ic

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Article history:Received 14 November 2009Received in revised form4 June 2010Accepted 22 June 2010

developing microdosimetric detectors are that they i) have tobe used in unknown and highly intense elds, ii) have to be cali-brated to generally accepted radiation quantities, iii) have to besafe for use in clinical applications. The miniaturized tissue-equivalent proportional counter (mini TEPC), developed at

level. On the other hand, the development of a particle-tracksimulation code requires the knowledge of low-energy electron-scattering cross sections (down to a few electron volts), which isavailable only for a limited number of materials. Moreover, an ad-hoc particle-track simulation code can hardly be used invery complex geometries, due to the huge amount of collisionswhich highly increase computing time. Therefore, it is worthwhileto study the applicability of multi-purposeMC-codes for simulatingradiation transport at intermediatedistances, namelyatmicrometer

* Corresponding author.

Contents lists availab

Radiation Me

ls

Radiation Measurements 45 (2010) 1330e1333E-mail address: colautti@lnl.infn.it (P. Colautti).1. Introduction

One of the great challenges of current applied radiation physicsis the dosimetry of ionizing radiation in cases where the pattern ofionization in tissue may be extremely inhomogeneous (for examplein radionuclide therapy or hadrontherapy). In such cases, macro-scopic quantities, like absorbed dose, are not sufciently accurate todetermine the radiation quality of the eld (ICRU, 1983;Grosswendt, 2007). Therefore, microdosimetric quantities have tobe introduced, to properly assess radiation quality in radiationtherapy (Wambersie et al., 2007). The major requirements for

LNLeINFN (Legnaro, Italy) in the last few years (DeNardo et al.,2004; Moro et al., 2006), satises these requirements. Therefore,the study of its radiation detection efciency by means of MonteCarlo (MC) simulations plays an important role.

General-purpose MC codes have proved to be very useful tocalculate the energy deposition due to ionization in macroscopictargets, even in various complex radiation elds. However, thetheoretical models implemented in these codes for simulatingparticle transport, based on multiple-scattering theory, arevalid only for electron energies above a few keV. This restrictstheir applicability for simulating radiation transport at a nanometricKeywords:TEPCTissue equivalent proportional counterFLUKA1350-4487/$ e see front matter 2010 Published bydoi:10.1016/j.radmeas.2010.06.055In the past few years, miniaturized tissue-equivalent gas detectors (mini TEPCs) have been developed forapplication of microdosimetry in radiotherapy. These mini-TEPCs are characterised by millimetricdimensions. They are equipped neither with an internal calibration source nor with electric eld tubes,which would properly dene the sensitive volume hence the simulated site size. In spite of these lacks,mini TEPCs working in gas ow conditions have proven to be precise and reliable detectors. However, forfuture therapeutic plans including microdosimetric data, consistency between experimental and calcu-lated data is important. Existing general-purpose Monte Carlo codes have proven to be very useful tocalculate the energy deposition due to ionization in macroscopic targets, even in various complexradiation elds. However, theoretical models implemented in these codes for simulating electrontransport and straggling are valid only for energies above a few keV. This restricts their applicability forsimulating radiation transport at a micrometric level, where low-energy electrons play a dominant role.In this work, we calculate frequency distributions of deposited energy in a mini TEPC (with sizesequivalent to 1 and 2 mm) due to photons using the Monte Carlo code FLUKA. Comparisons betweensimulated and experimental data show a rather good agreement. Differences due to different FLUKAsettings are discussed.

2010 Published by Elsevier Ltd.a r t i c l e i n f o a b s t r a c tMonte Carlo simulation of mini TEPC mInuence of low energy electrons

S. Rollet a,*, P. Colautti b, B. Grosswendt c, D. Moro b

aAIT-Austrian Institute of Technology, Donau-City-Strae 1, A-1220 Vienna, Austriab INFN Laboratori Nazionali di Legnaro, I-35020 Legnaro, Padova, Italyc Physikalisch-Technische Bundesanstalt, Bundesallee 100, D-38116 Braunschweig, GermdUniversity Medical Center Hamburg-Eppendorf, 20246 Hamburg, Germanye Physics Department of Padova University, Padova, Italy

journal homepage: www.eElsevier Ltd.rodosimetric spectra:

. Gargioni d, V. Conte b, L. DeNardo e

le at ScienceDirect

asurements

evier .com/locate/radmeas

level. In this work, we compare the microdosimetric spectraobtained with numerical simulations using the Monte Carlo codeFLUKA, with those measured with a mini TEPC in two differentphoton elds. Different types of particle-transport algorithms andenergy thresholds havebeen adopted in the code in order to study indetail how these can affect the results.

