Feasibility Of Graphite Calorimetry In A Modulated Low-Energy Clinical Proton Beam

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1 Feasibility Of Graphite Calorimetry In A Modulated Low-Energy Clinical Proton Beam H. Palmans a, R. Thomas a, M. Simon a, S. Duane a, A. Kacperek b, J. Seco c, R. Nutbrown a, D. Shipley a, A. DuSautoy a, F. Verhaegen d a Centre for Acoustics and Ionising Radiation, National Physical Laboratory, Teddington, UK b Douglas Cyclotron, Clatterbridge Centre of Oncology, Wirral, UK c Royal Marsden Hospital, Institute of Cancer Research, London, UK d Medical Physics Unit, McGill University, Montreal, Canada Abstract This paper describes the first application of a graphite calorimeter to absolute dosimetry of an ocular proton beam. NPL s existing portable graphite calorimeter, used for high-energy photon and electron beams, is adapted for use in a low-energy proton beam. The equivalence of graphite and water is investigated. Monte Carlo simulations are used to calculate fluence, gap and volume averaging corrections. 1. Introduction Proton therapy offers an attractive alternative to conventional high-energy photon and electron therapy due to the characteristic dose distributions for a proton beam, exhibiting a typical Bragg peak (BP) as shown in figure 1. Due to the ballistic properties of protons, they also undergo a limited amount of lateral scatter. 100 modulated percent dept dose non-modulated z (cm) Figure 1. Percent depth dose profiles for 100 MeV protons in water (solid lines). For comparison, the dashed line represents the depth dose distribution for a 10 MV x-ray beam and the shaded areas indicate the regions where a modulated proton beam offers a physical advantage in aiming to spare healthy tissue. 1

2 Moving the BP by adding extra material in the form of a plastic modulator wheel, a spread out Bragg peak (SOBP) is achieved, a uniform dose over an extended depth, resulting in a physically advantageous depth dose distribution compared to that of a high-energy photon beam. The shaded areas in figure 1 illustrate this. Proton therapy used to be mostly an experimental technique and side occupation at research accelerators until about ten years ago. Since then, a number of dedicated proton therapy centres have been established raising the number of centres currently treating patients to 27 or to express it with the words of Goitein et al.: Once an obscure area of academic research, proton therapy is developing into an effective treatment option for use in hospitals [1]. At least ten more centres will start treatments in the next few years and several more are planned by the end of the decade [2]. Calorimetry is generally recommended as primary dosimetry method for clinical proton beams and given the growing number of proton therapy centres worldwide, the development of a set of standard calorimeters for protons would be very valuable. Another reason for developing calorimeters for proton beams is that in a recent code of practice, IAEA TRS-398 [3], preference is given to using absorbed dose calibration factors for ionisation chambers obtained in proton beams or, equivalently, to using measured beam quality correction factors k Q. Despite this, no long-term primary calorimetry based standards for protons exist at present. The feasibility of calorimetry for dosimetry of clinical high-energy proton beams as well as for relatively low-energy beams has been demonstrated. Calorimeters with a double absorber consisting of aluminium or copper and A-150 to determine the chemical heat defect of A-150 have been used [4-7] and a similar design was used to confirm within the experimental uncertainty that the chemical heat defect in graphite is zero [6]. The heat defect for water calorimetry has been investigated in an absolute way using a two-component absorber consisting of water and copper [7] and by relative measurements with different chemical water systems [8,9]. Comparison of ionization chamber dosimetry with water calorimeters [9-11] and an A-150 calorimeter [12] has yielded indispensable information on the average energy required to produce an ion pair in dry air by protons which is recommended in IAEA TRS-398 and some more water calorimetry measurements have been reported [13-14]. For low-energy proton beams used for the treatment of ocular melanoma, on the other hand, the feasibility of calorimetry has not been explored mainly because of the short range of these beams (lower then 3.5 cm) and their limited lateral extension (a few cm in diameter). At NPL, graphite calorimeters have been developed for photon and electron beam dosimetry. A portable device was developed which is used in clinical photon and electron beams. In this work, the feasibility of adapting the NPL portable graphite calorimeter for dosimetry of a modulated low-energy proton beam is investigated. The equivalence of graphite and water for proton beam dosimetry will be discussed and the construction of a new portable calorimeter for small field dosimetry will be described as well as preliminary experimental results obtained with the device. 2. Materials and methods 2.1. Basic interaction data Stopping power data were obtained from ICRU report 49 [15] and non-elastic nuclear cross section data from ICRU report 63 [16]. Figure 2 shows the water to graphite stopping power ratios and non-elastic nuclear interaction cross section ratios. The non-elastic nuclear 2

