A windowless ionization chamber for soft X-ray dosimetry

Nuclear Instruments and Methods in Physics Research B 268 (2010) 92–96

Contents lists available at ScienceDirect

Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb

A windowless ionization chamber for soft X-ray dosimetry S. Pszona a,*, K. Wincel a, B. Zare˛ba a, W. Bulski b, P. Ulkowski b, M. Traczyk a a b

The Andrzej Soltan Institute for Nuclear Studies, 05-400 Otwock/Swierk, Poland Center of Oncology, Maria Sklodowska-Curie Memorial Institute, Warsaw, Poland

a r t i c l e

i n f o

Article history: Received 3 August 2009 Received in revised form 23 September 2009 Available online 1 October 2009 Keywords: Ionization chamber Free air ionization chamber Soft X-ray dosimetry

a b s t r a c t A new simplified model of a free air ionization chamber called a windowless air ionization chamber (WIC), for kerma in air measurements from the soft X-ray sources, has been designed and tested. The design is based on Monte Carlo calculations. The assembled WIC for testing has the electrodes in the form of half cylinders (internal diameter 36 mm; internal length 85 mm). The volume of the collecting sector of this chamber is around 1 cm3. An entrance aperture has 6 mm diameter. The results of MC calculations and tests for X-ray qualities: ranging 0.3–0.7 mm Al HVL are given. Ó 2009 Elsevier B.V. All rights reserved.

1. Introduction Recent developments of so-called electronic X-ray sources, designed especially for brachytherapy purposes [1–3] create the need for adequate dosimetric methods for their standardization. These sources operate on 40–50 kV voltages and can be categorized as soft X-rays. Generally, an obligation for standardization of these sources follows from the international recommendations such as American Association of Physicists in Medicine (AAPM) [4,5] as well the International Atomic Energy Agency (IAEA) [6] protocols. One of the basic measurable quantities needed by these protocols is the kinetic energy released in matter (kerma) in air. The recommended detectors for such standardization are based on ionization chambers namely, the free air ionization chambers, FAC, and the walled ionization chambers. The free air ionization chambers are in use for kerma in air standardization [7,8] at the level of primary standards laboratories. Generally, FAC, even for low X-rays are too cumbersome and therefore impractical for standardization purposes in field use. Even at the level of secondary standard dosimetry laboratories (SSDL), these devices are not applied. On the other hand, the full air equivalence of this type of chamber is sufficiently attractive for standardization purposes that considerable effort toward a new and improved design as a portable instrument for use in the field have been stimulated. Therefore, studies on a simplified design of the FAC have been undertaken with the aim out of elaborating a model of a windowless ionization chamber, WIC, which retains many of the basic characteristics of the original FAC. It is hoped that such a simplified construction will be applied as a * Corresponding author. Tel.: +48 227180565; fax: +48 227793481. E-mail address: [email protected] (S. Pszona). 0168-583X/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2009.09.037

portable instrument in many areas e.g. mammography, brachytherapy as well in stereotactic radiotherapy. It has been assumed, for this study that, due to the large departure from rigorous constraints which must be applied in designing a FAC, the response of a windowless model chamber to X-rays must be determined by a SSDL. The walled ionization chambers for in field kerma determination in air have entrance windows [9,10]. In the usual case the thickness and the elementary composition of the entrance windows are poorly defined. This causes some energy spectrum filtration of unknown magnitude when investigating soft X-ray sources. The energy response of these chambers depend very largely on the wall materials which, in many cases, are unstable (influence of humidity and time processes). This paper describes the work carried out (design and results) on a simplified model of a free air ionization chamber known as a windowless ionization chamber, WIC. 2. Materials and methods 2.1. Monte Carlo modeling The MC calculations aimed at elucidating an optimal position of a collecting volume of a model chamber with respect to the entrance and exit wall for a given range of photon energies. A schematic view of a windowless ionization chamber, applied for Monte Carlo modeling, is presented in Fig. 1. This model has a cylindrical shape with an inner diameter of 40 mm and total length of 85 mm. The air cone seen by a source of photons (distance from an entrance slit 60 cm) is defined by an entrance aperture of 6 mm (diameter) in a 5 mm thick lead entrance wall. The air cone, inside the modeled chamber, is divided into segments (slices) of 5 mm

93

S. Pszona et al. / Nuclear Instruments and Methods in Physics Research B 268 (2010) 92–96

Y, mm

20 10 1 2

5 6 7 8 9 10 11 12 13 14 15 16 17

X (0.5cm)

Fig. 1. Cross section of a windowless ionization chamber as used for the purpose of Monte Carlo modeling.