2. Materials and methods

A TEPC is a specialized proportional counter used to determinethe radiation quality of unknown radiation elds and basicallyconsists of a spherical or cylindrical chamber, with wall materialsand lling gas composition matching the elemental composition of

S. Rollet et al. / Radiation Measurebiological tissue. The use of a TEPC in microdosimetry is based onthe assumption that the spatial distribution of ionization eventsin the gas-lled cavity is the same as in geometrically similarregions (or sites) of equivalent effective dimensions, i.e. equalproduct of diameter and density (Rossi and Zaider, 1996; Dietze andPihet, 1995).

The mini-TEPC designed at LNLeINFN (DeNardo et al., 2004;Moro et al., 2006) has been characterized by means of MC simu-lations using a simplied detector geometry, consisting of a cylin-drical cavity, 0.9 mm in diameter, lled with a low-pressurepropane-based tissue equivalent (TE) gas, as schematically shownin Fig. 1. The 0.7 mm thick cavity walls are made of A-150 plasticand Rexolite (both tissue-equivalent materials), and are surroundedby a 0.2 mm titanium layer. The gas density is varied in order tosimulate sites that, at a density of 1 g/cm3, would have a diametervarying from 1 mm to 2 mm. The parallel-plane photon beamconsidered in the simulation to calculate the detector response, hasthe same area as the detector side and is directed as shown in Fig. 1.

Due to the small dimensions of the detector and to the very lowgas density (ranging approximately from 1 103 g/cm3 to2 103 g/cm3), the number of photon-interaction events takingplace in the gas cavity is negligible. Therefore, the energy depositedinside the gas cavity is mainly due to electrons created in thedetector wall. When the gas density rgas corresponds to a sitediameter D 2 mm at requiv 1 g/cm3 (i.e. D rgas 2 104 g/cm2) only electrons having an energy less than about 8 keVare, on average, fully absorbed. For D 1 mm and D 0.5 mm, thathappens to electrons having an energy of less than 5 keV and 3 keVrespectively (Iskev et al., 1983). Therefore, the transport of low-energy (less than 10 keV) electrons inside the gas cavity cannot beneglected in the MC simulation.

3. Experimental measurements

The mini TEPC used for the measurements has a sensitivevolume of 0.9 mm of diameter and height in order to stand highFig. 1. Schematic view of the mini TEPC geometry and materials implemented in theMonte Carlo simulation.intensity radiation elds without pile-up spectral distortions. Thecounter is encapsulated in a 2.7 mm of external diameter 0.2 mmthick titanium shield. This size was designed for inserting thecounter in 2.7 mm inner diameter (the so called 8 French) cath-eters, which are used in interstitial surgery for introducing toolsinside the patient. The counter sensitive volume is dened by thecylindrical A-150 wall and by insulator disks which have a cavity inthe center (200 mmdeep and 150 mm in diameter cavity). The anodeis a 10 mm gold-plated tungsten wire. More details about the miniTEPC are given in reference (DeNardo et al., 2004).

The experiments have been carried out at the secondary stan-dard Centre of ENEA-Montecuccolino (Italy) in 60Co and 137Csphotons elds. Because of different source intensities, measure-ments were performed at 25 and 1 mGy/min respectively. There-fore, mini TEPC counting ratewas of about 4000 and 300 counts persecond. Measurements have been performed with the propane-based tissue-equivalent gas mixture owing in the counter at1 cc/min (@ STP conditions). The gas pressure was 617 mbar and1234 mbar for 1 mm and 2 mm site sizes respectively. Spectra havebeen collected and processed in the usual way, shaping the elec-tronic signal at 250 ns and using a CAMAC acquisition system. Thelineal energy calibration has been performed by using the secondderivative maxima, which appears in yd(y) spectra near the elec-tron edge (Moro et al., 2003) and by assigning them the values of12.2 keV/mm and 9.1 keV/mm for 1 mm and 2 mm sites respectively.

The lower detection threshold of these detectors was about0.15 keV/mm. To take into account the contribution under thethreshold, a linear extrapolation was performed in the frequencyf(y) spectra down to the 0.01 keV/mm value. The frequency-aver-aged yf and dose-averaged yd values have been calculated fromspectral distributions. Their overall uncertainties have beenassessed by using the error-propagation theory (Moro et al., 2003).

4. Numerical simulations

The simulation of the response of themini TEPC is donewith theFLUKA Monte Carlo code. FLUKA is a general-purpose code capableof transporting several types of particles in a wide energy range.An exhaustive description of the transport capabilities of thesecodes is beyond the purpose of this work and can be found in Fasset al. (2003) and Fass et al. (2005). Detailed descriptions of thenumerical set up with the FLUKA code to simulate the response ofa TEPC and the evaluation the relation between different quantitiesused in radiation protection in photon, neutron and also complexradiation elds are given in previous papers (Rollet et al., 2004,2006; Latocha, 2007; Rollet et al., 2007). In this paper, the FLUKAcode version 2008 is used for all the presented simulated results.The inner dimensions and the relevant thicknesses of themini TEPCare described in details by means of the FLUKA combinatorialgeometry, using various combinations of planes, cylinders andrectangular parallelepipeds. Simulation settings have been chosento ensure the most detailed treatment of electron and photontransport (DEFAULTs card: PRECISION). The energy cut-off forelectrons and photons is set at the lowest transport thresholdallowed in FLUKA, i.e. 1 keV. The scoring region is the gas chamberbut the particles are also tracked in the surrounding materials tocheck the scatterings and the energy spectra therein. Besideaverage quantities, FLUKA has the capability to score energydeposition on an event by event basis between given energy limitsdistributed over 1024 linear channels (with the DETECT card) or toscore each of them (with EVENTBIN card) used also for logarithmicbinning. Both these cards are used to score the energy depositedinside the mini-TEPC gas chamber as a function of lineal energy.

In FLUKA a single scattering option is availablewhen theMolire

ments 45 (2010) 1330e1333 1331multiple scattering algorithm becomes unreliable (at low energies

in high Z materials, when the number of scatterings is too low inthin layers or on boundaries between different materials in pres-ence of a magnetic eld). This is usually done automatically but it isalso possible to completely switch off the multiple scattering inselected materials with the option MULSOPT. In the presentsimulation, the inuence on the results of the single scatteringalgorithm and of the electron and photon transport thresholds hasbeen investigated thoroughly. The low pressure of the gas requireslarge numbers of MC calculations to achieve a reasonably statisticalaccuracy for the simulation results. The analysis of at least 10different runs with 1e5 107 source particles is used to estimatethe different moments in order to assess the statistical convergenceand to achieve an uncertainty on the total absorbed dose in the gasof 0.2e0.3%. The simulations are done using a Linux cluster, whichconsists of four nodes, each containing four Intel Core2-Quad2.4 GHz processors.

The CPU time for each calculation varies depending on theparticles transport threshold and the amount of the single scat-tering performed. Using the multiple scattering everywhere except

The absorbed dose distributions yd(y), as a function of linealenergy measured with the mini TEPC and simulated with theFLUKA code, are compared in Figs. 3 and 4 for 60Co and 137Cssources respectively. Fig. 3 shows the simulated absorbed dosedistribution for 60Co photon source for 1 mm (a) and 2 mm (b) sitediameter. The analogous spectra for a 137Cs source are presented inFig. 4 for site diameter of 1 mm (a) and 2 mm (b).

In general, comparison points out a satisfactory agreementbetween simulations and measurements. The simulated upperlimit of y, called electron edge, which is determined by themaximum energy loss by secondary electrons, agrees very wellwith measured data. The best agreement is achieved when thesingle scattering option is switched on everywhere. That increasesthe CPU time (by a factor of about three), but it makes calculatedand measured curves to almost coincide at lower energy (137Cs) asshown in Fig. 4. Some signicant differences are instead visiblewith the higher photon energy (60C). In this case, the electronenergy is higher and they have fewer collisions inside the gas(a cavity of 1 mm for Co is roughly equivalent to a 0.5 mm for Cs),hence the ionization uctuations around the average value can besignicant. The importance of the simulations treatment of theseuctuations and of the electrons below 1 keV must be investigatedwith analogue Monte Carlo codes like that one used, for instance,by Cesari et al. (2002).

Table 1 shows the frequency-averaged yf and the dose-averagedyd values. The spectral differences between calculated and

S. Rollet et al. / Radiation Measurements 45 (2010) 1330e13331332on the boundary between gas and A150 it varies from a minimumCPU time of 2 h (for 10 keV threshold), 3 h (5 keV), 4 h (3 keV), 7 h(2 keV) up to 16 h (for the lowest threshold at 1 keV).

The microdosimetric spectra to be compared with themeasurements areelaboratedasdescribed in (ICRU,1983). The linealenergy y is given by dividing the average deposited energy in eachchannel by the mean chord length of the microdosimetric volume.

5. Results and discussion

The variation of the microdosimetric spectrum with the trans-port threshold can be seen in Fig. 2. The contribution to the mainpeak around 0.3 keV/mm due to the particles crossing the gas(crossers) doesnt change but the lower energy threshold changessignicantly the spectrum in the 1e10 keV range. This is the regionmainly inuenced by the secondary particles produced in thematerials surrounding the gas and than stopped inside the gas(stoppers). The peak in the region 5e10 keV/mm is due to energyreleased in the gas by electrons having a range comparable with theTEPC mean chord length (exact stoppers). As the transportthreshold is lowered, more electrons are properly transported fromthe counter sensitive volume to the counter walls. Therefore, theyare no more exact stoppers, hence the 5-10 keV/mm event yielddecreases. This peak is further reduced when the single scatteringoption is applied everywhere (and not only at the boundary).Fig. 2. Inuence of electron transport simulation threshold on the microdosimetricspectra (Co 2 mm).Fig. 3. Absorbed dose distribution as a function of lineal energy as measured bya mini-TECP in a 60Co eld. The simulated curves with multiple scattering (grey) and

with Single Scattering (black, SS) are also shown (see text). The simulated site sizediameters are 1 mm in (a) and 2 mm in (b).

data for 1e2 mm sites. Signicant differences for events sizes of1e10 keV/mm are observed using a multiple scattering algorithmand higher transport thresholds for photons and electrons. Thesedifferences are greatly reduced when the lowest threshold is usedand the capability of FLUKA to switch-on the single scattering

S. Rollet et al. / Radiation Measurements 45 (2010) 1330e1333 1333measured data are smoothed in the mean values, which do notshow any signicant difference.

6. Conclusions

Microdosimetric photon spectra calculated by a general-purpose Monte Carlo code like FLUKA t rather well experimental

ping powers of electrons with energy between 20 eV and 10 keV. Phys. Med.Biol. 28, 535e545.

Latocha, M., 2007. The results of cosmic radiation in-ight TEPC measurementsduring the CAATER ight campaign and comparison with simulation. Radiat.

lineal energy distribution at the CERN high energy facility with a tissue-equivalent proportional counter. Radiat. Prot. Dosim. 125, 425e428.

Rossi, H.H., Zaider, M., 1996. Microdosimetry and Its Applications. Springer Berlin

Table 1137Cs and 60Co frequency-averaged and dose-averaged mean lineal energies,measured with the mini TEPC and calculated with FLUKA code. FLUKA-calculatedvalues have been obtained with the single scattering option everywhere.

Sourcetype

Simulatedsite size[mm]

Experimentalyf [keV/mm]

Calculatedyf [keV/mm]

Experimentalyd [keV/mm]

Calculatedyd [keV/mm]

137Cs 1 0.37 0.02 0.43 0.02 2.1 0.1 2.1 0.1137Cs 2 0.35 0.02 0.40 0.02 1.6 0.1 1.7 0.160Co 1 0.30 0.02 0.30 0.02 1.8 0.1 1.8 0.160Co 2 0.28 0.02 0.27 0.02 1.4 0.1 1.4 0.1

Fig. 4. Absorbed dose distribution as a function of lineal energy as measured bya mini-TECP in a 137Cs eld. The simulated curves with multiple scattering (grey) andwith Single Scattering (black, SS) are also shown (see text). The simulated site sizediameters are 1 mm in (a) and 2 mm in (b).Heidelberg.Wambersie, A., Hendry, J.H., Andreo, P., De Luca, P.M., Gahbauer, R., Menzel, H.,

Whitmore, G., 2007. The RBE issues in ion-beam therapy: conclusions of a jointIAEA/ICRU working group regarding quantities and units. Rad. Prot. Dosim. 122,463e470.Prot. Dosim 125, 412e415.Moro, D., Seravalli, E., Colautti, P., 2003. Statistical and overall uncertainties in BNCT

microdosimetric measurements, LNL-INFN Report-199.Moro, D., Colautti, P., Gualdrini, G., Masi, M., Conte, V., De Nardo, L., Tornielli, G.,

2006. Two miniaturised TEPCs in a single detector for BNCT microdosimetry.Radiat. Prot. Dosim. 122, 396e400.

Rollet, S., Beck, P., Ferrari, A., Pelliccioni, M., Autischer, M., 2004. Dosimetricconsiderations on TEPC FLUKA-simulation and measurements. Radiat. Prot.Dosim. 110, 833e838.

Rollet, S., Autischer, M., Beck, P., Latocha, M., 2007. Measurements and simulation ofeverywhere is fully implemented. In order to investigate thereasons of residual spectral differences, the treatment of electronswith energies smaller than 1 keV must be investigated withanalogue Monte Carlo codes.

Acknowledgments

Wewould like to thank Gianfranco Gualdrini, chairperson of theEURADOS Working Group 6 Computational Dosimetry andAlberto Fass for their precious suggestions. We thank as well the5th Scientic Commission of the Italian Institute of Nuclear Physics,which has supported the experimental measurements.

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Monte Carlo simulation of mini TEPC microdosimetric spectra: Influence of low energy electronsIntroductionMaterials and methodsExperimental measurementsNumerical simulationsResults and discussionConclusionsAcknowledgmentsReferences