The reliability of optimization under dose-volume limits.

PURPOSE: An optimization algorithm improves the distribution of dose among discrete points in tissues, but tolerance depends on the distribution of dose across a continuous volume. This report asks whether an exact algorithm can be completed when enough points are taken to accurately model a dose-volume constraint.

METHODS AND MATERIALS: Trials were performed using a 3-dimensional model of conformal therapy of lung cancer. Trials were repeated with different limits placed on the fraction of lung which could receive > 20 Gy. Bounds were placed on cord dose and target dose inhomogeneity. A mixed integer algorithm was used to find a feasible set of beam weights which would maximize tumor dose. Tests of feasibility and optimality are introduced to check the solution accuracy.

RESULTS: Solutions were optimal for points used to model tissues. An accuracy of 3-4% in a volume condition could be obtained with models of 450-600 points. The error improved to 2% with 800 points to model the lung. Solution times increased six-fold at this level of accuracy.

CONCLUSION: The mixed integer method can find optimum weights which respect dose-volume conditions in usually acceptable times. If constraints are violated by an excessive amount, the optimization model should be rerun with more points.