Comment on Proton beam monitor chamber calibration

Transcription

1 Physics in Medicine & Biology COMMENT on Proton beam monitor chamber calibration To cite this article: Hugo Palmans and Stanislav M Vatnitsky 216 Phys. Med. Biol View the article online for updates and enhancements. Related content - Reply to comment on Proton beam monitor chamber calibration Carles Gomà, Stefano Lorentini, David Meer et al. - Topical Review Christian P Karger, Oliver Jäkel, Hugo Palmans et al. - Experimental validation of beam quality correction factors for proton beams Carles Gomà, Bénédicte Hofstetter-Boillat, Sairos Safai et al. Recent citations - Consistency in quality correction factors for ionization chamber dosimetry in scanned proton beam therapy Jefferson Sorriaux et al - Beam monitor calibration in scanned lightion beams Hugo Palmans and Stanislav M. Vatnitsky - Reply to comment on Proton beam monitor chamber calibration Carles Gomà et al This content was downloaded from IP address on 8/5/218 at 18:14

2 6593 Institute of Physics and Engineering in Medicine Physics in Medicine & Biology doi:1.188/ /61/17/6585 on Proton beam monitor chamber calibration Hugo Palmans 1,2 and Stanislav M Vatnitsky 1 1 EBG MedAustron GmbH, A-27 Wiener Neustadt, Austria 2 National Physical Laboratory, Teddington, TW11 LW, UK hugo.palmans@npl.co.uk Received 4 August 215, revised 8 October 215 Accepted for publication 12 October 215 Published 18 August 216 Abstract We comment on a recent article (Gomà et al 214 Phys. Med. Biol ) which compares different routes of reference dosimetry for the energy dependent beam monitor calibration in scanned proton beams. In this article, a 3% discrepancy is reported between a Faraday cup and a plane-parallel ionization chamber in the experimental determination of the number of protons per monitor unit. It is further claimed that similar discrepancies between calorimetry and ionization chamber based dosimetry indicate that k Q -values tabulated for proton beams in IAEA TRS-398 might be overestimated. In this commentary we show, however, that this supporting argument misrepresents the evidence in the literature and that the results presented, together with published data, rather confirm that there exist unresolved problems with Faraday cup dosimetry. We also show that the comparison in terms of the number of protons gives a biased view on the uncertainty estimates for both detectors while the quantity of interest is absorbed dose to water or dose-areaproduct to water, even if a beam monitor is calibrated in terms of the number of protons. Gomà et al (214 Phys. Med. Biol ) also report on the discrepancy between cylindrical and plane-parallel ionization chambers and confirm experimentally that in the presence of a depth dose gradient, theoretical values of the effective point of measurement, or alternatively a gradient correction factor, account for the discrepancy. We believe this does not point to an error or shortcoming of IAEA TRS-398, which prescribes taking the centre of cylindrical ionization chambers as reference point, since it recommends reference dosimetry to be performed in the absence of a depth dose gradient. But these observations reveal that important aspects of beam monitor calibration in scanned proton beams are not addressed in IAEA TRS- 398 given that those types of beams were not widely implemented at the time of its publication /16/ $ Institute of Physics and Engineering in Medicine Printed in the UK 6585

3 Keywords: scanned proton beam, reference dosimetry, ionization chamber, Faraday cup, W air value, gradient correction (Some figures may appear in colour only in the online journal) ary The selection of a suitable calibration method for scanned proton beams is based on the requirements by the treatment planning system (TPS) used in the institution: in some cases this is a calibration in terms of the number of protons per monitor unit (MU), in other cases this can be a calibration in terms of dose or dose-area-product per MU (Moyers and Vatnitsky 212). Many aspects of this topic have been investigated in the past by Hartmann et al (1999), Jäkel et al (24), Pedroni et al (25), Lorin et al (28), Gillin et al (21) and Clasie et al (212) but there remain various issues still to be understood, among which the measurement of ion recombination (Palmans 214) and which is the preferred method for reference dosimetry (either a point measurement in a large scanned field or a dose-area-product measurement in a single pencil proton