Page 24 - ARNM-1-1

Advances in Radiotherapy &

Nuclear Medicine

ORIGINAL RESEARCH ARTICLE
Mathematic modeling of the dose in water for

calculating collimator scatter factor of flattening
filter and flattening filter free megavoltage

photon beams

1
1†
Yan-Cheng Ye , Zhang-Yan Shan , and Jia-Ming Wu 1,2,3† *
1 Heavy Ion Center of Wuwei Cancer Hospital, Gansu Wuwei Academy of Medical Sciences, Gansu
Wuwei Tumor Hospital, Wuwei City, Gansu Province, China
2 Department of Medical Physics, Chengde Medical University, Chengde City, Hebei Province, China
3 Department of Radiation Oncology, Yee Zen General Hospital, Taoyuan City, Taiwan

Abstract

This study presents an empirical method to model the percent depth dose (PDD)
curves of flattening filter (FF) and FF-free (FFF) high-energy photon beams using a
home-generated buildup function and tail function (buildup-tail function) in
radiation therapy. The modeling parameters n and μ of the buildup-tail function
† These authors contributed equally were used to characterize the collimator scatter factor (S ). The buildup function
c
to the work. was a quadratic function in the form of d with main parameters of d (depth
2
*Corresponding author: d + n
Jia-Ming Wu in water) and n, while the tail function was in the form of e −µ d and was composed
(jiaming.wu@chmsc.com) of an exponential function with d and μ. PDD was the product of buildup-tail
Citation: Ye Y, Shan Z, and Wu J, function and characterized by the buildup-tail function by adjusting the parameters
2023, Mathematic modeling of n and μ. The S of 6 and 10 MV in FF and FFF beams can be expressed simply by the
c
the dose in water for calculating modeling parameters n and μ. The main parameter n increases when photon
collimator scatter factor of flattening
filter and flattening filter free energy increases. Its physical meaning expresses the beam hardening of photon
megavoltage photon beams. Adv energy in PDD. The parameter μ can be treated as an attenuation coefficient in the
Radiother Nucl Med. tail function, decreasing when photon energy increases. The values of n and μ
https://doi.org/10.36922/arnm.0314 obtained from the fitted buildup-tail function were applied into an analytical
, S
Received: March 6, 2023 formula of S = n (S) 0.63 μ E c,FFF = n (S) 4.45 μ E c
to get the S of 6 and 10 MV in FF and
E
E
c,FF
μ
Accepted: June 6, 2023 FFF photon beams, with n , , S denoting n andμ at photon energy E of field size S.

E E
The calculated S was compared with the measured data and showed agreement,
c
Published Online: June 21, 2023 finding that the field difference was size within ±1%. This model can be used to
Copyright: © 2023 Author(s). parameterize the S for some clinical requirements. The modeling parameters n
c
This is an Open-Access article and μ can be used to predict the S in either FF or FFF beams for the treatment
distributed under the terms of the c
Creative Commons Attribution monitor unit in double-check dose calculation. The technique developed in this
License, permitting distribution, study can also be used for systematic or random errors in the quality assurance
and reproduction in any medium, program, thus improving the clinical dose computation accuracy for patient
provided the original work is
properly cited. treatment.
Publisher’s Note: AccScience
Publishing remains neutral with Keywords: Photon; Percent depth dose; Buildup-tail function; S ; Flattening filter;
regard to jurisdictional claims in c
published maps and institutional Flattening filter free
affiliations.
Volume 1 Issue 1 (2023) 1 https://doi.org/10.36922/arnm.0314