Plan optimization with L0-norm and group sparsity constraints for a new rotational, intensity-modulated brachytherapy for cervical cancer

The aim of this work is to build a framework that comprehends inverse planning procedure and plan optimization algorithm tailored to a novel directional beam intensity-modulated brachytherapy (IMBT) of cervical cancer using a rotatable, single-channel radiation shield. Inverse planning is required for finding optimal beam emitting direction, source dwell position and dwell time, which begin with creating a kernel matrix for each structure based on Monte-Carlo simulated dose distribution in the rotatable shield. For efficient beam delivery and less transit dose, the number of source dwell positions and angles needs to be minimized. It can be solved by L0-norm regularization for fewest possible dwell points, and by group sparsity constraint in L2,p-norm (0 <= p<1) besides L0-norm for fewest active applicator rotating angles. The dose distributions from our proposed algorithms were compared to those of conventional tandem-based intracavitary brachytherapy (ICR) plans for six cervical cancer patients. The algorithmic performance was evaluated in delivery efficiency and plan quality relative to the unconstrained algorithm. The proposed framework yielded substantially enhanced plan quality over the conventional ICR plans. The L0-norm and (group sparsity+L0-norm) constrained algorithms reduced the number of source dwell points by 60 and 70% and saved 5 and 8 rotational angles on average (7 and 11 angles for highly modulated cases), relative to the unconstrained algorithm, respectively. Though both algorithms reduced the optimal source dwell positions and angles, the group sparsity constrained optimization with L0-norm was more effective than the L0-norm constraint only, mainly because of considering physical constraints of the new IMBT applicator. With much fewer dwell points compared to the unconstrained, the proposed algorithms led to statistically similar plan quality in dose volume histograms and iso-dose lines. It also demonstrated that the plan optimized by rotating the applicator resulted in much better plan quality than that of conventional applicator-based plans.