3 interaction cross sections are expressed per unit of atomic weight, which is roughly the same as expressing them per nucleon (a) 1.00 (b) s w,g [σnucl/a] w,g E+00 1.E+01 1.E+02 1.E+03 Energy (MeV) Energy (MeV) Figure 2. (a) Water to graphite stopping power ratios as a function of proton energy and (b) water to graphite non-elastic nuclear interaction cross section ratios as a function of proton energy. Figure 2a shows that the water to graphite stopping power ratio has an almost constant value of about 1.12 for energies between 5 and 250 MeV, which covers the entire range of clinical proton beam energies. This has the advantage that the shape of depth dose curves in graphite and water will be more or less the same if electromagnetic interactions are the dominant energy loss process. Another consequence is that proton spectra will be the same at equivalent depths in water and graphite, which is a prerequisite for applying a simple scaling theorem. In figure 2b, on the other hand, we can see that the overall water to graphite non-elastic nuclear interaction cross section ratios shows considerable energy dependence. However, the strongest variation occurs for energies below 100 MeV where the contribution of non-elastic nuclear interactions to the total dose is small Monte Carlo calculations Gap effects, volume averaging effects and fluence correction factors have been calculated using Monte Carlo simulations. The transport code used in this work is based on the proton Monte Carlo code PTRAN [17] that simulates mono-energetic pencil beams in homogeneous water without transport of secondary particles. Adaptations were made in order to simulate transport in low-z materials other than water, to allow the simulation of modulated proton beams, rectangular or circular beams and beams with a certain energy distribution [18,19]. The implementation of a boundary-crossing algorithm allowed the simulation of inhomogeneous geometries [19]. For the present work, two versions of the code were used: one which is almost equal to the original version of PTRAN, but which simulates protons in other homogeneous materials than water and a second version, which transports protons in two-dimensional cylindrical RZ-voxel geometry in which the materials in each voxel can be specified differently and the average dose over each voxel volume is scored. The effect of a plastic modulator wheel was simulated by adding an additional layer in front of the phantom, 3

4 the thickness of which is sampled from the distribution of the thickness in the wheel for each individual incident particle. Depth dose distributions in homogeneous graphite and water are compared in order to evaluate the equivalence of both materials. The depths in both materials should be scaled with range in both materials. It has been shown that a continuous slowing down approximation (csda) yields accurate results for the scaling of depths [20]. Thus, the water equivalent depth in water, z w, relates to the depth in graphite, z g, as z w = z g r 0,w / r 0,g (1) where r 0,w and r 0,g are the csda ranges in water and graphite respectively. Any difference in the proton fluence at equivalent depths in both materials will result in the need for a fluence correction factor Φ w,g to scale dose in graphite to dose to water. The most obvious way to assess these correction factors is by the following definition: D w (z w ) = D g (z g ) s w,g Φ w,g (2) where D w (z w ) is absorbed dose to water at the water equivalent depth z w, D g (z g ) is absorbed dose to graphite at the depth z g in graphite and s w,g is the water to graphite mass stopping power ratio for the spectral fluence distribution at the equivalent depths. However, it was shown that this definition does not account for the difference between the elastic and nonelastic interaction cross sections shown in figure 2 and that a better definition is given by D w (z w ) = [D g,c (z g ) s w,g + D g,n (z g ) σ w,g ] Φ w,g (3) where absorbed dose to graphite has been split in a contribution from Coulomb interactions, D g,c (z g ), and a contribution from non-elastic interactions, D g,n (z g ) and σ w,g is the water to graphite ratio of non-elastic nuclear cross sections per nucleon [20]. The practical problem with this definition is that if dose is measured in both materials, the relative contributions of both components are not very well known since the uncertainties on non-elastic nuclear cross section data could be up to 10% according to ICRU report 63 [16]. For the present work, fluence correction factors have been calculated according to both definitions using the previously described version of PTRAN and preliminary calculations have been performed with GEANT4 [21]. Only the definition given by equation (2) is used for the analysis of experimental data. It is worth noting that the effects responsible for the fluence correction factors are predominantly related to differences in non-elastic nuclear interaction cross sections as has been demonstrated before. The simulated geometries for the gap and volume averaging are shown in figure 3. The substituted gap correction factor, k gap,subst, is calculated as the ratio of the average dose over the core volume when the gap is filled up with graphite and the average dose when the gap is filled up with air. The compensated gap correction factor, k gap,comp, is defined as the average dose over the core volume when the core is moved towards the inner surface of the gap facing towards the beam source and the (new) gap is filled up with graphite and the average dose when the gap is filled up with air. The method with the compensated gap assures that, apart from the difference due to the air gap, the attenuation the particles that enter the core have undergone is the same for both dose determinations in the ratio. 4

5 substituted gap compensated gap volume averaging beam Figure 3. Side view of the geometries for the Monte Carlo calculation of the substituted gap correction factor, compensated gap correction factor and volume averaging correction factor. All geometries are axisymmmetric around the beam axis; all material is graphite, except the shaded areas, which are air or graphite; the scoring region is the core volume in all three cases. Volume averaging correction factors, k vol_av, were calculated as the ratio of the dose in a point at the centre of the core to the average dose in the core volume without the presence of the air gap (thus, also in homogeneous graphite). The dose in the centre of the core was evaluated by the reciprocity theorem from the integrated dose in an infinite slab due to a pencil beam. Simulations were performed for a modulated modulated mono-directional circular beam with a diameter of 3 cm and an incident energy of 60 MeV (mono-energetic) Experiment: 60 MeV beam at CCO The proton beam at Clatterbridge Centre of Oncology (CCO) is generated by a cyclotron and is used for the treatment of ocular melanoma. Details about the cyclotron and beam line can be found in reference [22]. The proton exit energy is 62 MeV allowing for a beam penetration of 31.9 ± 0.2 mm in water at the end of the beam line. A uniform beam is obtained by a double scattering tungsten foil system and an SOBP is obtained using rotating PMMA modulator wheels. The beam is monitored using two parallel plate transmission chambers. A light field and two x-ray tubes and film holders are installed in order to verify patient positioning. For the measurements in this work, circular brass collimators with diameters of 30 mm and 34 mm were used for the final collimation Experiment: graphite calorimetry and ionization chamber dosimetry The existing portable graphite calorimeter (PGC) has been designed for measurements in clinical high-energy photon and electron beams [23]. Figure 4 shows a schematic representation of the calorimeter. 5

6 front view of slab containing core beam core 90 mm (old) calorimeter graphite T controlled body styrofoam 30 mm (new) Figure 4. Schematic diagram of the portable calorimeter; left: side view, right: front view (adapted from reference [23]). The core consists of a disc with a thickness of 2mm and a diameter of 20 mm. Five sensing thermistors are embedded in the core, which is kept in place by styrofoam beads in the centre of a 4mm thick, 22 mm diameter disc shaped cavity within a graphite slab. This slab and a number of adjusting slabs for setting the depth of the core form the calorimeter body. This body is isolated from a larger graphite body which is temperature stabilized above room temperature at 27 ûc. On the right hand side of figure 3, a front view of the slab containing the core is shown. The slabs in the existing calorimeter had an octagonal shape with dimension of 90 mm and this calorimeter is referred to as old, in the sense that it existed prior to the present work. The core temperature is monitored by two sets of two calibrated thermistors coupled in two DC Wheatstone bridges and this is done continuously for a period of time starting before the first irradiation and ending after the last of a series of irradiation without any intermittent manipulation of the measuring assembly. A first set of measurements was performed in the modulated beam with the existing calorimeter, but we expected that large heat losses make it hardly possible to assess the radiation induced temperature rise accurately, since the surround of the core is only partially irradiated. A smaller version of the calorimeter body was constructed, with dimensions such that the modulated beam irradiated the whole graphite body in order to cope with the heat transfer phenomena. This version of the calorimeter is referred to as new in figure 3 and a second set of measurements was performed with this calorimeter in the modulated beam. For an additional set of measurements, a shielding brass cone was constructed with a diameter of 21 mm in order to shield the calorimeter core from the radiation field. This way, the heat transfer phenomena between the core and the surrounding graphite were studied. The graphite calorimeter measurements were compared with ionization chamber measurements using an NE2561 thimble chamber. Dose to water was obtained from the chamber measurements applying IAEA TRS-398 [3]. 3. Results and discussion 3.1. Water equivalence of graphite to water Figure 5 shows the graphite to water fluence correction factors calculated with PTRAN for a modulated 60 MeV beam according to both definitions in equations (2) and (3). It is obvious 6

