Page 31 - ARNM-1-1

Advances in Radiotherapy
& Nuclear Medicine Mathematic modeling of PDD for FF and FFF in photon

reduce the time of measurements and the confidence
to use interpolation. Knowing the smallest number of
measurements needed to characterize the S in either FF or
c
FFF high-energy X-ray beams would be helpful.
Acknowledgments

The author appreciates Professor Zhang-Yan Shan for his
great contribution to this study and is juxtaposed with first
author (co-first authors with equal contribution).
Funding

This work was supported by Science and Technology
Department, Gansu Province, China-funded projects:
Figure 5. The parameter n represents the photon beam hardening factor “The clinical application of carbon ion beams in radiation
in the buildup, and the parameter μ represents the attenuation coefficient oncology” (Grant no.: 22JR10KA029) and “The precise
of the photon beam in the medium. therapy platform of clinical and research for radiation
oncology in carbon ion therapy” (Grant no.: 22ZY1QH001).
used “collimator-scatter factor” was measured at d max for This work was also supported by Special project for popular
the TMR-based MU calculation algorithm. In this case, science of Gansu Province, China (The most significant
TG74 recommends using S , in-air output ratio as defined equipment in the field of radiotherapy- The fundamental
c
in this report, so long as S = S /S is determined using S principle, facility, and radiobiology in all aspects of carbon
c
cp
p
cp
measured at d . ion in radiation oncology 22JR10KA030).
max
A simple rule-of-thumb method has been developed by Conflict of interest
researchers for equating rectangular and square fields.
[19]
According to this rule, a rectangular field is equivalent to The authors declare no conflicts of interest.
a square field if they have the same area/perimeter (A/P). Author contributions
For example, the 18 × 12 cm field has an A/P of 14.4. The
2
square field that has the same 4 A/P is 14.4 × 14.4 cm . Conceptualization: Jia-Ming Wu
2
The PDD for irregular fields can also be applied using the Formal analysis: Zhang-Yan Shan
empirical buildup-tail function, and the results are listed Investigation: Yan-Cheng Ye
in the Figure S2. Writing – original draft: Zhang-Yan Shan, Jia-Ming Wu
Writing – review & editing: Yan-Cheng Ye, Zhang-Yan
5. Conclusions Shan, Jia-Ming Wu
The dosimetric quantities S either in FF or FFF beams, Ethics approval and consent to participate
c
and even the quantity S by dividing S with S , which are
c
cp
p
required for planning system measurement, or a MU check Not applicable.
methodology, were easily and accurately parameterized for
flattened and un-flattened beams using a simple mathematical Consent for publication
expression in this study. The data reproduced may be used Not applicable.
as expectation values for comparison when commissioning
similar beams, as there are scant published data on S in all FF Availability of data
c
or FFF photon beams from these accelerator types.
The data available following formal request from the
In this study, we presented an empirical method to corresponding author.
model the PDD curve for a high-energy photon beam
using the buildup-tail function in radiation therapy. The References
modeling parameters n and μ can also be used to predict S c 1. Khan FM, 2010, Dose distribution and scatter analysis.
in either FF or FFF beams for individual treatment MU to In: Khan FM, editor. The Physics of Radiation Therapy.
double check in patient dose calculation. 4 ed. Philadelphia, PA: Lippincott Williams and Wilkins,
th
The achievement of this study also provides a lot p140–157.
of help in double check of the measurement results to 2. Zhu TC, Ahnesjo A, Lam KL, et al., 2009, Report of

Volume 1 Issue 1 (2023) 8 https://doi.org/10.36922/arnm.0314