Antonella Fogliata, Antonella Stravato, Marco Pelizzoli, Francesco La Fauci, Pasqualina Gallo, Andrea Bresolin, Luca Cozzi, Giacomo Reggiori
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A novel formula is proposed for estimating the ESF to be used alongside the TRS-483 formalism for Field Output Factor (FOF) determination.</p><p><strong>Method: </strong>FOF for fields from 0.5 to 4 cm side shaped with MLC (jaws fixed to 4.4 × 4.4 cm<sup>2</sup>) were measured using two Varian TrueBeam (with Millennium and HD-MLC), at isocenter, 10 cm depth, with 6 and 10 MV beam energies, both with and without flattening filter, with microDiamond, DiodeE, and PinPoint3D detectors. Measured ratios were corrected using the OCF from the TRS-483 Tables to determine the FOF. The field size for each setting was determined as the FWHM of the scanning profiles acquired with the microDiamond detector. The ESF was determined using three methods: the Equivalent Area method (according to TRS-483), the Sterling Formula, and a new method according to the following formula: <math> <semantics><mrow><mi>E</mi> <mi>q</mi> <mi>S</mi> <mi>q</mi> <mi>F</mi> <mi>S</mi> <mo>=</mo> <mrow><mo>[</mo> <mrow><mn>2</mn> <mo>·</mo> <mi>m</mi> <mi>i</mi> <mi>n</mi> <msup><mrow><mo>(</mo> <mrow><mi>X</mi> <mo>,</mo> <mi>Y</mi></mrow> <mo>)</mo></mrow> <mi>a</mi></msup> <mo>·</mo> <mi>m</mi> <mi>a</mi> <mi>x</mi> <msup><mrow><mo>(</mo> <mrow><mi>X</mi> <mo>,</mo> <mi>Y</mi></mrow> <mo>)</mo></mrow> <mrow><mo>(</mo> <mrow><mn>2</mn> <mo>-</mo> <mi>a</mi></mrow> <mo>)</mo></mrow> </msup> </mrow> <mo>]</mo></mrow> <mo>/</mo> <mrow><mo>(</mo> <mrow><mi>X</mi> <mo>+</mo> <mi>Y</mi></mrow> <mo>)</mo></mrow> <mspace></mspace></mrow> <annotation>$EqSqFS = [ {2 \\cdot min{{( {X,Y} )}^a} \\cdot max{{( {X,Y} )}^{( {2 - a} )}}} ]/( {X + Y} )\\;$</annotation></semantics> </math> , with <math><semantics><mi>a</mi> <annotation>$a$</annotation></semantics> </math> here empirically set to 1.12.</p><p><strong>Results: </strong>Corrected FOF for square fields showed good agreement among the detectors with the Equivalent Area as ESF, validating the TRS-483 procedure. For even slightly elongated fields data demonstrated the inadequacy of the equivalent area method. The Sterling formula improved the results but still exhibits substantial differences for the smallest fields. The proposed EqSqFS effectively addresses these shortcomings, showing a description very close to the physical one provided by Ringholtz with the pencil beam method, which utilizes a kernel model to characterize both primary and scatter components of the dose.</p><p><strong>Conclusions: </strong>A new approach for ESF estimation is introduced, which is valid for elongated small fields, to be used in combination with TRS-483 OCF.</p>","PeriodicalId":94136,"journal":{"name":"Medical physics","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Small elongated MLC fields: Novel equivalent square field formula and output factors.\",\"authors\":\"Antonella Fogliata, Antonella Stravato, Marco Pelizzoli, Francesco La Fauci, Pasqualina Gallo, Andrea Bresolin, Luca Cozzi, Giacomo Reggiori\",\"doi\":\"10.1002/mp.17806\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><strong>Purpose: </strong>This study evaluates different approaches for estimating the equivalent square field size (ESF) to derive the Output Correction Factors (OCF) according to the IAEA TRS-483 protocol, for small fields, focusing on rectangular fields generated by MLCs. A novel formula is proposed for estimating the ESF to be used alongside the TRS-483 formalism for Field Output Factor (FOF) determination.</p><p><strong>Method: </strong>FOF for fields from 0.5 to 4 cm side shaped with MLC (jaws fixed to 4.4 × 4.4 cm<sup>2</sup>) were measured using two Varian TrueBeam (with Millennium and HD-MLC), at isocenter, 10 cm depth, with 6 and 10 MV beam energies, both with and without flattening filter, with microDiamond, DiodeE, and PinPoint3D detectors. Measured ratios were corrected using the OCF from the TRS-483 Tables to determine the FOF. The field size for each setting was determined as the FWHM of the scanning profiles acquired with the microDiamond detector. The ESF was determined using three methods: the Equivalent Area method (according to TRS-483), the Sterling Formula, and a new method according to the following formula: <math> <semantics><mrow><mi>E</mi> <mi>q</mi> <mi>S</mi> <mi>q</mi> <mi>F</mi> <mi>S</mi> <mo>=</mo> <mrow><mo>[</mo> <mrow><mn>2</mn> <mo>·</mo> <mi>m</mi> <mi>i</mi> <mi>n</mi> <msup><mrow><mo>(</mo> <mrow><mi>X</mi> <mo>,</mo> <mi>Y</mi></mrow> <mo>)</mo></mrow> <mi>a</mi></msup> <mo>·</mo> <mi>m</mi> <mi>a</mi> <mi>x</mi> <msup><mrow><mo>(</mo> <mrow><mi>X</mi> <mo>,</mo> <mi>Y</mi></mrow> <mo>)</mo></mrow> <mrow><mo>(</mo> <mrow><mn>2</mn> <mo>-</mo> <mi>a</mi></mrow> <mo>)</mo></mrow> </msup> </mrow> <mo>]</mo></mrow> <mo>/</mo> <mrow><mo>(</mo> <mrow><mi>X</mi> <mo>+</mo> <mi>Y</mi></mrow> <mo>)</mo></mrow> <mspace></mspace></mrow> <annotation>$EqSqFS = [ {2 \\\\cdot min{{( {X,Y} )}^a} \\\\cdot max{{( {X,Y} )}^{( {2 - a} )}}} ]/( {X + Y} )\\\\;$</annotation></semantics> </math> , with <math><semantics><mi>a</mi> <annotation>$a$</annotation></semantics> </math> here empirically set to 1.12.