7 that with equation (2) the result cannot be a real fluence correction factor since the fluence at the surface is equal for both simulations (assuming there is no significant component of backscattered protons) and consequently the fluence correction factor should be unity. Applying equation (3) we find a more sensible fluence correction factor of unity at the surface, but we repeat that we are able to do this calculation only because we can separate the dose components in the Monte Carlo simulation and can convert both components using the cross section data we used in the simulations. Still, the simulated contributions might not correspond well with the physical values of these relative contributions given the large uncertainties on the non-elastic cross section data, which makes it practically easier to use the correction factors calculated with equation (2) (a) (b) fluence correction factor water-equivalent depth (cm) water-equivalent depth (cm) Figure 5. Graphite to water fluence correction factors as a function of water equivalent depth for a 60 MeV modulated proton beam calculated with the version of PTRAN described in section 2.2., (a) according to equation (2) and (b) according to equation (3) (a) (b) (c) fluence correction factor water equivalent depth (cm) water equivalent depth (cm) water equivalent depth (cm) Figure 6. Graphite to water fluence correction factors as a function of water equivalent depth for a 60 MeV non-modulated proton beam calculated according to equation (2), (a) using the version of PTRAN described in section 2.2. and (b) using GEANT4 with the QGSP_BIC dataset and (c) using MCNPX. In figure 6, similar fluence correction factors have been calculated for a non-modulated 60 MeV proton with PTRAN, GEANT4 and MCNPX. For the GEANT4 simulations, the physics 7

8 data set denoted with QGSP_BIC is used which is shown to give better results than other data sets [24]. It is clear that there are substantial differences in the correction factors obtained from the three codes, though the order of magnitude of the corrections is similar (of the 1% level at the measurement depth of 15 mm). It must be noted that the stopping powers needed in equation (2) were taken from ICRU report 49 for the three Monte Carlo calculations, though they do not necessary use the same data. Until we have extracted the stopping powers used by each of the codes, this might contribute to these differences. Another likely source of differences are the non-elastic nuclear interaction models used in the three codes. This illustrates the uncertainty that is involved with interaction section data used in the Monte Carlo simulations and will contribute significantly to the overall uncertainty of dose to water derivation from the graphite calorimetry measurements. Careful absolute measurements with ionization chambers in graphite and water will be required for giving a decisive answer about the fluence correction factors Gap and volume correction factors for graphite calorimetry Gap and volume correction factors for a modulated 60 MeV beam, calculated with PTRAN, are shown in figure 7. Both substituted and compensated gap corrections are smaller than 0.1% except when part of the core is in the distal fall off region of the SOBP (a) (b) k gap k vol depth in graphite (cm) depth in graphite (cm) Figure 7. (a) Gap correction factors and (b) volume averaging correction factors as a function of depth calculated using the version of PTRAN described in section 2.2. for a modulated 60 MeV beam. Diamonds represent the substituted gap and triangles the compensated gap correction factors. The volume averaging corrections are smaller than a few tenths of a percent at the reference depth, demonstrating that accurate dosimetry is possible. Nevertheless, the corrections and the variation of it might be a larger than expected given the flat dose profile shown in figure 1. However, we must bear in mind that the reference dose for this calculation, the dose at a point, is very sensitive to small fluctuations or ripples in the SOBP. This is reflected in the fluctuations for the volume averaging correction factors shown in figure 9b and will contribute to the uncertainty of the dose measurement, especially when in a future stage of this work a comparison with a plane-parallel chamber is performed. 8

