S. Agosteo 1,A. Porta 1, L. Ulrici 2

Transcription

1 Monte Carlo Simulations for the Design of a Hadrontherapy Centre S. Agosteo 1,A. Porta 1, L. Ulrici 2 1 Dipartimento di Ingegneria Nucleare, Politecnico di Milano, via Ponzio 34/3, Milano, Italy. 2 CERN, Geneva 23, Switzerland. 1

2 INTRODUCTION: HADRONTHERAPY Hadrontherapy exploits the physical selectivity of charged hadrons for conforming the dose to the target volume: protons are used mainly for their ballistic precision; in addition light ions can provide superior radiobiological properties (RBE, OER). 2

3 QUADOS INTRODUCTION: IMRT VS PROTONS Between the eyes Abdomen Brain 3

4 MONTE CARLO SIMULATIONS The MC simulations discussed here refer to: the shielding design (including the maze); the estimate of the radioactivity induced in the materials interacting with the primary beam; the possible activation of the groundwater. MC simulations were also performed for calculating: the unwanted dose delivered to the patient by secondary radiation; neutron and proton fluence for the estimate of the activation of the air. We will refer to the National Centre of Hadrontherapy (CNA) as a practical application. 4

5 THE NATIONAL CENTRE OF HADRONTHERAPY The construction of the CNA was financed by the Italian government in The CNA will be built in Pavia and is based on a synchrotron capable of accelerating protons and carbon ions up to 250 MeV and 400 MeV/u, respectively. Level 1: Clinic and diagnostic area Surface building: Offices and patient reception Level 2: accelerator bunker 5

6 THE NATIONAL CENTRE OF HADRONTHERAPY: ACCELERATOR BUNKER (LEVEL 2) Synchrotron hall AREA TECNICA χ 3 9 ϖ ο 6 Power supply system 13 Treatment rooms ν 17' 2 ALIMENTAZIONI ι 7 Mechanical workshop Store Dosimetry room SALA 3 σ P7=220 DEPOSITI 19 ξ P11=130 τ CTRL P4=200 AMBUL. 15 ψ P9=270 ρ 14 DOSIMETRIA FARMACIA µ 17 P2'=200 ϕ SALA κ δ P8=150 SALA CONTR. 16 SPOGL. P3=200 λ γ P10=100 ω D θ E CAP P2=150 SALA 1 β SPOGL. CTRL 21 P6=250 π CAP SPOGL. 1 P5=300 SALA CONTR. ε SPOGL. SPOGL. OCCHIO C SALA DI CONTROLLO PRINCIPALE INFORM. RECEPTION A SPOGL. OCCHIO AREA DI ATTESA 8 SORGENTI OFFICINE P1=150 α WC B RAFFREDDAMENTO SCAMBIATORI WC Cooling system Main control room Control room (treat. Room no.1) Patient positioning Dressing room Waiting room 6

7 THE NATIONAL CENTRE OF HADRONTHERAPY: TREATMENT ROOMS The treatment rooms are equipped with fixed beams capable of delivering both protons and ions. Room no. 1 (height 4.2 m): horizontal beam (deepseated tumours); Room no. 2 (height 8 m): horizontal and vertical beams for treating deepseated tumours; Room no. 3 (height 4.2 m): horizontal beam for treating eye melanomas and for experimental radiobiology. All rooms will be served by active beam delivery systems. 7

8 SHIELDING DESIGN: GENERAL ASPECTS The areas accessible to the personnel during the accelerator operation must be shielded mainly against the secondary radiation generated in the interactions of the primary beam with the structural materials of the machine and of the beam transport lines. The barriers of the treatment rooms should be estimated also considering the patient as a secondary radiation source, since: the primary beam is completely absorbed in the patient. Neutrons are the main secondary radiation to be considered for intermediate energy accelerators devoted to medical applications. 8

9 SHIELDING DESIGN FEATURES The shielding design of the CNA was performed for both: 250 MeV protons; 400 MeV/u carbon ions. Although the average beam current delivered to the patient is higher for protons: 1.0 na (250 MeV protons); 0.25 na (400 MeV/u carbon ions). the yield and energy distribution of secondary neutrons from C ions rule the design of the majority of the shields. 9

