Shani G. Radiation Dosimetry: Instrumentation and Methods
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80 Radiation Dosimetry: Instrumentation and Methods
within all target volumes throughout the tissue of inter-
est. The importance and relevance of this pursuit will
depend upon the properties of the radionuclide emissions
and the spatial distribution of the radionuclide relative
to the target volumes.
When the distribution of radiolabeled antibody is non-
uniform, techniques of dose-averaging over volumes
greater in size than the individual target volumes can
become inadequate predictors of the biological effect.
The most fundamental parameter in microdosimetry
is the energy deposition
1
, from a single event (track
intersection) with a target volume. Given a specific irra-
diation geometry, target size and shape, and particle type,
the entire probability distribution of energy deposits
within the target volume from single traversals is
referred to as a single-event energy deposition spectrum.
A more commonly used quantity is the single-event spe-
cific energy . The quantity is the energy deposition
divided by the mass of the target volume m. The quan-
tity has been calculated and also measured, using a
Rossi proportional counter, for a number of radiations. For
high-dose radiation fields, of concern for therapy, one is
primarily interested in multiple-event spectra, where the
stochastics of individual target hits is convoluted with the
hit probability distribution. The microdosimetric quantity,
specific energy z, used to denote the stochastic energy
deposition per unit mass from multiple track traversals, is
the microdosimeter analogue of absorbed dose. Indeed,
the frequency mean of a multiple-event specific
energy spectrum f(z) is, under most circumstances, equal
to the absorbed dose. However, identical resulting from
differing specific energy spectra do not imply equitoxicity.
This notion is of immense importance for radioimmuno-
therapy, since microdosimetry can predict widely differing
tissue toxicities resulting from identical average tissue
doses. [60]
The full three-dimensional distribution of activity as
a function of time is required for the exact evaluation of
a microdosimetric spectrum. Such spectra have been cal-
culated from theoretical distributions.
An alternative approach is the point dose summation
methods by Monte Carlo or other methods. A distribution
of sources (which may be located extracellular, on the cell
surface, or intracellular) may be simulated or obtained
from digitized images of autoradiographs. Each source
decay is simulated, with an energy and direction of the
emission chosen. For a-particles the tracks are assumed
to be straight. If the line intersects a biological target, the
specific energy z deposited is determined by [60]
(2.234)
where
m is the target mass, dE/dx is the energy deposited
per unit track length, and and are the entrance and
exit coordinates of the track through the target. If the track
ends in the target, is the coordinate of the end of range
of the particle. If a track begins in the target, is zero.
The total distribution of specific energy f(z) for the
cellular targets represents a complete description of the
physical dose deposition throughout the target volume.
These physical data can be combined with a biological
cell inactivation model to estimate the fraction of cell
survivors. Such inactivation models evaluate the fraction
FIGURE 2.62 Distribution of
-particle dose calculated by the Fourier convolution method to tumor cell nuclei from
211
At and its
daughter
211
Pa for a 3.7 10
4
Bq/g specific activity after complete decay. Cells were assumed to be tightly packed and all the activity
distributed uniformly on the cell surface. Cell and cell nuclei are of 8 and 5
m in diameter, respectively. The mean specific energy
is 159 cGy. (From Reference [60]. With permission.)
f
1
()
z
1
z
1
1
z
1
z
F
()
z
F
z
1
m
----
Ed
dx
------
xd
t
1
t
2
t
1
t
2
t
2
t
1
Ch-02.fm Page 80 Friday, November 10, 2000 10:53 AM
Theoretical Aspects of Radiation Dosimetry 81
of cell survivors within each energy deposition bin and
then perform a weighted sum of these surviving fractions
over the cell populations.
Two methods are employed for the calculation of
microdosimetric spectra for internal radionuclides: the
Fourier convolution technique developed by Roesch [61]
and applied to problems with radiolabeled antibodies
by Fisher [74], and the application of full Monte Carlo
simulation by Humm [60] and by Roeske. [62] Examples
of specific energy spectra calculated by both methods are
illustrated in Figures 2.62 and 2.63.
Figure 2.62 is a specific energy spectrum calculated
by the Fourier convolution method for a population of
tightly packed cells, diameter 8
m, nuclear diameter 5
m,
uniformly labeled on the cell surface, after the complete
decay of 3.7 10
4
Bq/g of
211
At with
211
Po daughter. The
mean specific energy to the nucleus is 158 cGy, and the
fraction of cell nuclei receiving zero dose (delta) is 0.17.
Figure 2.63 is an a-particle hit and specific energy
spectrum calculated by the Monte Carlo method for a
uniform 7.4 10
4
Bq/g extracellular distribution of
211
At
labeled antibody with 25 radiolabeled antibodies bound
per cell surface. The cell and cell nuclear diameters are
10
m and 7.5
m, respectively. These are only two
examples of many different types of calculations that are
possible. The shape of microdosimetric spectra depends
on a number of parameters: the shape and size of the target
volume, the geometry of the source distribution relative
to the targets, the energy emission spectrum of the radio-
nuclide, etc.
FIGURE 2.63 Hit distribution (a) and specific energy spectrum (b) for the cell nucleus obtained by the Monte Carlo method, assuming
a uniform extracellular specific activity of 7.4
10
4
Bq/g of
211
At after complete decay of parent and daughter, within 25 decays
per cell surface. The stopping power table of Janni for protons, scaled for
-particles, was used to determine energy deposition. Cell
and cell nuclear diameters of 10 and 7.5
m, respectively, were used. Resultant distributions are based on 1000 iterations, and
the data is smoothed. The average number of hits is 10.3, and the average specific energy is 388 cGy with a standard deviation of
144 cGy. (From Reference [60]. With permission.)
Ch-02.fm Page 81 Friday, November 10, 2000 10:53 AM
82 Radiation Dosimetry: Instrumentation and Methods
The Medical Internal Radiation Dose (MIRD) Com-
mittee of the Society of Nuclear Medicine has provided
guidance on methods for calculating radiation-absorbed
dose estimates since 1968. The MIRD Primer gives a
complete explanation of the schema, which is a series of
general equations adaptable for use with either simple or
complex anatomical and kinetic models. By definition, the
absorbed dose is the energy absorbed from ionizing radi-
ation per unit mass of tissue. Because absorbed dose from
internally distributed radionuclides is never completely
uniform, the MIRD equations give the average, or mean,
absorbed dose to a volume of tissue. [63]
Microdosimetric techniques that account for statistical
aspects of particle track structures and energy distribution
patterns in microscopic volumes can be used to express
energy deposition in tissues from materials labeled with
alpha-particle or Auger-electron emitters, particularly
those incorporated within cells. The equation for calculat-
ing the absorbed dose may be written in various forms,
depending on available information, such as: [63]
(2.235)
where is the mean absorbed dose in a target
region from activity in a source region is the
cumulated activity (time integral of activity over the time
interval of interest) in the source; is the mean energy
emitted by a radionuclide per nuclear transition;
!
i
is the absorbed fraction (fraction of energy emitted in region
that is absorbed in region ); and is the mass of
the target r
k
. The absorbed fraction divided by the mass
may be represented by , the specific absorbed
fraction. The total mean absorbed dose in a target region
is calculated by summing the doses from all source regions
to the target.
Each type of radiation emitted by a radionuclide is
characterized by its own mean energy per particle and
its own intensity or number of particles emitted per tran-
sition . The mean energy emitted per transition, , is
equal to , where k is a constant that depends on the
units used for the terms in Equation (2.235).
The absorbed fraction varies with the type and energy
of the radiation, the type of material through which the
radiation passes, and geometric configuration and compo-
sition of the source and the target. If the amount of energy
imparted to any target other than the source is so insig-
nificant as to have little effect on the absorbed dose, the
radiation is considered to be nonpenetrating.
The product of and is a constant for a given
radionuclide and a given source-target combination, a
value designated by the MIRD Committee as the S value.
The mean absorbed dose equation can thus be written as
(2.236)
where
The cumulated activity represents the total number
of nuclear transformations occurring during the time of
interest in the source region and may be expressed in
units of microcurie hours, Becquerel seconds, or an appro-
priate multiple of these units. A compilation of cumulated
activities for various radionuclides or radioactive com-
pounds has not been published by the MIRD Committee
because the source regions differ for each radiolabeled
material, and the source regions and their cumulated activ-
ities often change as new research results become available.
Autoradiographic studies have clearly shown nonuni-
form distribution of radiolabeled monoclonal antibodies
in tumors. The MIRD schema can be used to estimate
absorbed doses for nonuniform distributions if the neces-
sary data are obtained. The limitation is in the lack of an
adequate model rather than in the schema. As the volume
for which the absorbed dose is calculated becomes
smaller, the nonuniformity of dose within that volume also
becomes smaller. [63]
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Ch-02.fm Page 83 Friday, November 10, 2000 10:53 AM
85
3
Ionization Chamber Dosimetry
CONTENTS
I. Introduction ...........................................................................................................................................................85
II. Correction Factors.................................................................................................................................................93
A. Plane-Parallel Ionization Chambers ...............................................................................................................93
B.
k
Q
Factors........................................................................................................................................................97
C. Cylindrical Ionization Chambers..................................................................................................................100
D. Other Correction Factors ..............................................................................................................................101
E. Monte Carlo Calculated Correction..............................................................................................................108
III. Build-Up Cap and Build-Up Region ..................................................................................................................110
IV. Charge Collection, Ion Recombination, and Saturation.....................................................................................119
V. Detector Wall Effect............................................................................................................................................140
VI. Chamber Polarity Effect......................................................................................................................................145
VII. Detector Perturbation ..........................................................................................................................................151
VIII. Displacement Correction.....................................................................................................................................155
IX. Ionization Chamber Calibration..........................................................................................................................162
X. Liquid Dielectric Ionization Chambers ..............................................................................................................181
XI. Technical Data for Some Ionization Chambers..................................................................................................196
XII. Portable Ionization Chambers.............................................................................................................................199
XIII. Other Ionization Chambers .................................................................................................................................203
References .......................................................................................................................................................................219
I. INTRODUCTION
The most commonly used dosimeters for dose measure-
ments and calibration of photon and electron beams
are exposure-calibrated ionization chambers. One dis-
advantage of ionization chambers for electron-beam
dosimetry is that the ionization-to-dose conversion fac-
tors, such as stopping-power ratios and perturbation fac-
tors, depend strongly upon electron energy and depth in
the phantom.
The ionization chamber should have low leakage cur-
rent as well as negligible stem and cable effects. Irradia-
tion of the chamber’s stem, collecting electrode, or cable
by high-energy electrons can lead to emission of second-
ary electrons or collection of electrons that could produce
a spurious ionization current.
Both cylindrical and plane-parallel ionization cham-
bers have been used for determining central-axis depth-
dose curves for electron beams. For thin plane-parallel
chambers, it is generally accepted that the effective point
of measurement is the front surface of the collecting
volume. For a cylindrical chamber, the effective point of
measurement is displaced toward the source from the cen-
ter of the chamber.
The following procedure is recommended for deter-
mining relative depth-dose values in a homogeneous phan-
tom using an ionization chamber. [1]
• Leakage: Leakage should be less than 0.1% of
maximum signal.
• Stability: Variation in sensitivity should not be
greater than 1%.
• Data collection
• Polarity
• Ion recombination
• Incorporate the above corrections of polarity
and ion recombination to determine the cor-
rected ionization charge
Q
corr
.
• Depth correction
• From the plot
Q
corr
vs.
d
, obtain the depth of
50% ionization
R
50
and practical range
R
p
, and
then determine the mean incident energy
and mean energy , as a function of depth
d
.
• Determine the mean restricted mass collision
stopping power ratio, , for the mean
E
0
E
d
E
d
E
0
1 dR
p
()
L
()
air
wate
r
Ch-03.fm(part 1) Page 85 Friday, November 10, 2000 11:58 AM
86
Radiation Dosimetry: Instrumentation and Methods
incident electron beam energy at each corrected
depth of measurement.
• Determine chamber replacement factor.
The central axis percent depth dose, %
D
, is given by
Plane-parallel chambers are usually characterized by
the following constructional details. The air volume is a
disc-shaped right circular cylinder, one flat face of which
constitutes the entrance window. The inside surface of the
entrance window is electrically conducting and forms the
outer electrode. The inner electrode is a conducting cir-
cular disc inset in the body insulator which forms the other
flat face of the cylinder opposite to the entrance window.
The sensitive volume is that fraction of the total air volume
through which the lines of electrical force between the
inner and outer electrodes pass. The inner and outer elec-
trodes are mounted in a supporting block of material (the
chamber body) to which the connecting cable is attached.
The cable usually exits the body in a direction parallel to
the entrance window. The sensitive volume is typically
between 0.05 and 0.5 cm
3
. The polarizing potential is
applied to the outer electrode, and the signal charge is
collected from the inner electrode. There is usually a third
electrode surface between the other two electrodes which
is not connected electrically to either of them but which
is designed to be held at the same potential as the inner
electrode. If the chamber assembly is fully guarded, this
third electrode will be present in the air volume as a ring
around the inner electrode. Plane-parallel chambers for
electron radiation have the following typical dimensions:
the entrance window thickness is 1 mm or less; the dis-
tance between the inner and outer electrode is 2 mm or
less; and the diameter of the inner (collecting) electrode
is 20 mm or less.
For measurements in electron beams of energies
below
10 MeV, plane-parallel ionization chambers
are recommended, and they must be used below
5
MeV. However, plane-parallel chambers are also suitable
for use above
10 MeV. The chambers should pref-
erably be designed for measurements in water, and the
construction should be as homogeneous and water equiv-
alent as possible; i.e., mass stopping powers and linear
scattering powers should be similar to those of water. It
is especially important to consider backscattering effects
from the rear wall of the chamber. Chambers designed for
measurements in solid phantoms should, accordingly, be as
phantom-equivalent as possible. Some chambers, however,
have a design that includes several materials, resulting
FIGURE 3.1
Diagram of a well-designed plane-parallel ionization chamber. Indicated in the diagram are height
a
and diameter
d
of the air cavity (1), diameter
m
of the collecting electrode (2), and width
g
of the guard ring (3). (From reference [8]. With permission.)
%Dd() 100
D
med
d()
D
med
d
max
()
--------------------------
E
0
E
0
E
0
Ch-03.fm(part 1) Page 86 Friday, November 10, 2000 11:58 AM
Ionization Chamber Dosimetry
87
in a significant departure from homogeneity. In these cases,
there is no simple rule for the selection of phantom mate-
rial. One of the main advantages of plane-parallel chambers
for electron beam dosimetry is the possibility of minimiz-
ing in-scattering perturbation effects,
P
cav
. Plane-parallel
ionization chambers may be designed so that the chamber
samples the electron fluence incident through the front
window, the contribution of electrons entering through the
side walls being negligible. This design justifies consid-
ering the effective point of measurement
P
eff
to be at the
center of the front surface of the air cavity. For practical
purposes, it is also convenient to choose the reference
point of the chamber at the same position. In order to
fulfill the requirements concerning
P
cav
and
P
eff
within a
reasonable approximation, plane-parallel chambers must
have a flat cavity; i.e., the ratio of cavity diameter and
cavity depth must be large (of the order of ten), the cavity
height should not exceed 2 mm, and the collecting
electrode should be surrounded by a guard electrode hav-
ing a width not smaller than 1.5 times the cavity height.
Such dimensions are reported to sufficiently reduce the
in-scattering perturbation effect. [2] Furthermore, the
diameter of the collecting electrode should not exceed
20 mm in order to reduce the influence of radial nonuni-
formities of the beam profile. The thickness of the front
window should be restricted to 1 mm at most to make
measurements at shallow depths possible. It is also nec-
essary for the air cavity to be vented so that it will equil-
ibrate rapidly with the external pressure and temperature.
An overview of desirable plane-parallel chamber prop-
erties is compiled in Table 3.1. Characteristics of several
commercial parallel chambers are shown in Table 3.2.
The mean energy at the phantom surface, , is
required for the evaluation of quantities and parameters
used in the formalism and mainly affects the choice of
stopping power ratios of water to air,
s
w,air
, at the reference
depth, namely
s
w,air
. For dosimetry purposes it
has become customary to specify the quality of electron
beams in terms of the mean energy at the surface of the
phantom, , determined from empirical relationships
between electron energy and the half-value depth in water,
R
50
. [3] The recommendation is to determine by using
the energy-range relationship [4]
where
C
2.33 MeV cm
1
and
R
50
in cm in water is
obtained from a depth-dose distribution measured with
constant source-chamber distance.
A photon beam is characterized by the ratio of
absorbed doses at depths of 20 and 10 cm for a constant
source-detector distance and a 10-cm
10-cm field at the
plane of the chamber, . Attention should be paid to
the use of certain solid-state detectors (some types of
diodes and diamonds) to measure depth-dose distributions
for the purpose of deriving . Significant discrepan-
cies between the reading of some detectors and that of a
reference ionization chamber at different depths have been
reported, which in certain cases might result in absorbed
dose deviations above 1% (see Figure 3.2). [5] A solid-
state detector whose response has been regularly verified
against a reference detector (ion chamber) should be
selected for these measurements.
The formalism for the determination of the absorbed
dose to water in high-energy photon and electron beams
is based on the use of an ionization chamber having a
calibration factor in terms of air kerma,
N
K
. The reference
quality
Q
0
is usually gamma rays from a
60
Co source. From
the chamber’s
N
K
value, the absorbed dose to air chamber
factor at the reference quality,
N
D
,
air
,
Q
0
, is obtained.
The formalism is based on the assumptions that the
volume of air in the sensitive region of the chamber cavity
and the average energy required to produce an ion pair,
W
air
,
are identical in the user’s beam quality
Q
and at the cali-
bration quality
Q
0
. Therefore,
N
D,air,Q
N
D,air,Q
0
N
D,air
.
The absorbed dose to water
D
w, Q
in the user’s beam
of quality
Q
, when the effective point of measurement of
the ionization chamber
P
eff
is positioned at the reference
depth, is given by
(3.1)
where
M
Q
is the reading of the ionization chamber and
electrometer system in the user’s beam, corrected for influ-
ence quantities (temperature, pressure, humidity, and sat-
uration);
N
D
,
air
is the absorbed dose to air chamber factor;
(
s
w
,
air
)
Q
is the stopping power ratio, water to air, in the
user’s beam; and
p
Q
is an overall perturbation factor for
TABLE 3.1
Desirable Properties for a Plane-Parallel Chamber
in Electron Radiation
Chamber Dimensions
Front window thickness
1 mm
Collecting electrode diameter
20 mm
Ratio of guard ring width to
cavity height
1.5
Cavity height
2 mm
In-scattering perturbation effect,
1%
Wall and backscattering
perturbation effects,
1%
Polarity effect
1%
Leakage current
A
Long-term stability
0.5%
a
Source:
From reference [8]. With permission.
E
0
p
cav
p
wall
10
14
E
0
, z
ref
()
E
0
E
0
E
0
MeV[]CR
50
TPR
10
20
TPR
10
20
D
w, Q
P
eff
() M
Q
N
D, air
s
w, air
()
Q
P
Q
Ch-03.fm(part 1) Page 87 Friday, November 10, 2000 11:58 AM
88
Radiation Dosimetry: Instrumentation and Methods
TABLE 3.2
Characteristics of Plane-Parallel Chamber Types (as stated by manufacturers)
Chamber Materials
Window
Thickness
Electrode
Spacing (mm)
Collecting
Electrode
Diameter
(mm)
Guard Ring
Width (mm)
Polarity
Effect
a
(%)
Leakage
Current
a
(A)
Long-Term
Stability
a
(%)
Recommended
Phantom
Material
Vinten 631 Aluminized mylar foil 1 mg/cm
2
2
1 20 3
0.2 larger PMMA
(Pitman 631) window, graphited mylar 0.006 mm cavity height reported [73] (phantom
foil electrode, styrene 2 integrated)
co-polymer, rear wall,
PMMA body
NACP01 Graphite window, 90 mg/cm
2
2 10 3
0.5 larger
0.5 Polystyrene,
(Scanditronix) graphited rexolite electrode, 0.5 mm reported [73] graphite,
Calcam-1 graphite body (back wall), water (with
(Dosetek) rexolite housing waterproof
housing)
NACP02 Mylar foil and graphite 104 mg/cm
2
2 10 3
0.5 larger
0.5 Water,
(Scanditronix) window, graphited rexolite 0.6 mm reported [74] PMMA
Calcam-2 electrode, graphite body
(Dosetek) (back wall), reloxite
housing
Markus chamber Graphite polyethylene foil 102 mg/cm
2
2 5.3 0.2
0.5 larger Water,
PTW 23 343 window, graphited 0.9 mm reported [75] larger reported PMMA
NA 30-329 polystyrene collector, (incl. cap)
NE 2534 PMMA body, PMMA cap
Holt chamber Graphited polystyrene wall 416 mg/cm
2
2 25 5
1 larger
0.5 Polystyrene
(Memorial) and electrode, polystyrene 4 mm reported [76] (phantom
NA 30-404 body integrated)
PS-033 Aluminized mylar foil 0.5 mg/cm
2
2.4 16.2 2.5
1 Polystyrene
(Capintec) window, carbon impregnated 0.004 mm
air equivalent plastic
electrode, polystyrene
body
10
14
10
14
210
16
10
15
10
14
Ch-03.fm(part 1) Page 88 Friday, November 10, 2000 11:58 AM
Ionization Chamber Dosimetry
89
Exradin 11 Conducting plastic wall and P11: 2 20 5.1 P11: poly-
electrodes,
model Pll: polystyrene
104 mg/cm
2
styrene, water
equivalent; model A11:
C552, air equivalent; 1 mm
model T11: A 150,
tissue equivalent
Roos chamber PMMA, 118 mg/cm
2
2 16 4
0.5 Water,
PTB FK6 graphited electrodes 1 mm PMMA
PTW 34001
Wellhöfer IC40
Attix chamber Kapton conductive film 4.8 mg/cm
2
1 12.7 13.5
0.3 Solid water
RMI 449 window, graphited
polyethylene collector, solid
water body
0.025 mm 0.7
reported
Schulz chamber Graphited polymide foil 60 mg/cm
2
2
1.5 19 3
0.5 Water
PTW 23346 electrodes, PMMA window 0.5 cavity
and body height: 5
Memorial pipe Graphited mylar window, 5 mg/cm
2
2.5 11.3
2.5 5 Polystyrene
rectangular graphite layer on 0.03 mm
polystyrene collector
Memorial pipe Graphited mylar window, 5 mg/cm
2
2.5 10 5 Polystyrene
circular graphite layer on 0.03 mm
polystyrene collector
a
Blanks correspond to no information available.
Source:
From Reference [8]. With permission.
10
15
10
14
3 10
14
10
14
Ch-03.fm(part 1) Page 89 Friday, November 10, 2000 11:58 AM