Using Integer Programming to Reduce Side Effects of High Dose Rate Brachytherapy
Timmy Siauw, Adam Cunha, Alper Atamtürk, I-Chow Hsu, Jean Pouliot and Ken Goldberg
High Dose Rate Brachytherapy (HDRB) is a radiation therapy for prostate cancer where radiation is delivered directly to the prostate via temporarily inserted needles. Although HDRB is an effective treatment, it is also an invasive procedure that can have negative side effects. These side effects are related to the number of needles inserted and the puncturing of organs near the prostate. Our research utilizes integer programming to generate HDRB needle insertion patterns that have fewer needles than standard patterns, avoid puncturing healthy organs, and meet treatment goals. Given anatomy data, an initial of set of needles is generated to densely cover the prostate volume and avoid intersecting nearby organs. Each needle is associated with a binary variable, xk, 1 iff nk is chosen to be in the needle pattern. The prostate volume is discretized into evenly spaced points, pi. Given a parameter, δ, let Cik(δ) be 1 iff there is a dwell position, dj, in nk such that ||pi – dj||2 < δ, and 0 otherwise. Then a needle pattern is the solution to Needle Placement Integer Program (NPIP): NPIP(δ): minimize Σ xk
subject to: Σ Cik(δ) xk ≥ 1
xk binary On average, physician-generated patterns use 16 needles and puncture the penile bulb 7 times. We used NPIP to compute needle patterns for 18 patients with initial needle sets ranging from 245 to 490 needles. The parameter δ was chosen adaptively to suit the size of the prostate. If an optimal solution was not found, the best solution was returned after 2000 branch and bound relaxations. Every NPIP needle pattern was within 1 needle of optimum. NPIP needle patterns contained an average of 8 needles, none puncturing a nearby organ. A treatment plan meeting established treatment objectives was computed for every NPIP needle pattern. For details, visit http://goldberg.berkeley.edu.
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