beam). In a recent article, Gomà et al (214) address the topic of beam monitor calibration for scanned proton beams by investigating mainly two aspects of this topic in quasi-monoenergetic proton beams (they use the term pseudo-mono-energetic in their paper): (i) the agreement of reference dosimetry using Faraday cups and ionization chambers and (ii) the agreement of reference dosimetry using cylindrical and plane-parallel ionization chambers. They present interesting data on both of those aspects but, in our opinion, various statements in the interpretation and discussion of the experimental results are a bit misleading and in some cases incorrectly representing the literature, which is what we want to clarify in the present commentary. Before discussing those, there are also a few smaller comments we want to make: - The authors claim that the beam monitor for scanned proton beams can only be calibrated by a measurement in the entrance region. Nevertheless, at the same institute Pedroni et al (25) developed a method based on a measurement with a thimble ionization chamber in a box irradiation field which is obviously an alternative way of calibrating the beam monitor. - The authors cross-calibrate the plane-parallel chamber in the spread-out Bragg peak (SOBP) of a passively scattered proton beam. They then derive a value of unity for the beam quality correction factor k Q of this chamber. The symbol k Q is defined in IAEA TRS-398 (Andreo et al 2) as a short notation for k QQ, in the case the calibration beam quality Q is 6 Co. However, it is not clear if the k Q Gomà et al (214) quote is really referring to a 6 Co calibration (in this case the value of unity is not correct) or if it should refer to the cross calibration proton beam quality Q cross, in which case the symbol k QQ, should be used. Later in the paper the symbol k cross QQ, is used where probably again it should be k QQ, since the chamber is not calibrated in a calibration beam quality Q cross in a standards laboratory. These inconsistencies in notation within the paper, as well as when compared to the IAEA TRS-398 formalism, are very confusing for the understanding of the presented discussions. - The authors mention that an energy-independent reference depth z ref is advisable from the practical point of view but we would strongly object to this statement. For example, it is not rational to use a depth of 2 cm for a 6 MeV beam; the gradient is just too large and would even with plane-parallel chambers results in large positioning uncertainty. 6586

4 More generically we believe that for energies below 1 MeV the reference depth should be as shallow as possible. If this is not possible, it is preferable to develop a calibration procedure based on a measurement in the SOBP. 1. Faraday cup versus ionization chamber based reference dosimetry In their abstract, Gomà et al (214) state that good agreement was found between planeparallel ionization chamber and Faraday cup based reference dosimetry and that the difference of 3% is within the uncertainty of the comparison which is of similar size. However, we believe that this uncertainty is dominated by the data used in the conversion factor to derive the particle fluence from a dose determination using the ionization chamber. The comparison can thus, with a much smaller uncertainty, determine this overall conversion factor and demonstrate that the data used are inconsistent with the measurements without necessary being able to indicate what data contribute most to this inconsistency. Before entering into more detailed discussion, it must be noted that Gomà et al (214) based the comparison of the two methods to calibrate the beam monitor on the determination of the number of protons in the pencil beam. The most common approach in dose calculation algorithms for scanned proton beams is, indeed, to derive the dose distribution for each spot from beam parameters normalized per proton. From this point of view it would seem obvious to compare different dosimetric methods by comparing the number of protons they estimate in the beam. However, it must be realized that the quantity of interest is absorbed dose to water and in the dose calculation the proton fluence is essentially multiplied with the mean mass electronic stopping power for water to obtain absorbed dose to water. From this point of view it is more logical to compare different methods by considering the determination of absorbed dose to water. To clarify this further, we treat these two