Page 27 - ARNM-1-1

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

d A
PDD = e · − µ d (I)
b-t
d + n
2
PDD (the abbreviation of PDD buildup-tail ) is described
b-t
separately as buildup function and tail function in the
following:
(i). Buildup function: d , where d is the depth in
d + n
2
water along the central axis in unit cm, n is a unitless
beam hardening factor scalar.
(ii). Tail function: e , where d is the depth in water along
-μd
the central axis in unit cm, μ is a linear attenuation B
coefficient factor in unit cm for adjusting the slope
-1
-μd
of the tail. The tail function in the form of e was
composed of an exponential function with main
parameters of d and μ.
The empirical function of PDD is the combination of
these two functions, denoted as PDD .
b-t
The PDD in FF and FFF beams of two photon energies
of 6 and 10 MV was modeled by the buildup-tail function
by adjusting the parameters n and μ to get the best fitting
for FF and FFF beams.
All PDDs of two high energy FF and FFF photon beams
with different field sizes at SSD = 100 cm were adjusted by
the main parameters of n and μ to get the best fitting. Figure 1. The fitting results of percent depth dose curves of flattening
filter beams for photon energies (A) 6 and (B) 10 MV, respectively.
3. Results
Table 1. The best fitting parameters n and μ for FF and FFF
3.1. The best fitting of PDD by empirical function in in two photon energies
two photon energies
Parameters 6 MV 10 MV 6 MV 10 MV
The converted curves of PDD in FF and FFF beams of FF FF FFF FFF
two photon energies of 6 and 10 MV measured by the ion n 0.208 0.495 0.21 0.51
chamber were coincident with film measurements. The
PDD in FF and FFF beams of two photon energies of 6 μ 0.0515 0.0458 0.0565 0.0498
and 10 MV adopted in this study was already measured Abbreviations: FF: Factor of flattening filter; FFF: Flattening filter free;
by the water phantom previously and was compared to n: μ.
the measurements in this study. By adjusting the main
0.63 μ
parameters of n and μ, the best fitting in FF beams for PDD S c,E,FF = n ·(FS) E (II)
E
of two photon energies at the field sizes of 10 cm×10 cm S = n ·(FS) (III)
4.45 μ
E
E
were listed in Figure 1A and B. S c,E,FFF and S indicate that the S can be fitted by
c,E,FF
c,E,FFF
c
Figure 1 shows the fitting results of PDD curves of FF the dominant parameters n and μ generated in buildup-
beams for photon energies of 6 and 10 MV. Figure 2 shows the tail function in FF and FFF beams for different photon
fitting results of PDD curves of FFF beams for photon energies energies, respectively. n and μ denote the best fitting
E
E
of 6 and 10 MV. Table 1 lists the best fitting parameters n and parameters n and μ of FF and FFF beams in buildup-
μ in FF and FFF beams for two photon energies. tail function at photon energy E. Figure 3 shows the best
3.2. The S expressed by the parameters n and μ fitting of the S by the S c,E,FF equation and Table 2 shows the
c
c
generated in the empirical buildup-tail function of comparison of measured and calculated S in FF beams of
c
photon energies 6 and 10 MV photon energies of 6 and 10 MV.
The S in FF and FFF beams for photon energies of 6 and Figure 4 shows the best fitting of the S by the S c,E,FFF
c
c
10 MV can be expressed by the parameters n and μ in the equation and Table 3 shows the comparison of measured
empirical buildup-tail function by Equations II and III: and calculated S in flattening filter free of photon energy
c
Volume 1 Issue 1 (2023) 4 https://doi.org/10.36922/arnm.0314