Total perturbation correction factor for PTW and NACP plane parallel chambers in electron beams

Radiotherapy and Oncology, 21 (1991) 135-140 © 1991 Elsevier Science Publishers B.V. 0167-8140/91/$03.50

135

RADION 00836

Total perturbation correction factor for PTW and NACP plane parallel chambers in electron beams C. Cinos, M. C. Lizuain a n d M. I. F e b r i a n Servicio de Fisica y Proteccibn Radiolbgica, Hospital de Bellvitge "Principes de Espa~a", L'Hospitalet de Ll., Barcelona, Spain (Received 16 March 1989, revision received 31 January 1991, accepted 5 February 1991)

Key words: Perturbation correction factor; Pu.pp; Plane parallel chambers; Electron beam; Recombination factor

Summary The international protocols of electron dosimetry published by the Nordic Association of Clinical Physics and the Sociedad Espafiola de Fisica M6dica recommend the use of a total perturbation correction factor Pu, pp which is constant for all plane parallel chambers. In this work we have compared the dose measured with the PTW-Markus and NACP plane parallel chambers in respect to a cylindrical one. The obtained results indicate that for the ionization chamber NACP the value of pu, pp = 1.000 + 0.005 is adequate while for the ionization chamber PTW the observed difference is explained by considering an individual total perturbation correction factor variable with the mean energy at depth z, Ez, as the fluence perturbation correction factor Pr is usually given for cylindrical chambers.

Introduction The knowledge of the absorbed dose to air calibration factor ND is necessary in order to determine the absorbed dose to a phantom from the ionization produced by the radiation beam in an ionization chamber. This factor can be calculated from the air kerma calibration factor, submitted by a calibration laboratory, by using the expression:

N D = NK'(1 - g ) ' k m ' k a s ' - -

1

(1)

ks" kst where g is the fraction of energy of secondary charged particles that is lost to bremsstrahlung, at the calibration energy; km is the factor to take account of non-air equivalence (at the calibration quality) of the ionization chamber wall and build-up cap materials; kas is the factor to allow for attenuation (absorption and scattering) in the walls of an ionization chamber and build-

up cap irradiated for calibration purposes; k s is the factor to allow for lack of saturation of charge collection (due to ion recombination) in an ionization chamber; kst is the factor to take account of the stem effect. In principle the value o f N D for plane parallel chambers can be calculated according to formula (1). However, most commercial available plane parallel chambers are made of heterogeneous wall materials. Therefore, the theoretical determination of kas and k m will have a large uncertainty. For some plane parallel chambers the product kas *km has been determined experimentally [ 8,9]. The actual recommended method to determine the N D value of plane parallel chambers is an experimental method based on the doses measured in an electron beam with mean electron energy Eo equal or greater than 18 MeV [8]. The obtained results are compared with those corresponding to a cylindrical chamber whose N D is known. When N O is determined, the absorbed dose to a point P of an extense medium, m, due to an electron beam,

Address for correspondence: C. Cinos, Servicio de Fisica y Protecci6n Radiol6gica, Hospital de Bellvitge "Principes de Espafia', 08907 L'Hospitalet de LI, Barcelona, Spain.

136 will be calculated by using the expression:

(2)

D m ( e ) = M* "ND "Sm, air" Pf" Pal" Pwall

where M* is the corrected reading of the ionization chamber system; N D absorbed dose to air chamber factor; Sm. air ratios of average restricted stopping powers for material m to air; pf correction factor for the perturbation of the electron fluence next to the measuring point; pg correction factor for the displacement of the effective point of measurement of the ionization chamber ;pwaH correction factor to take into account the perturbation due to the chamber wall. Pd is equal to the unity if the effective point of measurement is applied. PwaH does not depend on the wall material for thin chamber walls, therefore, it can be considered equal to the unity too [5]. These three correction factors can be grouped together in the total perturbation factor, Pu, pp, that is similar to the factor Pr for all the chambers that verify the above conditions as the plane parallel chambers do. In a comparative study between the plane parallel chambers PTW and NACP [7], a difference was observed in the determined doses for the two chambers at several points of a phantom irradiated with an electron beam. In a posterior work, it was observed that these differences seemed to increase with the decrease in the mean electron energy at depth z, E z [ 3 ]. It was thought that this phenomenon could be due to the fact

that the total perturbation correction factor for these chambers Pu, pp, considered constant with value equal to 1.000 + 0.005 [ 10] was not applicable to all models of plane parallel chambers. The study was continued in order to determine a perturbation factor variable with Ez, as the fluence perturbation correction factor pf is usually given for cylindrical chambers [5,6]. To determine the variation of Pu factor with E z the absorbed dose to different points of a phantom has been determined for different energies by using a cylindrical ionization chamber and the plane parallel chambers studied. Materials and methods