10 MC CODES FOR SHIELDING DESIGN The generalised Monte Carlo codes applicable for radiation protection calculations, such as FLUKA, MCNPX and MARS do not generally treat secondary particle production from ions with mass larger than one atomic mass unit. Development work is under way to implement ion transport in both FLUKA and MARS, but the new versions of the codes have not yet been released; In FLUKA ion transport above a few GeV is well advanced and a model to transport ions down to energy of about 50 MeV per nucleon is presently under implementation. Therefore, the simulations for shielding the secondary neutrons from C ion beams were performed by using experimental doubledifferential distributions. 10

11 SHIELDING DESIGN: SOURCES OF SECONDARY NEUTRONS 250 MeV protons on iron Neutrons per primary ion (sr 1 MeV 1 ) MeV/u C ions on Cu Neutron yield (neutrons per impinging particle) carbon ions on Cu 0 90 (forward 2π) carbon ions on C 0 90 (forward 2π) protons on Fe (4π) protons on tissue (4π) Projectile energy (MeV) Neutrons per primary ion (sr 1 MeV 1 ) MeV/u C ions on C x10 4 1x Neutron energy (MeV) 11

12 MC SIMULATIONS FOR THE ATTENUATION CURVES The double differential TTYs of neutrons generated by 400 MeV/u C ions on Cu and C targets at several angles between 090 (Kurosawa et al. Nucl. Sci. Eng. 132 (1999) 3057) were used as sources for R=90 m 23 fictitious shells of concrete subdivided into: Polar sectors angular distribution MC simulations with the FLUKA code: The fluence of outward directed particles was scored in cosineweighted boundary xings; Neutrons, photons, secondary protons and pions were scored; The H*(10) was estimated with the conversion factors by Ferrari and Pelliccioni; Geometry splitting and Russian Roulette were employed; R=90 m to minimize curvature effects and the contribution of scattered neutrons 1/(πR 2 ) 12

13 SOURCE TERMS AND ATTENUATION LENGTHS: CLASSICAL FITTING FORMULA Usually the attenuation curves of 400 MeV/u carbon ions on carbon and copper are fitted with the classical twoparameter formula for angles up to 50º (40 for 400 MeV/u C ions on lead): H0(E H(E p, θ,d/ λϑ) = 2 r d α r θ p, θ) exp λ θ ϑ d g( α) H = H*(10) beyond the shield; E p = primary particle energy; θ = angle between the dose scoring direction and beam axis; d = shield thickness; r = distance between the radiation source and scoring position; α = angle between the dose scoring direction and the normal to the shield surface. g(α)=1 for the spherical geometry used in the simulations. otherwise g(α)=cosα 13

14 SOURCE TERMS AND ATTENUATION LENGTHS: SPECTRUM EQUILIBRIUM Total H*(10) (Sv per carbon ion) 1x x x x deg. H=H0/r 2 *exp(d/lambda) Chi^2 = R^2 = H0=(8.7898± )X10 13 Sv m 2 per ion lambda= ± g cm Concrete depth (cm) 400 MeV/u C ions on Cu (0 10 ) Buildup at low depths The equilibrium of the neutron spectrum is achieved above 60 cm Φ(E)*E (cm 2 per carbon ion) Φ(E)*E (cm 2 per carbon ion) 7.0x MeV/u carbon ions on Cu 010 deg. 6.0x x x x x x x x x x x x x10 9 concrete depth 10 cm 20 cm 30 cm 40 cm 60 cm concrete depth 60 cm 80 cm 100 cm 120 cm 140 cm 160 cm 180 cm 200 cm Neutron energy (GeV) 400 MeV/u carbon ions on Cu 010 deg Neutron energy (GeV) Φ(E)*E (cm 2 per carbon ion) Φ(E)*E (cm 2 per carbon ion) Neutron energy (GeV) 1x10 7 1x10 8 1x10 9 1x cm 80 cm 100 cm 120 cm 140 cm 160 cm 180 cm 200 cm concrete depth 10 cm 20 cm 30 cm 40 cm 60 cm 400 MeV/u carbon ions on Cu 010 deg. 400 MeV/u carbon ions on Cu 010 deg Neutron energy (GeV) 14