1.E-01

fluence [cm-2 ]

Photons

1.E-02

10keV 20keV

1.E-03

30keV 40keV 50keV

1.E-04

1.E-05

1.E-06

1.E-07 0

1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18

position of an air segment Fig. 2. Dependence of electron fluence in a given air segment of the modeled ionization chamber (see Fig. 1) generated by parallel monoenergetic photons 10– 50 keV energy as a function of its distance from the entrance aperture. MC results for parallel beam, planar photon source situated at 2 cm from a conical entrance aperture.

1.E-03

50keV, with exit aperture 50keV, no exit aperture

1.E-04

fluence [cm-2 ]

thick for the purpose of the calculations. The surrounding walls are radially distanced from an axis of the air cone by 20 mm leaving enough space for stopping the secondary electrons. Polymethylmethacrylate (PMMA) was used for the exit and side walls. The position of an air segment with respect to an entrance aperture is defined by Cartesian axis as shown in Fig. 1. The length of an air cone inside chamber is 85 mm. Based on this geometrical model, the electron fluencies, generated and crossed each air slice by monoenergetic photons, ranged 10–50 keV, were calculated based on the Monte Carlo method. The MCNP5 [11] Monte Carlo code with the MCNP5DATA [12] cross section library was used. Electron fluences were calculated using track length estimation of the cell flux tally. The total electron fluence is the sum of all electrons generated or crossing a given air slice, with energy cut off 1 keV. The total electron fluencies at each segment of the modeled chamber are the sources of ionizations within this segment. Therefore, it is enough to study the shape of the electron flux (fluence) across the modeled chamber in order to elucidate an optimal position for a collection volume with respect to an exit wall as well as the entrance aperture. The role of the entrance and exit sections is to stop all scattered electrons generated by photons in the entrance aperture and exit wall. The number of simulated histories was 6 billions. The estimated relative uncertainties achieved for the calculated results are usually <2% and frequently <1%. The MCNP code was run using a computer with a cluster of 48 cores with Message Passing Interface software. The Linux operating system (Gentoo) and a Fortran compiler (Intel version 10) were used. All calculations were carried out for a source strength of one photon at a distance of 600 mm from the entrance to the chamber. The results of the calculations – the total fluence of electrons at an air slice generated by monoenergetic photons of given energy emitted from a source with a given air slice, as well as, generated in an entrance aperture and in an exit wall, are seen in Figs. 2–4. Fig. 2 shows the fluence of electrons at a given air slice as a function of its distance from an entrance wall for a parallel beam of photons of 10, 20, 30, 40 and 50 keV emitted by a planar source at position of 2 cm from a back surface of a conical entrance aperture. An influence of an exit wall on the number of generated electrons due to the scattered radiation from an exit wall is clearly seen. A parallel beam of photons was deliberately selected to show the importance of a backing wall on the level scattered radiation. An aperture (hole) in an exit wall reduces the effect of scattering from it almost completely as seen in Fig. 3 (for 50 keV photons). As expected, the optimal position and length of a collecting volume are a function of the energy of the photons. As seen from Figs. 2 and 3, for a parallel beam of 50 keV mono energetic photons the influence of an exit wall is larger than the entrance one (case for a conical shape of an entrance aperture). The next set of results of MC

1.E-05

1.E-06

1.E-07 0

1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18

position of an air segment Fig. 3. Dependence of electron fluence in a given air segment of the modeled ionization chamber (see Fig. 1) generated by monoenergetic 50 keV photons for two cases: with and without exit aperture. MC results for parallel beam from a planar photon source situated 61 cm from an entrance aperture. Entrance aperture: conical.

calculations were carried out for a point source distanced 60 cm from an entrance aperture. In practice, an X-ray source cannot be considered a point source and the position of a WIC could deviate from a central line i.e. source–chamber axis. This effect has been studied as a case when an entrance aperture has cylindrical shape. The results of the calculations for such case are seen in Fig. 4. Here,

