{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T05:59:55Z","timestamp":1791352795219,"version":"4.3.1"},"reference-count":27,"publisher":"Wiley","issue":"11","license":[{"start":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T00:00:00Z","timestamp":1762214400000},"content-version":"vor","delay-in-days":3,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"},{"start":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T00:00:00Z","timestamp":1761955200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"content-domain":{"domain":["aapm.onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Medical Physics"],"published-print":{"date-parts":[[2025,11]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:sec>\n                    <jats:title>Background<\/jats:title>\n                    <jats:p>Multi\u2010collimator proton minibeam radiation therapy (MC\u2010pMBRT) has recently emerged as a versatile technique for dose shaping, enabling the formation of peak\u2010valley dose patterns in organs\u2010at\u2010risk (OAR) while maintaining a uniform dose distribution in tumor targets. MC\u2010pMBRT leverages a set of generic multi\u2010slit collimators (MSCs), each with different center\u2010to\u2010center (ctc) distances. However, the current method for minibeam aperture optimization (MAO), that is, the selection of MSC per beam angle to optimize plan quality, is manual and heuristic, resulting in computational inefficiencies and no guarantee of optimality.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Purpose<\/jats:title>\n                    <jats:p>This work introduces a novel mixed integer programming (MIP) approach to MAO for optimizing MC\u2010pMBRT plan quality.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Methods<\/jats:title>\n                    <jats:p>The proposed MIP approach jointly optimizes dose distributions and peak\u2010to\u2010valley dose ratio (PVDR) and selects the optimal set of MSC per beam angle. The optimization problem includes decision variables for MSC selection per beam angle and spot weights. The proposed MIP approach is a two\u2010step process: in the first step, the values of binary variables are determined to select MSC for each beam angle; in the second step, the continuous variables are solved to determine the spot weights. Both steps utilize iterative convex relaxation (ICR) and the alternating direction method of multipliers (ADMM) to solve the optimization problems efficiently.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Results<\/jats:title>\n                    <jats:p>The proposed MIP method to solve MAO (MIP\u2010MAO) was validated against the conventional heuristic method (CONV) for MC\u2010pMBRT treatment planning. Results indicate that MIP\u2010MAO enhances the conformity index (CI) for the target and improves PVDR for OAR. For instance, in a head\u2010and\u2010neck (HN) case, CI improved from 0.61 (CONV) to 0.70 (MIP\u2010MAO); in an abdomen case, CI improved from 0.78 (CONV) to 0.83 (MIP\u2010MAO). Additionally, MIP\u2010MAO reduced mean doses in the body and OAR.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Conclusions<\/jats:title>\n                    <jats:p>A novel MIP approach for MAO in MC\u2010pMBRT is presented, showing demonstrated improvements in plan quality and PVDR compared to the heuristic method.<\/jats:p>\n                  <\/jats:sec>","DOI":"10.1002\/mp.70129","type":"journal-article","created":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T01:32:51Z","timestamp":1762306371000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A mixed integer programming approach to minibeam aperture optimization for multi\u2010collimator proton minibeam radiotherapy"],"prefix":"10.1002","volume":"52","author":[{"given":"Nimita","family":"Shinde","sequence":"first","affiliation":[{"name":"Department of Radiation Oncology University of Texas Southwestern Medical Center  Dallas Texas USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Weijie","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Radiation Oncology University of Kansas Medical Center  Kansas City Kansas USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuting","family":"Lin","sequence":"additional","affiliation":[{"name":"Department of Radiation Oncology University of Texas Southwestern Medical Center  Dallas Texas USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hao","family":"Gao","sequence":"additional","affiliation":[{"name":"Department of Radiation Oncology University of Texas Southwestern Medical Center  Dallas Texas 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