Neutron spectral fluence and dose distribution inside a NYLON 6 phantom irradiated with pencil beam of high energy protons

Accepted Manuscript Neutron spectral fluence and dose distribution inside a NYLON 6 phantom irradiated with pencil beam of high energy protons J. Šolc, V. Vondráček, Z. Vykydal, M. Králík PII:

S1350-4487(17)30368-2

DOI:

10.1016/j.radmeas.2017.12.006

Reference:

RM 5865

To appear in:

Radiation Measurements

Received Date: 29 May 2017 Revised Date:

17 November 2017

Accepted Date: 27 December 2017

Please cite this article as: Šolc, J., Vondráček, V., Vykydal, Z., Králík, M., Neutron spectral fluence and dose distribution inside a NYLON 6 phantom irradiated with pencil beam of high energy protons, Radiation Measurements (2018), doi: 10.1016/j.radmeas.2017.12.006. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Neutron spectral fluence and dose distribution inside a NYLON 6 phantom irradiated with pencil beam of high energy protons

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J. Šolca,*, V. Vondráčekb, Z. Vykydala, M. Králíka

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Czech Metrology Institute, Okružní 31, 638 00 Brno, Czech Republic

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Proton Therapy Center Praha, Budínova 1a, 180 00 Praha 8, Czech Republic

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* E-mail: [email protected]

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Monte Carlo (MC) simulations using the MCNPX™ code supported by measurements were exploited

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for detailed characterization of secondary neutrons generated by high energy protons during pencil beam

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proton therapy. The study focused on the estimation of the distribution of secondary neutron points of

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origin, their average initial energy, and the distribution of absorbed dose and equivalent dose from

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neutrons and photons inside the NYLON 6 phantom (diameter of 25.5 cm, length of 31.0 cm) irradiated

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with a proton beam with the energies of 100, 150 and 200 MeV. Validation of the MC model and the used

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methods was done by comparison of calculated responses of the extended-range Bonner Sphere

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Spectrometer at several positions outside the phantom with the measured ones. The results show that high

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energy neutrons predominate in the direction of the proton beam and more neutrons are generated by

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higher energy protons. The MC simulations also demonstrated that the majority of high energy neutrons is

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generated at the beginning of the proton trajectory in the phantom and the neutron yield and neutron initial

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average energy decrease with increasing depth. Therefore, attention should be paid not only to the tissues

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behind the irradiated volume, but also to the preceding ones. However, the neutron spectral fluence in the

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vicinity of the treated tissue can only be determined by calculation, mainly due to the dimensions of the

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neutron spectroscopic instrumentation.

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The calculation of the spatial distribution of the radiation weighting factor for neutrons allowed us to

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estimate the distribution of the neutron equivalent dose inside the phantom. The maximal value of the

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neutron equivalent dose within the phantom reached 42, 24, and 15 pSv per one primary 100, 150, and

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200 MeV proton, respectively, and occurred on the beam axis roughly at the half of the proton range. With

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respect to the proton dose, these maximal values of the neutron equivalent dose correspond to 2.1%, 1.3%,

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and 1.4% of the proton dose in the Bragg peak for these proton energies. Moreover, equivalent doses of

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secondary induced photons were more than 3 orders of magnitude lower that the neutron ones.

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32 Keywords

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proton therapy; dose distribution in phantom; neutron spectral fluence; neutron equivalent dose;

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extended-range Bonner Sphere Spectrometer; radiation weighting factor

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1. Introduction

During the therapy with high energy photons, an accelerator, usually a linac, is also a source of

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secondary neutrons which lead to unwanted exposure of patients. In hadron therapy, the source of

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unwanted neutrons is the accelerator (cyclotron or synchrocyclotron) and the patient tissues. Neutrons

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generated in the accelerator are relevant during passive beam delivery because the beam of protons is

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formed by scatterers and collimators. When the active (pencil) beam technique is applied, the number

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of neutrons generated in the beam delivery system is reduced significantly (Stichelbaut et al, 2014). As

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this technique is now prevailing, it is reasonable to pay attention to neutrons generated in the patient’s

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tissues and to assess the influence on them.

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High-energy protons undergo nuclear interactions in the tissue before they stop and the result of these

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interactions is a loss of proton fluence, generation of neutrons and other particles, and short‐lived

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radioactive isotopes. The probability of interactions occurring is determined by the measured cross section

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data or nuclear models. This paper concentrates on the evaluation of the consequences caused by neutrons.

