Документ взят из кэша поисковой машины. Адрес оригинального документа : http://www.mce.biophys.msu.ru/archive/doc150378/eng.pdf Дата изменения: Thu Feb 28 22:38:02 2013 Дата индексирования: Thu Feb 28 22:38:02 2013 Кодировка:

OPTIMIZATION WITH PENNES' BIOHEAT EQUATION AS CONSTRAINT Malek A., Abbasi GH.
1

Department of Applied Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, P.O. Box 14115-134, Iran, +98(21)82883445, E-mail: mala@modares.ac.ir 1 Department of Applied Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, P.O. Box 14115-134, Iran, +98(21)82883445, g.abbasi@modares.ac.ir

In this paper, an energy optimization problem with Pennes' bioheat equation as a constraint is solved numerically. The solution of optimal control problem for the Pennes ' bioheat equation involving boundary function of continuous time variable in its energy function is proposed. A specific direct approach based on Control parameterization method is suggested to solve optimal boundary control for Pennes' bioheat equation. Using space discretization one obtains an ODE which is then solved by using fourth-order Runge-Kutta formula. Now we deal with a linear system of algebraic equations based on , = 1, ... , , the unknown parameters of control function, in which they are considered as constraints in the optimization problem. This optimization problem has nonlinear objective function with linear constraints that is solved by Rosen's gradient projection technique. Calculation of the optimal values for parameters yields to the optimal control for the unknown boundary function. Numerical results for this process of optimization with PDE (Pennes' Eq.) constraints are presented. References
1. 2. 3. Malek, A., Momeni-Masuleh, S.H., A mixed collocation-finite difference method for 3D microscopic heat transport problems, Journal of Computational and Applied Mathematics, Vol. 217, Issue 1, 2008. Pp. 137-147. H. Heidari, H. Zwart, A. Malek, Controllability and Stability of 3D Heat Conduction Equation in a Submicroscale Thin Film. Department of Applied Mathematics, University of Twente, Netherlands, 2010. Pp. 1-21. Momeni-Masuleh, S.H., Malek, A., Hybrid pseudospectral -finite difference method for solving a 3D heat conduction equation in a submicroscale thin film, Numerical Methods for Partial Differential Equations, Vol. 23, Issue 5, 2007. Pp. 1139-1148. A. Malek, Applications of Nonstandard Finite Difference Methods to Nonlinear Heat Transfer Problems, Chapter 8 of the book: Heat Transfer - Mathematical Modelling, Numerical Methods and Information Technology, Edited by Aziz Belmiloudi, InTech, 2011. F. Xu, M. Lin, T.J. Lu. Modeling skin thermal pain sensation: Role of non-Fourier thermal behavior in transduction process of nociceptor // Computers in Biology and Medicine, Vol. 40. 2010. Pp. 478 ­486. J. Liu, Xu. Chen, L. X. Xu. New Thermal Wave Aspects on Burn Evaluation of Skin Subjected to Instantaneous Heating // IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, Vol. 46, NO. 4, 1999. Pp. 420-428.

4.

5. 6.