15 SOURCE TERMS AND ATTENUATION LENGTHS: SPECTRUM EQUILIBRIUM Total H*(10) (Sv per carbon ion) x x x x x MeV/u C ions on Cu 8090 deg. H=H0/r 2 *exp(d/lambda) H0=(1.351± )X10 15 Sv m 2 per ion lambda= ± g cm Concrete depth (cm) Φ(E)*E (cm 2 per carbon ion) 1x10 9 1x x x x x MeV/u carbon ions on Cu 8090 deg. 20 cm 40 cm 60 cm 80 cm 100 cm 120 cm 140 cm 160 cm 180 cm 200 cm x10 5 1x Neutron energy (GeV) 400 MeV/u C ions on Cu (80 90 ) No buildup is observed at larger angles and small depths (up to about 60 cm), where the curves decrease with a slope steeper than at equilibrium. 15

16 NEUTRON MEAN ENERGY WITH CONCRETE DEPTH Depth (cm) Mean Energy (MeV) 400 MeV/u C ions on Cu MeV/u C ions on Cu At large angles, the lower energy components of the spectrum are attenuated mostly up to about 100 cm concrete depth with a short attenuation length, giving rise to a harder and more penetrating spectral distribution (even if less intense), which is characterised by a larger attenuation length. The attenuation can be described by doubleexponential curves. 16

17 DOUBLEEXPONENTIAL FITTING FUNCTION A doubleexponential function was used for fitting the attenuation curves of 400 MeV/u carbon ions on carbon and copper for angles above 50º : H(E p, θ,d/ λ ϑ ) = H (E 1 r 2 p, θ) exp λ 1, ϑ d g( α) + H 2 (E r 2 p, θ) exp λ 2, ϑ d g( α) The second term of this expression describes the attenuation above cm and obviously cannot be applied at lower depths, because it would lead to an underestimate of the ambient dose equivalent. In practice, this expression includes the singleexponential functions by setting H 0 =H 2, λ θ = λ 2, θ and setting the first term to zero (i.e., H 1 = λ 1, θ =0). 17

18 H 1,2 AND λ 1,2 FOR 400 MeV/u C IONS ON Cu Angular bin H 1 (Sv m 2 per ion) λ 1 (g cm 2 ) H 2 (Sv m 2 per ion) λ 2 (g cm 2 ) 010 (8.79±0.12)x ± (2.13±0.01)x ± (8.75±0.06)x ± (3.58±0.01)x ± (1.93±0.02)x ± (1.11±0.13)x ±2.28 (8.10±0.09)x ± (7.83±0.56)x ±2.63 (2.91±0.10)x ± (6.78±0.51)x ±2.05 (1.88±0.06)x ± (7.67±0.29)x ±1.42 (1.30±0.04)x ±

19 SOURCE TERMS AND ATTENUATION LENGTHS: FICTITIOUS SHELL APPROXIMATION Fluence scoring in each boundary xing inside the concrete shell accounted only for outward directed particles; this minimizes the effect of reflection from the outer shells (especially for neutrons). Anyway reflection is not eliminated completely, in this way, because, as a second order effect neutrons can be backscattered more than once. n n n Prompt γ 19

20 SOURCE TERMS AND ATTENUATION LENGTHS: FICTITIOUS SHELL APPROXIMATION The effect of the fictitious shell approximation was investigated with separate simulations considering shells with different thickness for C ions on Cu. Angular bin Fictitious shell approx. Shells of different thickness H 2 (Sv m 2 per ion) λ 2 (g cm 2 ) H 2 (Sv m 2 per ion) λ 2 (g cm 2 ) 010 (8.79±0.12)x ±0.43 (8.15±0.22)x ± (2.13±0.01)x ±0.14 (2.03±0.03)x ± (8.75±0.06)x ±0.19 (8.34±0.02)x ± (3.58±0.01)x ±0.15 (3.82±0.01)x ± (1.93±0.02)x ±0.19 (1.71±0.01)x ± (8.23±0.07)x ±0.17 (7.38±0.03)x ± (3.39±0.06)x ±0.29 (3.23±0.03)x ± (2.22±0.04)x ±0.22 (2.17±0.02)x ± (1.35±0.03)x ±0.21 (1.43±0.01)x ±0.13 The source terms resulted to be slightly lower, as expected. The difference of the attenuation lengths is lower. The data obtained with the fictitious shell approximation are sufficiently representative of the situation referring to the correct thickness, if the nonstatistical uncertainties are taken into account. 20

21 SOURCE TERMS AND ATTENUATION LENGTHS: SECONDARY PARTICLES The ratio of the H*(10) due to each secondary particle to the total shows that: secondary protons are a non negligible fraction of the dose MeV/u C ions on copper 010 degrees 10 0 H*(10) particle /H*(10) total x10 4 1x neutrons photons protons positive pions negative pions Concrete depth (cm) 21

22 SOURCE TERMS AND ATTENUATION LENGTHS: SECONDARY PARTICLES Φ(E)*E (cm 2 per carbon ion) 1.8x MeV/ucarbon ions on Cu 010 deg. 1.6x10 8 depth in concrete: 100 cm 1.4x x x x x x x x10 5 1x Neutron energy (GeV) Φ(E)*E (cm 2 per carbon ion) 5.0x MeV/ucarbon ions on Cu 010 deg. 4.0x10 8 depth in concrete: 100 cm 3.0x x x Photon energy (GeV) Φ(E)*E (cm 2 per carbon ion) 1.2x MeV/ucarbon ions on Cu 010 deg. 1.0x x x x x10 10 depth in concrete: 100 cm Proton energy (GeV) Φ(E)*E (cm 2 per carbon ion) 5.5x x MeV/ucarbon ions on Cu 010 deg. 4.5x10 12 depth in concrete: 100 cm 4.0x x x x x x x x Positive pion energy energy (GeV) Φ(E)*E (cm 2 per carbon ion) x MeV/ucarbon ions on Cu 010 deg. depth in concrete: 100 cm 2.0x x x x Negative pion energy (GeV) Spectral fluence of secondary particles at 1 m depth in concrete. Photons are mainly from neutron capture on H; Protons are mainly from INC. 22

23 SHIELDING DESIGN OF THE CNA The shielding thickness d required for attenuating the H*(10) below the limiting value H M is (singleexponential function): d H0(Ep, θ) S H0(Ep, θ) I floss tloss U T = ln = λ θ α 2 ln 2 ( )g( ) H& M r H& M r d α r θ S = I f loss t loss T U; I = beam particles per unit time; f loss = beam loss factor; t loss = duty factor; T = occupancy factor; U= use factor. g(α)=cosα 23

24 SHIELDING DESIGN OF THE CNA AN EXAMPLE: switching magnet d H λ( θ)g( α)ln (E, θ) S H (E = λ θ α 2 ( )g( )ln r, θ) I f H& 0 p 0 p loss = 2 H& M M r d θ r WD t loss U T 10 <θ < 20 α = 0 H o = Sv m 2 per ion; ρ = 2.31 g cm 3 ; λ = g cm 2 ; f loss = 0.005; t loss = 4 h d 1 ; T = 1; U= 1; r = 8.89 m; I = part/spill = / 1 (s) x 3600 (s h 1 ) = part h 1 ; WD = 220 d y 1 ; H M = 2 msv y 1. = 127 cm 24

25 ACCESS MAZE TO THE TREATMENT ROOM The design is ruled by secondary neutrons produced in the beam delivery system and in the patient. The lengths of the access maze of the CNA were estimated with the following expression (Agosteo et al., NIM A 382 (1996) ), resulting from the simulations of mazes of different dimensions: H k+ 1 = H Cr k α k p 1 (r k ;w, l) p (r ;w, l) = 1 k 1 2 l 2 l r 2 k tan w rk l r + 1 k w 2 w r 2 k tan w l 2 r r k 2 k + 1 p 1 (r k, w,l) is the 2 nd coefficient of the Legendre expansion for the solution of the Hubbel integral for a rectangular source. it is related to a diffused rectangular source (the beginning of each maze leg in this case) and a surfacetype detector parallel to the source plane. 25

26 ACCESS MAZE TO THE TREATMENT ROOM H 3 H 2 r 3 H 4 r 2 H 1 r 1 H k = H*(10) at the beginning of the kth leg, k=1,2,3; r k = length of the kth leg (m); w = width of the maze section (m); l = height of the maze section (m); α<1, C = parameters obtained by fitting the results of simulations of mazes of different dimensions. 26

27 ACCESS MAZE TO THE TREATMENT ROOM: MC SIMULATIONS The C and α parameters were determined for an isocentric gantry delivering 250 MeV protons pointing downward and horizontally towards and opposite the maze and rotating in a plane parallel to the maze mouth: a passive beam delivery system constituted by a lead scatterer, a copper collimator and a softtissue phantom was considered. The highest ambient dose equivalent was found for the beam pointing opposite to the maze. 27

28 ACCESS MAZE TO THE TREATMENT ROOM FITTING PARAMETERS First Leg Second Leg Third Leg Gantry direction α C α C α C Opposite to the maze 1.02± ± ± ± ± ±0.004 Towards the maze 1.23± ± ± ± ± ±0.002 Downward 1.38± ± ± ± ± ±

29 ACCESS MAZE TO THE TREATMENT ROOM ASSUMPTIONS FOR ION BEAMS Since the calculation of a new set of parameters for 400 MeV/u C ions and other beam directions is very time consuming, the following assumptions were made: the H*(10) at the maze mouth can be roughly estimated by scaling the source terms H 0 (for C ions on C) with the distance from the source of beam loss (the patient in this case); the C and α relating to the beam pointing opposite to the maze mouth were used, since α gives the lowest attenuation in the first leg; the energy distribution of neutrons generated from 400 MeV/u C ions on C is different from that relating to 250 MeV protons. Anyway, as stated in [Dinter at al., NIM A 333 (1993) ] and confirmed in [Agosteo et al. NIM A 382 (1996) ], in the second leg of the maze the spectra of neutrons generated either by high energy protons or by an AmBe source are similar, extending the validity of the proposed formulas to all accelerators with energies high enough to produced neutrons with energies of a few MeV. 29

30 ACCESS MAZE TO THE TREATMENT ROOM AN EXAMPLE r 3 H 4 H 0 r 2 H 3 H 2 r H 1 r 1 60 <θ < 70 r = 5.3 m; H o = Sv m 2 per ion; w = 2 m; l = 3 m r 1 = 2.5 m; r 2 = 6 m; r 3 = 1.3 m; f loss = 1; t loss = 2 h d 1 ; I = part/spill = / 1 (s) x 3600 (s h 1 ) = part h 1 ; WD = 220 d y 1 ; H 1 = H 0 /r 2 I t loss f loss WD = 0.13 Sv y 1 ; H 2 = 23.7 msv y 1 ; H 3 = 0.37 msv y 1 ; H 4 = 16.4 µsv y 1. 30

31 ESTIMATE OF THE INDUCED ACTIVITY : METHODS The calculation of the induced radioactivity in water can be performed with the following methods: Tracklength method: calculate the tracklength fluence of the producing particle in a specified region and fold it with the inelastic crosssections, integrated over the particle energy; Residual nuclei method: The residual nuclei scoring in FLUKA can directly give the induced radioactivity in a material. This scoring card is based on the INC model. Residual nuclei are scored when fully deexcited to their ground or isomeric state. Radioactive decay is not treated directly by FLUKA, but can be performed with an offline code (USRSUW3) provided with the code package; 31

32 ESTIMATE OF THE INDUCED ACTIVITY : METHODS * star density method (highenergy): stars" are defined as inelastic interactions by hadrons of energy larger than 50 MeV; The hypothesis of a probable simple proportionality between star density and induced radioactivity is based on the observed constant asymptotic value of the hadron inelastic cross section and on an assumed equilibrium between the fluence of starproducing highenergy hadrons and that of other particles contributing to activation (neutrons below 50 MeV). The supposed equilibrium exists only outside thick shielding, but experience has shown that the contribution of low energy particles is generally small compared to that of starproducing hadrons; the proportionality factors (omega factors) were established experimentally by measuring the gamma dose rate at the surface of small blocks of material directly irradiated by a proton beam. 32

33 ESTIMATE OF THE ACTIVITY INDUCED IN THE GROUNDWATER: WATER COMPOSITION Elements Compounds Mass fraction Elements Compounds Mass fraction N F Na Mg Al P S Ammoniac, nitrites, nitrates, cyanides Fluorides Pesticides, detergents Sulfates, detergents 2x x x x x x10 4 Mn Fe Ni Cu Zn Cd Sn Hg Pb 5x x x10 9 2x10 9 1x10 8 5x x x x10 9 Cl Chlorides, HOCl, pesticides, etc. 1.5x10 4 K 1x10 6 Ca 8x

34 ESTIMATE OF THE ACTIVITY INDUCED IN THE GROUNDWATER Three main points were identified: the beam directed into the room 3 is pointing towards the external wall. It has been supposed that a consistent reserve of groundwater is positioned just after the 50 cm thick concrete external wall; the extraction septa where the probability of beam losses is higher than in the rest of the accelerator; the beam dumps installed into the synchrotron ring. Simulations were performed only for 250 MeV protons. Geometrysplitting and RussianRoulette were used as variance reduction techniques. 34

