Biomedical Engineering Reference
In-Depth Information
approximately one-half the maximum given by Eq. (9.3). These relationships facil-
itate the calculation of a “first-collision” dose from fast neutrons in soft tissue. The
first-collision dose is that delivered by neutrons that make only a single collision
in the target. The first-collision dose closely approximates the actual dose when the
mean free path of the neutrons is large compared with the dimensions of the tar-
get. A 5-MeV neutron, for example, has a macroscopic cross section in soft tissue
of 0.051 cm
-1
, and so its mean free path is
1/0.051
20
cm. Thus, in a target the
size of the body, a large fraction of 5-MeV neutrons will not make multiple col-
lisions, and the first-collision dose can be used as a basis for approximating the
actual dose. The first-collision dose is, of course, always a lower bound to the actual
dose. Moreover, fast neutrons deposit most of their energy in tissue by means of
collisions with hydrogen. Therefore, calculating the first-collision dose with tissue
hydrogen often provides a simple, lower-bound estimate of fast-neutron dose.
=
Example
Calculate the first-collision dose to tissue hydrogen per unit fluence of 5-MeV neu-
trons.
Solution
The density of H atoms is
N
=
10
22
cm
-3
(Table 12.3) and the cross section
for scattering 5-MeV neutrons is
σ
= 1.61 × 10
-24
cm
2
5.98
×
(Fig. 9.2). The mean energy
loss per collision,
Q
avg
=
2.5 MeV, is one-half the incident neutron energy. The dose
per unit neutron fluence from collisions with hydrogen is therefore (tissue density
ρ
=
1gcm
-3
)
5.98 × 10
22
cm
-3
× 1.61 × 10
-24
cm
2
N
σ
Q
avg
ρ
× 2.5 MeV
D
=
=
1gcm
-3
10
-13
JMeV
-1
10
-3
kg g
-1
= 3.85 × 10
-11
Gy cm
2
.
1.6
×
×
(12.31)
Note that the units of “Gy per (neutron cm
-2
)” are Gy cm
2
.
Similar calculations of the first-collision doses due to collisions of 5-MeV neu-
trons with the O, C, and N nuclei in soft tissue give, respectively, contributions of
0.244
10
-11
Gy cm
2
, representing in total about an
additional 10%. Detailed analysis shows that hydrogen recoils contribute approxi-
mately 85-95% of the first-collision soft-tissue dose for neutrons with energies be-
tween 10 keV and 10 MeV. Table 12.6 shows the analysis of first-collision neutron
doses.
Detailed calculations of multiple neutron scattering and energy deposition in
slabs and in anthropomorphic phantoms, containing soft tissue, bone, and lungs,
have been carried out by Monte Carlo techniques (Section 11.13). Computer pro-
grams are available, based on experimental cross-section data and theoretical algo-
rithms, to transport individual neutrons through a target with the same statistical
10
-11
, 0.079
10
-11
,and0.024
×
×
×
