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Using weighted power mean for equivalent square estimation.

Publication ,  Journal Article
Zhou, S; Wu, Q; Li, X; Ma, R; Zheng, D; Wang, S; Zhang, M; Li, S; Lei, Y; Fan, Q; Hyun, M; Diener, T; Enke, C
Published in: J Appl Clin Med Phys
November 2017

PURPOSE: Equivalent Square (ES) enables the calculation of many radiation quantities for rectangular treatment fields, based only on measurements from square fields. While it is widely applied in radiotherapy, its accuracy, especially for extremely elongated fields, still leaves room for improvement. In this study, we introduce a novel explicit ES formula based on Weighted Power Mean (WPM) function and compare its performance with the Sterling formula and Vadash/Bjärngard's formula. METHODS: The proposed WPM formula is ESWPMa,b=waα+1-wbα1/α for a rectangular photon field with sides a and b. The formula performance was evaluated by three methods: standard deviation of model fitting residual error, maximum relative model prediction error, and model's Akaike Information Criterion (AIC). Testing datasets included the ES table from British Journal of Radiology (BJR), photon output factors (Scp ) from the Varian TrueBeam Representative Beam Data (Med Phys. 2012;39:6981-7018), and published Scp data for Varian TrueBeam Edge (J Appl Clin Med Phys. 2015;16:125-148). RESULTS: For the BJR dataset, the best-fit parameter value α = -1.25 achieved a 20% reduction in standard deviation in ES estimation residual error compared with the two established formulae. For the two Varian datasets, employing WPM reduced the maximum relative error from 3.5% (Sterling) or 2% (Vadash/Bjärngard) to 0.7% for open field sizes ranging from 3 cm to 40 cm, and the reduction was even more prominent for 1 cm field sizes on Edge (J Appl Clin Med Phys. 2015;16:125-148). The AIC value of the WPM formula was consistently lower than its counterparts from the traditional formulae on photon output factors, most prominent on very elongated small fields. CONCLUSION: The WPM formula outperformed the traditional formulae on three testing datasets. With increasing utilization of very elongated, small rectangular fields in modern radiotherapy, improved photon output factor estimation is expected by adopting the WPM formula in treatment planning and secondary MU check.

Duke Scholars

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Published In

J Appl Clin Med Phys

DOI

EISSN

1526-9914

Publication Date

November 2017

Volume

18

Issue

6

Start / End Page

194 / 199

Location

United States

Related Subject Headings

  • Radiotherapy Planning, Computer-Assisted
  • Radiotherapy Dosage
  • Radiology
  • Photons
  • Particle Accelerators
  • Nuclear Medicine & Medical Imaging
  • Neoplasms
  • Humans
  • Data Collection
  • 5105 Medical and biological physics
 

Citation

APA
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Zhou, S., Wu, Q., Li, X., Ma, R., Zheng, D., Wang, S., … Enke, C. (2017). Using weighted power mean for equivalent square estimation. J Appl Clin Med Phys, 18(6), 194–199. https://doi.org/10.1002/acm2.12201
Zhou, Sumin, Qiuwen Wu, Xiaobo Li, Rongtao Ma, Dandan Zheng, Shuo Wang, Mutian Zhang, et al. “Using weighted power mean for equivalent square estimation.J Appl Clin Med Phys 18, no. 6 (November 2017): 194–99. https://doi.org/10.1002/acm2.12201.
Zhou S, Wu Q, Li X, Ma R, Zheng D, Wang S, et al. Using weighted power mean for equivalent square estimation. J Appl Clin Med Phys. 2017 Nov;18(6):194–9.
Zhou, Sumin, et al. “Using weighted power mean for equivalent square estimation.J Appl Clin Med Phys, vol. 18, no. 6, Nov. 2017, pp. 194–99. Pubmed, doi:10.1002/acm2.12201.
Zhou S, Wu Q, Li X, Ma R, Zheng D, Wang S, Zhang M, Li S, Lei Y, Fan Q, Hyun M, Diener T, Enke C. Using weighted power mean for equivalent square estimation. J Appl Clin Med Phys. 2017 Nov;18(6):194–199.

Published In

J Appl Clin Med Phys

DOI

EISSN

1526-9914

Publication Date

November 2017

Volume

18

Issue

6

Start / End Page

194 / 199

Location

United States

Related Subject Headings

  • Radiotherapy Planning, Computer-Assisted
  • Radiotherapy Dosage
  • Radiology
  • Photons
  • Particle Accelerators
  • Nuclear Medicine & Medical Imaging
  • Neoplasms
  • Humans
  • Data Collection
  • 5105 Medical and biological physics