approaches to the comparison in a formal way. We consider a single-layer square field, large enough to achieve lateral charged particle equilibrium, with constant spot spacings, x and y, in both directions lateral to the beam axis and a constant number of particles, n, per spot. In the case the comparison of the two dosimetric methods is based on a determination of absorbed dose to water at the reference depth, z ref, the equation for the derivation of this quanti ty using an ionization chamber is: Dw, Q( zref) = MN Q D,w, Q k Q, Q (1) where M Q is the electrometer reading of the ionization chamber in the beam with quality Q corrected for influence quantities other than beam quality, ND,w, Q is the ionization chamber s calibration coefficient in terms of absorbed dose to water at the calibration beam quality Q, is the beam quality correction factor to correct for the difference between the response of the ionization chamber in the beam qualities Q and Q. The beam quality correction factors tabulated in IAEA TRS-398 are calculated as k QQ, k QQ, k QQ, ( Wair) Q( sw,air) QpQ = ( W ) ( s ) p air Q w,air Q Q where W air is the mean energy expended per ion pair formed in dry air, s w,air is the Spencer- Attix water-to-air stopping power ratio and p is the overall perturbation correction factor for the ionization chamber. Using a Faraday cup to determine the number of protons, n, in a single static spot, absorbed dose to water at the reference depth in the single-layer square field is given by: (2) 6587

5 D n Φ( zref)( Sel/ ρ) w( z ) ( z ) = ref x y Φ () w, Q ref p where Φ( z ref ) is the total charged particle fluence (protons + heavier secondary ions produced in non-elastic nuclear interactions) at the reference depth, ( Sel/ ρ) w( z ref ) is the average mass electronic stopping power of the charged particle spectrum at the reference depth and Φp () is the primary proton fluence at the phantom surface. The ratio Φ( zref)( Sel/ ρ) w( z ref )/ Φ p () is the dose to water at the reference depth per unit of incident proton fluence at the phantom surface (or alternatively, as denoted by Gomà et al (214), the integral dose per proton). In the case the comparison is based on a measurement of the number of protons, the Faraday cup provides a direct measurement of this quantity. From a measurement with an ionization chamber at the reference depth, z ref, the overall equation for the derivation of the number of protons at the phantom surface can be derived from equations (1) and (3) and is given by: n = M N k x y Q D,w, Q QQ, Φ( zref)( Sel / ρ) w( z ref ) Φp() From equations (1) (4) it is clear that any difference between Faraday cup and ionization chamber in the determination of either Dw, Q( zref ) or n demonstrates an inconsistency n between the ratio of measured data, / MN x y Q D,w, Q, and the ratio of theoretical data, Φ( zref)( Sel / ρ) w( z ref ) / k Φp() QQ,. Given that total reaction cross sections are estimated to be accurate within 1% and those of angle-integrated secondary particle production cross sections within 3% (ICRU 2) and given that the dose contribution from secondary particles produced in non-elastic nuclear interactions amount up to 12% of the total dose in the highest-energy clinical beams (Laitano et al 1996), it can be assumed that the relative standard uncertainty on the Monte Carlo calculated ratio Φ( zref)/ Φp ( ) amounts up to 2%. There is also a considerable uncertainty on ( Sel/ ρ) w( z ref ), in part because of the stopping power data with typical uncertainties of 1 2% (ICRU 1993), but also because of the influence of non-elastic interactions on the charged particle spectrum (Laitano et al 1996). This is as opposed to the water to air stopping power ratios which are only marginally affected by the secondary particles produced in nuclear interactions (Medin and Andreo 1997). IAEA TRS-398 quotes an uncertainty of about 2% on k Q values for plane-parallel chambers. The ( W air ) Q value used for the calculation of those values was later confirmed by the value of Jones (26) derived from calorimetry data, but one must realize that from calorimetry/ionometry comparisons actually the product ( Wair) Q( sw,air ) QpQ is derived. This means that if a code of practice uses the same data for ( sw,air ) Q and p Q as those that were used to derive the value of ( W air ) Q from the product ( Wair) Q( sw,air ) QpQ, the resulting k Q values are automatically consistent with calorimetry. This is, for example, the case with IAEA TRS- 398 in which Spencer-Attix stopping power ratios based on ICRU Report 49 data are used (ICRU 1993) and the assumption is made that pq = 1. If other data for ( sw,air ) Q would be used a re-evaluation of the derived ( W air ) Q value is required and, consequently, the k Q values would remain unchanged (Andreo et al 213). Gomà et al (214) claim that the discrepancy observed between Faraday cup and ionization chambers is possibly due to the k Q data used in IAEA TRS-398 (and they give the strong impression that this is the most likely source). The basis for this statement is the disagreement between Faraday cup and ionization chamber and a supporting discussion gives the impression (3) (4) 6588

6 that calorimeters show a similar discrepancy with ionization chambers. The latter argument, however, is based on an inappropriately biased interpretation of literature data. For a start, as mentioned already, since ( W air ) Q has been derived from averaging a substantial number of comparisons between calorimeters and ionization chambers, there is on average (logically) a very good agreement between both techniques. But, most of these data are based on passively scattered beams, so one could raise the question if this agreement is worse for scanned beams. Gomà et al (214) refer to the only three experimental comparisons of calorimetry with ionometry in scanned proton beams reported in the literature so far: Gagnebin et al (21), Medin (21) and Sarfehnia et al (21). Let s have a closer look at those data in figure 1. The first result that Gomà et al (214) quote to support that calorimetry exhibits a lower response is the result of Gagnebin et al (21). While it is numerically correct that this value is about 3% lower than the IAEA TRS-398 value, it is obvious in figure 1 that this data point has a very large uncertainty. Noteworthy is that this large uncertainty is dominated by the type-a uncertainty of the experiment given that it is based on a very small number of calorimetry data (1 runs to be precise; in comparison, most of the other data points are based on more than hundred, sometimes hundreds, of calorimetry runs). The second data point that Gomà et al (214) quote is the result obtained in a passively scattered beam from Medin et al (26) while ignoring all the other data points obtained in scattered beams. The data point from Medin et al (26) is one of the lowest of the entire distribution but is not an outlier; it is consistent with the distribution of data points. Gomà et al (214) then quote the two other data points obtained in scanned beams by Medin (21) and Sarfehnia et al (21), but from figure 1 it is clear that those are very consistent with all the other data. It can be concluded that none of the calorimetry data support the suggestion by Gomà et al (214) that the k Q data in IAEA TRS-398 are overestimated. We now come back to the question which quantity (n or Dw, Q( zref )) should be compared. Since the delivery information provided by most treatment planning systems includes the number of particles per spot, the corresponding beam monitor calibration is also performed in terms of the number of particles in a single pencil proton beam. Then, it may seem logical to use a Faraday cup which is the most direct instrument to measure this quantity. Using a well-designed Faraday cup this can indeed be done with a low uncertainty of.5% (Gomà et al 214). With the ionization chamber the number of particles can also be determined, but in an indirect way as shown in equation (4). The measurement of absorbed dose to water using a plane-parallel ionization chamber has an intrinsic uncertainty of 2.3% (IAEA TRS-398). As can be seen in equation (4) the determination of the relevant area (from the spot spacing) will also contribute an uncertainty and so does the integral dose per proton. This results in an uncertainty of about 3% on the proton fluence incident at the phantom surface as derived from a reference dose measurement using an ionization chamber at a depth of 2 cm in water. This way of presenting the comparison, as is done by Gomà et al (214), gives the impression that the ionization chamber is an inferior dosimeter for the quantity of interest. However, in a dose calculation algorithm this particle fluence will have to be multiplied with the stopping power for the charged particle spectrum in the phantom/patient or an experimentally determined dose to fluence ratio. Using the number of protons determined with an ionization chamber, the equation for dose to water at a depth z becomes: Φ()( z Sel / ρ) w( z) Φp() w, Q Q D,w, Q Q, Q Φ( zref)( Sel / ρ) w( z ref ) D () z = M N k while using a Faraday cup the overall equation is: Φp() (5) 6589