9 3.3. Graphite calorimetry measurements Figure 8 shows some of the measurement series performed with both calorimeters. Figure 8a was recorded with the old photon and electron PGC in a series of irradiations in a 60 MEV modulated proton beam. The total scale is about 20 mk. Each vertical increase in the temperature corresponds with a dose of about 12 Gy delivered in 12 s and irradiation were delivered with 6 min time intervals except after the first and sixth runs. After each irradiation there is obviously a kind of bi-exponential behaviour. The is explained by the partial irradiation of the surround of the core; the very steep decrease of the temperature immediately after the irradiations is associated with the redistribution of heat in the surround of the core and the second, less steep, decrease is associated with the heat losses towards the surrounding styrofoam, which have a much longer time constant. Since it proves to be difficult to model these heat loss phenomena very accurately, the uncertainty on the extrapolation of the drift curves would be large and therefore we conclude that the old PGC is not suitable for measurements in these small proton beam as well as in small beams in general. (a) (b) (c) (d) Figure 8. (a) Series of measurements with the old calorimeter, (b) series of measurements with the new calorimeter, (c) one of the measurements with the fitting procedure illustrated, (d) series of measurements with the core shielded from the radiation field. Figure 8b shows a series of measurements with the new PGC, again for a number of successive 12 Gy irradiations of 12 s with 6 min time intervals except between the fifth and sixth runs where an interrupted irradiation occurred. This time the drift curves after each irradiation are almost linear. The calorimeter body is now given a more or less uniform dose 9

10 and the drift curves after each irradiation are predominantly due to the heat losses to the surrounding styrofoam. Noticeable is also that after a few irradiation runs, an almost steady regime is achieved in which the heat loss over a long time equals the average irradiative heat generated in the calorimeter. The average temperature rise per monitor unit for the nine last runs was used to determine the dose response of the calorimeter. The standard deviation on these nine runs was 0.28%. A similar set of measurements was done at a four times lower dose rate, for which the standard deviation set was consistently 0.65%. This lower dose rate was the one used for the ionization chamber measurements. The extrapolation procedure is illustrated in figure 8c; a quadratic fit is applied to the pre- and post-irradiation drift curves and extrapolated linearly to mid-run. Figure 8d shows a series of irradiations where the core has been shielded from the radiation field with a brass cylinder. Each abrupt change in slope corresponds with the start of an irradiation after which an exponential-like temperature increase is observed corresponding with the heat which is transferred from the surround to the core. Another paper in these proceedings discusses these heat transfer phenomena in more detail [25]. Dose to water obtained from the calorimeter measurements was compared with the ionization chamber measurements in a dummy phantom. Due to a difference in the amount of styrofoam in front of the dummy phantom and in front of the calorimeter, the source to detector distance was about 1 cm different in both measurements. Dose to water at the water equivalent depth of the ionization chambers was derived from the temperature rise T measured with the calorimeter applying the following expression: D w (z w ) = T c g s w,g Φ w,g k SDD (4) where c g is the specific heat capacity at the operating temperature, which was measured at NPL [26] and amounts to J kg -1 K -1 at 27.3 ûc, s w,g is the water to graphite stopping power ratio which was taken from ICRU report 49 [15] and is at this beam quality, the Φ w,g calculated using PTRAN and equation (2) was used, being and k SDD is the correction factor for the difference in SDD distance which is assuming an SDD of 155 cm, which was the physical distance of the core from the scattering foil. Since the modulating wheel for obtaining the SOBP is located closer to the isocentre the SDD might be smaller, but this has still to be evaluated and warrants a repeat of the measurements with equal SDD in both calorimetry and ionization chamber measurements. For the ionization chamber measurements in the graphite phantom, the fluence correction factors have to be applied as well, such that they essentially cancel out. Compared with the higher dose rate measurements showed in figure 10b, the ratio of the calorimetric dose and the ionometric dose was 1.00 ± 0.02 for the NE2561 and 1.01 ± 0.03 for the NACP02. Compared with the lower dose rate calorimeter measurements, the ratios were 0.99 ± 0.02 for the NE2561 and 1.00 ± 0.03 for the NACP02. The quoted uncertainties contain uncertainties for the ionization chamber measurements based on IAEA TRS-398 [3] and for the various factors in equation (3) but have to be considered as a preliminary assessment. From a comparison of calorimetry measurements with ionization chamber measurements, the value of the product of the graphite to air proton stopping power ratio, average energy required to produce an ion pair in dry air by protons and the ionization chamber perturbation factor for protons can be derived. When further measurements are performed, a careful uncertainty analysis on the determination of that product will be performed. 10

