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

Optimization in treatment planning of high dose-rate brachytherapy - Review and analysis of mathematical models

Treatment planning in high dose-rate brachytherapy has traditionally been conducted with manual forward planning, but inverse planning is today increasingly used in clinical practice. There is a large variety of proposed optimization models and algorithms to model and solve the treatment planning problem. Two major parts of inverse treatment planning for which mathematical optimization can be used are the decisions about catheter placement and dwell time distributions. Both these problems as well as integrated approaches are included in this review. The proposed models include linear penalty models, dose-volume models, mean-tail dose models, quadratic penalty models, radiobiological models, and multiobjective models. The aim of this survey is twofold: (i) to give a broad overview over mathematical optimization models used for treatment planning of brachytherapy and (ii) to provide mathematical analyses and comparisons between models. New technologies for brachytherapy treatments and methods for treatment planning are also discussed. Of particular interest for future research is a thorough comparison between optimization models and algorithms on the same dataset, and clinical validation of proposed optimization approaches with respect to patient outcome.

Verification of the plan dosimetry for high dose rate brachytherapy using metal-oxide-semiconductor field effect transistor detectors

The feasibility of a recently designed metal-oxide-semiconductor field effect transistor (MOSFET) dosimetry system for dose verification of high dose rate (HDR) brachytherapy treatment planning was investigated. MOSFET detectors were calibrated with a 0.6 cm3 NE-2571 Farmer-type ionization chamber in water. Key characteristics of the MOSFET detectors, such as the energy dependence, that will affect phantom measurements with HDR 192Ir sources were measured. The MOS-FET detector was then applied to verify the dosimetric accuracy of HDR brachytherapy treatments in a custom-made water phantom. Three MOSFET detectors were calibrated independently, with the calibration factors ranging from 0.187 to 0.215 cGy/mV. A distance dependent energy response was observed, significant within 2 cm from the source. The new MOSFET detector has a good reproducibility (<3%), small angular effect (<2%), and good dose linearity (R2=1). It was observed that the MOSFET detectors had a linear response to dose until the threshold voltage reached approximately 24 V for 192Ir source measurements. Further comparison of phantom measurements using MOSFET detectors with dose calculations by a commercial treatment planning system for computed tomography-based brachytherapy treatment plans showed that the mean relative deviation was 2.2 +/- 0.2% for dose points 1 cm away from the source and 2.0 +/- 0.1% for dose points located 2 cm away. The percentage deviations between the measured doses and the planned doses were below 5% for all the measurements. The MOSFET detector, with its advantages of small physical size and ease of use, is a reliable tool for quality assurance of HDR brachytherapy. The phantom verification method described here is universal and can be applied to other HDR brachytherapy treatments.

Optimization of HDR brachytherapy dose distributions using linear programming with penalty costs

Prostate cancer is increasingly treated with high-dose-rate (HDR) brachytherapy, a type of radiotherapy in which a radioactive source is guided through catheters temporarily implanted in the prostate. Clinicians must set dwell times for the source inside the catheters so the resulting dose distribution minimizes deviation from dose prescriptions that conform to patient-specific anatomy. The primary contribution of this paper is to take the well-established dwell times optimization problem defined by Inverse Planning by Simulated Annealing (IPSA) developed at UCSF and exactly formulate it as a linear programming (LP) problem. Because LP problems can be solved exactly and deterministically, this formulation provides strong performance guarantees: one can rapidly find the dwell times solution that globally minimizes IPSA's objective function for any patient case and clinical criteria parameters. For a sample of 20 prostates with volume ranging from 23 to 103 cc, the new LP method optimized dwell times in less than 15 s per case on a standard PC. The dwell times solutions currently being obtained clinically using simulated annealing (SA), a probabilistic method, were quantitatively compared to the mathematically optimal solutions obtained using the LP method. The LP method resulted in significantly improved objective function values compared to SA (P = 1.54 x 10(-7)), but none of the dosimetric indices indicated a statistically significant difference (P < 0.01). The results indicate that solutions generated by the current version of IPSA are clinically equivalent to the mathematically optimal solutions.

Optimization of dose distribution for HDR brachytherapy of the prostate using Attraction-Repulsion Model

PURPOSE

To optimize dose distribution for high-dose-rate brachytherapy for prostate cancer, we have developed a new algorithm named Attraction-Repulsion Model (ARM). In this study, we compared the ARM with geometric optimization (GO).

METHODS AND MATERIALS

The ARM was used to optimize the dose distribution by finding the best dwell time combination. ARM requires grids inside the clinical target volume (CTV) and critical organs. These grids generate attraction or repulsion based on specific dose constraints. After calculations were performed repeatedly until the attraction and repulsion forces reached equilibrium, the optimal dwell time distribution was established. We compared the ARM with GO for 10 patients using dose-volume histograms.

RESULTS

The CTV ranged from 23 to 48 cc, and the CTV V150 ranged from 52% to 79%, and 23% to 44% for GO and ARM, respectively. This indicates that the dose homogeneity indices, as well as the conformal indices, were higher for ARM than for GO. The urethra V150 was 0-99% and 0-1% for GO and ARM, respectively.

CONCLUSION

The ARM proved to be superior to GO in minimizing the dose to normal structures and in improving dose homogeneity for the target while reducing the dose to normal tissues.

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.