Purpose: To consider the uncertainty in the construction of target boundaries for optimization, and to demonstrate how the principles of mathematical programming can be applied to determine and display the effect on the tumor dose of making small changes to the target boundary.
Methods: The effect on the achievable target dose of making successive small shifts to the target boundary within its range of uncertainty was found by constructing a mixed-integer linear program that automated the placement of the beam angles using the initial target volume.
Results: The method was demonstrated using contours taken from a nasopharynx case, with dose limits placed on surrounding structures. In the illustrated case, enlarging the target anteriorly to provide greater assurance of disease coverage did not force a sacrifice in the minimum or mean tumor doses. However, enlarging the margin posteriorly, near a critical structure, dramatically changed the minimum, mean, and maximum tumor doses.
Conclusion: Tradeoffs between the position of the target boundary and the minimum target dose can be developed using mixed-integer programming, and the results projected as a guide to contouring and plan selection.
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