11 4. Conclusions The feasibility of graphite calorimetry as an absolute dosimetry method for a modulated lowenergy clinical beam has been demonstrated. A new PGC body has been constructed, devoted to small field low-energy proton beams and potentially other small field beams. The small size assures that the whole calorimeter body is irradiated, which brings problems with heat losses under control. Measurements at a dose rate of 1 Gy s -1 resulted in a standard deviation of 0.28%. A repetition of the measurement is warranted because of some unnecessary corrections and uncertainties in the experiment described here. An improved version of the PGC is under design, in which the temperature-controlled body is smaller than in the old PGC will allow a better control of the instrument. The equivalence of graphite and water was evaluated using Monte Carlo simulations and results in graphite to water fluence corrections of the order of 1% or smaller. Gap and volume averaging corrections are small for a modulated beam, though the local fluctuations in the SOBP introduces significant scatter of a few tenths of a percent on the ratio of dose at a point and dose averaged over the core. A careful analysis of the uncertainty on the product of stopping power ratio, average energy required to produce an ion pair in dry air and ionization chamber perturbation factor derived form the comparison will be performed. Acknowledgement This work is funded as part of NPL s Strategic Research Programme. The authors would also like to thank Andy, Brian, Ian and Tony of the Clatterbridge Centre of Oncology for their technical support and assistance. References [1] Goitein, M. et al, Treating Cancer With Protons, Physics Today, 55(9), (2002). [2] Sisterson, J., Particles Newsletter, 32. ( [3] Andreo, P. et al, Absorbed Dose Determination In External Beam Radiotherapy: An International Code Of Practice For Dosimetry Based On Standards Of Absorbed Dose To Water, Technical Report Series 398, IAEA, Vienna (2000). [4] Fleming, D.M. and Glass, W.A., Endothermic Processes In Tissue-Equivalent Plastic, Radiat. Res., 37, (1969). [5] McDonald, J.C. and Goodman, L.J., Measurements Of The Thermal Defect For A-150 Plastic, Phys. Med. Biol., 27, (1982). [6] Schulz, R.J. et al, The Thermal Defect Of A-150 Plastic And Graphite For Low-Energy Protons, Phys. Med. Biol., 35, (1990). [7] Brede, H.J. et al, Measurement Of The Heat Defect In Water And A-150 Plastic For High- Energy Protons, Deuterons, And α Particles, Radiat. Prot. Dosim., 70, (1997). [8] Seuntjens, J. et al, Water Calorimetry For Clinical Proton Beams, Proceedings of the NPL Calorimetry Workshop, NPL, Teddington (1994). 11