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Up to now, a lot of neutron measurements have been done at hadron facilities around different

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phantoms at various irradiation conditions, e.g. (Mares et al, 2016), (Vykydal et al, 2016, 2017), (Farah et

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al, 2015), (Howell and Burgett, 2014), but practically none inside the phantom because the known neutron

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detectors have inappropriate dimensions and do not always cover the required energy range. Derivation of

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the spatial dose distribution caused by neutrons in the phantom from the measurement outside is hardly

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feasible, so it is necessary to rely on Monte Carlo (MC) calculations. This approach has limitations caused

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mainly by uncertainties of nuclear data in the energy region relevant for hadron therapy, i.e. hundreds of

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MeV. Nuclear data for energies below ~20 MeV are confirmed by lots of experiments. Above this energy

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the experimental data are sparse and very rare in the region of hundreds MeV. This paper presents a

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thorough calculation study of neutron spectral fluence and dose distributions in the NYLON 6 phantom.

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Since the same phantom was used in the work (Vykydal et al, 2016, 2017) orientated to the measurement

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of neutron spectral fluence outside the phantom, the results presented here are a complement devoted to

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the phantom interior.

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2. Materials and Methods

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2.1 Measurement of Neutron Fluence around Phantom To support the reliability of Monte Carlo simulations of neutron doses and neutron spectral fluences

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inside the phantom, the measured responses of all spheres of the extended-range Bonner Sphere

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Spectrometer (EBS) obtained during measurements of neutron spectral fluences around the phantom

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(Vykydal et al, 2016, 2017) were compared with the calculated ones. The measurements were performed

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for proton beams with the energies of 100, 150, and 200 MeV.

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The used EBS consisted of a set of polyethylene moderators with the diameters of 3, 3.5, 4, 4.5, 5, 6,

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7, 8, 10 and 12, traditionally given in inches (1 inch = 2.54 cm). To this set, three spheres with metallic

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layer inside the polyethylene were added: one with tungsten (7W) and two with lead (7Pb, 9Pb). As the

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detector of thermal neutrons inside the spheres, a proportional counter filled with 3He (LMT-0.5NH1/1KF,

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LCC Thomson CSF, France) was used. 3

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The phantom was a right circular cylinder made of NYLON 6 (polycaprolactam) with the density of

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1.14 g⋅cm-3 (McConn et al, 2011), diameter of 25.5 cm, and length of 31 cm. It was placed on the

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treatment coach so that its axis was identical with the axis of the proton beam and the iso-centre laid at the

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centre of its circular surface where the protons enter the phantom. In the further text, this wall is referred

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to as the front wall. The other circular surface is referred to as the rear wall.

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The measurements were carried out in a Fixed Beam Treatment Room (FBTR) at the Proton Therapy

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Center Prague (PTC), Czech Republic, in 6 positions under the angles of 0°, 30°, 45°, 60°, 90°, and 120°

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from the beam axis at the distance of 1 m from the iso-centre. The measured detector responses were

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obtained as the number of pulses above a specified threshold (Vykydal et al, 2016, 2017).

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2.2 Conversion of Monitor Units to the Number of Protons

Two ionization chambers, referred to as IC2/3, mounted on a nozzle monitored the current of the

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delivered protons in the so-called monitor units (MU). At the used nozzle, 1 MU corresponded to the

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collected ionization charge 1.5 nC produced by the passing-through protons. From the IBA staff at the

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PTC, we obtained the conversion coefficient between MU and the number of protons as 8.150×107,

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1.089×108, and 1.325×108 protons/MU, for 100, 150, and 200 MeV proton beams.

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An independent check of these conversion coefficients was performed by MC simulations of the

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monitor chamber response. A detailed MC model of IC2/3 was based on the information published by

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Courtois et. al (2017) and supported by confidential drawings provided by the IBA. The simulated

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quantity was the energy distribution of fluence of protons and charged ions in the sensitive volume of the

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chamber. Similar to the procedure described by Paganetti (2006), the spectral fluence of each type of

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particles calculated by MC was convoluted with the appropriate energy-dependent electronic stopping

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power function in air (NIST PSTAR, 2017) and summed up over particle energies to get the total

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ionization energy deposited in the chamber by each type of particles. Then, the deposited energy was

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multiplied by air mass and elemental charge and divided by the mean energy Wair needed to produce one

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ion pair in air to get the charge created in the chamber. The following values of Wair were used: 33.97 J/C

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for electrons (Boutillon and Perroche-Roux, 1987), 34.2 J/C for protons (Siebers et al, 1995) as well as for

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deuterons and tritons, and 34.5 J/C for He-3 (Kanai et al, 1993) and also for He-4 and heavier ions. The

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charge created by each kind of particles per one primary proton was summed and compared to the charge

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of 1.5 nC/MU measured by IC2/3. No corrections to this value were applied as this value had already been

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corrected to reference conditions, saturation, etc. The resulting number of protons per 1 MU agreed with

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the values provided by the IBA within 0.5%, which is well within the uncertainties. The above-mentioned

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conversion from MU to the number of protons is confirmed and it is used within the present paper for

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normalization of the measured data to one primary proton.

