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Med. Biol."],"published-print":{"date-parts":[[2026,10,28]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    <jats:italic>Objective<\/jats:italic>\n                    . To show computational feasibility of a previously proposed probabilistic planning approach on a neuro-oncological patient group, we compared probabilistic plans with (automated) robust plans for one patient (group A) that could achieve sufficient clinical target coverage and for four patients (group B) where target coverage had to be compromised due to organ-at-risk (OAR) dose constraints.\n                    <jats:italic>Approach<\/jats:italic>\n                    . The probabilistic approach is percentile-based and uses the fact that a (dose) percentile can be approximated as a linear combination of its expected value and standard deviation. This allows us to formulate objectives and constraints with patient-specific acceptance probabilities. The optimization has a nested structure: the inner optimization optimizes the beam weights for a given percentile estimate, while an outer loop iteratively updates and improves the accuracy of the percentile estimate. For every outer iteration, the optimization is warm-started from the previous iteration. Percentiles are efficiently calculated by sampling a polynomial chaos expansion of the dose-influence matrix.\n                    <jats:italic>Main results<\/jats:italic>\n                    . The patient in group A achieved cumulative OAR dose reductions (of OAR-related DVH-metrics) of 23.1 GyRBE, for identical target coverage. Target coverage improved for all patients in group B (the 10th percentile of\n                    <jats:inline-formula>\n                      <jats:tex-math>\n                        \n                      <\/jats:tex-math>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mrow>\n                          <mml:msub>\n                            <mml:mi>D<\/mml:mi>\n                            <mml:mrow>\n                              <mml:mn>99.8<\/mml:mn>\n                              <mml:mi mathvariant=\"normal\">%<\/mml:mi>\n                            <\/mml:mrow>\n                          <\/mml:msub>\n                        <\/mml:mrow>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    increased up to 0.61 GyRBE), at the same time reaching cumulative OAR dose reductions (of OAR-related DVH-metrics) up to about 40 GyRBE. Probabilistic plans were optimized in 44 h to 226 h. For two representative patients, eliminating warm-starting (i.e. the outer loop) from the approach reduced total optimization times to below 10 h (which took originally 80 h and 141 h).\n                    <jats:italic>Significance<\/jats:italic>\n                    . Compared to robust optimization methods, the probabilistic approach achieves improved trade-offs between probabilistic target coverage and OAR sparing, potentially leading to better treatments.\n                  <\/jats:p>","DOI":"10.1088\/1361-6560\/aeb08b","type":"journal-article","created":{"date-parts":[[2026,10,16]],"date-time":"2026-10-16T07:39:13Z","timestamp":1792136353000},"page":"205008","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Direct probabilistic IMPT treatment planning with setup and range errors for neuro-oncological patients"],"prefix":"10.1088","volume":"71","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-1963-7377","authenticated-orcid":true,"given":"J R","family":"de Jong","sequence":"first","affiliation":[{"name":"Section Medical Physics and Technology"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"data-curation","vocabulary":"credit"},{"role":"formal-analysis","vocabulary":"credit"},{"role":"investigation","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"},{"role":"software","vocabulary":"credit"},{"role":"validation","vocabulary":"credit"},{"role":"visualization","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8954-4554","authenticated-orcid":true,"given":"S","family":"Breedveld","sequence":"additional","affiliation":[{"name":"University Medical Center Rotterdam"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"resources","vocabulary":"credit"},{"role":"software","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-1168-3479","authenticated-orcid":true,"given":"S J","family":"M Habraken","sequence":"additional","affiliation":[{"name":"Holland Proton Therapy Centre Delft"},{"name":"Leiden University Medical Center"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4264-9903","authenticated-orcid":false,"given":"M S","family":"Hoogeman","sequence":"additional","affiliation":[{"name":"Holland Proton Therapy Centre Delft"},{"name":"University Medical Center Rotterdam"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"funding-acquisition","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-4787-4242","authenticated-orcid":true,"given":"J I","family":"de Jong","sequence":"additional","affiliation":[{"name":"Holland Proton Therapy Centre Delft"},{"name":"University Medical Center Rotterdam"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"resources","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3810-1926","authenticated-orcid":true,"given":"D","family":"Lathouwers","sequence":"additional","affiliation":[{"name":"Section Medical Physics and Technology"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"},{"role":"project-administration","vocabulary":"credit"},{"role":"resources","vocabulary":"credit"},{"role":"supervision","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0975-4226","authenticated-orcid":true,"given":"Z","family":"Perk\u00f3","sequence":"additional","affiliation":[{"name":"Section Medical Physics and Technology"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"funding-acquisition","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"},{"role":"project-administration","vocabulary":"credit"},{"role":"resources","vocabulary":"credit"},{"role":"supervision","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"}]}],"member":"266","published-online":{"date-parts":[[2026,10,16]]},"reference":[{"key":"pmbaeb08bbib1","doi-asserted-by":"publisher","first-page":"5467","DOI":"10.1088\/0031-9155\/55\/18\/013","type":"journal-article","article-title":"Interior point algorithms: guaranteed optimality for fluence map optimization in IMRT","volume":"55","author":"Aleman","year":"2010","journal-title":"Phys. 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