94

S. Pszona et al. / Nuclear Instruments and Methods in Physics Research B 268 (2010) 92–96

the collecting volume from the influence of electrons released from the entrance and exit slits. An exit aperture (20 mm diameter) in the exit wall (bottom cover) has a insert which can be removed to study the influence of scattered radiation from the exit walls. The chamber is surrounded by a 5 mm thick lead shield as indicated in the schematic cross section to avoid the fluence of scattered radiation on the collected charge readings. The prototype chamber [13] differs from the model one by the length of the air path inside the chamber (85 mm vs. 60 mm). The energy response of the assembled chamber was studied using X-ray beams at the secondary standard dosimetry laboratory, SSDL at the Oncology Center in Warsaw. The calibration coefficients, Nk (mGy/nC), were derived from comparison with a reference ionization chamber (type 40001-1020703M-T, Radcal Corporation) having a certificate of calibration issued by the SSDL of the International Atomic Energy Agency [14].

fluence [cm -2 ]

1.E-06

1.E-07

1.E-08

1.E-09 0

1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18

position of an air segment Fig. 4. Dependence of electron fluence in a given air segment of the modeled ionization chamber (see Fig. 1) generated by monoenergetic 50 keV photons. Without exit aperture. MC results for photon beam from a point photon source situated 61 cm from an entrance aperture. Entrance aperture: cylindrical.

for a 50 keV photon point source one can observe the large scattering effect of photons on the surfaces of an entrance aperture, resulting in electrons production, extending up to 30 mm into the chamber depth. The results in Fig. 4 also show the effects of electron production by these photons on an exit wall of the chamber (case where exit aperture is closed). Based on the results of MC modeling, seen in Figs. 2–4 the optimal distances for positioning a collection volume from an entrance aperture as well from an exit wall, can be evaluated as a function of the range of photon energies to be encompassed by the chamber to be constructed. 2.2. Experimentals Based on the results of Monte Carlo modeling, two WIC’s have been assembled for tests with X-rays of different qualities, namely a model one and a prototype one. In the tests i.e. kerma in air measurements, the mammography qualities of X-rays have been employed. A final layout of a WIC is seen in Fig. 5. An assembled chamber has three sectors, namely: entrance, collector and exit. The electrodes of this chamber have the form of half cylinders with 36 mm internal diameter separated by the guard electrodes. The chamber is made of PMMA covered (internally facing surfaces) by a conducting layer of graphite that forms an ionization chamber divided into three sectors, entrance, collector and exit. The entrance wall is made of 5 mm thick lead with a conical aperture (6 mm diameter). The collector section, 25 mm in length, is separated from other sectors by guard electrodes. The length of the entrance and exit sectors are 20 mm (model) and 30 mm (prototype) and, as seen from the modeling results, is sufficient for separating

3. Results and discussion The energy response of an assembled model of WIC was studied in X-ray fields with qualities, in the range of 0.3 mm Al to 0.71 mm Al of HVL. Two series of measurements aimed at measuring the kerma in air coefficient (Nk) were carried out (i) the exit aperture of investigated chamber is open and, (ii) with this aperture closed. The results are presented in Figs. 6 and 7. As seen from these figures; for the case i (open exit aperture) the energy response (in terms of HVL of Al) has tendencies to decrease for higher HVL down to 0.983 (in relation to a normalization point at 0.3 mm Al; for the case ii (closed exit aperture) the difference between the Nk for the closed aperture case are systematically lower, reaching 1.45% for X-rays with HVL 0.71 mm Al, the hardest spectrum used in these studies. The lower values for Nk in the modeled chamber (closed aperture) seem to be due to additional charges generated within the sensitive volume by scattered photons and electrons from the entrance aperture as well as from an exit wall. These results are, in fact, the effect of incomplete rejection of scattered electrons from the entrance and exit surfaces. Generally, these effects are at a level of <1.5% which seems to be acceptable. Taking into account the flatness of the energy responses of these two set ups i.e. with or without an exit aperture, they are within <0.7%, which seems to be very satisfactory at least for the X-ray qualities used in this experiment. To improve the energy dependence of this type of ionization chamber a prototypic WIC was assembled which differs from the model one by dimensions of entrance and exit sectors (having 85 mm total air path in chamber). A summary of the main dimensions of a prototype WIC is given in Table 1. All measurements were carried out for 250 V as supplying chamber voltage. For such voltage the correction factor for saturation was at the level of 1.016 (at the highest applied kerma rate of

SECTORS

ENTRANCE

COLLECTOR

ENTRANCE APERTURE

EXIT

EXIT APERTURE

SENSITIVE VOLUME Fig. 5. Cross section of an assembled prototypic WIC used in the verification studies.

