  Current inverse treatment planning methods that optimize both catheter
positions and dwell times in prostate HDR brachytherapy use surrogate linear or
quadratic objective functions that have no direct interpretation in terms of
dose-volume histogram (DVH) criteria, do not result in an optimum or have long
solution times.
  We decrease the solution time of existing linear and quadratic dose-based
programming models (LP and QP, respectively) to allow optimizing over potential
catheter positions using mixed integer programming. An additional average
speed-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 15
seconds, which confirms earlier results. We propose an iterative procedure for
QP that allows to prescribe the target dose as an interval, while retaining
independence between the solution time and the number of dose calculation
points. This iterative procedure is comparable in speed to the LP model, and
produces better plans than the non-iterative QP.
  We formulate a new dose-volume based model that maximizes $V_{100\%}$ while
satisfying pre-set DVH-criteria. This model optimizes both catheter positions
and dwell times within a few minutes depending on prostate volume and number of
catheters, optimizes dwell times within 35 seconds, and gives better DVH
statistics than dose-based models. The solutions suggest that the correlation
between objective value and clinical plan quality is weak in existing
dose-based models.