Experimental The experiment was carried out using the pulsed and swept electron beam of the Therac-20 Saturne linear accelerator at nominal energies 6, 9, 13, 17 and 20 MeV. In Table I the characteristics of these electron beams are reported. The nominal fluence rate was 100 monitor units/min (approximately 100 cGy/min at the point of the maximum depth dose). The radiation field was 20 x 8 cm 2 in order to minimize the stem effect. The absorbed dose was determined at several depths between the surface and the practical range Rp. In Table II some examples of the measuring depths in P M M A and their corresponding effective points in

TABLE I Characteristics of the Therac-20 electron beams. Nominal energy (MeV)

Mean electron energy at the surface Eo (MeV)

R50 (cm)

Rp (cm)

6 9 13 17 20

5.38 8.15 11.78 16.16 19.15

2.25 3.46 5.01 6.77 8.06

2.78 4.31 6.08 8.16 9.82

TABLE II Some examples of measuring depths in PMMA and their corresponding effective depths in water for the nominal energy of 20 MeV for the three ionization chambers studied. NE 2571

NACP

PTW

ZpMMA(cm)

zefr (cm)

ZpMMA(cm)

z~er(cm)

ZpMMA (cm)

Zeer (cm)

1.000 2.000 3.000 5.000 7.200

0.979 2.129 3.289 5.610 8.160

0.800 1.800 2.800 4.800 7.000

1.029 2.179 3.339 5.659 8.209

0.800 1.800 2.800 4.800 7.000

0.956 2.106 3.266 5.587 8.137

137 water are shown, for 20 MeV and ionization chamber PTW. In the calculation of the effective depth in water it has been taken into account the corresponding ratio of the linear continuous slowing-down range, factor depending on Eo, the thickness of the entrance window in the case of plane parallel chambers and also the air cavity between the phantom plate above the chamber and chamber membrane in the case of the ionization chamber PTW, as the Markus construction characteristics indicate. Two 0.6cm 3 cylindrical chambers, NE2571 and NE2581, were used together with two plane parallel chambers, PTW M23343-187 and N A C P type 01, serial number 02-05. The electrometer employed was a Therados R D M - 2 A with two inputs. The high voltages applied to the ionization chambers were - 4 0 0 V , + 4 0 0 V and - 1 0 0 V . The P M M A phantom consisted of sheets of 30 x 30 cm 2 and of different thicknesses: 1, 0.5, 0.3 and 0.2cm. The NE2581 chamber was used as a monitor chamber (reference) and the collecting voltage was maintained constant at - 4 0 0 V during each series of measurements.

Determination of the absorbed dose In order to calculate the absorbed dose at the points referred to above, the leakage current, the polarity effect, the recombination correction factorps and the absorbed dose to air calibration factor ND were previously determined for each of the chambers PTW, N A C P and NE2571.

where Q + and Q_ are the charges measured with an opposite polarizing voltage ( - 400 V, + 400 V) is less than 0.3}'0 for all the studied chambers.

Recombination correction factor Ps The "two-voltage method" for pulsed and swept electron beams [ 1] was used for determining the Ps correction factor for each ionization chamber [2], with the following conditions: - Collecting voltages: Vl = - 4 0 0 V, V2 = - 100 V. Evaluation of the function q~(~, k), with the upper limit of integration k 2 = (Pmax/a)L Scale constant a of the Gaussian radial distribution of intensity at 100 cm distance from the position of the virtual electron source was determined by film (Kodak X-Omat V) exposed perpendicularly to the axis of the stationary electron beam. The optical density across the diameter of the circular blackened area was fitted to a Gaussian curve. The obtained values appear in Table III. - Correction for unsymmetrical field of integration because the irradiation field is 20 × 8 cmL To do this correction, the radiation field has been decomposed in 8 sectors: two of 122 °, two of 20 ° and four of 24 ° . The pulsed falling within each sector will be collected with the average efficiency obtained for the k value corresponding to the radius of the sector. The results ofps as a function of dose rate are shown in Fig. 1 for each one of the ionization chambers and for electron beam of 20 MeV. The nominal fluence rate in these cases was 100, 200, 300 and 400 monitor units/min. These values coincide with:

Leakage current The leakage current is very low and of minor significance during a period without irradiation. The obtained values are: PTW<8 x 10-14A N A C P < 4 x 10- 14 A NE2571 < 15 x 10-14A The post-irradiation leakage current is very difficult to determine due to its rapid descent. In order to avoid this effect the measurements were taken at intervals equal to those used to take the other measurements.