95

S. Pszona et al. / Nuclear Instruments and Methods in Physics Research B 268 (2010) 92–96 1.05 N k=28.4mG y/nC for HVL 0.3 mm

1.01

N k (HVL)/N k mean

N k (HVL)/N k(HVL=0,3)

N k mean =31.49mGy/nC

1

0.95 0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.99

0.97 0.2

0.3

Fig. 6. Response (relative) of an assembled model WIC to X-rays of different qualities.

N k no aperture/N k with aperture

1

0.95 0.2

0.3

0.4

0.5

0.6

0.7

0.8

HVL [mm Al] Fig. 7. Ratio of the response of an assembled, model WIC to X-rays of different qualities with and without an exit aperture.

Table 1 Main dimensions of the prototype WIC. Aperture diameter (mm) Air path length (mm) Collecting length (mm) Measuring volume geometrical (cm3) Internal diameter of sectors (mm) External diameter (with shielding) (mm) Total external length (mm)

0.4

0.5

0.6

0.7

0.8

HVL [mm Al]

HVL [mm Al]

6 85 25 0.890 36 60 95

0.75 cGy/s). The final energy response (as a ratio to the mean value of Nk) of this prototypic WIC is seen in Fig. 8. As seen from this figure the energy response of the WIC is flat and resembles that of a free air ionization chamber, being dependent only on the mass of air inside the collector section. The degree of flatness of energy response of the WIC determined here by comparison with the reference chamber is limited to the accuracy of its response characteristics. These characteristics have apparently two regions with the respect to HVL, namely 0.3–0.39 mm Al and 0.59– 0.71 mm Al with a different range of uncertainties (anticipated from the results of measurements). The uncertainties stated in calibration certificate(14) was 0.8%. The reproducibility of the measuring results was 0.2%. A summary of the calibration results of the prototypic WIC is given in Table 2. An interesting point to note is that the mass of air calculated based on the experimentally determined Nk coefficient is higher by a factor of 1.02 from that estimated from the geometry of chamber. This is an unexpected result which means that no large

Fig. 8. Response (relative) of an assembled, prototypic WIC to X-rays of different qualities.

distortion of the electric field exists and, as a consequence of that, an enlargement of the sensitive volume of the assembled chamber is not dramatic. This could be assumed as a small departure from the rigorous principles of designing FAC. However, no attempts have been carried to discover a method to take into account the full influence of electric field effects on the collection volume of such a chamber. In our case it was performed deliberately to achieve a simpler construction without loosing too much of the basic performance of a FAC chamber as far as its performance for Kerma in air measurements, is concerned. As a consequence the modeled chambers have to be calibrated at SSDL as, indeed, any ionization chamber does which seeks permission to be used for standardization procedures. Similar to a FAC, the response of the WIC is valid only for a strictly defined distance from the center of the collection volume. This is due to the dependence of the mass of air seen by a source at the distance of the collecting volume from the source. In practice, this requirement is one of the obstacles to wider use of this type of chamber. To enlarge the range of distances source – chamber a correction factor derived experimentally was introduced. Under such conditions the Nk(r) factor is related to the derived Nk0 as:

Nk ðrÞ ¼ N k0 kðrÞ

ð1Þ

where Nk0 is the calibration factor derived through SSDL at a specified source detector distance, r0. Here, r0 = 610 mm. k(r) is the distance correction factor which accounts for the mass of air seen by a source as a function of source-detector distance. For r = 610 mm, k(r = 610) = 1. The distance correction factor, k(r) can be expressed by a relation which is a function (theoretical) of the distance, r (in mm), of the chamber from a source as seen in Eq. (1).

kðrÞ ¼ 0:7159 þ 0:0007r  4  107 r 2

ð2Þ

seen in Fig. 9 as solid line together with an experimental dependence derived based only on one point of measurements as:

kðrÞ ¼ 0:8537 þ 0:0002r

ð3Þ

This derived functions (2) and (3) are valid for the distance range 400 < r < 610 mm, where 610 mm is the calibration distance. The modeled WIC relative readings at 400 mm for two radiation qualities (0.3 and 0.7 mm Al HVL) are seen in Fig. 9. As seen from this figure the relation of chamber dependence on source–chamber distances does not exceed 5% even for distances which differ from the calibration distance by more than 35%. These results indicate that a WIC chamber may be applied for kerma in air measurements for source–detector distances which differs from the calibration distance when a correction factor is known.

