Ion recombination correction for very high dose-per-pulse high-energy electron beams F. Di Martino, M. Giannelli, A. C. Traino, and M. Lazzeri Citation: Medical Physics 32, 2204 (2005); doi: 10.1118/1.1940167 View online: http://dx.doi.org/10.1118/1.1940167 View Table of Contents: http://scitation.aip.org/content/aapm/journal/medphys/32/7?ver=pdfcov Published by the American Association of Physicists in Medicine Articles you may be interested in The Italian affair: The employment of parallel-plate ionization chambers for dose measurements in high dose-perpulse IORT electron beams Med. Phys. 37, 2918 (2010); 10.1118/1.3432601 Evaluation of Al 2 O 3 : C optically stimulated luminescence (OSL) dosimeters for passive dosimetry of highenergy photon and electron beams in radiotherapy Med. Phys. 35, 260 (2008); 10.1118/1.2816106 Absolute dose measurements by means of a small cylindrical ionization chamber for very high dose per pulse high energy electron beams Med. Phys. 34, 952 (2007); 10.1118/1.2436979 Reference dosimetry in clinical high-energy electron beams: Comparison of the AAPM TG-51 and AAPM TG-21 dosimetry protocols Med. Phys. 28, 2077 (2001); 10.1118/1.1405841 AAPM’s TG-51 protocol for clinical reference dosimetry of high-energy photon and electron beams Med. Phys. 26, 1847 (1999); 10.1118/1.598691
Ion recombination correction for very high dose-per-pulse high-energy electron beams F. Di Martino,a兲 M. Giannelli, A. C. Traino, and M. Lazzerib兲 U.O. Fisica Sanitaria—Sezione di Fisica Medica, Azienda Ospedaliera Universitaria Pisana, via Roma 67, 56126 Pisa, Italy
共Received 9 December 2004; accepted for publication 30 April 2005; published 15 June 2005兲 The parallel-plate ionization chamber is the recommended tool for the absorbed dose measurement in pulsed high-energy electron beams. Typically, the electron beams used in radiotherapy have a dose-per-pulse value less then 0.1 cGy/ pulse. In this range the factor to correct the response of an ionization chamber for the lack of complete charge collection due to ion recombination 共ksat兲 can be properly evaluated with the standard “two voltage” method proposed by the international dosimetric reports. Very high dose-per-pulse electron beams are employed in some special Linac dedicated to the Intra-Operatory-Radiation-Therapy 共IORT兲. The high dose-per-pulse values 共3 – 13 cGy/ pulse兲 characterizing the IORT electron beams allow to deliver the therapeutic dose 共10– 20 Gy兲 in less than a minute. This considerably reduces the IORT procedure time, but some dosimetric problems arise because the standard method to evaluate ksat overestimates its value by 20%. Moreover, if the dose-per-pulse value ⬎1 cGy/ pulse, the dependence of ksat on the dose-per-pulse value cannot be neglected for relative dosimetry. In this work the dependence of ksat on the dose-per-pulse value is derived, based on the general equation that describes the ion recombination in the Boag theory. A new equation for ksat, depending on known or measurable quantities, is presented. The new ksat equation is experimentally tested by comparing the absorbed doses to water measured with parallelplate ionization chambers 共Roos and Markus兲 to that measured using dose-per-pulse independent dosimeters, such as radiochromic films and chemical Fricke dosimeters. These measurements are performed in the high dose-per-pulse 共3 – 13 cGy/ pulse兲 electron beams of the IORT dedicated Linac Hitesys Novac7 共Aprilia—Latina, Italy兲. The dose measurements made using the parallelplate chambers and those made using the dose-per-pulse independent dosimeters are in good agreement 共⬍3 % 兲. This demonstrates the possibility of using the parallel-plate ionization chambers also for the very high dose-per-pulse 共⬎1 cGy/ pulse兲 electron-beam dosimetry. © 2005 American Association of Physicists in Medicine. 关DOI: 10.1118/1.1940167兴 Key words: dose-per-pulse, ion recombination, ksat, ionization chamber, IORT I. INTRODUCTION
ksat =
The parallel-plate ionization chamber is the dosimetry tool recommended by the international reports for the pulsed high-energy 共⬎5 MeV兲 electron-beam dosimetry. The charge collected by the chamber can be converted into dose to water 共Dw兲 in the reference point 共zref兲 by the equation1 Dw共zref兲 = M corrND,w,Q⬘kQ,Q⬘ksat ,
共1兲
where M corr = Mk p,tkhkpol is the reading of the chamber 共M兲 corrected for temperature/pressure 共k p,t兲, humidity 共kh兲, and polarity 共kpol兲; ND,w,Q⬘ is the calibration factor in terms of the absorbed dose to water for the ionization chamber at a reference beam quality Q⬘; kQ,Q⬘ is the correction factor for the difference between the response of an ionization chamber in the reference beam quality Q⬘ used for calibrating the chamber and in the actual used beam quality Q; ksat is the factor to correct the response of an ionization chamber for the lack of complete charge collection due to ion recombination. A basic equation for ksat derived from the ionrecombination Boag theory2,3 is 2204
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u , e pu − 1 ln 1 + p
冉
冊
共2兲
where p is the free-electron fraction, i.e., electrons that escape attachment to gas molecules and so reach the electrode as free electrons and u=
d 2q , V
共3兲
where 共mV/C兲 is a constant depending on the gas in the cavity chamber; d 共m兲 is the distance between the chamber plates; q 共C / m3兲 is the charge liberated in air per unit volume and per pulse; and V 共Volt兲 is the voltage supply of the chamber. The free-electron fraction p depends on the voltage supply and on other chamber properties, but it does not depend on the dose rate. The high-energy pulsed electron beams of interest in clinical dosimetry have usually a dose-per-pulse value of less than 0.1 cGy/ pulse. This means that q and, consequently, u 关Eq. 共3兲兴 are small for the usually employed plane-parallel ionization chambers. Thus Eq. 共2兲 can be expanded to first order, giving
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ksat ⬇
Di Martino et al.: ksat evaluation for very high dose-per-pulse electron-beams
u ; ln共1 + u兲
共4兲
Eq. 共4兲 does not depend on the value of the free-electron fraction p. This means that the contribution of the freeelectron fraction to ksat is neglected for usual dose-per-pulse electron beams. For dose-per-pulse values of less than 0.1 cGy/ pulse, ksat is less than 1.05 for each parallel-plate ionization chamber recommended by the international reports.4 Thus, Eq. 共4兲 can be approximated by the equation4 u ksat ⬇ 1 + . 2
共5兲
The standard “two voltage” method is derived from Eq. 共5兲. This is the classical method, suggested by the international dosimetry reports,1 for ksat evaluation. Moreover, for doseper-pulse ⬍0.1 cGy/ pulse, the change of ksat due to the change of the dose-per-pulse value can be neglected in the relative dosimetry measurements. This means that the ksat value can be fixed to ksat = 1 for relative dosimetry measurements. For pulsed high-energy electron beams with values of dose per pulse ⬎1 cGy/ pulse, Eq. 共2兲 cannot be approximated by Eq. 共5兲. Thus Eq. 共5兲 cannot be used and the calculation of ksat cannot be done using the standard “two voltage” method. This brings a difficulty in using the parallelplane ionization chambers for absolute dosimetry. Moreover, for pulsed high-energy electron beams with values of dose per pulse ⬎1 cGy/ pulse, the change of ksat due to the change of the dose per pulse cannot be neglected for the relative dosimetry. High dose-per-pulse electron beams of 3 – 13 cGy/ pulse 共about 100 times greater than conventional beams兲 are actually produced from some special Linac, dedicated to IntraOperatory-Radiation-Therapy 共IORT兲. IORT is a radiationtherapy treatment modality that involves the delivery of a single large radiation dose to the exposed tumor during the surgical exploration or to the bed of a resected tumor. A Linac dedicated to IORT is a special accelerator located near the surgery room, with the possibility to be moved toward the patient and to deliver the treatment dose. IORT with a dedicated Linac has many practical and clinical advantages, but it has several dosimetric problems. During the IORT procedure it is impossible to execute treatment planning. Thus the absolute dosimetry in the reference condition and the relative dosimetry 共output factors, percentage depth dose, airgap factors兲 are fundamental. The dosimetric problems due to the very high dose-perpulse value suggest to use dose-rate-independent dosimeters instead of the parallel-plate ionization chambers. The doserate-independent dosimeters most commonly used are the chemical Fricke dosimeters5,6 and the radiochromic films.7,8 The Fricke dosimeters have a low spatial resolution. This does not allow their use for the relative dosimetry. They have a low sensitivity, thus they need to be exposed to high dose values. They are expensive and they need a post-irradiation reading procedure to give the dose value. The radiochromic Medical Physics, Vol. 32, No. 7, July 2005
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films are sensitive to temperature, humidity, time after irradiation, and they need both a calibration procedure and a post-irradiation procedure to give the dose value. In comparison to the Fricke dosimeter and radiochromic films, the ionization chamber has a very good sensitivity, it is practical to use, and it gives the dosimetric information online. Thus the possibility to use ionization chamber has a practical relevance. The problems related to the parallel-plate ionization chamber use for high dose-per-pulse electron beams were previously described and investigated but not solved.9 In this work a new equation for ksat based on the general equation that describes the ion recombination in the Boag theory 关Eq. 共2兲兴 is derived. This new equation depends on known or measurable quantities. It allows us to use the parallel plate ionization chambers also in high dose-per-pulse electron beams, either for relative or absolute dosimetry. The new ksat evaluation method in very high dose-per-pulse electron beams is experimentally validated for both the parallelplate ionization chambers type Roos and Markus. II. MATERIAL AND METHODS A. Theory
ksat is the factor to correct the response of an ionization chamber for the lack of complete charge collection due to ion recombination. It can be defined as ksat =
QL , QR
共6兲
where QL is the total electric charge produced in the ionization-chamber cavity and QR is the electric charge 共M兲 collected by the ionization chamber. Taking into account Eq. 共6兲, it follows that q =
Mksat , vch
共7兲
where q共C / m3兲 is the charge liberated in air per unit volume and per pulse into the parallel plate ionization chamber; is the number of electron beam pulses and ch共m3兲 is the effective ionization chamber volume. From Eqs. 共2兲, 共3兲, and 共7兲, it follows that
␣ Mksat , ksat = e p␣Mksat/ − 1 ln 1 + p
冉
冊
共8兲
where ␣ = 共d2 / Vch兲 depends only on the ionizationchamber properties and on its voltage supply. Equation 共8兲 can be analytically solved, giving ksat =
兵ln关p共e␣M/ − 1兲 + 1兴其 . p␣ M
共9兲
Finally, from Eqs. 共1兲 and 共9兲, a general equation for the absorbed dose to water in the reference point 共zref兲 for a parallel plate ionization chamber can be obtained:
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TABLE I. Specific parameters of the used parallel-plate ionization chamber Markus and Roos. Ion. chamber
Measurement volume 共m3兲
Polarity votage 共V兲
Electrode distance 共m兲
ND,w,Q⬘ 共Gy/C兲
共mV/C兲
kQ,Q⬘ 7 Mev
 共Gy−1兲
Markus Roos
0.055⫻ 10−6 0.35⫻ 10−6
+300 +100
0.002 0.002
5.76⫻ 108 ± 2% 0.833⫻ 108 ± 2%
3.02⫻ 1010 3.02⫻ 1010
0.916± 2% 0.931± 2%
12.71± 2% 41.43± 2%
Dw共zref兲 =
兵ln关p共e␣M/ − 1兲 + 1兴其ND,w,Q⬘kQ,Q⬘k p,tkhkpol p␣
. 共10兲
Note that Eq. 共10兲 is derived directly from Eq. 共1兲 and from the general theory of Boag 关Eq. 共2兲兴 without any approximation. B. Measurements
The knowledge of the free-electron fraction p for the chamber in use is required to calculate Dw共zref兲 by Eq. 共10兲. The theoretical value of the free-electron fraction p is unknown for the commonly used parallel plate ionization chambers. A set of measurements of Dw at different dose-per-pulse values 共range 3 – 13 cGy/ pulse兲 were performed using the pulsed electron beams of a IORT dedicated Linac Hitesys Novac7 共Aprilia—Latina, Italy兲 using dosimeters independent on dose-per-pulse value. The pulse frequency is 5 Hz and their duration is 4 s. The collimation of the beam is obtained with special perspex cylindrical tools. Different dose-per-pulse values at a fixed energy at the build-up depth in water can be obtained using collimators of a different size. Experimental values of ksat at a different dose-per-pulse of a 7 MeV electron beam were evaluated using the following equation 关see Eq. 共1兲兴: ksat =
Dw , M corrND,w,Q⬘kQ,Q⬘
共11兲
where Dw is the absorbed dose to water in the reference point measured with dose-per-pulse-independent Fricke dosimeters. The quality Q共R50兲 of the high dose-per-pulse electron
beams used were evaluated using radiochromic films 共HS Gafchromic兲 placed vertically in a water phantom. Note that HS Gafchromic dosimeters are independent of dose-perpulse and of energy of the electrons in the range 1 – 9 MeV.8 They can be placed and irradiated directly in water. The radiochromic films employed were read using a scanner Epson-Expression-1680-Pro with a large spectrum 共white兲 light. A red filter was also used to obtain the maximum absorption range 共 = 660 nm兲. The radiochromic films were read before irradiation to know the basal optical density and 48 hours after irradiation to evaluate the change of optical density due to the absorbed dose. The curve that relates optical density and absorbed dose to water was obtained fitting the experimental dose values from a standard Linac electron beam with a second-order polynomial function. The kQ,Q⬘ factor is reported in the IAEA TRS-398 report as a function of R50 and the ionization chamber type.1 From Eq. 共2兲, Eq. 共8兲, and Eq. 共11兲 it follows that
u=
␣ ND,w,Q⬘kQ,Q⬘k p,tkhkpol
Dw, = Dw,,eff ,
where Dw, = Dw / is the dose-per-pulse to water in the ref共Gy−1兲 = ␣ / ND,w,Q⬘ and Dw,,eff erence point; = Dw, / k p,tkhkpolkQ,Q⬘.  depends only on the ionization chamber characteristics while the dose-per-pulse dependence is expressed by Dw,,eff. Finally, from Eq. 共2兲 and Eq. 共12兲, ksat can be expressed as a function of dose-per-pulse and p values as
TABLE II. Measured values of dose/pulse Dw,, M corr, and ksat for Markus and Roos parallel-plane ionization chambers. The dose/pulse values were measured using Fricke dosimeters.
Dose/pulse 共cGy/ pulse± 2 % 兲
Electric charge collected per pulse 共nC/ pulse± 0.5% 兲 Markus
Electric charge collected per pulse 共nC/ pulse± 0.5% 兲 Roos
ksat共±3.5% 兲 Markus
ksat共±3.5% 兲 Roos
3.97 5.02 6.93 8.24 8.77 9.34 10.62 12.36
0.0654 0.0793 0.1034 0.1201 0.1259 0.1331 0.1480 0.1650
0.3240 0.3785 0.4728 0.5286 0.5516 0.5735 0.6169 0.6811
1.15 1.20 1.27 1.30 1.32 1.33 1.36 1.42
1.58 1.71 1.89 2.01 2.05 2.10 2.22 2.34
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共12兲
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FIG. 1. The relationship between ksat and the dose per pulse for the Markus parallel-plate ionization chamber.
ksat =
Dw,,eff . e pDw,,eff − 1 ln 1 + p
冉
冊
共13兲
The p value was evaluated for both the parallel-plate ionization chamber Markus 共PTW type 23343兲 and Roos 共PTW type 34001兲 by fitting with Eq. 共13兲 the ksat values evaluated at a different dose per pulse 关Eq. 共11兲兴. The absorbed dose values to water Dw共zref兲 were measured using Fricke dosimeters for two high dose-per-pulse electron-beams with two different effective energies 共6.3 MeV and 6.96 cGy/ pulse, 7.2 MeV and 7.74 cGy/ pulse兲. To test Eq. 共10兲, these measured values were compared to the dose Dw共zref兲 calculated by Eq. 共10兲 using the experimental p values previously estimated. The water percentage depth dose 共PDD兲 of a high doseper-pulse 共9.34 cGy/ pulse at buildup in water兲 electron beam 共effective energy 7 MeV兲 was measured using radiochromic films 共HS Gafchromic兲. The PDD was also measured using a Markus and Roos parallel-plate ionization chamber. The ksat value was calculated either by Eq. 共9兲 or fixing its value as a
costant 共ksat = 1兲, as usually assumed for the conventional pulsed high-energy electron beams. The PDD was calculated correcting the charge collected values M for the stoppingpower ratio at a different depth. III. RESULTS The characteristics of the ionization chambers used are reported in Table I. The ksat values evaluated using Fricke dosimeters at a different dose-per-pulse value 关Eq. 共11兲兴 are reported in Table II. The charge per pulse collected 共M / 兲 using both the Markus and Roos ionization chamber are also reported in Table II. ksat increases with dose per pulse and it is generally greater for the Roos than the Markus ionization chamber. The general ksat equation 关Eq. 共13兲兴 derived from the ion recombination Boag theory very well fits the experimental ksat values for both Markus 共R2 = 0.994, 2 = 0.024兲 and Roos 共R2 = 0.999, 2 = 0.026兲 ionization chambers. The freeelectron fraction values p estimated fitting experimental data are, respectively, p = 共0.354± 0.005兲 for Markus ionization
FIG. 2. The relationship between ksat and dose per pulse for the Roos parallel-plate ionization chamber.
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TABLE III. A comparison between Dw, measured by Fricke dosimeters and calculated by Eq. 共10兲 using Markus and Roos electric-charge/pulse measurements. Markus
Effective energy 共MeV兲 6.3 7.2
Depth water of the measurement point zref 共mm兲 15 17
Dose/pulse 共cGy/pulse兲 by Fricke dosimeters 6.96 7.74
ND,w,Q⬘kQ,Q⬘ 共cGy/nC兲 52.92 52.73
Charge/pulse 共nC/pulse兲 0.1037 0.1162
Dose/pulse 共cGy/pulse兲 by 关Eq. 共10兲兴 6.90 7.91
兩1-Dw,,Markus/ Dw,Fricke兩 0.9% 2.2%
Charge/pulse 共nC/pulse兲 0.4697 0.5112
Dose/pulse 共cGy/pulse兲 by 关Eq. 共10兲兴 6.88 7.81
兩1-DW,,Roos/ DW,,Fricke兩 1.1% 0.9%
Roos
Effective energy 共MeV兲 6.3 7.2
Depth in water of the measurement point Zref 共mm兲 15 17
Dose/pulse 共cGy/pulse兲 by Fricke dosimeters 6.96 7.74
ND,W,Q⬘kQ,Q⬘ 共cGy/nC兲 7.79 7.75
chamber and p = 共0.179± 0.002兲 for Roos ionization chamber. The fitting of experimental data are reported in Fig. 1 共Markus兲 and Fig. 2 共Roos兲. The Dw共zref兲 values measured by Fricke dosimeter are in good agreement with the doses measured by parallel-plate ionization chambers and calculated using Eq. 共10兲 and the p values experimentally evaluated. The absorbed dose differences 共Table III兲 are less than 2.2% for Markus and less than 1.1% for the Roos ionization chamber. In Figs. 3 共Markus兲 and 4 共Roos兲 are reported the water PDD measured by means of radiochromic films and the charge collected by ionization chambers, respectively, with ksat = 1 共as usually assumed for the conventional pulsed highenergy electron beams兲 and ksat estimated using the general equation derived from the Boag theory 关Eq. 共9兲兴. The PDD calculated using recombination factor values derived from Eq. 共9兲 are in good agreement with PDD measured with radiochromic films. On the other hand, the PDD values calculated using ksat = 1 overestimate significantly the PDD values
measured with radiochromic films. This overestimation effect increases with depth and is more evident for the Roos than for the Markus ionization chamber. IV. DISCUSSION AND CONCLUSION The international dosimetry reports suggest using a parallel-plate ionization chamber for the measurement of the absorbed dose in high-energy 共⬎5 MeV兲 electron beams. The correct absorbed dose value can be estimated correcting the ionization chamber response for the lack of complete charge collection due to ion recombination by means of ksat. The standard “two voltage” method for ksat evaluation fails when applied to high dose-per-pulse 共⬎1 cGy/ pulse兲 electron beams: this method significantly overestimates the ksat value 共up to 20% for the Markus ionization chamber兲.9 High dose-per-pulse electron beams are actually produced by some special Linac dedicated to IORT. The dosimetric characterization of high dose-per-pulse electron beams must
FIG. 3. A comparison between PDD in water evaluated using Gafchromic HS films and calculated using a parallel-plate Markus ionization chamber. The measurements are obtained with ksat = 1 and ksat calculated by Eq. 共9兲.
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FIG. 4. A comparison between PDD in water evaluated using Gafchromic HS films and calculated using a parallel-plate Roos ionization chamber. The measurements are obtained with ksat = 1 and ksat calculated by Eq. 共9兲.
be made using dose rate-independent dosimeters 共like Fricke dosimeters and radiochromic films兲 but some problems arise due to low sensitivity, calibration, or post-irradiation reading. In this paper a new method for the ksat evaluation and an appropriate use of parallel-plate ionization chamber also in high dose-per-pulse electron beams was proposed. The problems due to the impossibility of using the standard “two voltage” method for the ksat evaluation were solved, deriving an equation for ksat directly from the general equation for the ion recombination in the Boag theory. It follows a new general equation 关Eq. 共10兲兴 for the absorbed dose 共Dw兲 measured by a parallel plate ionization chamber in very high dose-per-pulse high-energy electron beams. Equation 共10兲 depends only on chamber characteristics 共p , ␣兲, correction 共ND.w,Q⬘ , kQ,Q⬘ , k p,t , kh , kpol兲, and measured data 共 , M兲. Note that Eq. 共10兲 does not contain ksat explicitly since ksat is now a function 关Eq. 共9兲兴 of the ionization chamber characteristics and charge per pulse 共M / 兲 collected. M / is a directly measurable quantity. Equation 共10兲 allows us to evaluate the absorbed dose if the free-electron fraction 共p兲 is known. The p value for both a Markus and a Roos parallel-plate ionization chamber was derived fitting experimental ksat values obtained using doseper-pulse-independent dosimeters 关Eq. 共11兲兴. Experimental ksat values increase with the dose-per-pulse value. For a given value of dose per pulse, ksat is larger for the Roos than for the Markus chamber because of the lower potential on which the Roos chamber is operated. This is also confirmed by the lower free-electron fraction for the Roos than for the Markus ionization chamber. The absorbed dose to water measured by Fricke dosimeters is in very good agreement with the dose calculated using Eq. 共10兲. This is true for the experimental points used for the free-electron fraction evaluation 共with an effective energy of 7 MeV and a dose-per-pulse value in the range 3.97– 12.36 cGy/ pulse兲 and for two other points of measurement of effective energies of 6.3 and 7.2 MeV and dose per pulse of 6.96 and 7.74 cGy/ pulse. Medical Physics, Vol. 32, No. 7, July 2005
The PDD measurements showed that using a parallelplate ionization chamber in high dose-per-pulse electron beams can be misleading also for relative dosimetry. Considering ksat as a constant 共ksat = 1兲, PDD is significantly overestimated. The dose per pulse decreases with depth. Therefore, ksat is not constant and decreases with depth as well. Assuming ksat constant 共ksat = 1兲, the PDD values at a greater depth are increasingly overestimated. This effect is greater for the Roos than for the Markus chamber. The correct PDD can be obtained, correcting ionization chamber reading for the ksat values at a different depth and dose-per-pulse values 关Eq. 共9兲兴. In conclusion, a general equation that allows us to calculate the absorbed dose to water using an ionization chamber was derived from the basic ion recombination Boag theory. Based on this equation a new method for the use of a parallel plate ionization chamber in high-energy high dose-per-pulse electron beams for absolute and relative dosimetry was presented. This method needs only the knowledge of the freeelectron fraction 共p兲 and the direct measurement of the charge per pulse collected by the ionization chamber. The p parameter depends only on chamber characteristics and can be estimated experimentally. The new proposed method was successfully validated for two parallel-plate ionization chambers 共Markus and Roos兲 in high dose-per-pulse electron beams produced by a special Linac dedicated to IORT. Author to whom correspondence should be addressed. Phone: 共⫹兲 共39兲 050 992219; Fax: 共⫹兲 共39兲 050 992513. Electronic mail: [email protected] b兲 Also at U.O. Fisica Sanitaria, Azienda Ospedaliera Universitaria Pisana, via Roma 67, 56126 Pisa, Italy. 1 IAEA TRS-398, “Absorbed dose determination in external beam radiotherapy: An international code of practice for dosimetry based on standards of absorbed dose to water,” 21 March 2000. 2 J. W. Boag, “Ionization measurements at very high intensities. Pulsed radiation beams,” Br. J. Radiol. 23, 601–611 共1950兲. 3 J. W. Boag, E. Hochhäuser, and O. A. Balk, “The effect of free-electron a兲
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collection on the recombination correction to ionization measurements of pulsed radiation,” Phys. Med. Biol. 41, 885–897 共1996兲. 4 D. T. Burnst and M. R. McEwen, “Ion recombination corrections for the NACP parallel-plate chamber in a pulsed electron beam, Phys. Med. Biol. 43, 2033–2045 共1998兲. 5 AIFB, “Protocollo per la dosimetria di base nella radioterapia con fasci di fotoni ed elettroni con Emax tra 1 e 40 MeV,” Notiziario della AIFB, 共1988兲, Vols. 1 and 2. 6 ICRU, The dosimetry of pulsed radiation, Report 34, 1982. 7 AAPM 共American Association of Physicist in Medicine兲, Radiation Therapy Committee Task Group 55, Radiochromic Dosimetry: Recomen-
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dation of AAPM Radiation Therapy Committee Task Group 55, 1996. 8 W. L. McLaughlin, C. Y. Dong, C. G. Soares, A. Miller, G. Van Dyk, and D. F. Lewis, “Sensitometry of the response of a new radiochromic film dosimeter to gamma radiation and electron-beams,” Nucl. Instrum. Methods Phys. Res. A 302, 165–176 共1991兲. 9 A. Piermattei, S. Delle Canne, L. Azario, A. Russo, A. Fidanzio, R. Miceli, A. Soriani, A. Orvieto, and M. Fantini, “The saturation loss for plane parallel ionization chambers at high dose-per-pulse value,” Phys. Med. Biol. 45, 1869–1883 共2000兲.
Ion recombination correction for very high dose-per-pulse high-energy electron beams F. Di Martino,a兲 M. Giannelli, A. C. Traino, and M. Lazzerib兲 U.O. Fisica Sanitaria—Sezione di Fisica Medica, Azienda Ospedaliera Universitaria Pisana, via Roma 67, 56126 Pisa, Italy
共Received 9 December 2004; accepted for publication 30 April 2005; published 15 June 2005兲 The parallel-plate ionization chamber is the recommended tool for the absorbed dose measurement in pulsed high-energy electron beams. Typically, the electron beams used in radiotherapy have a dose-per-pulse value less then 0.1 cGy/ pulse. In this range the factor to correct the response of an ionization chamber for the lack of complete charge collection due to ion recombination 共ksat兲 can be properly evaluated with the standard “two voltage” method proposed by the international dosimetric reports. Very high dose-per-pulse electron beams are employed in some special Linac dedicated to the Intra-Operatory-Radiation-Therapy 共IORT兲. The high dose-per-pulse values 共3 – 13 cGy/ pulse兲 characterizing the IORT electron beams allow to deliver the therapeutic dose 共10– 20 Gy兲 in less than a minute. This considerably reduces the IORT procedure time, but some dosimetric problems arise because the standard method to evaluate ksat overestimates its value by 20%. Moreover, if the dose-per-pulse value ⬎1 cGy/ pulse, the dependence of ksat on the dose-per-pulse value cannot be neglected for relative dosimetry. In this work the dependence of ksat on the dose-per-pulse value is derived, based on the general equation that describes the ion recombination in the Boag theory. A new equation for ksat, depending on known or measurable quantities, is presented. The new ksat equation is experimentally tested by comparing the absorbed doses to water measured with parallelplate ionization chambers 共Roos and Markus兲 to that measured using dose-per-pulse independent dosimeters, such as radiochromic films and chemical Fricke dosimeters. These measurements are performed in the high dose-per-pulse 共3 – 13 cGy/ pulse兲 electron beams of the IORT dedicated Linac Hitesys Novac7 共Aprilia—Latina, Italy兲. The dose measurements made using the parallelplate chambers and those made using the dose-per-pulse independent dosimeters are in good agreement 共⬍3 % 兲. This demonstrates the possibility of using the parallel-plate ionization chambers also for the very high dose-per-pulse 共⬎1 cGy/ pulse兲 electron-beam dosimetry. © 2005 American Association of Physicists in Medicine. 关DOI: 10.1118/1.1940167兴 Key words: dose-per-pulse, ion recombination, ksat, ionization chamber, IORT I. INTRODUCTION
ksat =
The parallel-plate ionization chamber is the dosimetry tool recommended by the international reports for the pulsed high-energy 共⬎5 MeV兲 electron-beam dosimetry. The charge collected by the chamber can be converted into dose to water 共Dw兲 in the reference point 共zref兲 by the equation1 Dw共zref兲 = M corrND,w,Q⬘kQ,Q⬘ksat ,
共1兲
where M corr = Mk p,tkhkpol is the reading of the chamber 共M兲 corrected for temperature/pressure 共k p,t兲, humidity 共kh兲, and polarity 共kpol兲; ND,w,Q⬘ is the calibration factor in terms of the absorbed dose to water for the ionization chamber at a reference beam quality Q⬘; kQ,Q⬘ is the correction factor for the difference between the response of an ionization chamber in the reference beam quality Q⬘ used for calibrating the chamber and in the actual used beam quality Q; ksat is the factor to correct the response of an ionization chamber for the lack of complete charge collection due to ion recombination. A basic equation for ksat derived from the ionrecombination Boag theory2,3 is 2204
Med. Phys. 32 „7…, July 2005
u , e pu − 1 ln 1 + p
冉
冊
共2兲
where p is the free-electron fraction, i.e., electrons that escape attachment to gas molecules and so reach the electrode as free electrons and u=
d 2q , V
共3兲
where 共mV/C兲 is a constant depending on the gas in the cavity chamber; d 共m兲 is the distance between the chamber plates; q 共C / m3兲 is the charge liberated in air per unit volume and per pulse; and V 共Volt兲 is the voltage supply of the chamber. The free-electron fraction p depends on the voltage supply and on other chamber properties, but it does not depend on the dose rate. The high-energy pulsed electron beams of interest in clinical dosimetry have usually a dose-per-pulse value of less than 0.1 cGy/ pulse. This means that q and, consequently, u 关Eq. 共3兲兴 are small for the usually employed plane-parallel ionization chambers. Thus Eq. 共2兲 can be expanded to first order, giving
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ksat ⬇
Di Martino et al.: ksat evaluation for very high dose-per-pulse electron-beams
u ; ln共1 + u兲
共4兲
Eq. 共4兲 does not depend on the value of the free-electron fraction p. This means that the contribution of the freeelectron fraction to ksat is neglected for usual dose-per-pulse electron beams. For dose-per-pulse values of less than 0.1 cGy/ pulse, ksat is less than 1.05 for each parallel-plate ionization chamber recommended by the international reports.4 Thus, Eq. 共4兲 can be approximated by the equation4 u ksat ⬇ 1 + . 2
共5兲
The standard “two voltage” method is derived from Eq. 共5兲. This is the classical method, suggested by the international dosimetry reports,1 for ksat evaluation. Moreover, for doseper-pulse ⬍0.1 cGy/ pulse, the change of ksat due to the change of the dose-per-pulse value can be neglected in the relative dosimetry measurements. This means that the ksat value can be fixed to ksat = 1 for relative dosimetry measurements. For pulsed high-energy electron beams with values of dose per pulse ⬎1 cGy/ pulse, Eq. 共2兲 cannot be approximated by Eq. 共5兲. Thus Eq. 共5兲 cannot be used and the calculation of ksat cannot be done using the standard “two voltage” method. This brings a difficulty in using the parallelplane ionization chambers for absolute dosimetry. Moreover, for pulsed high-energy electron beams with values of dose per pulse ⬎1 cGy/ pulse, the change of ksat due to the change of the dose per pulse cannot be neglected for the relative dosimetry. High dose-per-pulse electron beams of 3 – 13 cGy/ pulse 共about 100 times greater than conventional beams兲 are actually produced from some special Linac, dedicated to IntraOperatory-Radiation-Therapy 共IORT兲. IORT is a radiationtherapy treatment modality that involves the delivery of a single large radiation dose to the exposed tumor during the surgical exploration or to the bed of a resected tumor. A Linac dedicated to IORT is a special accelerator located near the surgery room, with the possibility to be moved toward the patient and to deliver the treatment dose. IORT with a dedicated Linac has many practical and clinical advantages, but it has several dosimetric problems. During the IORT procedure it is impossible to execute treatment planning. Thus the absolute dosimetry in the reference condition and the relative dosimetry 共output factors, percentage depth dose, airgap factors兲 are fundamental. The dosimetric problems due to the very high dose-perpulse value suggest to use dose-rate-independent dosimeters instead of the parallel-plate ionization chambers. The doserate-independent dosimeters most commonly used are the chemical Fricke dosimeters5,6 and the radiochromic films.7,8 The Fricke dosimeters have a low spatial resolution. This does not allow their use for the relative dosimetry. They have a low sensitivity, thus they need to be exposed to high dose values. They are expensive and they need a post-irradiation reading procedure to give the dose value. The radiochromic Medical Physics, Vol. 32, No. 7, July 2005
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films are sensitive to temperature, humidity, time after irradiation, and they need both a calibration procedure and a post-irradiation procedure to give the dose value. In comparison to the Fricke dosimeter and radiochromic films, the ionization chamber has a very good sensitivity, it is practical to use, and it gives the dosimetric information online. Thus the possibility to use ionization chamber has a practical relevance. The problems related to the parallel-plate ionization chamber use for high dose-per-pulse electron beams were previously described and investigated but not solved.9 In this work a new equation for ksat based on the general equation that describes the ion recombination in the Boag theory 关Eq. 共2兲兴 is derived. This new equation depends on known or measurable quantities. It allows us to use the parallel plate ionization chambers also in high dose-per-pulse electron beams, either for relative or absolute dosimetry. The new ksat evaluation method in very high dose-per-pulse electron beams is experimentally validated for both the parallelplate ionization chambers type Roos and Markus. II. MATERIAL AND METHODS A. Theory
ksat is the factor to correct the response of an ionization chamber for the lack of complete charge collection due to ion recombination. It can be defined as ksat =
QL , QR
共6兲
where QL is the total electric charge produced in the ionization-chamber cavity and QR is the electric charge 共M兲 collected by the ionization chamber. Taking into account Eq. 共6兲, it follows that q =
Mksat , vch
共7兲
where q共C / m3兲 is the charge liberated in air per unit volume and per pulse into the parallel plate ionization chamber; is the number of electron beam pulses and ch共m3兲 is the effective ionization chamber volume. From Eqs. 共2兲, 共3兲, and 共7兲, it follows that
␣ Mksat , ksat = e p␣Mksat/ − 1 ln 1 + p
冉
冊
共8兲
where ␣ = 共d2 / Vch兲 depends only on the ionizationchamber properties and on its voltage supply. Equation 共8兲 can be analytically solved, giving ksat =
兵ln关p共e␣M/ − 1兲 + 1兴其 . p␣ M
共9兲
Finally, from Eqs. 共1兲 and 共9兲, a general equation for the absorbed dose to water in the reference point 共zref兲 for a parallel plate ionization chamber can be obtained:
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TABLE I. Specific parameters of the used parallel-plate ionization chamber Markus and Roos. Ion. chamber
Measurement volume 共m3兲
Polarity votage 共V兲
Electrode distance 共m兲
ND,w,Q⬘ 共Gy/C兲
共mV/C兲
kQ,Q⬘ 7 Mev
 共Gy−1兲
Markus Roos
0.055⫻ 10−6 0.35⫻ 10−6
+300 +100
0.002 0.002
5.76⫻ 108 ± 2% 0.833⫻ 108 ± 2%
3.02⫻ 1010 3.02⫻ 1010
0.916± 2% 0.931± 2%
12.71± 2% 41.43± 2%
Dw共zref兲 =
兵ln关p共e␣M/ − 1兲 + 1兴其ND,w,Q⬘kQ,Q⬘k p,tkhkpol p␣
. 共10兲
Note that Eq. 共10兲 is derived directly from Eq. 共1兲 and from the general theory of Boag 关Eq. 共2兲兴 without any approximation. B. Measurements
The knowledge of the free-electron fraction p for the chamber in use is required to calculate Dw共zref兲 by Eq. 共10兲. The theoretical value of the free-electron fraction p is unknown for the commonly used parallel plate ionization chambers. A set of measurements of Dw at different dose-per-pulse values 共range 3 – 13 cGy/ pulse兲 were performed using the pulsed electron beams of a IORT dedicated Linac Hitesys Novac7 共Aprilia—Latina, Italy兲 using dosimeters independent on dose-per-pulse value. The pulse frequency is 5 Hz and their duration is 4 s. The collimation of the beam is obtained with special perspex cylindrical tools. Different dose-per-pulse values at a fixed energy at the build-up depth in water can be obtained using collimators of a different size. Experimental values of ksat at a different dose-per-pulse of a 7 MeV electron beam were evaluated using the following equation 关see Eq. 共1兲兴: ksat =
Dw , M corrND,w,Q⬘kQ,Q⬘
共11兲
where Dw is the absorbed dose to water in the reference point measured with dose-per-pulse-independent Fricke dosimeters. The quality Q共R50兲 of the high dose-per-pulse electron
beams used were evaluated using radiochromic films 共HS Gafchromic兲 placed vertically in a water phantom. Note that HS Gafchromic dosimeters are independent of dose-perpulse and of energy of the electrons in the range 1 – 9 MeV.8 They can be placed and irradiated directly in water. The radiochromic films employed were read using a scanner Epson-Expression-1680-Pro with a large spectrum 共white兲 light. A red filter was also used to obtain the maximum absorption range 共 = 660 nm兲. The radiochromic films were read before irradiation to know the basal optical density and 48 hours after irradiation to evaluate the change of optical density due to the absorbed dose. The curve that relates optical density and absorbed dose to water was obtained fitting the experimental dose values from a standard Linac electron beam with a second-order polynomial function. The kQ,Q⬘ factor is reported in the IAEA TRS-398 report as a function of R50 and the ionization chamber type.1 From Eq. 共2兲, Eq. 共8兲, and Eq. 共11兲 it follows that
u=
␣ ND,w,Q⬘kQ,Q⬘k p,tkhkpol
Dw, = Dw,,eff ,
where Dw, = Dw / is the dose-per-pulse to water in the ref共Gy−1兲 = ␣ / ND,w,Q⬘ and Dw,,eff erence point; = Dw, / k p,tkhkpolkQ,Q⬘.  depends only on the ionization chamber characteristics while the dose-per-pulse dependence is expressed by Dw,,eff. Finally, from Eq. 共2兲 and Eq. 共12兲, ksat can be expressed as a function of dose-per-pulse and p values as
TABLE II. Measured values of dose/pulse Dw,, M corr, and ksat for Markus and Roos parallel-plane ionization chambers. The dose/pulse values were measured using Fricke dosimeters.
Dose/pulse 共cGy/ pulse± 2 % 兲
Electric charge collected per pulse 共nC/ pulse± 0.5% 兲 Markus
Electric charge collected per pulse 共nC/ pulse± 0.5% 兲 Roos
ksat共±3.5% 兲 Markus
ksat共±3.5% 兲 Roos
3.97 5.02 6.93 8.24 8.77 9.34 10.62 12.36
0.0654 0.0793 0.1034 0.1201 0.1259 0.1331 0.1480 0.1650
0.3240 0.3785 0.4728 0.5286 0.5516 0.5735 0.6169 0.6811
1.15 1.20 1.27 1.30 1.32 1.33 1.36 1.42
1.58 1.71 1.89 2.01 2.05 2.10 2.22 2.34
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共12兲
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FIG. 1. The relationship between ksat and the dose per pulse for the Markus parallel-plate ionization chamber.
ksat =
Dw,,eff . e pDw,,eff − 1 ln 1 + p
冉
冊
共13兲
The p value was evaluated for both the parallel-plate ionization chamber Markus 共PTW type 23343兲 and Roos 共PTW type 34001兲 by fitting with Eq. 共13兲 the ksat values evaluated at a different dose per pulse 关Eq. 共11兲兴. The absorbed dose values to water Dw共zref兲 were measured using Fricke dosimeters for two high dose-per-pulse electron-beams with two different effective energies 共6.3 MeV and 6.96 cGy/ pulse, 7.2 MeV and 7.74 cGy/ pulse兲. To test Eq. 共10兲, these measured values were compared to the dose Dw共zref兲 calculated by Eq. 共10兲 using the experimental p values previously estimated. The water percentage depth dose 共PDD兲 of a high doseper-pulse 共9.34 cGy/ pulse at buildup in water兲 electron beam 共effective energy 7 MeV兲 was measured using radiochromic films 共HS Gafchromic兲. The PDD was also measured using a Markus and Roos parallel-plate ionization chamber. The ksat value was calculated either by Eq. 共9兲 or fixing its value as a
costant 共ksat = 1兲, as usually assumed for the conventional pulsed high-energy electron beams. The PDD was calculated correcting the charge collected values M for the stoppingpower ratio at a different depth. III. RESULTS The characteristics of the ionization chambers used are reported in Table I. The ksat values evaluated using Fricke dosimeters at a different dose-per-pulse value 关Eq. 共11兲兴 are reported in Table II. The charge per pulse collected 共M / 兲 using both the Markus and Roos ionization chamber are also reported in Table II. ksat increases with dose per pulse and it is generally greater for the Roos than the Markus ionization chamber. The general ksat equation 关Eq. 共13兲兴 derived from the ion recombination Boag theory very well fits the experimental ksat values for both Markus 共R2 = 0.994, 2 = 0.024兲 and Roos 共R2 = 0.999, 2 = 0.026兲 ionization chambers. The freeelectron fraction values p estimated fitting experimental data are, respectively, p = 共0.354± 0.005兲 for Markus ionization
FIG. 2. The relationship between ksat and dose per pulse for the Roos parallel-plate ionization chamber.
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TABLE III. A comparison between Dw, measured by Fricke dosimeters and calculated by Eq. 共10兲 using Markus and Roos electric-charge/pulse measurements. Markus
Effective energy 共MeV兲 6.3 7.2
Depth water of the measurement point zref 共mm兲 15 17
Dose/pulse 共cGy/pulse兲 by Fricke dosimeters 6.96 7.74
ND,w,Q⬘kQ,Q⬘ 共cGy/nC兲 52.92 52.73
Charge/pulse 共nC/pulse兲 0.1037 0.1162
Dose/pulse 共cGy/pulse兲 by 关Eq. 共10兲兴 6.90 7.91
兩1-Dw,,Markus/ Dw,Fricke兩 0.9% 2.2%
Charge/pulse 共nC/pulse兲 0.4697 0.5112
Dose/pulse 共cGy/pulse兲 by 关Eq. 共10兲兴 6.88 7.81
兩1-DW,,Roos/ DW,,Fricke兩 1.1% 0.9%
Roos
Effective energy 共MeV兲 6.3 7.2
Depth in water of the measurement point Zref 共mm兲 15 17
Dose/pulse 共cGy/pulse兲 by Fricke dosimeters 6.96 7.74
ND,W,Q⬘kQ,Q⬘ 共cGy/nC兲 7.79 7.75
chamber and p = 共0.179± 0.002兲 for Roos ionization chamber. The fitting of experimental data are reported in Fig. 1 共Markus兲 and Fig. 2 共Roos兲. The Dw共zref兲 values measured by Fricke dosimeter are in good agreement with the doses measured by parallel-plate ionization chambers and calculated using Eq. 共10兲 and the p values experimentally evaluated. The absorbed dose differences 共Table III兲 are less than 2.2% for Markus and less than 1.1% for the Roos ionization chamber. In Figs. 3 共Markus兲 and 4 共Roos兲 are reported the water PDD measured by means of radiochromic films and the charge collected by ionization chambers, respectively, with ksat = 1 共as usually assumed for the conventional pulsed highenergy electron beams兲 and ksat estimated using the general equation derived from the Boag theory 关Eq. 共9兲兴. The PDD calculated using recombination factor values derived from Eq. 共9兲 are in good agreement with PDD measured with radiochromic films. On the other hand, the PDD values calculated using ksat = 1 overestimate significantly the PDD values
measured with radiochromic films. This overestimation effect increases with depth and is more evident for the Roos than for the Markus ionization chamber. IV. DISCUSSION AND CONCLUSION The international dosimetry reports suggest using a parallel-plate ionization chamber for the measurement of the absorbed dose in high-energy 共⬎5 MeV兲 electron beams. The correct absorbed dose value can be estimated correcting the ionization chamber response for the lack of complete charge collection due to ion recombination by means of ksat. The standard “two voltage” method for ksat evaluation fails when applied to high dose-per-pulse 共⬎1 cGy/ pulse兲 electron beams: this method significantly overestimates the ksat value 共up to 20% for the Markus ionization chamber兲.9 High dose-per-pulse electron beams are actually produced by some special Linac dedicated to IORT. The dosimetric characterization of high dose-per-pulse electron beams must
FIG. 3. A comparison between PDD in water evaluated using Gafchromic HS films and calculated using a parallel-plate Markus ionization chamber. The measurements are obtained with ksat = 1 and ksat calculated by Eq. 共9兲.
