Optimization of beam weights under dose-volume restrictions.

A basic problem in treatment planning is the selection of weights for a set of beams which will yield the largest tumor dose under constraints limiting the doses received in specified fractions of different normal tissue structures. This report describes a method for formulating and solving this optimization problem as a combinatorial linear program. An illustration is provided by a problem in planning treatment of a thoracic tumor, in which no more than 1/2 or 2/3 of the lung is permitted to receive greater than 20 Gy and no part of the spinal cord allowed to receive greater than 45 Gy. The optimization technique was applied to this example to determine how the maximum tumor dose is affected by changes in the normal tissue constraints and the addition of a tumor dose homogeneity restriction. The linear programming technique yielded a rigorous and efficient determination of the beam weights for the thoracic plan considered. An exhaustive specification of all the underlying linear programs allows problems of moderate dimensions to be solved, while developments in mathematical programming and computer processing suggest approaches to problems of greater complexity.