96

S. Pszona et al. / Nuclear Instruments and Methods in Physics Research B 268 (2010) 92–96

Table 2 Summary of calibration results for the prototype WIC. Added filtration

HV (kV)

HVL (mm) Al.

Nk (mGy/nC)

Nk mean (mGy/nC)

Nk/Nk mean

0.03 mm 0.03 mm 0.03 mm 0.03 mm 0.03 mm 0.03 mm 0.03 mm

28 30 35 40 28 30 35

0.30 0.33 0.36 0.39 0.57 0.65 0.71

31.42 31.45 31.51 31.61 31.45 31.47 31.53

31.49

0.9977 0.9987 1.0006 1.0038 0.9987 0.9993 1.0012

Mo Mo Mo Mo Mo + 2 mm Al. Mo + 2 mm Al. Mo + 2 mm Al.

dardization purposes at the level of SSDL as well as in field measurements.

1.05 k(r) = 0.8537 + 0.0002r - practical - dashed -7 2

k(r)= 0.7159 + 0.0007r - 4*10 r - theoritical - solid

k(r )=N k (r )/N k0

Acknowledgements 1

This work was supported by Grants R13 005 003 and NN 401 216134 of the Ministry of Science and Education of Poland. The authors are indebted to B. Kocik, E. Jaworska and A. Dudzinski for their technical assistance.

0.95

References 0.9 350

610

400

450

500

550

600

650

700

r, mm Fig. 9. The distance correction factor, k(r) as a function (theoretical) of the distance, r, (solid line) and an experimental dependence (dashed line).

4. Conclusions A novel, simplified construction of a free air ionization chamber called a windowless ionization chamber has been designed, assembled and tested. The design was based on Monte Carlo modeling. The resulting prototype detector has a cylindrical shape with 36 mm internal diameter with an internal air path of 85 mm. with the sensitive volume around 1cm3. Its external dimensions are: 60 mm diameter and 95 mm length. It was tested in X-ray fields with qualities between HVL 0.3 mm and 0.7 mm Al which correspond to the qualities commonly used in mammography. The energy response of the tested prototypic chamber is flat, within <0.6% deviation (max. to min.). The results indicate that the newly designed windowless, cylindrically shaped ionization chamber is well suited for kerma in air measurements of soft X-rays for stan-

[1] Axxent HDR X-ray source. Xoft Inc., Product information, www.xoftinc.com. [2] J. Beatty, P.J. Biggs, K. Gall, P. Okunieff, F.S. Pardo, K.J. Harte, M.J. Dalterio, A.P. Sliski, A new miniature X-ray device for interstitial radiosurgery: dosimetry, Med. Phys. 23 (1) (1996) 53–62. [3] M. Słapa, W. Stras´, M. Traczyk, et al., X-ray tube with needle-like anode, Nukleonika 47 (3) (2002) 101. [4] J.F. Williamson, B.M. Coursey, L.A. DeWerd, L.A. Hanson, R. Nath, Dosimetric prerequisites for routine clinical use of new low energy photon interstitial brachytherapy sources, Med. Phys. 25 (1998) 2269–2270. [5] M.J. Rivard, B.M. Coursey, L.A. DeWerd, et al., Update of AAPM Task Group No. 43. A revised protocol for brachytherapy dose calculations, Med. Phys. 31 (2004) 633–674. [6] Calibration of brachytherapy sources, IAEA–TECDOC-1079, IAEA, 1999. [7] R. Loevinger, Wide angle free air chamber for calibration of low energy brachytherapy sources, Med. Phys. 20 (1993) 907. [8] H.-J. Selbach, H.-M. Kramer, W.S. Culberson, Realization of reference air – kerma rate for low-energy photon sources, Metrologia 45 (2008) 422–428. [9] D.S. Biggs, E.S. Thomson, Radiation properties of a miniature X-ray device for radiosurgery, Br. J. Radiol. 69 (1996) 544–547. [10] P.J. Biggs, Long term stability of a 50 kV X-ray unit for stereotactic irradiation, JACMP 7 (3) (2006) 12–20. [11] MCNP – A general Monte Carlo N – Particle Transport Code, Version 5, X-5 Monte Carlo Team LANL, 2003. [12] MCNP5DATA: Standard Neutron Photoatomic, Photonuclear, and Electron Data Libraries for MCNP5 (CCC-710). [13] Patent application.P.388458, Patent Office of Poland, 2009. [14] Calibration Certificate Nr POL/01/02, IAEA 21-02-2003.