Drug Diffusion in Optimizing Control and Its Numerical Method
|School||Changsha University of Science and Technology|
|Keywords||Effective diffusion coefficient Drug Releasing Gauss-Newton Method Diffusion coefficient Optimization algorithm|
Many practical problems in physics, medicine, chemical, biological process can be used to be describe by the diffusion equation. In order to prove that the drug effective ingredients of drugs and spread the bioavailability and efficacy of drug research, determine the appropriate inversion diffusion coefficient, this paper is done. Because it is difficult to obtain the diffusion coefficient of the drug diffusion problem, we shall propose the optimization control model in the different containers and the corresponding mathematical methods for inversing the simulation process.The structure of this paper is outlined as follows:The first chapter is an introduction, which describes the research background, the motivation of thesis as well as the research content, method and innovation.The second chapter proposes two optimization methods. One is to estimate the diffusion parameters in the cylinder transfer device model, the other is to estimate the effective time dependent diffusion coefficient parameter in the cylinder transfer device. Examples show that the proposed methods are valid.Aimed at two dimensional devices: the disc and spherical, some methods based on the separation variables idea and the least square method in the third chapter are given to compute the linear diffusion problems. We obtain the analytical solutions of the linear diffusion problem and some examples illustrate their convergence and validity.In the fourth chapter for the nonlinear diffusion problems in two dimensional releasing disc or spherical device, substituting the linear diffusion process for the nonlinear diffusion process, we obtain the semi-analytical solution of the nonlinear diffusion problem. The results also show the effectiveness of the proposed algorithm.In the fifth chapter we summarize the advantages and disadvantages of the methods for the linear diffusion problem and nonlinear diffusion problems of the drug releasing process. At last, some future work is listed.