Optimizing Radiation Dose for Brachytherapy Cancer Treatment

HDR LP solution

Isodose curves for the LP solution for a patient undergoing HDR brachytherapy. CT scan shows the prostate (dark blue), urethra (magenta), rectum (gray), and catheters (red dots). Isodose curves for 50% (green), 100% (outer yellow), 120% (inner yellow), and 150% (cyan) of prostate minimum prescribed dose are plotted. Ideally, the dose to the prostate should be between 100% and 150% of the minimum prescribed dose and the dose to the urethra and surrounding tissues should be minimized.

Prostate cancer is increasingly treated with high-dose-rate (HDR) brachytherapy, a type of radiation therapy in which a radioactive source is guided through catheters temporarily implanted in the prostate. As part of this treatment, the physician uses an image of the patient anatomy and specifies radiation dose prescriptions to the tumor and surrounding tissues. Clinicians must then set dwell times for the radioactive source inside the catheters. The goal is to set the dwell times such that the resulting dose delivered to the tumor and surrounding tissues satisfies the physician prescription as best as possible, maximizing dose to the tumor and minimizing dose to surrounding healthy tissue.

The primary contribution of this project 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 seconds per case on a standard PC.


  1. Ron Alterovitz, Etienne Lessard, Jean Pouliot, I-Chow Joe Hsu, James F. O'Brien, and Ken Goldberg, "Optimization of HDR brachytherapy dose distributions using linear programming with penalty costs," Medical Physics, vol. 33, no. 11, pp. 4012-4019, Nov. 2006. (Download PDF)
  2. Ron Alterovitz, Etienne Lessard, Jean Pouliot, I-Chow Joe Hsu, James F. O'Brien, and Ken Goldberg, "High-dose-rate Brachytherapy Dose Optimization for Prostate Cancer Using Linear Programming," Institute for Operations Research and the Management Sciences (INFORMS) Annual Meeting, San Francisco, CA, Nov. 2005.