7 Figure 1. ( W air ) Q for proton beams derived from the literature. The numbered squares are the data points based on calorimetry used by Jones (26) where the numbers refer to the source of the data: (1) Schulz et al (1992), (2) Siebers et al (1995), (3) Palmans et al (1996), (4) Delacroix et al (1997), (5) Brede et al (1999), (6) Hashemian et al (23) and (7) Palmans et al (24). The other points are more recent data published after Jones (26), measured in passively scattered beams (grey-filled symbols) and scanned beams (black-filled symbols). The grey horizontal line represents the (W air ) p value used in IAEA TRS-398 whereas the grey dashed line is 3% lower, representing the (W air ) p that would results from the Faraday cup/ionization chamber comparison by Gomà et al (214). D w,q n Φ()( z Sel/ ρ) w( z) () z = x y Φ () p It is clear that the numerator and denominator in the last factor on the right hand side of equation (5) are highly correlated and that the uncertainty on the dose determination is thus approximately equal to that of a direct dose determination using IAEA TRS-398. In equation (6), on the other hand, the substantial uncertainties on x y and Φ()( z Sel/ ρ) w ( z) propagate directly and the uncertainty can then be expected to be larger when based on a Faraday cup than when based on a reference dose measurement using a calibrated ion chamber. This is also confirmed by Pedroni et al (25), in the same institute of Gomà et al (214), who corrected the beam monitor calibration curve derived from a Faraday cup measurement to the dose derived using a thimble ionization chamber in a box irradiation field. This is actually another way of saying that the quantity of interest is absorbed dose to water. For some it may appear counterintuitive at first but for the dose calculation it is more accurate to derive fluence from a dose measurement than to measure fluence directly, provided the same stopping power data are used in the derivation of fluence from dose as are used in the dose calculation. In conclusion, our opinion is that the source of the discrepancy should likely be related to the Faraday cup measurement itself or to the conversion of particle fluence to dose. Various problems with dosimetry based on Faraday cup dosimetry reported in the literature (Palmans and Vynckier 22, Karger et al 21), combined with the agreement of calorimeter and ionization chambers support our view that Faraday cup based dosimetry is not recommended (6) 659

8 as the primary method for beam monitor calibration. For the same reason it is also not recommended by ICRU Report 78 (ICRU 28). 2. Cylindrical versus plane-parallel ionization chambers Another observation made by Gomà et al (214) is related to the disagreement between dosimetry based on cylindrical and plane-parallel ionization chambers and indicates that in the presence of a depth dose gradient, dosimetry using cylindrical ionization chambers is in better agreement with dosimetry using plane-parallel chambers when the effective point of measurement of the ion chamber is taken into account rather than the centre of the chamber. This obviously results from the fact that in IAEA TRS-398 the displacement correction factor is taken to be unity given that one of the conditions for reference dosimetry mentioned is the absence of a substantial depth dose gradient. The data presented by Gomà et al (214) on this confirm earlier experimental results by Mobit et al (2) and Palmans et al (21) and theoretical predictions by Palmans et al (21) and Palmans (26). The authors use this finding to suggest that the recommendations in IAEA TRS-398 are inadequate. However, we believe this is not the case as IAEA TRS-398 does not promote reference dosimetry in the presence of substantial depth dose gradients. The recommendation of TRS-398 is that reference dosimetry should be performed in the centre of the SOBP. For plateau irradiations an exception is made but that refers to a specific application of so-called cross-fire irradiation where the plateau part of depth dose is used for stereotactic radiosurgery using protons (Konnov 1987). Gomà et al (214) are right that if dosimetry in the entrance region (we wouldn t call it plateau region since there is a gradient) is the preferred reference condition for scanned beams, then it would be