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

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#### Authors

- Ron Alterovitz
- Etienne Lessard
- Jean Pouliot
- I-Chow Joe Hsu
- James F. O'Brien
- Ken Goldberg

### Abstract

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 * 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.

### Citation

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*, 33(11):4012–4019, November 2006.