Biomedical Engineering Reference
In-Depth Information
The curves from the TRIM code [
66
] are also shown for comparison purposes.
Differences into the depth-dose distributions come mainly from the different values
of the stopping power provided by each model (shown in Fig.
15.6
); if the energy-
loss straggling were not included in the simulations, the Bragg peak would be
sharper and deeper.
All the models we have presented here (except the results from SRIM) predict
the same mean ionization energy, I
79:4 eV, because their common starting point
was the OELF derived from the IXSS data [
16
]. For energies larger than 10 MeV the
SEICS code uses the Bethe stopping power. However there are still discrepancies in
the Bragg peak position predicted by the different models.
The depth-dose distribution obtained from the Ritchie-Howie [
17
], the Ashley
[
18
] and the MELF-GOS [
19
,
22
] models are rather similar, since their stopping
power is comparable at proton energies larger than 200 keV. However, the Bragg
peak calculated from the damped Ritchie [
21
]andtheIED[
20
,
60
] for 1 MeV and
10 MeV proton beams are shifted deeper as compared to the previous ones, since
these models provide smaller values for the stopping power at energies lower than
several MeV (see Fig.
15.6
). However for 75 MeV proton beams, the depth-dose
distributions obtained from all the models are quite similar since a large portion
of the energy loss (as the projectile energy decreases from 75 MeV to 10 MeV) is
evaluated with the same stopping power, namely the one provided by the Bethe
formula with I
D
79:4 eV (which is common to all models).
Therefore, it is important to notice that for high incident energies the position of
the Bragg peak is mostly determined at the millimeter scale by the value of the mean
excitation energy into the Bethe formula. But differences in the stopping power
values provided by the different extension algorithms at proton energies less than a
few MeV imply shifts in the Bragg peak of the order of micrometers (
D
4mwhen
E
D
1 MeV;
100 mwhenE
D
10 MeV and
300 mwhenE
D
75 MeV),
which could have microdosimetric implications.
15.5
Conclusions
The electronic energy deposited by a proton beam in liquid water has been evaluated
for several extended optical-data models currently used in the literature. We describe
diverse methodologies based on Drude's, Lindhard's and Mermin's ELF. The choice
of the current OELF data (either REF [
15
]orIXSS[
16
]) for liquid water has
a significance of
10% around the maximum stopping power. Nonetheless the
procedure to extend the OELF to non-zero momentum transfer is crucial to obtain
ELF values consistent with available experimental data at finite momentum transfer
[
42
,
43
]. Only the MELF-GOS [
19
,
22
]andtheIED[
20
,
60
] models satisfactorily
reproduce the experimental Bethe surface.
We want to call the attention on the influence into the stopping magnitudes
(especially at proton energies around and lower than the maximum stopping) of
the different methodologies used to extend the OELF at finite momentum transfer.