advisable to use plane-parallel chambers when the gradient is too large or cylindrical ionization chambers with a displacement correction (or the alternative use of an effective point of measurement) provided the gradient is modest. The authors are also right to observe that IAEA TRS-398 has not addressed specific aspects that are essential for monitor calibration in scanned beams since those types of beams were not widely implemented at the time of its publication. Among those aspects are the determination of ion recombination (Palmans 214) and the determination of dose-area-product in a single pencil proton beam using a point dose measurement with a small-volume ionization chamber in a single-layer scanned field (Hartmann et al 1999, Jäkel et al 24, Clasie et al 212) or using a large-area ionization chamber in the single pencil proton beam (Gillin et al 21). 3. Conclusions Gomà et al (214) observe an unexplained 3% discrepancy between Faraday cup and ionization chamber based beam monitor calibration of a scanned proton beam. Their interpretation that literature data supports the existence of a similar discrepancy between calorimetry and ionization chamber based dosimetry is incorrect and misleading. This commentary shows, on the contrary, that from the current literature can be inferred that calorimeters and ionization chambers agree in both passively scattered and actively scanned proton beams. The conclusion of Gomà et al (214) that their results combined with literature data indicate that k Q -values tabulated in IAEA TRS-398 for proton beams might be overestimated, is thus unwarranted. It must rather be concluded that there still exist unresolved problems with Faraday cup dosimetry which need further investigation before reconsidering this method for reference dosimetry; ICRU Report 78 (ICRU 28), for example, does not recommend its use. This commentary also explains why, with respect to the analysis of uncertainty contributions, 6591

9 a fair comparison between Faraday cup and ionization chamber should preferably be based on the quantity absorbed dose to water rather the number of protons as Gomà et al (214) do. Furthermore, while they claim that the beam monitor for scanned proton beams can only be calibrated by a measurement in the entrance region, Pedroni et al (25) have demonstrated the use of a Faraday cup based calibration corrected by a reference dose measurement using a thimble chamber in a box irradiation field as an alternative method. Gomà et al s findings on the effective point of measurement for cylindrical ionization chambers are very valuable and confirm earlier results in the literature. These, however, do not undermine the recommendations of IAEA TRS-398 in the reference conditions it prescribes, since these imply the absence of a depth dose gradient. Gomà et al (214) are right to observe that important aspects of beam monitor calibration in scanned proton beams are not addressed in IAEA TRS-398 given that those types of beams were not widely implemented at the time of its publication. References Andreo P, Burns D T, Hohlfeld K, Huq M S, Kanai T, Laitano F, Smyth V G and Vynckier S 2 Absorbed dose determination in external beam radiotherapy: an international code of practice for dosimetry based on standards of absorbed dose to water IAEA Technical Report Series 398 IAEA, Vienna Andreo P, Wulff J, Burns D T and Palmans H 213 Consistency in reference radiotherapy dosimetry: resolution of an apparent conundrum when 6 Co is the reference quality for charged-particle and photon beams Phys. Med. Biol Brede H J, Greif K D, Hecker O, Heeg P, Heese J, Jones D T, Kluge H and Schardt D 26 Absorbed dose to water determination with ionization chamber dosimetry and calorimetry in restricted neutron, photon, proton and heavy-ion radiation fields Phys. Med. Biol Brede H J, Heinemann E, Binns P J, Langen K M, Jones D T L and Schreuder A N 1999 Water calorimetry and ionization chamber dosimetry in the proton therapy beam National Accelerator Annual Report (Faure: National Accelerator Centre) pp Clasie B, Depauw N, Fransen M, Gomà C, Panahandeh H R, Seco J, Flanz J B and Kooy H M 212 Golden beam data for proton pencil-beam scanning Phys. Med. Biol Delacroix S et al 1997 Proton dosimetry comparison involving ionometry and calorimetry Int. J. Radiat. Oncol. Biol. Phys Gagnebin S, Twerenbold D, Pedroni E, Meer D, Zenklusen S and Bula C 21 Experimental determination of the absorbed dose to water in a scanned proton beam using a water calorimeter