Abstract
The intensity-modulated radiation therapy optimization algorithm presented here is based on linear algebra. This is a hybrid method with the deterministic property of linear algebra and the stochastic property of random iteration. The objective function is the quadratic summation of negative beam weights, instead of the quadratic differences between the desired and the computed doses. It is minimized by searching for physically realizable beams. Instead of iterating the beam weights, as most of the optimization algorithms do, this algorithm iterates the doses in the dose matrix within the ranges given. The dose matrix is composed of dose voxels from an arbitrary selection of dose points from target volumes, critical organs or from surrounding tissue. The prescriptions for each category of the dose points do have the given dose ranges corresponding to the tolerances, biological indices and/or minimum and maximum dose requirements. Doses from primary, internal scatter radiation in each voxel can all be considered in the model. The process will simultaneously iterate doses in a batch of dose voxels within the given dose windows. From the inversely calculated beam weights, the optimization process would gradually minimize the objective function and eventually converge near the global minimum. The algorithm is tested with hypothetical targets in two-dimensional setups. The calculated doses conform well to the complex targets and protect the critical organs. The calculated results were verified with film measurements and CORVUS verification plans, and have shown excellent matches in dose distributions. This algorithm is feasible and can easily be implemented to solve complex target problems.