Article ID Journal Published Year Pages File Type
4602931 Linear Algebra and its Applications 2008 20 Pages PDF
Abstract

We consider an inverse problem related to external radiation therapy treatment planning. The dose calculation (the forward problem) is based on the Boltzmann Transport Equation (BTE) which models exactly the transport of charged particles in tissue. The inverse planning (the inverse problem) is formulated as an optimal boundary control problem. The optimal control variable is the incoming (external) flux and the output is the dose distribution in patient domain. Both physical and biological cost functions are defined but here we concentrate on the physically based optimization. The discretization is done by finite element approximations for which the BTE is expressed in its variational form. In the optimization process of the discrete model we apply so called parametrization (which may essentially diminish the decision variables in optimization) of the matrix equations. Parametrization is based on certain linear algebraic decompositions of matrices. One simulation is presented which show the functionality of the developed methods.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory