Shani G. Radiation Dosimetry: Instrumentation and Methods

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160 Radiation Dosimetry: Instrumentation and Methods

where D is the percent depth dose and d is the depth at

which the chamber central axis is located. P

repl

values are

shown in Table 3.20.

Ma and Nahum [80] investigated the displacement-

effect corrections for ionization chambers calibrated in air

in terms of air kerma and used at a depth in a phantom

irradiated by medium energy x-ray beams for tube poten-

tials between 100 and 300 kV. The Monte Carlo code

system was used to simulate the coupled transport of pho-

tons and electrons.

The air kerma at a point, usually the center of the air

cavity of the chamber on an air cavity axis, that has a volume

deﬁned by the outer dimensions of the ionization chamber

and the stem in the water phantom can be written as:

(3.149)

The air kerma at the depth of the chamber center in

water in the absence of the chamber can be written as

(3.150)

where

dis

is the displacement correction factor that

accounts for the effect of the displacement of water by the

ionization chamber. Equation (3.150) deﬁnes p

dis

as a ratio

of air kermas.

The air kerma K

air,u

can be converted to the water

kerma at the same point in water, K

w, u

, through the ratio

of the mass energy absorption coefﬁcients for water to air

averaged over the photon ﬂuence at the same point in the

undisturbed phantom, ( /



)

w,air

In order to obtain the displacement correction factor,

dis

, one must ﬁrst calculate air kermas K

air,u

and .

(3.151)

and

(3.152)

where and are averaged over the

photon ﬂuence’ and primary and scattered, respectively.

In general, the difference between and

is very small and therefore, according to Equa-

tion (3.150), we have

(3.153)

K

air u,



air, u

 p

dis

()k

dis





TABLE 3.20

repl

factors for photon beams

Energy a

k (mm

–1

)

b c

Co 0.0040 0.0043 0.0030

5 MV 0.0040 0.0043 0.0026

8 MV 0.0031 0.0037 0.0022

16 MV 0.0024 0.0027 0.0020

42 MV 0.0025 0.0026 0.0016

Note: The measurement point was assumed to be at the central axis

of chamber, located at a depth of 5 cm for

Co and 10 cm for other

beams.

repl

 1 kr, where r is chamber radius in mm; a: from

measured data of Johansson et al;

b: from Equation (3.148), using

BJR 17 depth-dose data; c: from AAPM TG-21 protocol.

Source: From Reference [78]. With permission.

K

air, u

K

wu,

K

air u,





()

w air,



wu,

air u,





()

w air,







()

w air,





()

w air,





()

w air,





()

w air,

dis

air,u

/K

air u,

wu,

/K

wu,



FIGURE 3.72 Experimental values of P

repl,pp,E

for the ﬁve parallel-plate chambers studied in this work. Error bars are 1%. (From

Reference [77]. With permission.)

Ch-03.fm(part 2) Page 160 Friday, November 10, 2000 11:59 AM

Ionization Chamber Dosimetry 161

Figure 3.73 gives the values, calculated using the

simple attenuation and scattering method for a stemless

NE2571 chamber of 7.4-mm outer diameter and 26-mm

length for photon beams incident from different angles.

varies with both photon energy and incident angle.

It decreases rapidly with photon energy for low-energy

photons.

Figure 3.74 shows the dependence of on chamber

length for photons incident at a 90° angle. At 200 kV,

is 1.011 for 100-mm length but decreases to 1.003 for the

dimensions of an NE2571 chamber. For

Co gamma-rays,

increases with chamber length and stabilizes at about

0.994  0.001 for chamber length greater than 50 mm.

Further calculations show that for a 7.4-mm diameter and

FIGURE 3.73 The displacement corrections for an NE2571 chamber, calculated using the simple attenuation and scattering method

as ratios of the water kerma in a water cylinder of 7.4-mm diameter and 26-mm length, , to the water kerma in a low-density

(the same as that of air) water cavity, , for x-ray beams incident from either the side or the end of the water cylinder, or at a

45° angle (note that the quality of the

Co beam does not correspond to the HVL value). The statistical uncertainty in the calculated

kerma ratios is about 0.2%. (From Reference [80]. With permission.)

FIGURE 3.74 The variation of the displacement correction factor with chamber length for a chamber of 7.4-mm outer diameter,

calculated using the simple attenuation and scattering method for 70, 200, and 300-kV photons and

Co gamma-rays incident from

the side (90°). The statistical uncertainty in the calculated kerma ratios is about 0.1%. (From Reference [80]. With permission.)

wu,

K

wu,

p

dis

p

dis

p

dis

p

dis

p

dis

Ch-03.fm(part 2) Page 161 Friday, November 10, 2000 11:59 AM

162 Radiation Dosimetry: Instrumentation and Methods

7.4-mm long cylinder, is 0.991, while decreases

to 0.988 if the beam is incident on the end wall of the

cylinder (i.e., 0°) rather than on the side wall (i.e., 90°).

For a cylinder of 7.4-mm diameter and 7.4-mm length,

values are smaller than unity for photon energies

throughout the medium-energy range.

IX. IONIZATION CHAMBER CALIBRATION

Several methods for the calibration of plane-parallel

chambers have been reported in the literature. These are

shown in Figure 3.75 and can be described as follows. [81]

1. Calibration with high-energy electrons in phan-

tom. The location of the point of measurement

is taken as the center of the cylindrical chamber

and the inner surface (of the wall that is prox-

imal to the source) of the plane-parallel cham-

ber, respectively. The point for each chamber is

placed at

max

for the ionization curve, as deter-

mined by measurement for the electron beam

being used, and the ﬁeld size is measured at the

phantom surface Figure 3.75a.

2. ‘‘In-air” calibration of a plane-parallel cham-

ber using a

Co beam with a ﬁxed source-to-

detector distance (SDD) and ﬁeld size (FS),

p

dis

p

dis

p

dis

FIGURE 3.75 Schematic illustration of the irradiation geometries used for making calibrations of parallel-plate chambers with

cylindrical chambers. (A) Calibration with 20-MeV electrons. The cylindrical chamber is aligned with the midpoint of its collecting

volume, located on the beam axis at

max

, and its axis of rotation, perpendicular to the beam axis. The midpoint of the inner surface

of the front wall of the plane-parallel chamber is located on the beam axis, and the chamber walls are perpendicular to that

axis. (B) ‘‘In-air” calibration of a parallel-plate chamber using a

Co beam. Point of measurement taken as the chamber center.

Co beam. Both chambers are placed in phantoms at depth of 5 g/cm

. Point of

measurement taken as the center of the cylindrical chamber and the inner surface of the proximal electrode of the plane-parallel

chamber. (D) Calibration ‘‘in phantom at dose maximum,” with a

Co beam. The parallel-plate chamber was placed in the phantom

with full backscatter at

max

(determined by measurement). Point of measurement taken as the chamber center. In all cases, the

cylindrical chamber is shown on the left and the plane-parallel chamber is on the right. (From Reference [81]. With permission.)

Ch-03.fm(part 2) Page 162 Friday, November 10, 2000 11:59 AM

Ionization Chamber Dosimetry 163

measured at the SDD, with the point of mea-

surement being taken as the chamber center, and

with build-up cap required for both chambers

(Figure 3.75b).

3. Calibration ‘‘in phantom at depth,” with a

beam, both chambers being placed in phantoms

at depth d  5 g/cm

. The point of measurement

is taken as the center of the cylindrical chamber

and at the inner surface (of the wall that is

proximal to the source) of the plane-parallel

chamber Figure 3.75c.

4. Calibration ‘‘in phantom at dose maximum,”

with a

Co beam. The plane-parallel chamber

is placed in the phantom at d

max

with full back-

scatter (determined by measurement). The

point of measurement is taken as the chamber

center. The SDD and ﬁeld size are the same as

for the ‘‘in-air” method. The comparison is

made with a cylindrical chamber irradiated in

air (Figure 3.75d).

5. Method (d) is essentially the same as method (b),

the two being related by the backscatter factor.

There are only three independent methods, (a),

(b), and (c), and these are described in this

report; method (d) is not recommended.

Method (a) employs high-energy electrons,

method (b) makes use of a

Co gamma-ray beam

with the chambers located at a point in air, and

method (c) also employs a

Co beam but with

the chambers placed at depth in a phantom.

gas

for a plane-parallel chamber may be determined

as follows. Using the highest electron-beam energy avail-

able and the cylindrical chamber for which N

gas

is known,

determine the response per monitor unit at d

max

. Next,

place the plane-parallel chamber into the same dosimetry

phantom, taking care to position the inner surface of its

proximal electrode at the depth of the central axis of the

cylindrical chamber, and determine its response per mon-

itor unit. The cavity gas calibration factor for the plane-

parallel chamber is given by [82]

(3.154)

where the terms in the numerator apply to the cylindrical

chamber and those in the denominator apply to the plane-

parallel chamber.

gas

is the dose to the gas in the chamber

per electrometer reading (Gy/C or Gy/scale division) M,

ion

is the factor that corrects for ionization recombination

losses, and P

repl

is the replacement correction factor. M is

the electrometer reading (C or scale division), and it rep-

resents the measured average ionization for positive and

negative polarities, in Coulombs or scale division, cor-

rected to air density at 22°C, 760 mm Hg, but not corrected

for relative humidity, assuming it to be typical of labora-

tory conditions (50%  25%).

The highest electron-beam energy available must be

high enough to make the P

repl

value for the cylindrical

chamber no smaller than 0.98. For a typical Farmer-type

cylindrical chamber of inner diameter 6.3 mm, an electron

beam is required, with a mean energy of at least 10 MeV

at d

max

, the depth of the measurement required. The mean

energy at depth is related approximately to the mean inci-

dent energy.

Electron-beam diameters should be large enough to

provide complete in-scattering to the beam axis. Conser-

vatively, this requires a beam diameter of twice the range

R of the electrons in the phantom medium. Thus, a beam

diameter (cm) numerically equal to the incident electron

energy (MeV) is ample, assuming unit density.

The quantity in Equation (3.154) is derived from

the NIST calibration value of or for the chamber.

TABLE 3.21

Recommended Values of /(N  A

ion

)

and /(N

 A

ion

)

for Five Commercially

Available Plane-Parallel Chambers

Chamber

Build-up

material

or phantom material A

wall

comp

and /(N

ion

)

(10

–3

Gy/R) /(N

ion

)

Capintec Polysty 1.0022 0.960 8.84 1.005

PS-033

Exradin P-11 Polysty 1.0016 1.000 8.48 0.964

Holt Polysty 1.0097 1.000 8.55 0.972

NACP Graphite 1.0016 1.027 8.45 0.961

PTW-Markus Acrylic 1.0030 1.000 8.59 0.977

Factors to be applied in the calibration and use of plane-parallel chambers.

The build-up material of thickness 0.5 g/cm

is added to the front face of the chamber, except for the Holt in which the

build-up material is inherent in the design.

Source: From Reference [81]. With permission.

gas

wall

gas

ion

repl

()

cyl

/ MP

ion

()



gas

cyl

Ch-03.fm(part 2) Page 163 Friday, November 10, 2000 11:59 AM

164 Radiation Dosimetry: Instrumentation and Methods

Equation (3.155) relates to , based on the con-

ditions present during the NIST calibration of the chamber

in a

Co gamma-ray beam:

(3.155)

where is stated in R/C, R/scale division, Ckg

1

/C, or

Ckg

1

/scale division; k  2.58  10

4

CKg

1

or unity

if exposure is stated in Ckg

1

; and (W/e)

gas

 33.7 J/C.

ion

is the ion-collection efﬁciency, at the time of calibra-

tion. A

wall

is the correction factor for attenuation and scat-

tering of gamma-rays in the chamber wall and buildup

cap.



wall

is the quotient of absorbed dose by the collision

kerma in the chamber wall;



wall

1.005 for

Co gamma-

rays. is the mean restricted mass stopping power

ratio for the chamber wall material, relative to the gas

(ambient air) inside. is the mean mass energy

absorption coefﬁcient ratio for dry air relative to the cham-

ber wall material. K

comp

corrects for the composite nature

of the chamber and build-up cap. For a cylindrical cham-

ber and buildup cap, it is given by [81]

(3.156)

where



is the fraction of ionization due to electrons

arising from photon interactions in the chamber wall and





) is the fraction of ionization due to electrons arising

from photon interactions in the build-up material.

If the NIST calibration of the cylindrical chamber is

stated as an air-kerma calibration factor, N

in Gy/C, the

value of N

, in R/C for use in Equation (3.155), can be

obtained from

(3.157)

where

g is the average fraction of secondary electron

kinetic energy that is spent in bremsstrahlung production.

NIST takes g as 0.0032 and (W/e)

air

for dry air as 33.97

J/C for

Co gamma-rays. Thus, for these values, N



113.7N

. Recommended values of N

gas

ion

for the

cylindrical chambers commonly used can be found in

Gastorf et al. [83] N

gas

ion

values can be determined

using Equation (3.157).

In the

Co in-air method, the intercomparison between

the plane-parallel chamber and the NIST calibrated spher-

ical or cylindrical chamber is performed in a

Co gamma-

ray beam in air. An exposure or air-kerma calibration factor

or will be obtained for the plane-parallel chamber

by direct comparison with the spherical or cylindrical

chamber and is obtained from given

values. The following procedures should be followed: [81]

1. The plane-parallel chamber should be submit-

ted to the ADCL for calibration with the nec-

essary dose build-up material in place, unless

the proximal wall is already thick enough, as

is the case for the Holt chamber. The added

build-up material should have the same outer

diameter as the chamber and be of the material

speciﬁc in Table 3.21; its thickness should

be 0.5 g/cm

to ensure charged-particle equi-

librium, exclude electro-contamination that

may be present in the

Co beam, and match

the calculated A

wall

values given in Table 3.21.

2. The

Co beam should be 10  10 cm

at the

chamber measurement location, at a distance of

at least 80 cm from the source.

3. The correct alignment of the plane-parallel

chamber for the intercomparison is with the

midpoint of its ion-collecting volume located

on the beam axis at the measurement location

and its ﬂat chamber walls perpendicular to that

axis. This is the point of measurement for in-air

calibrations only and is required by the ion

chamber theory used to extract N

gas

. Similarly,

the use-provided build-up cap material must be

in place for the in-air calibration only.

In the

Co in-phantom method, the intercompari-

son between the plane-parallel chamber and the NIST-

calibrated cylindrical chamber is performed in a

gamma-ray beam at a depth of 5 g/cm

in a phantom of

material selected to match that of the plane-parallel cham-

ber. is related to the known value of by

(3.157)

where

cyl

and M

are, respectively, the meter readings

of the cylindrical and plane-parallel chambers under the

above conditions, corrected for temperature and pressure,

and M

is the average of each polarity. A

ion

is the ion-

collection efﬁciency at the time of calibration; is

obtained from the NIST calibration value of or ;

repl

is the correction factor for the replacement of phan-

tom material by the cavity of the ionization chamber [P

repl

is taken as unity in the 1983 AAPM protocol for plane-

parallel chambers, so it does not appear on the left-hand

side of Equation (3.157)]; and P

wall

is the correction factor

to account for the chamber material being different from

that of the phantom.

wall

for the plane-parallel chamber is difﬁcult to deter-

mine. In the ideal case, where the plane-parallel chamber

gas

cyl

gas

cyl

kW/e()

gas

ion

wall



wall



()

gas

wall





()

wall

air

comp

cyl

----------------------------------------------------------------



cyl

L



()

gas

wall





()

wall

air

comp

cyl





()

gas

wall





()

wall

air



()L/



()

gas

cap





()

cap

air





()

gas

wall





()

wall

air

------------------------------------------------------------------------------------------------------------------------



1 g() We()

air



gas

/ N

ion

()

gas

cyl

M/A

ion

()

gas

wall

()

M/A

ion

()

cyl

gas

repl

wall

()

cyl



gas

cyl

Ch-03.fm(part 2) Page 164 Friday, November 10, 2000 11:59 AM

Ionization Chamber Dosimetry 165

is made of only a single material that is identically matched

by the phantom medium, P

wall

equals unity. However, the

construction of plane-parallel chambers usually employs

more than one material. Thus, the phantom medium should

be selected to match whichever material is the most impor-

tant contributor of the secondary electrons that produce the

measured ionization.

If the chamber has a very thin front wall (for which



is nearly zero), its inﬂuence can be ignored because

practically all of the electrons then originate in the phan-

tom medium. That medium should be selected to match

the principal material of which the thicker rear wall is

constructed. Since secondary electrons are projected pref-

erentially in the forward hemisphere by

Co gamma-ray

interactions, the electron backscattering ability of the rear

wall (a strong function of atomic number) will be the most

important inﬂuence on the ionization. If the chamber has

a thicker front wall, for



which is signiﬁcantly greater

than zero, the phantom medium should be made of that

same material. However, if the back wall differs apprecia-

bly in atomic number, this in-phantom procedure should

not be expected to yield a satisfactory result, due to the

difference in electron backscattering from the back wall

in comparison with the phantom medium.

Once has been calculated, the determination of

absorbed dose for the user’s beam will proceed according

to TG-21. Since these chambers are designed primarily

for use with electron beams, calibration of those beams

only will be presented. When the chamber is placed in a

suitable phantom (medium), the dose to the medium will

be given by

(3.158)

where M is the electrometer reading (Coulombs or scale

division corrected to 22°C, 760 mm Hg). is the

ratio of the mean, restricted collision mass stopping power

of the phantom material to that of the chamber gas (ambi-

ent air). P

ion

is the factor that corrects for ionization recom-

bination losses that occur at the time of calibration of the

user’s electron beam.

In the 1983 AAPM protocol, the replacement correc-

tion factor P

repl

is taken as unity for plane-parallel cham-

bers, irrespective of electron-beam energy. Two of the

commercial chambers (Capintec and Markus) show clear

experimental evidence that P

repl

decreases with decreasing

electron energy. The Netherlands Commission on Radia-

tion Dosimetry, in their Code of Practice of the Dosimetry

of High-Energy Electron Beams, considered this situation

for the Markus chambers and recommended the following

equation for P

repl

(designated p

in their protocol):

(3.159)

For ﬁve commonly used parallel-plate ion chambers,

Monte Carlo calculations of the wall attenuation and

scatter correction factors (

wall

 or ) and the

correction for nonhomogeneous composition of the cham-

ber (K

comp

or related to k

) were presented by Rogers.

[84] The chambers were assumed to have 0.5 g/cm

build-up caps made of the predominant material in each

chamber. These correction factors are needed if air-

kerma calibration factors are used to deduce the cham-

ber’s cavity-gas calibration factor, N

gas

. The scatter from

the material around the cavity more than compensates

for the attenuation in the front wall and, hence, K

wall

values are less than unity. Thin collectors or insulators

behind the collecting volume can have a major effect

because electron backscattering depends strongly on

material.

The AAPM’s TG-21 dosimetry protocol recommends

calibrating parallel-plate ion chambers by establishing the

dose in a high-energy electron beam using a calibrated

cylindrical ion chamber and then using this dose to estab-

lish the calibration of the parallel-plate chamber. By equat-

ing the dose measured at

max

in an electron beam using

cylindrical and parallel-plate ion chambers, one ﬁnds by

following TG-21 that

(3.160)

where the charge readings from ion chambers are repre-

sented by

M and are understood to be corrected for tem-

perature, pressure, ion recombination, and polarity effects.

If an electron beam is not to be used, there are two

options: base the calibration on an in-air air-kerma cali-

bration factor, , or base

the calibration on an in-phantom absorbed-dose calibra-

tion factor, N

, or equivalent.

If the in-air route is chosen, N

gas

is determined from

(3.161)

where N

is the air-kerma calibration factor, is the

fraction of the electron’s energy lost by radiative pro-

cesses, K

wall

( ) corrects for the lack of charged-

particle equilibrium in the chamber walls (caused mostly

by photon attenuation and scatter), corrects for any

charge-collection losses in the calibration beam, and K

comp

corrects for any components in the chamber made of mate-

rials different from the wall material.

If the calibration of the parallel-plate chamber is done

starting from an absorbed-dose measurement in a phantom,

gas

med

gas



()

gas

med

ion

repl





()

gas

med

repl

1 0.041e

0.4E





wall

1

att

1

wall

gas cyl,

cyl

repl

cyl

wall

cyl

repl

wall

------------------------------

Gy/C()

W/e

air

()()[]

gas

1 g()



()

air

wall





()

wall

air

wall

comp

ion

-------------------------------------------------------------------------------

GyC

1

()

wall

1

ion

Ch-03.fm(part 2) Page 165 Friday, November 10, 2000 11:59 AM

166 Radiation Dosimetry: Instrumentation and Methods

one has [84]

(3.162)

where N

is the absorbed dose to the phantom material

per unit charge from the parallel-plate chamber (corrected

for ion recombination and polarity effects), P

wall

corrects

for the replacement of the phantom material by the mate-

rial in the ion chamber, and P

repl

corrects for the effects

of the cavity on the electron ﬂuence in the phantom at the

point of measurement. This equation is the basis of many

proposals and measurements related to determining N

gas

for parallel-plate ion chambers, where N

is usually deter-

mined using a calibrated cylindrical ion chamber in the

same phantom. In most cases, the phantom material is the

same as the material of the parallel-plate chamber and,

hence, P

wall

is taken as unity, as is P

repl

. Note, however,

that in a

Co beam for an ion chamber in a phantom or

free in air with a build-up cap of the phantom material,

wall

and K

comp

correct for the same physical effect. K

comp

corrects the chamber response for the fact that not all of

the chamber is made of the same material as the build-up

cap.

Results for the standard conﬁgurations are shown in

Table 3.22. The K

wall

factors are all less than unity, which

means that photon scatter is more important than attenu-

ation. With the exception of the Holt chamber, which

comes in a slab-phantom, the chambers have a K

wall

value

within 0.1% of 0.998. This should be compared to a typ-

ical value of 1.010 for a cylindrical thimble chamber with

a 0.5 g/cm

wall, in which case the photon attenuation

dominates the scatter. The value of 0.9904 for the Holt

chamber is 0.3% greater than the previous value published

using this computer code. This may be attributed mainly

to improved statistical precision (0.04% here vs. 0.2%

previously) and somewhat (0.1%) to the fact that the cur-

rent calculations are for a 100-cm

beam, whereas the

previous ones were for a broad beam.

The effects of using different buildup caps have been

investigated for the Markus, NACP, and Capintec cham-

bers. The results in Table 3.23 show some results. Effects

of the build-up caps on the calculated values of k

for

heterogeneous chambers do not follow what is expected

from a naive theory, in which the k

value of the chamber

is assumed to behave as the k

value of the cap. [84]

It was shown by Rogers [85] that basing clinical

dosimetry on absorbed-dose calibration factors N

leads

to considerable simpliﬁcation and reduced uncertainty in

dose measurement. A quantity k

is deﬁned which relates

an absorbed-dose calibration factor in a beam of quality

to that in a beam of quality Q. For 38 cylindrical ion

chambers, two sets of values were presented for N

TABLE 3.22

Calculated Values of K

wall

 and K

comp

for the 5 Parallel-Plate

Chambers, Each with a 0.5-g/cm

Build-Up Cap of the Chamber’s

Predominant Material Added to the Front Face (except for the Holt

chamber)

Chamber Cap Material K

wall

 k

att

comp

att

Capintec polystnoy 0.9978(4) 1.0022(4)

1.020(4)

0.952(4) 1.022(4)

Exradin P

11b

polystnoy 0.9984(3) 1.0016(3) 0.971(4) 1.000(4) 0.973(4)

Holt

b,d

polystnoy 0.9904(4) 1.0097(4) 0.974(5) 0.997(5) 0.983(5)

Markus

PMMA 0.9970(6) 1.0030(6) 0.982(4) 1.000(4) 0.985(4)

NACP graphite 0.9984(2) 1.0016(2) 0.973(3) 1.027(3) 0.975(3)

Note: The collector and/or insulators were included in the calculations. All cases are for a point source

with a

Co spectrum at a distance of 80 cm from the front face of the build-up cap. For in-air

measurement, the point of measurement is the midpoint of the air cavity. One-standard-deviation

statistical uncertainties in the last digit are shown in brackets. Estimated systematic uncertainties are

1% for k

and K

comp

and 0.05% for K

wall

or A

wall

Results for the Capintec chamber using a radius of 1. 6 cm are 0.1% less, i.e., insigniﬁcantly different.

This means the approximation of a square detector by a circular one has no effect on these results.

Recall that stem effect corrections must be used with this detector.

No insulator.

Note: N

gas

 k

att

(l  g) where g  0.003. Alternatively, N

gas

 (W/e)k

att

[J/C] for N

C/kg or N

gas

 8.764  10

–3

att

[Gy/R] for N

in R/C.

Holt chamber results are for a beam area of 100 cm

Source: From Reference [84]. With permission.

att

1

att

1

,

gas

wall

repl



()

air

water

[]

--------------------------------------------------------

GyC()

Ch-03.fm(part 2) Page 166 Friday, November 10, 2000 11:59 AM

Ionization Chamber Dosimetry 167

and N

gas

, and for k

for photon beams with beam qual-

ity speciﬁed by the ratio. One set is based on TG-

21’s protocol to allow the new formalism to be used while

maintaining equivalence to the TG-21 protocol. To dem-

onstrate the magnitude of the overall error in the TG-21

protocol, the other set uses corrected versions of the

TG-21 equations and the more consistent physical data of

the IAEA Code of Practice.

Given , the absorbed dose-to-water calibration

factor for an ion chamber in a beam of quality Q, and

under reference conditions of ﬁeld size and depth:

(3.163)

where is the absorbed dose to water at the location

of the center of the ion chamber when it is absent; the ion

chamber reading M has been corrected to reference con-

ditions of temperature and pressure; and corrects for

lack of complete charge collection in the user’s beam and

must be measured for each beam quality. This deﬁnition

of is analogous to the deﬁnition of the exposure cal-

ibration factor given by , where X is the

exposure at the location of the center of the ion chamber

(except that in the absorbed-dose equation, the cor-

rection is made explicit because its effects are not negli-

gible, unlike the normal case for exposure measurements).

The following dose equation from the AAPM protocol

also applies:

(3.164)

In the case where the absorbed-dose calibration factor

is known in some other beam quality , let be

a factor which accounts for changes in the calibration

factor between beam quality and

Q; i.e.,

(Gy/c) (3.165)

and from Equation (3.163):

(Gy) (3.166)

Equations (3.163) and (3.164) give

(Gy/c) (3.167)

Eliminating from this equation by using the analogous

equation for a beam of quality allows one to solve for :

(3.168)

The quantity relates the absorbed-dose calibration fac-

tor in a beam of quality

Q to that for a beam of quality

in the same medium. From the user’s point of view,

this is the simplest possible approach since it uses a cor-

rection factor which is conceptually very straightfor-

ward yet takes into account all of the physics.

A computer program, called PROT, has been written

to calculate and other protocol-related quantities for

photon beams as a function of beam quality Q for an

arbitrary ion chamber in a phantom of water, PMMA, or

polystyrene. The program calculates using the equa-

tions and data of the original TG-21 protocol or using the

TG-21 equations with the more consistent physical data

of the IAEA Code.

Conversion from to (in a

Co beam) gives

(Gy/R) (3.169)

where is in R/C [divide by

(C/kg)/R to get the result in Gy/(C/kg), for use with

when using the SI unit for exposure C/kg]. The

formalism can be applied to cases of electron beams

as well as photon beams. Conceptually, it loses its sim-

plicity somewhat because different quantities are involved

in the ratio for for electron and photon beams and

because becomes a function of both the beam quality

Q and the depth of dose maximum.

To investigate the relative merits of using an absorbed

dose calibration–based approach vs. an in-air calibration

factor–based approach, one must ﬁrst deﬁne the optimal

approach based on the in-air calibration factors. This can

TABLE 3.23

Calculated Effect on k

and K

wall

of Changing the

Material of the 0.5-g/cm

Build-Up Cap for the

NACP, Markus, and Capintec Chambers

Chamber k

wall

att

Capintec

polyst cap 1.020(4) 0.9978(4) 1.022(4)

PMMA cap 1.008(3) 0.9981(4) 1.010(3)

graphite cap 1.018(3) 0.9964(4) 1.022(3)

Markus

polyst cap 1.000(4) 0.9972(4) 1.003(4)

PMMA cap 0.982(4) 0.9970(6) 0.985(4)

graphite cap 0.984(3) 0.9949(4) 0.989(3)

NACP

polyst cap 0.984(3) 1.0003(3) 0.982(3)

PMMA cap 0.977(5) 1.0007(3) 0.976(5)

graphite cap 0.974(3) 0.9984(2) 0.975(3)

Source: From Reference [84]. With permission.

TPR

water

ion



water

ion

XMN



ion

water

ion

gas

wall

repl

L 



()

air

water

[]



water

ion



gas

wall

repl

L



()

air

water

[]



gas

wall

repl

L



()

air

water

[]

wall

repl

L



()

air

water

[]

----------------------------------------------------



-------

gas

---------

wall

repl

L 



()

air

water

[]



N

2.58 10

4



1

Ch-03.fm(part 2) Page 167 Friday, November 10, 2000 11:59 AM

168 Radiation Dosimetry: Instrumentation and Methods

best be done by starting from an air-kerma calibration

factor and deﬁning a single

factor, , to relate the ion-chamber readings in phantom

M to the dose to the medium; i.e., is deﬁned such that:

(Gy) (3.170)

This is usually accompanied by requiring use of one of a

few speciﬁed types of ion chambers. Using Equation

(3.164) for the dose to the medium and substituting the

relationship between and gives:

(3.171)

One of the advantages of using this approach rather than

the and approach is that is within about 10%

of unity.

The approach was introduced to make use of an

in-air calibration as simple as possible and analogous to

the procedure in practical terms. This bypasses the

equivalent, now traditional approach of the AAPM TG-21

protocol where Equation (3.170) can be written:

(Gy) (3.172)

with a corrected equation for given by

(Gyc

1

) (3.173)

where has the standard meaning but has been written

in terms of the air-kerma calibration factor. In using this

approach, the complexities of using an in-air calibration

factor are handled within the factor .

Figure 3.77 shows the size of the differences between

the AAPM value of and the effective value of

used by the IAEA Code for a cavity diameter typical of

a Farmer-like chamber. In photon beams, this is the only

difference between the physics in the AAPM TG-21 pro-

tocol and IAEA Code of Practice (ignoring aluminum

electrode differences, after corrections, and using the same

data sets).

Note that the IAEA’s effective for

Co is not on

the curve for the values commonly found for

beams because the offset for

Co beams is different than

for all other beams. The net effect is that values for

the IAEA Code do not go to unity for values near

0.57, which is a typical value for a

Co beam. [85]

Figure 3.78 presents a comparison of various ,

correction factors as a function of cavity diameter in a

Co beam. The upper curve is that from the TG-21 pro-

tocol. The long dashed and solid curves are those given

by the IAEA offsets in the effective point of measurement,

as deﬁned explicitly for a

Co beam (long dash) or assum-

ing a general beam with of 0.57 (solid). The ﬁnal

dashed-dot curve represents the values implied by the

original data of Johanson et al. [72], on which the IAEA’s

offsets are based. These are signiﬁcant differences which

deserve further research.

Figure 3.79 presents curves for a more restricted

situation, namely for Farmer-like chambers. In this case

FIGURE 3.76 Plots vs. of TG-21 equivalent values of and values for the chambers discussed by Rogers. There is

a reduction in chamber-to-chamber variation obtained by using the approach, although the functional shape for a given detector

is the same in each case. (From Reference [85]. With permission.)

TPR

 N

We()

air

1 g()[]

med

ion



1 g()P

wall

repl

L



()

air

med

[]

L



()

air

wall







()

wall

air

wall

comp

ion

[]

--------------------------------------------------------------------------------------------



gas

med

ion

gas

wall

repl

L



()

air

med

[]



gas

1 g()

L



()

air

wall







()

wall

air

ion

------------------------------------------------------------



gas

repl

TPR

repl

TPR

Ch-03.fm(part 2) Page 168 Friday, November 10, 2000 11:59 AM

Ionization Chamber Dosimetry 169

there is only a 0.7% variation about a “neutral” median

value. This is given accurately by any of the PMMA-

walled Farmer chambers, which are what make up the

dark central group in Figure 3.79. Alternatively, the

formula

(3.174)

FIGURE 3.77 Comparison of the AAPM TG-21 values of and the value of the equivalent correction in the IAEA Code of

Practice for a 6.4-mm diameter Farmer-like chamber as a function of beam quality, speciﬁed as . The symbols show the values

speciﬁed for

Co beams. (From Reference [85]. With permission.)

FIGURE 3.78 Comparison, as a function of chamber diameter, of the effective values of the replacement correction factor given by

a variety of approaches. The upper short-dash curve is that given by TG-21. The long-dash curve is equivalent to the offset

recommended by the IAEA for a

Co beam, whereas the solid curve is the same quantity for a beam with a value of 0.57.

The dot-dash curve is based directly on the data of Johansson

et al., upon which the IAEA approach was based. (From Reference

[85]. With permission.)

repl

TPR

Q() 1.0 0.0215 TPR 0.57()

0.736 TPR 0.57()

Ch-03.fm(part 2) Page 169 Friday, November 10, 2000 11:59 AM