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2.3 Monte Carlo Calculations

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2.3.1 Model of the Problem Geometry

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The model of the geometry consisted of the phantom and the treatment room. In specific calculations,

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the model also included EBS spheres. The treatment room was modelled according to the available

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drawings, positioned and oriented with respect to the iso-centre. The MC model included walls, floor, and

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ceiling of real thicknesses, and also took into account an approximation of the treatment coach. Since

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information on the composition of the concrete was not available, concrete structures were described using

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the elemental composition of Portland concrete with the density of 2.3 g/cm3 taken from McConn et al.

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(2011) as already used in shielding studies in PTC Prague by Stichelbaut (2007) and later by Urban and

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Kluson (2012). Nozzle and other parts of the beam line were not modelled.

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2.3.2 Description of the Proton Beam

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Proton energies of 100, 150, and 200 MeV were chosen in accordance with the experiment (Vykydal

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et al, 2016, 2017). Monoenergetic parallel single spot proton beams were defined by a 2D Gaussian

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transversal profile with respect to the beam axis, with the full-width at half maximum of 1.68, 1.28, and

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0.96 cm for 100, 150, and 200 MeV beams, respectively. The source of protons was placed in air at the

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distance of 50 cm from the phantom front wall.

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2.3.3 The Monte Carlo Code and Data Tables Calculations were performed by means of the general-purpose Monte Carlo code MCNPX™ in

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version 2.7.E (Pelowitz et al, 2011). The following cross-section tables were used: continuous-energy

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photoatomic data library MCPLIB84 (White, 2012), electron data library el03, photonuclear reaction

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library ENDF/B-VII.0 (Chadwick et al, 2006), and neutron data library ENDF/B-VII.0 at 293.6 K

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(Chadwick et al, 2006) with the table-based physics cut-off set to mix and match (parameter “tabl” equal

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to -1 on the PHYS:N card). The transport of protons of all energies was done by the intranuclear cascade

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model BERTINI (Bertini, 1969; Prael and Liechtenstein, 1989) with the Dresner evaporation model. The

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choice of BERTINI model was based on the results of a detailed comparison of various proton cross-

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section tables, proton physics models, and their combinations available in the MCNPX™ code. The

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details of this comparison fall out of the scope of this study and will be published in a separate paper. In

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the specific simulations, additional particles were also tracked, i.e., light ions (deuterons, tritons, He-3,

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and He-4) and heavy ions. The transport of these particles was treated by ISABEL physics model (Yariv

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and Fraenkel, 1979; Prael and Liechtenstein, 1989). Vavilov model was used for ions straggling

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description by setting the parameter “istrg” to 0 on the corresponding PHYS card. Table 1 summarizes the

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list of the tracked particles in the phantom and their cut-off energy (minimum energy for their transport)

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depending on the goal of the simulation. Outside the phantom, only primary protons were transported

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before entering the phantom, and neutrons in the simulation of the EBS response.

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Table 1: Tracked particles in the phantom and their cut-off energy depending on the goal of the simulation

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(N – neutrons, P – photons, H - protons, E - electrons, D - deuterons, T - tritons, A – He-4, S – He-3, V –

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heavy ions). Neutron cut-off was always 0 MeV, except if explicitly stated otherwise. Tracked particles

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EBS spheres response

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Primary protons DD(1)

H, A, D, T, S, V

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Generating and storing of N, H, A, D, T, S, V

N: 210 MeV(2), others: 10

neutrons points of origin

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Secondary neutrons DD(1)

N, H, A, D, T, S, V

Secondary photons DD(1)

N, P, H, E, D, T, A, S, V 10 keV

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(1)

DD: Spatial dose distribution in phantom;

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(2)

The neutrons were generated, their parameters were recorded in the PTRAC file, but the neutrons were not tracked.

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2.3.4 Response of the Bonner Sphere Spectrometer

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The reason of MC simulations of the EBS spectrometer was to validate the MC model for the

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calculation of the neutron dose distribution in the phantom and, more generally, for the validation of the

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MC model setup and procedures used to generate secondary neutrons. The validation was done by direct

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comparison of the measured and the simulated number of counts in LMT-0.5NH1/1KF neutron detector

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per one primary proton. Although it requires much more computer time, the full modelling of the EBS

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response in this specific measurement geometry allows us to avoid an additional uncertainty introduced by

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unfolding of neutron spectra.

