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Current inverse treatment planning methods that optimize both catheterpositions and dwell times in prostate HDR brachytherapy use surrogate linear orquadratic objective functions that have no direct interpretation in terms ofdose-volume histogram (DVH) criteria, do not result in an optimum or have longsolution times.  We decrease the solution time of existing linear and quadratic dose-basedprogramming models (LP and QP, respectively) to allow optimizing over potentialcatheter positions using mixed integer programming. An additional averagespeed-up of 75% can be obtained by stopping the solver at an early stage,without deterioration of the plan quality. For a fixed catheter configuration,the dwell time optimization model LP solves to optimality in less than 15seconds, which confirms earlier results. We propose an iterative procedure forQP that allows to prescribe the target dose as an interval, while retainingindependence between the solution time and the number of dose calculationpoints. This iterative procedure is comparable in speed to the LP model, andproduces better plans than the non-iterative QP.  We formulate a new dose-volume based model that maximizes $V_{100\%}$ whilesatisfying pre-set DVH-criteria. This model optimizes both catheter positionsand dwell times within a few minutes depending on prostate volume and number ofcatheters, optimizes dwell times within 35 seconds, and gives better DVHstatistics than dose-based models. The solutions suggest that the correlationbetween objective value and clinical plan quality is weak in existingdose-based models.

Mixed integer programming improves comprehensibility and plan quality in inverse optimization of prostate HDR-brachytherapy