Biomedical Engineering Reference
In-Depth Information
Fig. 8.14
Rate of energy absorption per unit mass in thin slab
(dose rate,
D
) is equal to the product of the incident intensity
and mass energy-absorption coefficient.
duced by the photons are stopped in the slab. Under these conditions, the trans-
mitted intensity in Fig. 8.10 is given by
˙
=
˙
0
e
-
µ
en
x
.
(8.59)
1
, which is consistent with our assumptions, one can write
e
-
µ
en
x
For
µ
en
x
≈
1-
µ
en
x
. Equation (8.59) then implies that
˙
0
-
˙
=
˙
µ
en
x
.
(8.60)
0
With reference to Fig. 8.14, the rate at which energy is absorbed in the slab over an
area
A
is
(
˙
˙
)
A
=
˙
µ
en
xA
. Since the mass of the slab over this area is
ρAx
,
where
ρ
is the density, the rate of energy absorption per unit mass,
0
-
0
D
,intheslab
is
˙
µ
en
xA
ρAx
0
µ
en
ρ
0
D
=
=
˙
.
(8.61)
The quantity
D
is, by definition, the average dose rate in the slab. As discussed in
Chapter 12, under the condition of electronic equilibrium Eq. (8.61) also implies
that the dose rate at a point in a medium is equal to the product of the intensity, or
energy fluence rate, at that point and the mass energy-absorption coefficient.
The mass energy-transfer coefficient can be employed in a similar derivation.
The quantity thus obtained,
0
µ
tr
ρ
K
=
˙
(8.62)
,
is called the average
kerma rate
in the slab. Equation (8.62) also gives the kerma rate
at a point in a medium in terms of the energy fluence rate at that point, irrespective
of electronic equilibrium. As described in Section 12.10, kerma is defined generally
as the total initial kinetic energy of all charged particles liberated by uncharged
radiation (photons and/or neutrons) per unit mass of material.