35 ESTIMATE OF THE ACTIVITY INDUCED IN THE GROUNDWATER: ASSUMPTIONS The following assumptions were made: The groundwater is supposed to be stagnant and positioned just outside the external wall; A cylindrical approximation is used to increase the statistics of the problem and reduce the simulation time; Only the patient is considered in the treatment room (no support for the patient, no other material scattering the beam etc.); No electromagnetic interaction was considered. Concrete Primary proton beam Target Secondary particles Ring of water 35

36 ESTIMATE OF THE ACTIVITY INDUCED IN THE GROUNDWATER: IRRADIATION CYCLES The following cases were treated: CASE A (one treatment session): Irradiation: 3 minutes ON + 17 minutes OFF; Cycle: 12 h Decay: 12 h CASE B (realistic annual operation): Irradiation: 5 days ON + 2 days OFF; Cycle: 220 days Decay: 145 days CASE C (pessimistic!): Irradiation: 5 days ON + 2 days OFF; Cycle: 365 days Decay: 1day. 36

37 ESTIMATE OF THE ACTIVITY INDUCED IN THE GROUNDWATER: RESULTS FOR THE TREATMENT ROOM A (one session) B (annual operation) C (conservative) Nuclide T 1/2 Specific Activity (Bq l 1 ) Uncert. (%) Specific Activity (Bq l 1 ) Uncert. (%) Specific Activity (Bq l 1 ) Uncert. (%) 3 H y Be d C 5729 y F 1.83 h Na h P d S d Ar d Fe 2.73 y Co d m Cd y Au d Hg h

38 BEAM DUMP ACTIVATION Corrector Beam dump Quadrupole Simulations were performed only for 250 MeV protons; Activation of the beam dump (in W) was estimated with the RESNUCLE card (FLUKA); The contribution of the corrector (upstream) and quadrupole magnet (downstream) was also taken into account. 38

39 BEAM DUMP ACTIVATION: SIMULATION GEOMETRY Semiasse minore 37mm SUPERELLISSE Profilo Interno Superelliss e The ellipsoidal shape of the dump crosssection was approximated as the intersection of three ellipses whose parameters were estimated with the MATLAB code Semiasse maggiore 70mm Dump crosssection 100 SUPERELLISSE Profilo Interno Semiasse minore 37mm Semias se maggiore 70mm Simulation geometry 39

40 BEAM DUMP ACTIVATION Nuclide (Activity>10 8 Bq) T 1/2 Activity [x10 8 Bq] Uncert. (%) Nuclide (Activity>10 8 Bq) T 1/2 Activity [x10 8 Bq] Uncert. (%) 185 W 75 d Ta 665 d W d Ta 2.45 h W 38 m Ta 56.6 h W 22 d Ta 8 h W 2.25 h Ta 10.5 h W 2.5 h Ta 1 h W 35.2 m Hf 70 d W 31 m Hf 23.6 h All nuclides: saturation activity; 173 Lu 1.37 y Proton intensity= 8.95x10 9 s 1 beam off 40

41 BEAM DUMP ACTIVATION The spectrum of the most probable gamma rays was considered in a MICROSHIELD calculation for estimating the dose equivalent; The source volume for MICROSHIELD, i.e. the part of beam dump which may contribute to activation, was estimated with the SRIM code; The dose equivalent rate without any shield was estimated to be about 150 µsv h 1 m from the dump immediately after the beam is switched off. The activity was considered at saturation for all nuclides. 41

42 BEAM DUMP SHIELDING Iron shield thickness (cm) Dose equivalent rate (µsv h 1 1m (@beam off) The activation of the iron shield (8 cm) contributes to an additional dose equivalent rate of 3.3 µsv h 1 m; The activation of the corrector (upstream) and quadrupole magnet (downstream) contributes to additional dose rates of 0.2 and 2.85 µsv h 1, respectively ; Therefore, the total dose equivalent rate with an iron shield 8 cm thick is 7.35 µsv h 1 m from the dump immediately after the beam is switched off. 42

43 CONCLUSIONS MC simulations are fundamental for the design of a hadrontherapy centre; Data from the literature are fairly scarce for hadrons of intermediate energies, especially for material activation; A conservative approach is mandatory when experimental data are not available; Parametric formulae are helpful, but the real geometry should be simulated when the design is frozen. 43