12 [9] Palmans, H. et al, Water Calorimetry And Ionization Chamber Dosimetry In An 85-Mev Clinical Proton Beam, Med. Phys., 23, (1996). [10] Schulz, R.J. et al, Water Calorimeter Dosimetry For 160 Mev Protons, Phys. Med. Biol., 37, (1992). [11] Siebers, J.V. et al, Deduction Of The Air W Value In A Therapeutic Proton Beam, Phys. Med. Biol., 40, (1995). [12] Delacroix, S. et al, Proton Dosimetry Comparison Involving Ionometry And Calorimetry, Int. J. Radiat. Oncol. Biol. Phys., 37, (1997). [13] Jones, A.Z. et al, Comparison Of Indiana University Cyclotron Facility Faraday Cup Proton Dosimetry With Radiochromic Films, A Calorimeter, And A Calibrated Ion Chamber, IEEE T Nucl Sci, 46, (1999). [14] Brede, H.J. et al, An Absorbed Dose To Water Calorimeter For Collimated Radiation Fields, Nucl. Instrum. Meth. A, 455, (2000). [15] ICRU, Stopping Powers And Ranges For Protons And Alpha Particles, International Commission on Radiation Units and Measurements Report 49, ICRU, Bethesda (1993). [16] ICRU, Nuclear Data For Neutron And Proton Radiotherapy And For Radiation Protection Dose, International Commission on Radiation Units and Measurements Report 63, ICRU, Bethesda (2000). [17] Berger, M.J., Proton Monte Carlo Transport Program Ptran, National Institute for Standards and Technology Report NISTIR 5113, NIST, Gaithersburg (1993). [18] Palmans, H. and Verhaegen, F., Calculated Depth Dose Distributions For Proton Beams In Some Low-Z Materials, Phys. Med. Biol., 42, (1997). [19] Palmans, H. and Verhaegen, F., Monte Carlo Study Of Fluence Perturbation Effects On Cavity Dose Response In Clinical Proton Beams, Phys. Med. Biol., 43, (1998). [20] Palmans, H. et al, Fluence Correction Factors In Plastic Phantoms For Clinical Proton Beams, Phys. Med. Biol., 47, (2002). [21] Geant4, developed at CERN, is available free at [22] Bonnett, D.E. et al, The 62 Mev Proton Beam For The Treatment Of Ocular Melanoma At Clatterbridge, Br. J. Radiol. 66, (1993). [23] McEwen, M.R. and Duane, S., A Portable Calorimeter For Measuring Absorbed Dose In The Radiotherapy Clinic, Phys. Med. Biol., 45, (2000). [24] Verhaegen, F. et al, A Comparison Of Hadron Monte Carlo Transport Codes (Ptran, Mcnpx, Geant) For Clinical Protons, CD-ROM Proceedings of the World Congress on Medical Physics and Biomedical Engineering, Sydney (2003). 12

13 [25] Duane, S., Thermal Modelling Of Graphite Calorimeters, These proceedings, paper 23 (2003). [26] Williams, A.J. et al, Measurement of the specific heat capacity of the electron beam graphite calorimeter, NPL Report RSA(EXT)40, National Physical Laboratory, Teddington, (1993). Discussion Akifumi Fukumura How big is the field size of the proton beam? Hugo Palmans This proton beam? Three cm diameter. Akifumi Fukumura How about the uniformity of dose in the beam? Hugo Palmans It s within one percent as I showed on the measured Bragg curve. Only at the end of the Bragg curve you have that bump which is of the order of a few percent. Malcolm McEwen What s the radial non-uniformity like? Hugo Palmans The radial uniformity is a bit worse since there s a dip in the middle. Russell [Thomas] will actually discuss this tomorrow, because you have to account for it when you compare ion chamber measurements with calorimeter measurements. It is about two percent or so and it is due to the cross wires; the attenuation of the beam due to the cross wires. Malcolm McEwen This question perhaps (relates) to some of what Simon was doing. It looks like you were doing that test where you blocked out (the) centre of the beam. I know getting access to the cyclotron s not easy, but that might be a nice way of testing some of your thermal modelling. Hugo Palmans We actually did some more experiments that I can discuss. We can produce very thin beams with a small collimator and just irradiate the surroundings at various distances from the core, and so you get information on the time constants of the heat distribution in the surrounds and also on the time constants between the surrounds and the core. Malcolm McEwen And you could use that for water calorimetry as well I guess, if it s heating particular bits of the water volume in the calorimeter. Hugo Palmans I think the smallest diameter we could achieve was 2mm. 13