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In this simulation, only protons, neutrons, and charged light ions were tracked (see Table 1). While

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neutrons were tracked in the whole modelled geometry, protons and ions were tracked in the phantom

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only. The potential contribution of photonuclear interactions, as well as the detector response to photons

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and recoiled ions, was neglected considering that in the measurement, the latter effects were suppressed by

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setting an appropriate discrimination of detector pulses.

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Particle splitting variance reduction technique was utilized for neutrons in the EBS spheres to

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increase the probability of reaching the detector of thermal neutrons placed at the centre of the spheres.

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The calculated quantity was the number of 3He(n, p)3H reactions in the detector and it was scored with the

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F4-type tally modified by a multiplier converting the mean neutron fluence in the detector sensitive

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volume to the number of neutron capture reactions on 3He. The result stated per cm3 was multiplied by the 7

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detector sensitive volume (0.61 cm3) and normalized to the same number of protons as in the

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measurements. To balance the computational time and the statistical uncertainty of the result, the

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calculations were stopped when the uncertainty of the tally reached 1.75%.

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Dose distributions were obtained by means of the MESH tally. The phantom volume was divided

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with a cylindrical mesh into segments concentric around the phantom axis. In the direction of the cylinder

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axis, each segment was 0.25 cm thick, except for the simulation of the detailed proton depth-dose curve

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where the segment thickness was set to 0.025 cm. In the direction of the cylinder radius, the segments

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were 0.1 cm thick within 1.5 cm distance from the phantom axis and 0.25 cm thick at larger distances.

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To clearly distinguish the absorbed dose delivered by primary protons and their charged progenies

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from the absorbed dose caused by interactions of secondary neutrons and photons, several independent

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simulations were performed with different scored quantities and different sets of tracked particles.

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2.3.5.1 Dose from Primary Protons and Charged Progenies In the whole study, the proton dose consists of the contribution of protons and charged progenies

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directly created in elastic and inelastic interactions of primary protons. Light ions (protons, deuterons,

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tritons, alphas, He-3 ions) and heavy ions (all other nuclei) were tracked (see Table 1) only and their

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energy deposition was included in the total absorbed dose. Electrons were not tracked because the

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MCNPX™ does not include proton delta-rays production and therefore no electrons were generated.

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Neutrons and photons were not tracked either. The purpose was to remove the contribution of protons and

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other heavy-charged particles created by neutrons, and electrons created by photons to the proton dose.

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The absorbed dose was scored with the type 3 mesh tally with the DE/DX keyword. This definition allows

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to calculate average ionization energy losses from all the tracked charged particles per unit volume in each

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mesh segment. The parameter “recl” on the proton physics card PHYS:H was set equal to 1 to accurately

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account for ionization from recoiled protons in the total dose. Also, the parameter “efac” on the physics

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card of all the tracked heavy particles was set to 0.985 compared to the default value of 0.917 used in

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other simulations. At the expense of the increased processor time, the used value produces more points in

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the stopping power tables resulting in a smooth depth-dose curve calculated in a mesh with fine binning.

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The calculations were done for 1.3×107 primary protons resulting in the statistical uncertainty on the level

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of 0.15% in mesh segments close to the beam axis.

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The spatial distribution of the absorbed dose from secondary photons was scored with the type 1

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mesh tally for electrons with the PEDEP keyword. Such approach allows to calculate the average energy

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deposition per unit volume in each mesh segment by a selected type of particle, in this case by electrons.

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As the only mechanism to create an electron in this simulation is by photon interaction, the ionization

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energy losses caused by electron slowing-down are directly related to the absorbed dose caused by

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secondary photons. Neutrons, photons, electrons, and all ions were tracked to include all interaction

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processes which may generate a photon, see Table 1. As this study is not focused on photon dose, the

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authors did not validate simulations of the photon production and transport by the measurement, therefore

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the simulated photon data should be taken with caution and should be considered as a complementary

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information to neutron data.

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2.3.5.3 Dose from Secondary Neutrons

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Dose from secondary neutrons was determined in a two-step simulation. In the first step, a particle

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track (PTRAC) ASCII file of 1 GB size was generated that contained information about energy,

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coordinates, direction vectors, and weight of the total of 5×106 neutrons created by primary protons in the

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phantom. The cell-by-cell energy cut-off card ELPT:N for neutrons was applied in the phantom volume

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and its value was set higher than the highest proton energy. This ensured that the neutrons were created

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but were not tracked and so information about the neutrons produced by primary protons only was written

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The PTRAC file was processed with a purpose-written routine in the Matlab® software (The

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MathWorks, Inc., USA) to generate an ASCII file with a list of neutrons. In the second step, this ASCII

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file was read by the MCNPX™ and used as a neutron source in the new simulation. The spatial

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distribution of the absorbed dose from secondary neutrons was scored with the type 3 mesh tally with the

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DE/DX keyword. The neutrons written in the ASCII file were re-used 15 times as a source in one

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simulation, which resulted in the statistical uncertainty of the absorbed dose below 1% at most of mesh

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segments. The results were then normalized to one primary proton from the simulation performed in the

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first step.

