  Purpose: To provide a fast computational method, based on the proximal graph
solver (POGS) - a convex optimization solver using the alternating direction
method of multipliers (ADMM), for calculating an optimal treatment plan in
rotating shield brachytherapy (RSBT). RSBT treatment planning has more degrees
of freedom than conventional high-dose-rate brachytherapy (HDR-BT) due to the
addition of emission direction, and this necessitates a fast optimization
technique to enable clinical usage. // Methods: The multi-helix RSBT (H-RSBT)
delivery technique was considered with five representative cervical cancer
patients. Treatment plans were generated for all patients using the POGS method
and the previously considered commercial solver IBM CPLEX. The rectum, bladder,
sigmoid, high-risk clinical target volume (HR-CTV), and HR-CTV boundary were
the structures considered in our optimization problem, called the asymmetric
dose-volume optimization with smoothness control. Dose calculation resolution
was 1x1x3 mm^3 for all cases. The H-RSBT applicator has 6 helices, with 33.3 mm
of translation along the applicator per helical rotation and 1.7 mm spacing
between dwell positions, yielding 17.5 degree emission angle spacing per 5 mm
along the applicator.// Results: For each patient, HR-CTV D90, HR-CTV D100,
rectum D2cc, sigmoid D2cc, and bladder D2cc matched within 1% for CPLEX and
POGS. Also, we obtained similar EQD2 figures between CPLEX and POGS. POGS was
around 18 times faster than CPLEX. Over all patients, total optimization times
were 32.1-65.4 seconds for CPLEX and 2.1-3.9 seconds for POGS. // Conclusions:
POGS substantially reduced treatment plan optimization time around 18 times for
RSBT with similar HR-CTV D90, OAR D2cc values, and EQD2 figure relative to
CPLEX, which is significant progress toward clinical translation of RSBT. POGS
is also applicable to conventional HDR-BT.
