{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T20:30:10Z","timestamp":1770755410217,"version":"3.50.0"},"reference-count":20,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2022,12,26]],"date-time":"2022-12-26T00:00:00Z","timestamp":1672012800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"content-domain":{"domain":["aapm.onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Medical Physics"],"published-print":{"date-parts":[[2023,2]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:sec><jats:title>Purpose<\/jats:title><jats:p>We developed a method based on a physical pencil beam model for accurate equivalent square calculations for rectangular and irregular fields, for different definitions of equivalent squares, for beams with and without flattening filter, different photon energies, and depths in water.<\/jats:p><\/jats:sec><jats:sec><jats:title>Methods<\/jats:title><jats:p>We considered two equivalent square definitions: equal dose at a point on the beam axis and equal depth dose, measured as tissue phantom ratio at 20 and 10\u00a0cm depth (). As dose engine, we used an analytical pencil beam model. By integrating the pencil beam kernels, we assigned square fields to rectangular fields minimizing the dose, respectively, the  difference. The results were compared with measurements at 100\u00a0mm depth for nominal beam energies of 6 and 18\u00a0MV, the Sterling equation, the geometric mean, and data from BJR Suppl 25 (British Institute of Radiology, 1996).<\/jats:p><\/jats:sec><jats:sec><jats:title>Results<\/jats:title><jats:p>Pencil beam results were closest to the measurements. An energy dependence of several millimeters for small field dimensions and depth dependencies for very elongated fields were observed. For the assignment of WFF square to FFF rectangular fields, using the equal\u2010 definition, our method agrees with previously published results. For circular fields approximated by leaves, we found deviations to the data from BJR Suppl. 25 below 1\u00a0mm for diameters smaller than\u00a0200\u00a0mm.<\/jats:p><\/jats:sec><jats:sec><jats:title>Conclusions<\/jats:title><jats:p>Our study shows that the validity range for geometric mean and Sterling equation\u00a0is limited. Ergo, instead of specifying specific validity ranges, we suggest using the pencil beam method, valid for all aspect ratios, including elongated fields in the primary dose dominated regime. We published our method as python library and graphical user interface on GitHub. Users can choose between two definitions of equivalent square and between WFF and FFF fields. The implemented pencil beam method for irregular fields is also usable for quality assurance such as monitor unit\u00a0checks.<\/jats:p><\/jats:sec>","DOI":"10.1002\/mp.16069","type":"journal-article","created":{"date-parts":[[2022,10,27]],"date-time":"2022-10-27T03:05:06Z","timestamp":1666839906000},"page":"1242-1250","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Technical note: Determining equivalent squares of high\u2010energetic photon fields"],"prefix":"10.1002","volume":"50","author":[{"given":"Jonas","family":"Ringholz","sequence":"first","affiliation":[{"name":"Department of Radiation Oncology University of W\u00fcrzburg W\u00fcrzburg Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sonja","family":"Wegener","sequence":"additional","affiliation":[{"name":"Department of Radiation Oncology University of W\u00fcrzburg W\u00fcrzburg Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Otto Andreas","family":"Sauer","sequence":"additional","affiliation":[{"name":"Department of Radiation Oncology University of W\u00fcrzburg W\u00fcrzburg Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2022,12,26]]},"reference":[{"key":"e_1_2_7_2_1","unstructured":"International Atomic Energy Agency and American Association of Physicists in Medicine.Dosimetry of Small Static Fields Used in External Beam Radiotherapy: An International Code of Practice for Reference and Relative Dose Determination. International Atomic Energy Agency and American Association of Physicists in Medicine;2017."},{"key":"e_1_2_7_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.radonc.2013.10.002"},{"key":"e_1_2_7_4_1","doi-asserted-by":"publisher","DOI":"10.1259\/0007-1285-37-439-544"},{"key":"e_1_2_7_5_1","doi-asserted-by":"publisher","DOI":"10.1118\/1.595161"},{"key":"e_1_2_7_6_1","doi-asserted-by":"publisher","DOI":"10.1118\/1.597024"},{"key":"e_1_2_7_7_1","doi-asserted-by":"publisher","DOI":"10.1259\/bjr\/27713136"},{"key":"e_1_2_7_8_1","doi-asserted-by":"publisher","DOI":"10.1118\/1.596856"},{"key":"e_1_2_7_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.radonc.2006.02.002"},{"key":"e_1_2_7_10_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.radonc.2010.12.003"},{"key":"e_1_2_7_11_1","volume-title":"Central Axis Depth Dose Data for Use in Radiotherapy 1996: A Survey of This Supplement Depth Doses and Related Data Measured in Water Or Equivalent Media","author":"Radiology BI","year":"1996"},{"key":"e_1_2_7_12_1","doi-asserted-by":"publisher","DOI":"10.3109\/00016922109133336"},{"key":"e_1_2_7_13_1","doi-asserted-by":"publisher","DOI":"10.1038\/s41592-019-0686-2"},{"key":"e_1_2_7_14_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01386223"},{"key":"e_1_2_7_15_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-0427(00)00435-0"},{"key":"e_1_2_7_16_1","doi-asserted-by":"publisher","DOI":"10.1002\/mp.13501"},{"key":"e_1_2_7_17_1","doi-asserted-by":"publisher","DOI":"10.1118\/1.3562896"},{"key":"e_1_2_7_18_1","doi-asserted-by":"publisher","DOI":"10.1118\/1.4903757"},{"key":"e_1_2_7_19_1","doi-asserted-by":"publisher","DOI":"10.1118\/1.2734383"},{"key":"e_1_2_7_20_1","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6560\/aa83f5"},{"key":"e_1_2_7_21_1","doi-asserted-by":"publisher","DOI":"10.1259\/0007-1285-14-164-265"}],"container-title":["Medical Physics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/mp.16069","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/mp.16069","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/aapm.onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/mp.16069","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,21]],"date-time":"2023-08-21T00:26:28Z","timestamp":1692577588000},"score":1,"resource":{"primary":{"URL":"https:\/\/aapm.onlinelibrary.wiley.com\/doi\/10.1002\/mp.16069"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,26]]},"references-count":20,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2023,2]]}},"alternative-id":["10.1002\/mp.16069"],"URL":"https:\/\/doi.org\/10.1002\/mp.16069","archive":["Portico"],"relation":{},"ISSN":["0094-2405","2473-4209"],"issn-type":[{"value":"0094-2405","type":"print"},{"value":"2473-4209","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,12,26]]},"assertion":[{"value":"2021-07-02","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2022-07-25","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2022-12-26","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}