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Therefore, proton arc therapy has drawn significant interest in the Society of Radiation Oncology as a potentially efficient and optimal treatment option for cancer patients. However, state\u2010of\u2010the\u2010art spot\u2010scanning proton arc therapy (SPArc) still relies on single or dual\u2010 co\u2010planar arc trajectories, which limits its capacity to advance the treatment outcome further. There is an urgent need to explore particle beam therapy's full potential via 4pi.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Purpose<\/jats:title>\n                    <jats:p>This study aims to develop the first 4pi arc optimization algorithm that searches for efficient arc trajectories in 4pi space, explores the potential dosimetric improvements, and demonstrates its feasibility through simulation.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Method<\/jats:title>\n                    <jats:p>\n                      Dynamic Programming, originally from control theory, was translated into this new concept of the 4pi SPArc optimization algorithm (SPArc\n                      <jats:sub>\u20104pi<\/jats:sub>\n                      ) for the trajectory search and route decision\u2010making. It breaks down the complicated and high\u2010computational\u2010demand main problem into a series of small sub\u2010problems and searches for delivery\u2010efficient 4pi arc trajectories through an iterative approach. Five different disease sites, e.g., head &amp; neck, partial brain, clival brain chordoma, lung and pancreatic cancer, were used for testing purposes. Conventional Intensity Modulated Proton Therapy (IMPT) and 2D co\u2010planar arc (SPArc\n                      <jats:sub>\u20102d<\/jats:sub>\n                      ) plans were generated as a benchmark. Treatment delivery efficiency was evaluated through a published and validated dynamic arc system controller. Plan quality was assessed through target coverage and organ at risk (OAR) sparing.\n                    <\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Result<\/jats:title>\n                    <jats:p>\n                      The new SPArc\n                      <jats:sub>\u20104pi<\/jats:sub>\n                      demonstrated superior dosimetric performance across various evaluation metrics for all five disease sites. The simulation result shows that SPArc\n                      <jats:sub>\u20104pi<\/jats:sub>\n                      is able to be delivered within a reasonable time of around 5\u201311 mins, which is comparable to the SPArc\n                      <jats:sub>\u20102d<\/jats:sub>\n                      plans\n                    <\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Conclusion<\/jats:title>\n                    <jats:p>\n                      The study introduced the first optimization algorithm for SPArc\n                      <jats:sub>\u20104pi<\/jats:sub>\n                      technique. It not only showed SPArc\n                      <jats:sub>\u20104pi<\/jats:sub>\n                      \u2018s potential to improve the plan quality via a greater degree of freedom compared to the conventional IMPT and state\u2010of\u2010art 2D co\u2010planar SPArc\u20102d technique but also demonstrated its feasibility for future clinical implementation based on the current proton beam therapy system's machine characteristics.\n                    <\/jats:p>\n                  <\/jats:sec>","DOI":"10.1002\/mp.70639","type":"journal-article","created":{"date-parts":[[2026,8,19]],"date-time":"2026-08-19T05:42:07Z","timestamp":1787118127000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Develop a novel non\u2010coplanar trajectory optimization algorithm for an efficient 4pi spot\u2010scanning proton Arc (SPArc\n                    <sub>\u20104pi<\/sub>\n                    ) treatment delivery"],"prefix":"10.1002","volume":"53","author":[{"given":"Xiaoda","family":"Cong","sequence":"first","affiliation":[{"name":"Department of Radiation Oncology Corewell Health William Beaumont Hospital  Royal Oak Michigan USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shupeng","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Radiation Oncology Emory University  Atlanta Georgia USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peilin","family":"Liu","sequence":"additional","affiliation":[{"name":"Department of Radiation Oncology Corewell Health William Beaumont Hospital  Royal Oak Michigan USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peng","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Radiation Oncology Cleveland Clinic  Cleveland Ohio 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