Polarity effect The value of the ratio

PQ+I-IQ_I IQ+I+IQ

I

values obtained by using the extrapolation method applied to measures performed between 121 and 600 V for the cylindrical chambers and between 121 and 500 V for the plane chambers [2]. The values obtained applying the Weinhous and Meli polynomial, recommended in the IAEA protocol [4]. For electrons of 20 MeV, theps factor obtained by us,

- T h e

-

TABLE III Scale constant a of the Gaussian radial distribution of intensity at 100 cm distance from the position of the virtual electron source. Nominal energy (MeV)

a (cm)

6 9 13 17 20

13.6 9.9 7.2 5.9 5.1

138 1.05

1.00

"-x

b o gs

~. - - - + _ _ _

..... ~ x~×

....

~x

"k' ....

0.90 0 U

+ NACP ~ PTW X NE 2571 0,85

I 0

x~ [ 1

I 2 Dose

rote

I 3

I 4

I 5

I 6

(Gy/min)

Fig. I. Collection efficiency (at - 400 V) as a function of the dose rate for pulsed a n d swept 20 M e V electron b e a m : cylindrical c h a m b e r NE257 l ( ), plane parallel c h a m b e r s N A C P ( . . . . . ) a n d P T W ( ...... ).

applying the two-voltage method under the above described conditions, is 0.08 % less than the obtained by using the Weinhous and Meli expression. For electrons of 6 MeV is 0.08 % more. It is to be noticed that: - The collection efficiencyof NACP chamber is slightly higher than of PTW chamber. - The NE2571 cylindrical chamber has a collection efficiency lower than that of the two plane parallel chambers. Absorbed dose to air calibration factor N o The absorbed dose to air calibration factor N o of the plane parallel chambers was determined by comparison with NE2571 cylindrical ionization chamber in a high energy electron beam [4,8,11-13]. For this, the three chambers were irradiated in turn in an electron beam with mean electron energy at the phantom surface Eo = 19.15 MeV and a depth of the effective point of measurement 37 mm, which corresponds to the maximum of the depth dose distribution. The operation was performed 5 times and an uncertainty of 0.4% (1 S.D.) was obtained. The N o value for the cylindrical chamber NE2571 was calculated from the air kerma calibration factor ArK given by the Secondary Standard Dosimetry Laboratory (CIEMAT Madrid, 1987). Results and discussion

By studying the relation between the absorbed doses at each point obtained with the cylindrical chamber NE2571 and the chambers NACP and PTW and by supposing the certainty of all the factors in the Eqn. (2), excepting pf, we may conclude that the possible differences between the absorbed doses would mean that the

correction factor for the perturbation of the electronic fluence, pf, in the plane parallel chambers would not be neglectable and it could be determined. NACP plane parallel chamber. The absorbed doses obtained with the chambers NE2571 and NACP differ in a 0.5% for all the measuring points (Fig. 2a) then the factorpu" pp = 1.000 + 0.005 given as total perturbation correction factor for plane parallel chambers and electron beams [10,11-13] would be applicable to this model of chamber and for any energy of the irradiation beam. P T W plane parallel chamber. The difference between the calculated doses with the PTW and the NE2571 chambers is higher than that could be expected due to the uncertainty of the measurements. The ratio of the absorbed doses determined with both chambers has been calculated and the values of Pu obtained at several points of the depth dose distribution curve of electron beams of 6, 9, 13, 17 and 20 MeV are plotted as a function of Ez (Fig. 2b). The calculation of Ez has been performed from the values of 2 o and z/Rp by following the most recent dosimetry protocols [4,11-13 ] that have assumed the results obtained applying Monte Carlo simulation of electron transport by Andreo and Brahme 1981 and Andreo 1983. These values ofpu, that decreases with Ez, could correct the perturbation produced in the electron beam by the PTW chamber, and could replace the factor Pu, pp = 1.000 + 0.005 [9] recommended for plane parallel chambers [11-13] which is not suitable for the PTW chamber. The uncertainty for each one of the calculated values ofpu was less than 0.6% (1 S.D.). This was derived from quadratic summation of the statistical uncertainties of the ionization chamber readings and absorbed dose to air calibration factor ND.

139 1.02

]~

1.00

~I~]~TI !~ ~ ~ ~][ !