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FIG. 4. A comparison between PDD in water evaluated using Gafchromic HS films and calculated using a parallel-plate Roos ionization chamber. The measurements are obtained with ksat = 1 and ksat calculated by Eq. 共9兲.
be made using dose rate-independent dosimeters 共like Fricke dosimeters and radiochromic films兲 but some problems arise due to low sensitivity, calibration, or post-irradiation reading. In this paper a new method for the ksat evaluation and an appropriate use of parallel-plate ionization chamber also in high dose-per-pulse electron beams was proposed. The problems due to the impossibility of using the standard “two voltage” method for the ksat evaluation were solved, deriving an equation for ksat directly from the general equation for the ion recombination in the Boag theory. It follows a new general equation 关Eq. 共10兲兴 for the absorbed dose 共Dw兲 measured by a parallel plate ionization chamber in very high dose-per-pulse high-energy electron beams. Equation 共10兲 depends only on chamber characteristics 共p , ␣兲, correction 共ND.w,Q⬘ , kQ,Q⬘ , k p,t , kh , kpol兲, and measured data 共 , M兲. Note that Eq. 共10兲 does not contain ksat explicitly since ksat is now a function 关Eq. 共9兲兴 of the ionization chamber characteristics and charge per pulse 共M / 兲 collected. M / is a directly measurable quantity. Equation 共10兲 allows us to evaluate the absorbed dose if the free-electron fraction 共p兲 is known. The p value for both a Markus and a Roos parallel-plate ionization chamber was derived fitting experimental ksat values obtained using doseper-pulse-independent dosimeters 关Eq. 共11兲兴. Experimental ksat values increase with the dose-per-pulse value. For a given value of dose per pulse, ksat is larger for the Roos than for the Markus chamber because of the lower potential on which the Roos chamber is operated. This is also confirmed by the lower free-electron fraction for the Roos than for the Markus ionization chamber. The absorbed dose to water measured by Fricke dosimeters is in very good agreement with the dose calculated using Eq. 共10兲. This is true for the experimental points used for the free-electron fraction evaluation 共with an effective energy of 7 MeV and a dose-per-pulse value in the range 3.97– 12.36 cGy/ pulse兲 and for two other points of measurement of effective energies of 6.3 and 7.2 MeV and dose per pulse of 6.96 and 7.74 cGy/ pulse. Medical Physics, Vol. 32, No. 7, July 2005
The PDD measurements showed that using a parallelplate ionization chamber in high dose-per-pulse electron beams can be misleading also for relative dosimetry. Considering ksat as a constant 共ksat = 1兲, PDD is significantly overestimated. The dose per pulse decreases with depth. Therefore, ksat is not constant and decreases with depth as well. Assuming ksat constant 共ksat = 1兲, the PDD values at a greater depth are increasingly overestimated. This effect is greater for the Roos than for the Markus chamber. The correct PDD can be obtained, correcting ionization chamber reading for the ksat values at a different depth and dose-per-pulse values 关Eq. 共9兲兴. In conclusion, a general equation that allows us to calculate the absorbed dose to water using an ionization chamber was derived from the basic ion recombination Boag theory. Based on this equation a new method for the use of a parallel plate ionization chamber in high-energy high dose-per-pulse electron beams for absolute and relative dosimetry was presented. This method needs only the knowledge of the freeelectron fraction 共p兲 and the direct measurement of the charge per pulse collected by the ionization chamber. The p parameter depends only on chamber characteristics and can be estimated experimentally. The new proposed method was successfully validated for two parallel-plate ionization chambers 共Markus and Roos兲 in high dose-per-pulse electron beams produced by a special Linac dedicated to IORT. Author to whom correspondence should be addressed. Phone: 共⫹兲 共39兲 050 992219; Fax: 共⫹兲 共39兲 050 992513. Electronic mail: [email protected] b兲 Also at U.O. Fisica Sanitaria, Azienda Ospedaliera Universitaria Pisana, via Roma 67, 56126 Pisa, Italy. 1 IAEA TRS-398, “Absorbed dose determination in external beam radiotherapy: An international code of practice for dosimetry based on standards of absorbed dose to water,” 21 March 2000. 2 J. W. Boag, “Ionization measurements at very high intensities. Pulsed radiation beams,” Br. J. Radiol. 23, 601–611 共1950兲. 3 J. W. Boag, E. Hochhäuser, and O. A. Balk, “The effect of free-electron a兲
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collection on the recombination correction to ionization measurements of pulsed radiation,” Phys. Med. Biol. 41, 885–897 共1996兲. 4 D. T. Burnst and M. R. McEwen, “Ion recombination corrections for the NACP parallel-plate chamber in a pulsed electron beam, Phys. Med. Biol. 43, 2033–2045 共1998兲. 5 AIFB, “Protocollo per la dosimetria di base nella radioterapia con fasci di fotoni ed elettroni con Emax tra 1 e 40 MeV,” Notiziario della AIFB, 共1988兲, Vols. 1 and 2. 6 ICRU, The dosimetry of pulsed radiation, Report 34, 1982. 7 AAPM 共American Association of Physicist in Medicine兲, Radiation Therapy Committee Task Group 55, Radiochromic Dosimetry: Recomen-
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dation of AAPM Radiation Therapy Committee Task Group 55, 1996. 8 W. L. McLaughlin, C. Y. Dong, C. G. Soares, A. Miller, G. Van Dyk, and D. F. Lewis, “Sensitometry of the response of a new radiochromic film dosimeter to gamma radiation and electron-beams,” Nucl. Instrum. Methods Phys. Res. A 302, 165–176 共1991兲. 9 A. Piermattei, S. Delle Canne, L. Azario, A. Russo, A. Fidanzio, R. Miceli, A. Soriani, A. Orvieto, and M. Fantini, “The saturation loss for plane parallel ionization chambers at high dose-per-pulse value,” Phys. Med. Biol. 45, 1869–1883 共2000兲.