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The parameter “recl” on the neutron and proton physics card PHYS:N and PHYS:H was set equal to

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1 to generate recoiled ions and include ionization from these recoiled particles in the total dose. In both

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simulation steps, all particles were tracked except for photons and electrons. Neutrons generated in the

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phantom in photonuclear interactions were neglected.

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2.3.6 Estimation of Biological Effectiveness of Secondary Neutron and Photon Dose

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An effective radiation weighting factor for neutrons in the phantom,

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estimate of the biological effectiveness of the absorbed dose from neutrons in a patient by the transition

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from the absorbed dose (in grays) to the equivalent dose (in sieverts). The

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in each mesh segment to get information about its spatial distribution in the phantom with respect to the

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position of the single spot proton beam. In each mesh segment k, the effective radiation weighting factor

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for neutrons,

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distribution of neutron fluence in the given segment k, Φ

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was determined separately

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The wR as a function of neutron kinetic energy was taken from the ICRP Publication 103 (2007). Then, the

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spatial distribution of the neutron equivalent dose was obtained by convolution of the distribution of

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secondary neutron absorbed dose described in the previous paragraph with the distribution of

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As the photon radiation weighting factor is equal to 1 (ICRP Publication 103, 2007), the photon

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equivalent dose is numerically the same as the absorbed dose caused by secondary photons determined by

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the procedure described in the paragraph 2.3.5.2.

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Proton depth-dose distributions presented in the further text were obtained from the spatial

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distribution of the absorbed dose from primary protons. As the single spot-beam simulations resulted in

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steep dose gradients, the absorbed energy in mesh segments was integrated over the whole radius of the

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phantom. Then, the proton depth-dose curves presented in the figures are either in a relative scale only, or

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in absorbed ionization energy per unit depth in the phantom, in MeV/mm.

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2.3.8 Proton Reference Dose

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Apart from the normalization to one primary proton used in this study, the quantity proton reference

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dose was exploited for an additional normalization of photon and neutron equivalent doses to get a better

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picture of the photon and neutron contribution during proton treatment, with respect to the proton dose. As

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this study deals with a single spot irradiation rather than with a realistic irradiation plan, the therapy dose

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cannot be used. Instead, the reference proton dose was defined as the dose averaged over the cylindrical

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volume with the height of 1 mm (along the beam axis) and the diameter of 5 mm with the geometrical

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centre position on the beam axis at the Bragg peak maximum. This volume consists of 20 mesh tally

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voxels.

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3. Results and Discussion

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3.1 Validation of the MC Model 11

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Fig. 1 shows an example of the comparison of the measured and the simulated responses of the EBS

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outside the phantom at 1 m from the iso-centre at 45° degree from the beam axis, for 150 MeV protons.

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Excellent agreement was achieved with an average relative difference of 2%. Detailed view of the relative

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differences between the measured and the simulated responses of all EBS spheres at all measurement

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positions and for all studied proton energies is presented in Fig. 2. It is assumed that discrepancies that are

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a function of sphere diameter and material are caused by the difference between the real and the simulated

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neutron energy spectrum at the point of measurement. This implies that the energy distribution of

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secondary neutrons generated by the BERTINI intranuclear model, as shown later in Fig. 8, is not fully

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accurate, namely for high energies of protons. Similarly, the discrepancies that are a function of the

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measurement position (angle from the beam axis) may be attributed to the inaccuracy of the distribution of

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initial direction vectors of generated secondary neutrons shown later in Fig. 11. Mean relative differences

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(NMC/NEXP – 1) between the measured (NEXP) and the simulated (NMC) EBS responses averaged over all

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EBS spheres vary between -25% and +30% for all measurement positions, and proton energies.

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Considering that many sources of uncertainties occur in such a complex proton-neutron problem, the

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results show a reasonable agreement. Therefore, the MC model and the used methods for generation and

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transport of secondary neutrons within and outside the phantom were considered as validated and

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providing acceptable results.

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Fig. 1: An example of measured (circles) and simulated (triangles) responses of all EBS spheres in

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the neutron field at 1 m from the iso-centre at 45° degree from the beam axis generated in the phantom by

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150 MeV proton beam. Error bars are equivalent to data points size.

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Fig. 2: Relative differences (NMC/NEXP – 1) between measured (NEXP) and simulated (NMC) responses of all

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EBS spheres at all measurement positions for 100 MeV, 150 MeV, and 200 MeV proton beams.