</p><p><strong>Results: </strong>Corrected FOF for square fields showed good agreement among the detectors with the Equivalent Area as ESF, validating the TRS-483 procedure. For even slightly elongated fields data demonstrated the inadequacy of the equivalent area method. The Sterling formula improved the results but still exhibits substantial differences for the smallest fields. The proposed EqSqFS effectively addresses these shortcomings, showing a description very close to the physical one provided by Ringholtz with the pencil beam method, which utilizes a kernel model to characterize both primary and scatter components of the dose.</p><p><strong>Conclusions: </strong>A new approach for ESF estimation is introduced, which is valid for elongated small fields, to be used in combination with TRS-483 OCF.</p>\",\"PeriodicalId\":94136,\"journal\":{\"name\":\"Medical physics\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2025-04-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Medical physics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1002/mp.17806\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Medical physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1002/mp.17806","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
目的：本研究根据IAEA TRS-483协议，评估了估算等效方场大小（ESF）的不同方法，以获得小场的输出校正因子（OCF），重点是mlc产生的矩形场。提出了一个新的公式来估计ESF，与TRS-483公式一起用于确定现场输出因子（FOF）。方法：使用两台瓦里安TrueBeam (Millennium和HD-MLC)，在等中心，10 cm深度，6 MV和10 MV光束能量，带和不带平坦滤波器，使用microDiamond， DiodeE和PinPoint3D探测器，测量边长为0.5 ~ 4 cm的MLC（钳口固定为4.4 × 4.4 cm2）场的FOF。使用TRS-483表中的OCF对测量的比率进行校正以确定FOF。每个设置的场大小被确定为微金刚石探测器获得的扫描剖面的频宽m。欧洲证券化论坛决心使用三种方法:等效面积法(根据trs - 483),英镑公式,和一个新的方法根据以下公式:E q S q F S =[2·m我n (X, Y)·m X (X, Y) (2 - a ) ] / ( X + Y) $ EqSqFS = [{2 \ cdot分钟{{}({X, Y}) ^一个}\ cdot马克斯{{}({X, Y}) ^ {({2 - a } )}}} ]/( { X + Y } )\;$ , 这里是一个美元经验设置为1.12。结果：校正后的方形场FOF与等效面积（ESF）一致，验证了TRS-483程序。即使是稍微拉长的油田，数据也证明了等效面积法的不足。斯特林公式改进了结果，但对于最小的字段仍然显示出实质性的差异。提出的EqSqFS有效地解决了这些缺点，其描述非常接近Ringholtz用铅笔束方法提供的物理描述，该方法利用核模型来表征剂量的主要成分和散射成分。结论：结合TRS-483 OCF，提出了一种适用于细长小油田的ESF估计新方法。
Small elongated MLC fields: Novel equivalent square field formula and output factors.
Purpose: This study evaluates different approaches for estimating the equivalent square field size (ESF) to derive the Output Correction Factors (OCF) according to the IAEA TRS-483 protocol, for small fields, focusing on rectangular fields generated by MLCs. A novel formula is proposed for estimating the ESF to be used alongside the TRS-483 formalism for Field Output Factor (FOF) determination.
Method: FOF for fields from 0.5 to 4 cm side shaped with MLC (jaws fixed to 4.4 × 4.4 cm2) were measured using two Varian TrueBeam (with Millennium and HD-MLC), at isocenter, 10 cm depth, with 6 and 10 MV beam energies, both with and without flattening filter, with microDiamond, DiodeE, and PinPoint3D detectors. Measured ratios were corrected using the OCF from the TRS-483 Tables to determine the FOF. The field size for each setting was determined as the FWHM of the scanning profiles acquired with the microDiamond detector. The ESF was determined using three methods: the Equivalent Area method (according to TRS-483), the Sterling Formula, and a new method according to the following formula: , with here empirically set to 1.12.
Results: Corrected FOF for square fields showed good agreement among the detectors with the Equivalent Area as ESF, validating the TRS-483 procedure. For even slightly elongated fields data demonstrated the inadequacy of the equivalent area method. The Sterling formula improved the results but still exhibits substantial differences for the smallest fields. The proposed EqSqFS effectively addresses these shortcomings, showing a description very close to the physical one provided by Ringholtz with the pencil beam method, which utilizes a kernel model to characterize both primary and scatter components of the dose.
Conclusions: A new approach for ESF estimation is introduced, which is valid for elongated small fields, to be used in combination with TRS-483 OCF.
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