An Optimization Approach for Radiosurgery Treatment Planning

Abstract

We outline a new approach for radiosurgery treatment planning, based on solving a series of optimization problems. We consider a specific treatment planning problem for a specialized device known as the Gamma Knife, that provides an advanced stereotactic approach to the treatment of tumors, vascular malformations, and pain disorders within the head. The sequence of optimization problems involves nonlinear and mixed integer programs whose solution is required in a given planning time (typically less than 30 minutes). This paper outlines several modeling decisions that result in more efficient and robust solution. Furthermore, it outlines a new approach for determining starting points for the nonlinear programs, based on a skeletonization of the target volume. Treatment plans are generated for real patient data that show the efficiency of the approach.

Optimal configuration of gamma ray machine radiosurgery units: the sphere covering subproblem

“…Thus the configuration has one sphere per lattice cube. The sphere density for the limiting case r = r * is then τ = 4π(r * ) 3 3(∆ ) 3 , which is bounded above by π 6 .…”

“…3.3) for a detailed summary of existing approaches. In particular, the approach taken by Ferris and co-workers [3,5,4,17] formulates linear and nonlinear programming models where the decision variables are D w (x s , y s , z s , i, j, k), i.e. the dose of radiation delivered to the tumor "pixel" (i, j, k) by the shot of width w centered at (x s , y s , z s ).…”

Radiation Treatment Planning: Mixed Integer Programming Formulations and Approaches

“…The use of a modified Powell's method in conjunction with simulated annealing has also been proposed [31,52]. A mixed integer programming (MIP) and a nonlinear programming approach for the problem are presented in [17,18,19,37,39].…”

“…The conformity estimate C is passed to the basic model as an input parameter. Details can be found in [17].…”

Neuro-dynamic programming for fractionated radiotherapy planning

“…Intensity-Modulated Radiotherapy (IMRT) is one of the most powerful tools to deliver conformal dose to a tumor target [6,23,17]. The treatment process involves optimization over specific parameters, such as angle selection and (pencil) beam weights [8,9,16,18]. The organs near the tumor will inevitably receive radiation as well; the physician places constraints on how much radiation each organ should receive.…”