes of triangles that are constructed using a refinement/derefinement procedure in accordance with the variations of terrain surface and albedo. The selected methodology defines the terrain characteristics with a minimum number of points so that the computational cost is reduced for a given accuracy. The model can be used in atmospheric sciences as well as in other fields such as electrical engineering, since it allows the user to find the optimal location for maximum power generation in photovoltaic or solar thermal power plants. For this purpose, the effect of shadows is considered in each time step. The solar radiation is first computed for clear sky conditions considering the different components of the radiation. The real sky radiation is computed daily, starting from the results of clear sky radiation, in terms of the clear sky index. Maps for the clear sky index are obtained from a spatial interpolation of observational data that are available for each day at several points of the region under consideration. Finally, the solar radiation maps for a month are calculated from the daily results. The model can also be applied in solar radiation forecasting with the help of a forecasting meteorological model. This model takes into account the shadows cast, and allows the user to make a better estimation of the amount of solar power generation. Some numerical experiments related to the generation of solar radiation maps in Gran Canaria Island (Canary Islands, Spain) are presented.     

Existence and uniqueness of optimal solutions for multirate partial differential algebraic equations

The numerical simulation of electric circuits including multirate signals can be done by a model based on partial differential algebraic equations. In the case of frequency modulated signals, a local frequency function appears as a degree of freedom in the model. Thus the determination of a solution with a minimum amount of variation is feasible, which allows for resolving on relatively coarse grids. We prove the existence and uniqueness of the optimal solutions in the case of initial-boundary value problems as well as biperiodic boundary value problems. The minimisation problems are also investigated and interpreted in the context of optimal control. Furthermore, we construct a method of characteristics for the computation of optimal solutions in biperiodic problems. Numerical simulations of test examples are presented.     

A mathematical model for the effect of anti-angiogenic therapy in the treatment of cancer tumours by chemotherapy

A model consisting of a system of five ordinary differential equations to simulate the interactions between normal cells, cancer cells, endothelial cells, chemotherapy agent and anti-angiogenic agent in tumour growth is developed. By a partial analysis of the cancer-free subspace, it is shown how the anti-angiogenic agent may help the chemotherapy agent in controlling the cancer. This is illustrated by numerical examples and bifurcation diagrams.     

The Noise Prediction Model SATIN

This paper presents the noise prediction model SATIN (Statistical Approach to Turbulence Induced Noise) which is based on Lighthill's acoustic analogy. It allows to predict both, the far‐field noise radiation as well as near‐field wall‐pressure fluctuations. Far‐field noise radiation may result from the scattering of wall‐pressure fluctuations at geometrical discontinuities and is therefore important for many practical problems. Within this paper, we focus on the calculation of far‐field noise radiation. The required input values of SATIN are local properties of turbulence, namely the turbulent kinetic energy and the integral length scale which can be obtained by steady solutions of the Reynolds‐averaged Navier‐Stokes equations with a two equation turbulence model. It is assumed that the turbulence is axisymmetric and homogenous, which is taken into account by introducing two anisotropy parameters. The validation of SATIN is done for trailing‐edge noise originating from a thin flat plate using measurements of a phased array. As expected, the anisotropic formulation of SATIN improves the prediction quality considerably compared to isotropic turbulence.     

ECONOMICALLY OPTIMAL MARINE RESERVES WITHOUT SPATIAL HETEROGENEITY IN A SIMPLE TWO‐PATCH MODEL

Bioeconomic analyses of spatial fishery models have established that marine reserves can be economically optimal (i.e., maximize sustainable profit) when there is some type of spatial heterogeneity in the system. Analyses of spatially continuous models and models with more than two discrete patches have also demonstrated that marine reserves can be economically optimal even when the system is spatially homogeneous. In this note we analyze a spatially homogeneous two‐patch model and show that marine reserves can be economically optimal in this case as well. The model we study includes the possibility that fishing can damage habitat. In this model, marine reserves are necessary to maximize sustainable profit when dispersal between the patches is sufficiently high and habitat is especially vulnerable to damage.     

Two-dimensional cargo overbooking models

This paper introduces two-dimensional (weight and volume) overbooking problems arising mainly in the cargo revenue management, and compares them with one-dimensional problems. It considers capacity spoilage and cargo offloading costs, and minimizes their sum. For one-dimensional problems, it shows that the optimal overbooking limit does not change with the magnitude of the booking requests. In two-dimensional problems, the overbooking limit is replaced by a curve. The curve, along with the volume and weight axes, encircles the acceptance region. The booking requests are accepted if they fall within this region. We present Curve (Cab) and Rectangle (Rab) models. The boundary of the acceptance region in the Cab (resp. Rab) model is a curve (resp. rectangle). The optimal curve for the Cab model is shown to be unique and continuous. Moreover, it can be obtained by solving a series of simple equations. Finding the optimal rectangle for the Rab model is more challenging, so we propose an approximate rectangle. The approximate rectangle is a limiting solution in the sense that it converges to the optimal rectangle as the booking requests increase. The approximate rectangle is numerically shown to yield costs that are very close to the optimal costs.     

Long-Term Forecasts of Optimal Approximations to the Load Duration Curve

Little has been done by way of developing an objective technique for long-term forecasting of a utility load duration curve. This paper endeavours to rectify this situation by developing a methodology to provide forecasts of an economically optimal approximation to the load duration curve. A dynamic programming algorithm serves as the basis of the optimal approximations over a known horizon. These approximations are then forecast using time series analysis and an econometric model. The approach is implemented and the results are encouraging.     

An optimal control problem in cancer chemotherapy

We consider a mathematical model for the control of the growth of tumor cells which is formulated as a problem of optimal control theory. It is concerned with chemotherapeutic treatment of cancer and aims at the minimization of the size of the tumor at the end of a certain time interval of treatment with a limited amount of drugs. The treatment is controlled by the dosis of drugs that is administered per time unit for which also a limit is prescribed. It is shown that optimal controls are of bang-bang type and can be chosen at the upper limit, if the total amount of drugs is large enough.     

Fracture and Damage Analysis of Crimped Glass Fibre Truss Type Elements

The paper deals with the damage behaviour of special glass fibre reinforced plastic truss type elements, called Polystal profiles, which are widely used as load bearing cables. To connect these profiles with other structural elements steelmade hulls are crimped onto the profiles. The challenge is to detect the optimal crimping ratio (CR) to realize maximum longitudinal loads in restraint systems. By using scanning electron microscopy (SEM) several damage states like fibre pullout and matrix cracking could be observed. To describe the failure behaviour within the rod during crimping a 3D strain based fracture criterion was developed and implemented within the commercial finte element package Abaqus. The verification of this criterion is done by simulating the crimping process followed by tensile tests. The numerical results are compared with the experiments and with the results obtained by SEM. An outlook on further work to improve the failure prediction is given. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimal discrete long-term operation of nuclear-hydrothermal power systems

We discuss in this paper an algorithm for solving the optimal long-term operating problem of a hydrothermal-nuclear power system by application of the minimum norm optimization technique. The algorithm proposed here has the ability to deal with large-scale power systems and with equality and/or inequality constraints on the variables. A discrete model for the xenon and iodine concentrations is used, as well as a discrete model for hydro reservoirs. The optimization is done on a monthly time basis. For simplicity of the problem formulation, the transmission line losses are considered as a part of the load.This work supported by the Natural Sciences and Engineering Research Council of Canada, Grant No. A4146.     

Stochastic Policy Design in a Learning Environment with Rational Expectations

In this paper, we present a method for using rational expectations in a stochastic linear-quadratic optimization framework in which the unknown parameters are updated through a learning scheme. We use the QZ decomposition as suggested by Sims (Ref. 1) to solve the rational expectations part of the model. The parameter updating is done with the Kalman filter and the optimal control is calculated using the covariance matrix of the uncertain parameter.