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3.2 Proton Depth Dose

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Fig. 3 presents proton depth dose curves in NYLON 6 phantom for 100, 150, and 200 MeV proton

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beams normalized to one primary proton or to one monitor unit. The reference absorbed dose from protons

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in the Bragg peak maximum used later for the comparison to the dose from neutrons and photons was

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estimated to 1948 (±3%), 1710 (±3%), and 1115 (±2%) pGy/proton for 100, 150, and 200 MeV proton

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beams, respectively. The values in the brackets show the standard uncertainty of the dose that was

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averaged over 20 mesh segments.

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Fig. 3: 100, 150, and 200 MeV protons depth dose curves in MeV/mm normalized to 1 proton (left)

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and one monitor unit (right).

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3.3 Secondary Neutrons Characteristics

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3.3.1 Points of Origin

Fig. 4 shows projections of the distribution of points of origin of secondary neutrons in the phantom

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for 100, 150, and 200 MeV protons. In the figures, the neutrons generated by primary protons and their

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charged progenies are visually divided into groups of initial energy of 0-10 MeV, 10-100 MeV, and 100-

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200 MeV. The neutrons originated in other reactions, e.g. (n,2n), are visualized independently of their

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initial energy. Each figure shows the number of neutrons generated by 104 primary protons. The total

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number of neutrons visualized in the figures is 439, 1252, and 2088 for 100, 150, and 200 MeV protons,

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while the number of neutrons generated by primary protons only is 398, 1100, and 1821, respectively. The

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distributions follow the shape of proton beam in the phantom showing that the majority of secondary

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neutrons originates along the proton beam path.

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Fig. 4: Projections of positions where secondary neutrons are generated in NYLON 6 phantom for the

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total of 104 primary protons with the energies of 100 MeV, 150 MeV, and 200 MeV. The figure with a

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circle shows the projection to a plane perpendicular to the beam axis, the other figures show the projection

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to a plane along the beam axis. Corresponding proton depth-dose curves (in arbitrary units) are presented

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for comparison.

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3.3.2 Energy and Number of Secondary Neutrons

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Figs. 5 and 6 on the left side and Fig. 7 show the distribution of the number of neutrons generated by

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primary protons, their average initial energy, and the total initial energy as a function of the depth in the

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phantom, respectively, for 100, 150, and 200 MeV protons. The results present integrals over the phantom 15

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radius. Similarly, Figs. 5 and 6 on the right side visualize the first two quantities as a function of the

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distance from the beam axis at the depth corresponding to one third of the proton range, i.e. 2.2, 4.2, and

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7.5 cm, for 100, 150, and 200 MeV protons, respectively. The results are averaged over 1.5 cm depth.

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Summary information about the secondary neutrons generated in the phantom are presented in Table 2.

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Fig. 5: The total number of neutrons generated in the phantom by primary protons, per 1000 protons per 1 mm depth, as a function of the depth in the phantom (left), and per 1000 protons per 1 cm3 as a

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function of the phantom radius (right) at the depth related to one third of the proton range. Corresponding

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proton depth-dose curves (in arbitrary units) are presented for comparison.

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Fig. 6: Average energy of neutrons generated in the phantom by primary protons as a function of the

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depth in the phantom (left) and as a function of phantom radius (right), for 100, 150, and 200 MeV

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protons. Statistical errors at the distance from beam axis higher than 3 cm in plot at the right are large but

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they are not shown for easier readability of the figure. Corresponding proton depth-dose curves (in

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arbitrary units) are presented for comparison.

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Fig. 7: The total initial energy of neutrons generated in the phantom by primary protons, per 1000

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protons per 1 mm depth, as a function of the depth in the phantom, for 100, 150, and 200 MeV protons.

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Corresponding proton depth-dose curves (in arbitrary units) are presented for comparison.

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It is evident, that most neutrons are generated at the small depths in the phantom. Their number and average initial energy becomes smaller with decreasing energy of protons.

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3.3.3 Neutron Initial Energy Distribution The distribution of the initial energy of neutrons generated in the phantom by primary protons is

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presented in Fig. 8. Spectral fluence distribution of neutrons averaged over the whole volume of the

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phantom is shown in Fig. 9. This spectrum includes the peak of thermal neutrons slowed down by

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interactions in the phantom. Fig. 10 presents average spectral fluence distributions of neutrons leaving the

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cylindrical phantom through its walls. It is clearly visible that high energy neutrons move mainly forward,

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i.e. in the beam direction, and the fluence through the rear wall increases with the increasing proton

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energy. On the other hand, the neutron fluence through the front wall changes only insignificantly with

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proton energy.

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primary protons. The inserted plot has log scale on the axis of ordinates.

