Collimator position optimization for proton minibeam radiation therapy.

Proton minibeam radiation therapy (pMBRT) employs spatially fractionated dose distributions to reduce normal tissue toxicity. A key component is the multi-slit collimator (MSC), which shapes the beam into narrow, spatially separated minibeams. Small lateral shifts of the MSC relative to the beam direction can substantially alter peak-valley dose patterns, target coverage, and organs-at-risk (OAR) sparing, making MSC positioning a critical planning parameter. We develop a novel collimator position optimization (CPO) algorithm for pMBRT that allows independent lateral shifts of the MSC at each beam angle to improve plan quality. The problem is formulated as a mixed-integer programming (MIP) model that jointly optimizes MSC positions and spot intensities. Binary variables select candidate lateral shifts per beam angle, while continuous variables represent spot intensities. The resulting non-convex problem is solved using an augmented Lagrangian framework with iterative convex relaxation and alternating direction method of multipliers (ADMM) decomposition. In three clinical cases, the proposed method achieved near-optimal solutions with substantially reduced computation time compared to exhaustive enumeration (e.g., 700 s vs. 15,000 s for an abdominal case). Allowing multiple MSC positions per beam angle led to consistent dosimetric improvements, particularly in OAR sparing; for example, mean oral cavity dose in a head-and-neck case decreased from 6.5 Gy to 4.6 Gy. MSC position optimization enhances pMBRT plan quality and can be efficiently integrated into clinical treatment planning.