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.