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Fig. 8: Distribution of initial energy of neutrons generated in the phantom by 100, 150, and 200 MeV

Fig. 9: Spectral fluence distribution of all neutrons normalized to 103 protons and averaged over the whole volume of the phantom, for 100, 150, and 200 MeV proton beams.

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Fig. 10: Average spectral fluence distribution of neutrons leaving the cylindrical phantom through its

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three surfaces – rear wall, front wall, and cylindrical wall, normalized to 103 protons, for 100, 150, and

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200 MeV proton beams.

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3.3.4 Neutron Initial Angular Distribution Fig. 11 shows the distribution of an angle between the proton beam axis and the initial direction

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vector of secondary neutrons created by primary protons. The distribution is divided into three neutron

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energy groups: below 10 MeV, 10-100 MeV, and above 100 MeV. Practically all neutrons with the energy

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above 10 MeV are generated in the forward direction, the same as the majority of neutrons with the initial

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energy below 10 MeV.

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Fig. 11: Angular distribution of secondary neutrons originated in the phantom, for 100, 150, and 200 MeV

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proton beams. Radii represent relative number of emitted neutrons into the given angle (in degrees) from

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the beam axis.

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Table 2 summarizes the information about secondary neutrons generated in the NYLON 6 phantom

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by primary protons with the energies of 100, 150, and 200 MeV. It is evident that the number of secondary

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neutrons and the energy transferred to them significantly increase with the energy of impinging protons.

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This fact should be considered when the treatment with high energy protons is administered.

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Table 2: Summary information about secondary neutrons generated by 100, 150, and 200 MeV primary

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protons.

Proton energy:

100 MeV

150 MeV

200 MeV

The total number of neutrons generated by primary protons, per

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107

189

103 primary protons

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Relative number of generated neutrons with E > 10 MeV

47%

56%

60%

Fraction of proton energy transferred to initial energy of neutrons

0.88%

2.23%

3.88%

Average initial energy of neutrons

20.1 MeV

30.1 MeV

41.2 MeV

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3.4 Dose Distributions in Phantom

Fig. 12 visualizes 2D distribution of absorbed dose from primary protons in the NYLON 6 phantom.

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Fig. 12: The 2D distribution of the absorbed dose caused by primary protons and recoiled charged ions,

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for 100 MeV, 150 MeV, and 200 MeV primary proton beams. Values of the contour lines are stated in

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pGy/proton. The first two unlabelled contour lines are 800 and 500 pGy/proton. Corresponding proton

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depth-dose curves (in arbitrary units) are presented for comparison.

Fig. 13 presents spatial distributions of neutron effective radiation weighting factors

inside the

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phantom. The highest

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and nearly constant, with an exception of close distances to phantom surfaces where the effective

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increases, particularly at the front wall. Averaged over the whole phantom volume, the mean effective

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is 7.12, 6.75, and 6.57 Sv/Gy for 100, 150, and 200 MeV proton beams. A weak dependence of effective

values occur along the proton beam while at larger distances the

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is lower

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on proton energy and the spatial distributions of absolute values of

agrees with findings presented

by Schneider et al. (2016) for a large water phantom. The distribution of

in the phantom was used for the determination of spatial distributions of

neutron equivalent dose, which are visualized in Fig. 14. The maximum values occur at the proton beam

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path and reach up to 30 pSv/proton. The 2D maps also visualize the results presented in Fig. 11 showing

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that the majority of high energy secondary neutrons are emitted at angles between 15° and 45° with

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respect to the proton beam that is suggested by contour lines elongated at these angles. Finally, Fig. 15

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shows the spatial distribution of photon equivalent dose. A rough comparison with Fig. 14 reveals that the

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photon equivalent dose is about 3 orders of magnitude lower than the neutron one.

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Fig. 13: 2D distribution of neutron effective radiation weighting factor for 100 MeV, 150 MeV, and 200

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MeV primary proton beams. Contour line values are stated in Sv/Gy. Corresponding proton depth-dose

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curves (in arbitrary units) are presented for comparison.

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Fig. 14: 2D distribution of neutron equivalent dose for 100 MeV, 150 MeV, and 200 MeV primary proton

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beams. Contour line values are stated in pSv/proton. Corresponding proton depth-dose curves (in arbitrary

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units) are presented for comparison.

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Fig. 15: 2D distribution of photon equivalent dose for 100 MeV, 150 MeV, and 200 MeV primary proton

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beams. Contour line values are stated in pSy/proton. Corresponding proton depth-dose curves (in arbitrary

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3.5 Comparison of Neutron and Proton Dose This section presents the comparison of the neutron equivalent dose in the NYLON 6 phantom to the

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reference proton dose in the Bragg peak introduced in paragraph 3.2. Fig. 16 shows spatial distribution of

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the neutron equivalent dose normalized per reference proton dose in the Bragg peak, for 100, 150, and 200

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MeV proton beams.