U

_~

0.98

I1: U

0.96

g m ~ i-115

20

MeV

17

MeV

A

13

MeV

[]

9

MeV

+

6

MeV

X

0.94

.•

0.92

MEAN

1tO

ELECTRON

E N E R G Y AT

'

DEPTH

'

z

'

ll5

'

'

'

'

210

'

'

FZ ( M e V )

1.02

1O 0 U

g 7u uJ U

0.98

0.96

z 0 II1 ~:

20

MeV

17

MeV

/~

13

MeV

[]

9

MeV

+

6

MeV

X

094

092

,

,

I 0

,

,

,

MEAN

,

I 5

,

ELECTRON

,

,

I 10

ENERGY

AT

ll5 DEPTH

z

-)(-

210

r:z ( M e V )

Fig. 2. Perturbation correction factorpu as a function of the mean electron energy at depth z, ~'z. (a) NACP plane parallel chamber; (b) PTW plane parallel chamber.

1 02

If

i-t--

1.00

S

.~,

098

g_

o96,

,

;

. . . .

;

Mean electron

. . . . energy at

1'o depth

. . . .

z , Ez

1~' . . . .

/o

'

'

(MeV)

Fig. 3. Perturbation correction factor Pu for PTW plane parallel chamber as a function of the mean electron energy at depth z, ~'z, for points between the surface and the maximum absorbed dose.

140 The maximum value of Ez has been close to 17 MeV, corresponding to the nominal energy of 20 MeV, that is our maximum available energy. However, looking at the results we may see that above 10 MeV the value ofpu can be considered constant, and it is for lower energies that this value presents an appreciable variation. The lower value of Ez included is 2 MeV because the perturbation correction factor used in the calculation of the absorbed dose measured with the NE2571 chamber is only defined for Ez higher than 2 MeV [5,6]. We may observe a dispersion of the values ofpu for lower values of Ez. In this zone in Fig. 2b, a portion of the shown values correspond to zones of the depth ionization curve with strong gradient. Taking into account that usually the measures of the reference doses in electron beams are performed at the proximity of the maximum, in Fig. 3 are shown only the values of Pu corresponding to measuring points situated between the depth of the maximum of the absorbed dose and the surface, for the nominal energies studied. The nominal energy of 6 MeV is not included because the use of cylindrical ionization chambers, employed as a standard in the calculation of the correction factor Pu for plane parallel chambers, is not recommended in the case of low energies. The experimental values ofp~, shown in Fig. 3, are fitted to the function: Pu = 1 - a * e x p ( - b * E z )

(3)

TABLE IV Pertubation correction factor, Pu, for PTW plane parallel chamber as a function of the mean electron energy at depth z, Ez, for points between the surface and the maximum absorbed dose. Ez (MeV)

Pu

3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 8.0 9.0 10.0 17.0

0.978 0.983 0.987 0.990 0.992 0.994 0.995 0.996 0.997 0.998 0.999 0.999 0.999

being a = 0.0999 and b = 0.5061. The corresponding range of Ez is between 3 and 17 MeV. For example, in Table IV are shown some fitted values Ofpu obtained by using the function (3). This function is only valid for the measurement of the absorbed dose at the points close to the maximum of the depth dose distribution.

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8

9

10

11

12

13

Sociedad Espafiola de Fisica M6dica, San Lorenzo de E1 Escorial, 1985. Mattsson, L. O., Johansson, K. A. and Svensson~ H. Calibration and use of plane parallel ionization chambers for the determination of absorbed dose in electron beams. Acta Radiol. Oncol. 20: 385, 1981. Mijnheer, B. J., Wittk~imper, F. W. and Aalbers, A. H.L. D6termination de la dose absorb6e de r6f6rence dans les faisceaux de photons et d'61ectrons avec des chambres d'ionisation plates NACP et MARKUS. XXVIIIe Congr~s de la Soci&6 Fran~aise des Physiciens d'H6pital, Lyon, 1989. Morris, W. T. and Owen, B. An ionization chamber for therapy-level dosimetry of electron beams. Phys. Med. Biol. 20:718, 1975. NACP. Recommendations of the Nordic Association of Clinical Physics. Procedures in external radiation therapy dosimetry with electron and photon beams with maximum energies between 1 and 50 MeV. Acta Radiol. Oncol. 19: 55, 1980. NACP. Recommendations of the Nordic Association of Clinical Physics. Electron beams with mean energies at the phantom surface below 15 MeV. Acta Radiol. Oncol. 20: 403, 1981. Sociedad Espa~ola de Fisica M6dica. Procedimientos recomendados para la dosimetria de fotones y electrones de energias comprendidas entre 1 MeV y 50 MeV en radioterapia de haces externos. SEFM, Publ. hr. 1/1984, Madrid, 1984.