and an ionization chamber beam Nucl. Instrum. Methods B Gillin M T et al 21 Commissioning of the discrete spot scanning proton beam delivery system at the University of Texas MD Anderson Cancer Center, Proton Therapy Center, Houston Med. Phys Gomà C, Lorentini S, Meer D and Safai S 214 Proton beam monitor chamber calibration Phys. Med. Biol Hartmann G H, Jäkel O, Heeg P, Karger C P and Krießbach A 1999 Determination of water absorbed dose in a carbon ion beam using thimble ionization chambers Phys. Med. Biol Hashemian R, Foster C C, Murray K M, Landolt R L, Shaw S M and Bloch C 23 Measurement of W/e for protons in air 39th Meeting of the Particle Therapy Co-Operative Group (San Francisco, CA) ICRU 1993 Stopping Powers and Ranges for Protons and Alpha Particles (ICRU Report vol 49) (Bethesda, MD: International Commission on Radiation Units and Measurements) ICRU 2 Nuclear Data for Neutron and Proton Radiotherapy and for Radiation Protection Dose (ICRU Report vol 63) (Bethesda, MD: International Commission on Radiation Units and Measurements) ICRU 28 Prescribing, Recording, and Reporting Proton-Beam Therapy (ICRU Report vol 78) (Bethesda, MD: International Commission on Radiation Units and Measurements) Jäkel O, Hartmann G H, Karger C P, Heeg P and Vatnitsky S 24 A calibration procedure for beam monitors in a scanned beam of heavy charged particles Med. Phys Jones D T L 26 The w-value in air for proton therapy beams Radiat. Phys. Chem

10 Karger C P, Jäkel O, Palmans H and Kanai T 21 Dosimetry for ion beam radiotherapy Phys. Med. Biol. 55 R Konnov B A 1987 Proton therapy at Leningrad synchrocyclotron 1th Meeting of the Proton Therapy Co-Operative Group and 2nd Int. Charged Particle Therapy Workshop (12 14 October 1987) Laitano R F, Rosetti M and Frisoni M 1996 Effect of nuclear interactions on energy and stopping power in proton beam dosimetry Nucl. Instrum. Methods A Lorin S, Grusell E, Tilly N, Medin J, Kimstrand P and Glimelius B 28 Reference dosimetry in a scanned pulsed proton beam using ionisation chambers and a Faraday cup Phys. Med. Biol Medin J and Andreo P 1997 Monte Carlo calculated stopping-power ratios, water/air, for clinical proton dosimetry (5 25 MeV) Phys. Med. Biol Medin J, Ross C K, Klassen N V, Palmans H, Grusell E and Grindborg J E 26 Experimental determination of beam quality factors, k Q, for two types of Farmer chamber in a 1 MV photon and a 175 MeV proton beam Phys. Med. Biol Medin J 21 Implementation of water calorimetry in a 18 MeV scanned pulsed proton beam including an experimental determination of k Q for a Farmer chamber Phys. Med. Biol Mobit P N, Sandison G A and Bloch C 2 Depth ionization curves for an unmodulated proton beam measured with different ionization chambers Med. Phys Moyers M F and Vatnitsky S M 212 Practical Implementation of Light Ion Beam Treatments (Madison, WI: Medical Physics) Palmans H 26 Perturbation factors for cylindrical ionization chambers in proton beams: part I. Corrections for gradients Phys. Med. Biol Palmans H 214 Theoretical models for volume recombination in scanned proton beams Radiother. Oncol Palmans H, Seuntjens J, Verhaegen F, Denis J-M, Vynckier S and Thierens H 1996 Water calorimetry and ionization chamber dosimetry in an 85 MeV clinical proton beam Med. Phys Palmans H, Thomas R, Simon M, Duane S, Kacperek A, DuSautoy A and Verhaegen F 24 A smallbody portable graphite calorimeter for dosimetry in low-energy clinical proton beams Phys. Med. Biol Palmans H, Verhaegen F, Denis J M, Vynckier S and Thierens H 21 Experimental p wall and p cel correction factors for ionization chambers in low-energy clinical proton beams Phys. Med. Biol Palmans H and Vynckier S 22 Reference dosimetry for clinical proton beams Recent Developments in Accurate Radiation Dosimetry ed J P Seuntjens and P N Mobit (Madison, WI: Medical Physics) pp Pedroni E, Scheib S, Böhringer T, Coray A, Grossmann M, Lin S and Lomax A 25 Experimental characterization and physical modelling of the dose distribution of scanned proton pencil beams Phys. Med. Biol Sarfehnia A, Clasie B, Chung E, Lu H M, Flanz J, Cascio E, Engelsman M, Paganetti H and Seuntjens J 21 Direct absorbed dose to water determination based on water calorimetry in scanning proton beam delivery Med. Phys Schulz R J, Verhey L J, Huq M S and Venkataramanan N 1992 Water calorimeter dosimetry for 16 MeV protons Phys. Med. Biol Siebers J V, Vatnitsky S M, Miller D W and Moyers M F 1995 Deduction of the air w value in a therapeutic proton beam Phys. Med. Biol