{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T13:59:11Z","timestamp":1791381551884,"version":"4.3.3"},"reference-count":38,"publisher":"Wiley","issue":"8","license":[{"start":{"date-parts":[[2025,8,13]],"date-time":"2025-08-13T00:00:00Z","timestamp":1755043200000},"content-version":"vor","delay-in-days":12,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"},{"start":{"date-parts":[[2025,8,1]],"date-time":"2025-08-01T00:00:00Z","timestamp":1754006400000},"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":[[2025,8]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:sec>\n                    <jats:title>Background<\/jats:title>\n                    <jats:p>Treatment planning in proton therapy aims to deliver a conformal dose to the target while sparing normal healthy tissues. However, the range uncertainty of CT values and patient motion during delivery may compromise both target dose coverage and organ\u2010at\u2010risk (OAR) sparing.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Purpose<\/jats:title>\n                    <jats:p>This study proposes a novel optimization method, Regularized\u2010Multi\u2010Field Optimization (R\u2010MFO). R\u2010MFO which incorporates the single\u2010field uniform dose as a regularization term in the multi\u2010field optimization (MFO). The proposed method seeks to reduce the sensitivity to uncertainties while maintaining the high plan quality as MFO plans.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Methods<\/jats:title>\n                    <jats:p>R\u2010MFO combines the uniform dose distribution with the flexibility of MFO plans through an iterative process. Specifically, a dose equality constraint in the target volume for each field is introduced as a regularized term in the conventional MFO at every certain iteration. Robust optimization is performed with the range uncertainty of 3.5% and setup uncertainty of 3mm for the head and neck (HN) case and 5mm for the liver and lung cases. Due to the nonconvex constraints associated with minimum monitor unit (MMU) and active set, R\u2010MFO optimization is solved by iterative convex relaxation (ICR) and alternating direction method of multipliers (ADMM) algorithms. To demonstrate the effectiveness of our proposed R\u2010MFO, plan quality and robustness are compared with R\u2010MFO, MFO, and single\u2010field optimizations (SFO) across three clinical cases: HN, liver, and lung.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Results<\/jats:title>\n                    <jats:p>\n                      R\u2010MFO demonstrated significantly enhanced robustness compared to MFO, with narrower uncertainty bands (e.g., RV\n                      <jats:sub>95<\/jats:sub>\n                      : 7.8\u201310.0 vs. 9.6\u201310.5) and superior high\u2010dose tail performance, though slightly inferior to SFO in RV\n                      <jats:sub>100<\/jats:sub>\n                      (26.2\u201331.5 vs. 19.2\u201326.9). Plan quality analysis revealed R\u2010MFO achieved higher conformity indices (CI: 0.65\u20130.79) and improved dose coverage (D\n                      <jats:sub>95<\/jats:sub>\n                      \u226599.15%, D\n                      <jats:sub>max<\/jats:sub>\n                      \u2264111.90%) compared to SFO, approaching MFO performance. For OARs, both MFO and R\u2010MFO reduced esophageal D\n                      <jats:sub>max<\/jats:sub>\n                      , D\n                      <jats:sub>mean<\/jats:sub>\n                      , and D\n                      <jats:sub>5cc<\/jats:sub>\n                      in the lung case by leveraging dose distribution flexibility. However, R\u2010MFO incurred the longest computational time due to comprehensive voxel\u2010level optimization, whereas MFO remained the most time\u2010efficient.\n                    <\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Conclusions<\/jats:title>\n                    <jats:p>The proposed R\u2010MFO method successfully integrates the uniform dose characteristics of SFO with the flexibility of MFO, achieving enhanced robustness compared to MFO and superior plan quality compared to SFO.<\/jats:p>\n                  <\/jats:sec>","DOI":"10.1002\/mp.18046","type":"journal-article","created":{"date-parts":[[2025,8,14]],"date-time":"2025-08-14T04:25:16Z","timestamp":1755145516000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A regularized\u2010multi\u2010field optimization algorithm for robust IMPT"],"prefix":"10.1002","volume":"52","author":[{"given":"Ying","family":"Luo","sequence":"first","affiliation":[{"name":"Institute of Modern Physics Chinese Academy of Sciences  Lanzhou China"},{"name":"University of Chinese Academy of Sciences  Beijing China"},{"name":"Department of Radiation Oncology University of Kansas Medical Center Kansas City Kansas USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chao","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Radiation Oncology University of Kansas Medical Center Kansas City Kansas USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ya\u2010Nan","family":"Zhu","sequence":"additional","affiliation":[{"name":"Department of Radiation Oncology University of Kansas Medical Center Kansas City Kansas USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wangyao","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Radiation Oncology University of Kansas Medical Center Kansas City Kansas USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Daniel","family":"Johnson","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 Kansas Medical Center Kansas City Kansas USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"David","family":"Akhavan","sequence":"additional","affiliation":[{"name":"Department of Radiation Oncology University of Kansas Medical Center Kansas City Kansas USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Krishna","family":"Reddy","sequence":"additional","affiliation":[{"name":"Department of Radiation Oncology University of Kansas Medical Center Kansas City Kansas 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