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Fig. 16: Spatial distribution of the ratio of the neutron equivalent dose per proton reference dose, for 100,

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150, and 200 MeV proton beams. Contour line values are stated in percent of Sv/Gy. Corresponding

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proton depth-dose curves (in arbitrary units) are presented for comparison.

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A summary of the neutron equivalent dose at several selected positions in the phantom, normalized to the reference proton dose, is presented in Table 3.

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Table 3: A summary of the secondary neutron equivalent dose per one primary proton and the ratio

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between secondary neutrons equivalent dose and the reference proton dose, for the selected positions in

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the phantom. 24

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Neutron equivalent dose

Relative neutron equivalent dose (Sv/Gy)

(pSv/proton) 100 MeV 150 MeV

200 MeV

Bragg peak

18

8.2

4.0

0.90%

0.86

0.67

0.090%

24

12

1.70%

0.96

0.74

0.055%

5 cm behind Bragg 1.76

100 MeV

5 cm in front of Bragg 34

5 cm off-axis at Brag 1.07 peak depth Maximal

(1)

200 MeV 0.37%

0.050%

0.060%

1.30%

1.10%

0.056%

0.066%

equivalent 42 at 3.7 24 at 6.5 15 at 8.5 2.10% at 3.7 1.30% at 6.5 1.40% at 8.5

dose(1) 464

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Proton energy:

cm

cm

cm

cm

cm

cm

At the given depth of the phantom on the beam axis.

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The highest neutron equivalent dose per reference proton dose reached 2.1%, 1.3%, and 1.4% for

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100, 150, and 200 MeV protons, respectively. Such values occurred on the proton beam axis at the depth

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roughly equal to 56%, 48%, and 38% of the range of corresponding protons. At 5 cm distance from the

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beam axis and 5 cm behind the Bragg peak, the ratio decreases roughly by a factor of 25 to 0.04%-0.09%

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depending on the proton beam energy. In the Bragg peak, the neutron equivalent dose reaches 0.9, 0.45,

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and 0.37% of the proton dose, for 100, 150, and 200 MeV protons, respectively, that is more than two

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orders of magnitude lower than the dose delivered by protons. As already mentioned in paragraph 3.4, the

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photon equivalent dose is yet another 3 orders of magnitude lower.

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4. Conclusions

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To the controversies related to the exposure of patients to neutrons during proton therapy can be

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remarked in the following way: Machines (cyclotrons or synchrocyclotrons) with passively scattered 25

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proton beams, which themselves were sources of neutrons, are replaced with machines equipped with

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beam spot scanning mode enabling to paint the slices of the treated tissue. These systems practically

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eliminate generation of neutrons in the output of the proton beam. Then, the only significant source of

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neutrons is the treated patient.

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Monte Carlo simulations were used to assess the neutrons generated in the NYLON 6 phantom

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irradiated with a spot beam of 100, 150, and 200 MeV protons. The simulations predicted the number and

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positions of the generated neutrons, spectral fluence distributions, and spatial distribution of neutron and

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photon absorbed dose and equivalent dose.

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Most neutrons, and especially neutrons with the highest energies, are generated by protons in shallow

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layers of the phantom. The movement of high energy neutrons is prevalent in the direction of the proton

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beam. The equivalent dose of secondary neutrons generated in the phantom is 2 orders of magnitude lower

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than the proton dose in the Bragg peak and the equivalent dose of secondary photons is 5 orders of

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magnitude lower.

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Monte Carlo simulations provide important information about the transport of radiation in the studied

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object, but their uncertainties are greater especially for higher proton energies. As shown in the

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comparison with the measurements, the significant contribution to the overall uncertainty comes from

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proton interaction models that provide inaccurate angular and energy distributions of the originated

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neutrons.

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Acknowledgements

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The authors wish to thank the PTC and IBA staffs for valuable discussions and to the Czech Metrology

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Institute for their support.

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Neutron spectral fluence and dose distribution inside a NYLON 6 phantom irradiated with pencil beam of high energy protons

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J. Šolca,*, V. Vondráčekb, Z. Vykydala, M. Králíka

a

Czech Metrology Institute, Okružní 31, 638 00 Brno, Czech Republic

b

Proton Therapy Center Praha, Budínova 1a, 180 00 Praha 8, Czech Republic

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* E-mail: [email protected]

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Highlights

Secondary neutrons generated by protons in NYLON phantom studied by MC simulations.

Most neutrons, and with highest energies are generated in phantom shallow layers.

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Neutron equivalent dose is 2 orders of magnitude lower than proton dose.

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