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Advances in Radiotherapy
& Nuclear Medicine Different approaches for the computation of BED

The mean BED and mean EQD are defined by averaging Corporation, 2024: https://office.microsoft.com/excel).
2
these quantities for different voxels, that is, A two-tailed Student’s t-test was used to evaluate the
significance of the differences between these parameters
   for the DCA and VMAT plans.
1 N voxel   D j () 
BED mean = N ∑  D voxel () + voxel  and 3. Results
j 1
α
j=1 
voxel
β
     N f( )   
 
BED Table 1 contains the locations and volumes of the lung
EQD 2,� mean = mean (15) lesions for the studied SBRT cases. Figure 2 displays the
1+ 2 mean value and standard deviation of the target dose for
( ) the evaluated DCA and VMAT plans. The computed BEDs
α
β
are presented in Figure 3. The dashed and solid lines in
BED mean can also be written in a more succinct form: Figures 2 and 3 represent the sample means of the displayed
parameters for the DCA and VMAT plans, respectively.
  Table 2 contains the sample mean and sample standard
 D  σ 2 deviation of the computed dosimetric and radiobiological
BED mean = D mean 1 + mean  + (16)
α
α
  N f( )  ( ) parameters.

N
 β  f β
4. Discussion
where
1 N voxel 4.1. General properties of BED mean and BEDnud
D mean = N ∑ D voxel j () and BED mean always exceeds or equals BED nud (Appendix).
j=1
1 voxel 2 In addition, BED depends on both α and β, whereas
nud
N voxel
σ = ∑ (D − D ) j () (17) BED depends only on the ratio of these parameters. The
2
mean
N voxel = j 1 mean voxel third important difference between BED mean and BED is
nud
For a fixed mean dose to the target, BED mean increases their different dependencies on the variance of the target
2
with increasing variance of the target dose (Eq. (16). In dose σ . That is, if the mean dose in the target is fixed, then
contrast, as mentioned above, BED decreases with BED mean always increases with increasing σ. Conversely,
nud
increasing σ . In addition (see Appendix), BED mean always under the same condition, BED decreases when σ
2
nud
exceeds or equals BED . increases. The differences between BED mean and BED are
nud
nud
further discussed in the subsequent sections.
2.6. Computation of BED for clinical cases
4.2. BED vs. BED in SBRT plans with DCA
The BED was computed for 51 cases of non-small lung cancer mean nud
treated with stereotactic body radiation therapy (SBRT). The results confirm that the sample mean of BED mean is
The considered treatment plans were produced with 6MV greater than that of BED . For example, in the considered
nud
flattening filter-free beams using Eclipse TPS (version 15.6, cases, the sample mean of BED mean was 9% and 18% > the
−1
−1
Varian Medical Systems, Inc., Palo Alto, CA). For each case, sample mean of BED for α = 0.15 Gy and α = 0.35 Gy ,
nud
two plans were created using VMAT and DCAs. respectively (Table 2). The latter value of the alpha is
consistent with that in a recent study that compared the
41
The analytical anisotropic algorithm and a dose grid LQ model with several other radiobiological models for
of 1.25 mm were used to compute the planned dose. The nearly 3000 patients.
3
same treatment regimen 10 Gy × 5 = 50 Gy was used for all
cases with plan normalization such that at least 95% of the 4.3. BED mean vs. BED in SBRT plans with VMAT
nud
PTV received the prescribed dose. Compared with the DCA plans, the studied VMAT
The BED was calculated for different values of alpha plans were characterized by smaller values of D mean
and alpha/beta ratio of 10 Gy. To compute the BED and and σ (Figure 2). For the VMAT plans, we had
nud
BED mean , the planned DVHs in Eclipse were exported and D mean = 52.9 ± 0.9 Gy and σ = 1.6 ± 0.5 Gy (Table 2). The
analyzed offline using Excel and Python scripts developed corresponding values of D mean and σ for the DCA plans
in-house. were as follows: D mean = 56.1 ± 1.1 Gy and σ = 3.5 ± 0.7 Gy.
As in the DCA plans, the sample mean of BED for the
mean
2.7. Data analysis VMAT plans was greater than that of BED . However,
nud
The mean values and variances of D mean , σ, BED mean , and the difference between BED mean and BED was smaller
nud
BED were computed in Microsoft Excel (Microsoft for the VMAT plans than for the DCA plans. That is, for
nud
Volume 2 Issue 4 (2024) 5 doi: 10.36922/arnm.4826