Theoretical Aspects of Radiation Dosimetry 65
can be modulated to produce a flat high-dose region, the
spread-out Bragg peak, at any depth of the body with a
lower dose in entrance region. No dose is deposited past
the distal border of the spread-out Bragg peak. With this
characteristic depth-dose curve, protons have a considerable
potential for sparing normal tissue surrounding a tumor.
Two dosimetry protocols have been published: one by
the American Association of Physicists in Medicine TG
20 [75] and one by the European Clinical Heavy Particle
Dosimetry Group (ECHED) [76], both providing a prac-
tical procedure for the determination of absorbed dose to
tissue or water, in proton beams, using ionization cham-
bers calibrated in terms of air kerma in a
60
Co beam. Both
protocols give an uncertainty of about 4% on this absorbed
dose determination. Because protons undergo little scat-
tering in low-Z materials, it is generally assumed that
perturbations caused by the non-water equivalence of ion-
ization chambers must be very small.
In proton beam dosimetry the use of
N
k
-calibrated
ionization is well established. This is the procedure rec-
ommended by the ECHED dosimetry protocol for thera-
peutic proton beams when no calorimetric calibration of
the ion chamber is available. The American TG-20 protocol
also recommended this procedure as an alternative to cal-
orimetry or Faraday-cup-based dosimetry methods.
A method which reduces the final uncertainity in the
measured dose to water, is to calibrate the ionization
chamber in terms of absorbed dose to water.
Ionization chamber dosimetry of proton beams using
cylindrical and plane-parallel chambers was discussed by
Medin et al. [48]
The formalism in the IAEA Code of Practice for
photon and electron dosimetry [64] can be extended to
proton beams. The absorbed dose to water at the user’s
beam quality, , at the reference point of the ionization
chamber is generally given by
(2.172)
where is the reading of the electrometer plus ioniza-
tion chamber at the user’s beam quality corrected for
influence quantities (temperature, pressure, humidity, sat-
uration, etc.), is the ratio of the mean
energy required to produce an ion pair in the user’s proton
beam quality Q and in the calibration quality , and
is the water to air stopping power ratio in the
user’s beam. The factor contains the product of dif-
ferent perturbation correction factors of the ion chamber
at the user’s beam quality, which generally consists of the
factors , and . These correct, respec-
tively, for the lack of water equivalence of the chamber
wall, the influence of the central electrode of the chamber
both during calibration and in-phantom measurements,
and the perturbation of the fluence of secondary electrons
due to differences in the scattering properties between the
air cavity and water. If the concept of effective point of
measurement is not used and the determination of
absorbed dose is referred to the center of the ionization
chamber, a fourth factor has to be included in
to take into account the replacement of water by the
detector. is the absorbed dose to air chamber factor
at the beam quality used by the dosimetry laboratory,
which is defined by the well-known relation. [64]
(2.173)
In the formalism the absorbed dose to water at the
center of the chamber is given by the relationship
(2.174)
where is obtained at the standard laboratory from
the knowledge of the absorbed dose to water at the point
of measurement in water for the calibration quality,
(2.175)
The factor in Equation (2.174) corrects for the
difference in beam quality at the standard laboratory and
at the user’s facility and should ideally be determined
experimentally at the same quality as the user’s beam.
When no experimental data are available, can be
calculated according to the expression
(2.176)
It should be noted that the chamber-dependent correction
factors and are not included in the definition of .
Another potential advantage in the use of a calibration
factor in terms of absorbed dose to water is that the product
of and , referred to as
, can be determined
using calorimetry with a much higher accuracy than that
obtained when the two factors are considered indepen-
dently, yielding
(2.177)
The expression for of a plane-parallel ionization
chamber can be written as
(2.178)
N
D
D
wQ,
P
eff
D
wQ,
P
eff
() M
Q
N
DQ
0
,
W
air
()
Q
0
W
air
()
Q
0
[]S
w air,
()
Q
p
Q
M
Q
W
air
()
Q
W
air
()
Q
0
Q
0
s
wair,
()
Q
p
Q
P
ca
P
Q
N
DQ
,
N
DQ
0
,
N
KQ
0
,
1 g()k
air
k
m
N
w
N
wQ
0
,
N
wQ
0
,
D
wQ
0
,
M
Q
0
k
Q
k
Q
s
wair,
()
Q
s
wair,
()
Q
0
[]W
air
()
Q
0
W
air
()
Q
0
[]P
Q
P
Q
0
()
k
att
k
m
k
Q
W
air
N
D
N
Dx,
N
D ref,
M
ref
p
cav,ref
p
cel-gbl ref,
M
x
p
cav,x
p
wall,x
p
cel-glb x,
Ch-02.fm Page 65 Friday, November 10, 2000 10:53 AM