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Central to these problems is the dose influence matrix\u2014also known as the\n                      <jats:italic>dij<\/jats:italic>\n                      matrix or dose deposition matrix\u2014which quantifies the radiation dose delivered from each beamlet to each voxel. Our findings demonstrate that this matrix is highly compressible, enabling a compact representation of the optimization problems and allowing them to be solved more efficiently and accurately.\n                    <\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Purpose<\/jats:title>\n                    <jats:p>To develop a compressed radiotherapy treatment planning framework based on a sparse\u2010plus\u2010low\u2010rank matrix compression technique. This approach circumvents conventional sparsification methods that discard small matrix elements\u2014often representing scattering components\u2014and may compromise the quality of the treatment plan.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Methods<\/jats:title>\n                    <jats:p>We precompute the primary () and scattering () dose contributions of the dose influence matrix  separately for photon therapy, expressed as: . Our analysis reveals that the singular values of the scattering matrix  exhibit exponential decay, indicating that  is a low\u2010rank matrix. This allows us to compress  into two smaller matrices: , where  is relatively small (approximately 5\u201310). Since the primary dose matrix  is sparse, this supports the use of the well\u2010established \u201csparse\u2010plus\u2010low\u2010rank\u201d decomposition technique for the influence matrix , approximated as: . We introduce an efficient algorithm for sparse\u2010plus\u2010low\u2010rank matrix decomposition, even without direct access to the scattering matrix. This algorithm is applied to optimize treatment plans for ten lung and ten prostate patients, using both compressed and sparsified versions of matrix . We then evaluate the dose discrepancy between the optimized and final plans. We also integrate this compression technique with our in\u2010house automated planning system, ECHO, and evaluate the dosimetric quality of the generated plans with and without compression.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Results<\/jats:title>\n                    <jats:p>Compressed planning offers superior trade\u2010offs between accuracy and computational efficiency, adjustable through algorithm parameters. For example, we achieved average reductions in dose discrepancy and optimization time of 73% and 20%, respectively, for 10 prostate patients, and 83% and 13% for lung patients. By using the compressed matrix within our automated ECHO planning system, we maintained comparable PTV coverage while significantly enhancing the sparing of organs at risk. Specifically, mean doses to the bladder and rectum for prostate patients were reduced by 8.8% and 12.5%, respectively. For lung patients, mean doses to the lungs (left and right, excluding GTV) and heart were reduced by 10.8% and 11.2%, respectively, compared to plans generated with the sparsified matrix.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Conclusion<\/jats:title>\n                    <jats:p>The proposed framework enables rapid, high\u2010quality treatment planning without compromising data integrity and plan quality. By integrating that with recent advancements in AI\u2010driven influence matrix calculations, this platform has the potential to facilitate fast and efficient online adaptive radiotherapy treatment planning, enhancing both speed and accuracy in clinical workflows.<\/jats:p>\n                  <\/jats:sec>","DOI":"10.1002\/mp.17736","type":"journal-article","created":{"date-parts":[[2025,3,11]],"date-time":"2025-03-11T11:57:33Z","timestamp":1741694253000},"page":"4642-4656","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Compressed radiotherapy treatment planning: A new paradigm for rapid and high\u2010quality treatment planning optimization"],"prefix":"10.1002","volume":"52","author":[{"given":"Mojtaba","family":"Tefagh","sequence":"first","affiliation":[{"name":"Edinburgh Futures Institute University of Edinburgh  Edinburgh Scotland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gourav","family":"Jhanwar","sequence":"additional","affiliation":[{"name":"Department of Medical Physics Memorial Sloan Kettering Cancer Center, New York  New York USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Masoud","family":"Zarepisheh","sequence":"additional","affiliation":[{"name":"Department of Medical Physics Memorial Sloan Kettering Cancer Center, New York  New York USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2025,3,8]]},"reference":[{"key":"e_1_2_9_2_1","doi-asserted-by":"publisher","DOI":"10.1118\/1.4761864"},{"key":"e_1_2_9_3_1","doi-asserted-by":"publisher","DOI":"10.1118\/1.3574874"},{"key":"e_1_2_9_4_1","doi-asserted-by":"publisher","DOI":"10.1088\/1361\u20106560\/ace09e"},{"key":"e_1_2_9_5_1","doi-asserted-by":"publisher","DOI":"10.1287\/inte.2021.1095"},{"key":"e_1_2_9_6_1","doi-asserted-by":"publisher","DOI":"10.1088\/0031-9155\/54\/23\/011"},{"key":"e_1_2_9_7_1","doi-asserted-by":"publisher","DOI":"10.1088\/0031-9155\/52\/6\/009"},{"key":"e_1_2_9_8_1","doi-asserted-by":"publisher","DOI":"10.1118\/1.4720218"},{"key":"e_1_2_9_9_1","doi-asserted-by":"publisher","DOI":"10.1002\/mp.14544"},{"key":"e_1_2_9_10_1","doi-asserted-by":"publisher","DOI":"10.1088\/0031-9155\/53\/4\/011"},{"key":"e_1_2_9_11_1","doi-asserted-by":"publisher","DOI":"10.1088\/0031-9155\/53\/11\/002"},{"key":"e_1_2_9_12_1","doi-asserted-by":"publisher","DOI":"10.1002\/mp.14114"},{"key":"e_1_2_9_13_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.semradonc.2022.06.004"},{"key":"e_1_2_9_14_1","doi-asserted-by":"publisher","DOI":"10.1088\/1361\u20106560\/ac8d45"},{"key":"e_1_2_9_15_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijrobp.2023.06.2091"},{"key":"e_1_2_9_16_1","doi-asserted-by":"publisher","DOI":"10.1088\/1361\u20106560\/ad4b90"},{"key":"e_1_2_9_17_1","doi-asserted-by":"publisher","DOI":"10.1118\/1.1446112"},{"key":"e_1_2_9_18_1","doi-asserted-by":"publisher","DOI":"10.1088\/0031-9155\/56\/4\/N03"},{"key":"e_1_2_9_19_1","unstructured":"TianZ ZarepishehM JiaX JiangSB.The fixed\u2010point iteration method for IMRT optimization with truncated dose deposition coefficient matrix. arXiv [physics.med\u2010ph]. 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