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

1. Introduction contains both the collimator and phantom scatter that are
defined as the ratio of dose for the field of interest to that
The measurement of X-ray dose at the central axis for of a reference field for the same delivered MUs measured
flattening filter (FF) and FF free (FFF) beams in radiation under full scatter conditions in a large water tank at the
oncology is usually tabulated and used for clinical dose reference depth .
[11]
calculation. Percentage depth dose (PDD) and tissue-
phantom ratio (TPR) are dominated by the scattering There is scant S in the FFF beam for dose calculation
c
effect on the depth and field size . They consist mainly of scatter analysis. In this study, we proposed a simple
[1]
two parts: Primary fluence (adjusted for inverse square and mathematic equation to model the PDD for FF and FFF
beam hardening effects) and another part that represents beams using the buildup-tail function. The buildup-tail
the effects of attenuation. PDD and other quantities, such function includes two physical parameters, which are the
as TPR and field size factor (S ), are typically measured for beam-hardening coefficient n and the dose-averaged linear
cp
simple square-shaped fields for each therapy machine and attenuation coefficient μ. The modeling parameters n and
modality [2,3] . μ of buildup-tail function in PDD curve for FF and FFF
beams can also be used to characterize the S either in the
c
In modern treatment planning system (TPS), the head square field or the different individual upper jaw and lower
scatter is commonly taken into account by multi-source jaw setting separately for specific patient treatment MU
models [4-6] . The substantially reduced head scatter and calculation.
head scatter variation of FFF beams could simplify beam
modeling and consequently improve dose calculation 2. Materials and methods
accuracy. Especially intensity modulated radiation therapy,
which uses complex segment apertures, might benefit from 2.1. Experiment design and steps
the flat output factor variation. Several TPS model off-axis The experiment was conducted in the following steps:
softening uses an empirical correction formula derived (i). The mechanical isocenter check for verifying the
from 15 conventional/flattened photon beams delivered source axis distance (SAD) was conducted with the
by several linac models. Some researchers showed that wiggler point positioned at the nominal isocenter as
the variation of half value layer (HVL) values at an off- determined previously; another horizontal rod with
axis ray angle of 10° relative to on-axis HVL was reduced a fine point was held in a ring stand so that the two
from 12% to 5% after the removal of the FF . The third points coincided as best as possible. The other item
[7]
component that might influence the calculation accuracy is for checking the SAD precise position was to open the
electron contamination. As the largest portion of electron upper jaws of the collimator wide and close the lower
contamination originates in the FF, the FF is considered jaws to obtain a narrow slit of the minimum possible
the main source for the variation of d over field size .
[8]
max width. Using a new film, the above process was
It is important to distinguish the radiation absorbed repeated with the lower jaws open and the upper jaws
dose terminology for photon beam components of primary closed to a narrow slit. For an acceptable result, all the
[9]
and scattered photons , the quantities to quantify the lines should intersect or pass within a 2 mm-diameter
radiation fluence, and the quantities used to describe the circle.
radiation absorbed dose. It is often useful to separate the (ii). The PDD for two high photon energies of 6 and
radiation incident on the patient into different components 10 MV of Varian True Beam with FF and FFF
with distinguishable different dose deposition properties. was modeled in this study. The measurement data
obtained with 6 and 10 MV and previously published
Treatment planning systems and independent monitor
unit (MU) check systems of dosimetric data requirements data obtained with 4 and 18 MV were used for testing
the power of the mathematic modeling proposed in
for FF and FFF beams usually include variations of this study. The results of modeled PDD of 4 and 18
descriptors with field size . These may include the MV are demonstrated in the Figure S1, and no FF/
[10]
collimator scatter factors (S ), also known as head scatter FFF analysis is addressed in the contains.
c
factors, which account for the variation in beam output (iii). Measurement of photon beam PDD in FF and FFF
with field size from changes in direct and indirect radiation was conducted by Varian True Beam with two photon
from the head of the linac.
energies of 6 and 10 MV at a source-to-surface
The phantom scatter factor (S ) for FF and FFF distance (SSD)=100 cm with different field sizes. The
p
beams takes into account the change in scatter radiation quantity of PDD is defined as the quotient, expressed
originating in the phantom at a reference depth as the as a percentage, of the absorbed dose at any depth (d)
field size is changed. The term S for FF and FFF beams to the absorbed dose at a reference depth (usually at
cp

Volume 1 Issue 1 (2023) 2 https://doi.org/10.36922/arnm.0314