Calculation of mean central dose in interstitial brachytherapy using Delaunay triangulation

Optimization of MammoSite therapy

PURPOSE

Radiation source anisotropy causes about 10% of a spherically shaped planning target volume surrounding a MammoSite balloon to receive less than the prescribed dose. The principal dose-limiting factor for MammoSite therapy is the dose to the overlying skin. Additional limiting factors potentially include the dose to portions of the heart and lung. The goal of optimization is to deliver the prescribed dose to as much of the planning target volume as possible while avoiding toxicity to adjacent organs.

METHODS AND MATERIALS

An experimental CT-based high-dose-rate brachytherapy treatment planning system was used to investigate optimization strategies for MammoSite treatment. This system implements a linear optimization of high-dose-rate dwell times on the basis of constraints assigned to points of interest and a set of potential dwell positions.

RESULTS

The cylindrical symmetry of the MammoSite catheter limits the optimization process to creating spherical, ellipsoidal, or egg-shaped isodose distributions whose major axis is oriented along the catheter axis. If the dose to a limiting structure, such as skin, is not an issue, the use of multiple dwell positions can compensate for source anisotropy and create a more spherical isodose surface enclosing the planning target volume compared with a single dwell position. When skin becomes a dose-limiting factor, the catheter axis orientation, source anisotropy, dwell position, and dwell weighting can be exploited to limit the skin dose while simultaneously preserving the prescribed dose to as much of the target volume as possible.

CONCLUSION

Optimization of MammoSite therapy using multiple dwell positions within the balloon is both possible and practical.

The use of linear programming in optimization of HDR implant dose distributions

The introduction of high dose rate brachytherapy enabled optimization of dose distributions to be used on a routine basis. The objective of optimization is to homogenize the dose distribution within the implant while simultaneously satisfying dose constraints on certain points. This is accomplished by varying the time the source dwells at different locations. As the dose at any point is a linear function of the dwell times, a linear programming approach seems to be a natural choice. The dose constraints are inherently linear inequalities. Homogeneity requirements are linearized by minimizing the maximum deviation of the doses at points inside the implant from a prescribed dose. The revised simplex method was applied for the solution of this linear programming problem. In the homogenization process the possible source locations were chosen as optimization points. To avoid the problem of the singular value of the dose at a source location from the source itself we define the "self-contribution" as the dose at a small distance from the source. The effect of varying this distance is discussed. Test cases were optimized for planar, biplanar and cylindrical implants. A semi-irregular, fan-like implant with diverging needles was also investigated. Mean central dose calculation based on 3D Delaunay-triangulation of the source locations was used to evaluate the dose distributions. The optimization method resulted in homogeneous distributions (for brachytherapy). Additional dose constraints--when applied--were satisfied. The method is flexible enough to include other linear constraints such as the inclusion of the centroids of the Delaunay-triangulation for homogenization, or limiting the maximum allowable dwell time.