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Beam Orientation Optimization with Non-Convex Group Sparsity Penalty

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D O'Connor

D O'Connor*, D Nguyen , D Ruan , V Yu , K Sheng , UCLA School of Medicine, Los Angeles, CA


WE-RAM3-GePD-T-1 (Wednesday, August 2, 2017) 10:30 AM - 11:00 AM Room: Therapy ePoster Lounge

Purpose: A natural strategy for beam orientation optimization (BOO) starting from a pool of candidate beams is to penalize the number of active (nonzero) beams during fluence map optimization. The group sparsity approach to BOO uses the L2,1-norm as a convex surrogate for the intractable beam counting penalty. However, compressed sensing theory informs us that the L2,1-norm may be a poor surrogate when the group restricted isometry property is not satisfied. This is likely the case for BOO problems because adjacent block columns of the dose-calculation matrix (corresponding to adjacent beams) are highly correlated. In such cases, a nonconvex group sparsity penalty may be useful. Therefore, in this study we revisit the group sparsity approach to BOO using the nonconvex L2,1/2-penalty in place of the L2,1-norm.

Methods: Beam angles are selected by solving a fluence map optimization problem involving 500-700 non-coplanar candidate beams, with an additional nonconvex L2,1/2-penalty term that encourages most candidate beams to be inactive. The optimization problem is solved using an accelerated proximal gradient method (FISTA). The nonconvex group sparsity formulation is used to create noncoplanar treatment plans for a prostate case and a lung case, and the resulting treatment plans are compared with plans created using the convex group sparsity formulation.

Results: Mean dose was reduced by 2.1% of prescription dose (bladder), 2.1% (rectum), 21.0% (seminal vesicle), 19.2% (penile bulb), and 3.7% (proximal bronchus). Max dose was reduced by 7.6% of prescription dose (penile bulb), 7.5% (proximal bronchus), 5.7% (heart), and 4.5% (spine). On average, mean and max OAR dose were reduced by 4.1% and 3.0% of prescription dose, respectively. PTV homogeneity improved slightly. The average FISTA runtime was 5.1 minutes (non-convex formulation) and 3.75 minutes (convex formulation).

Conclusion: For both cases the non-convex BOO formulation provides superior dosimetry, with only a minor increase in runtime.

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