Author’s Accepted Manuscript Bioneutronics: Thermal scattering in organics tissues and its impact on BNCT dosimetry R.L. Ramos, M.L. Sztejnberg Gonçalves-Carralves, F. Cantargi www.elsevier.com/locate/apradiso
PII: DOI: Reference:
S0969-8043(15)30064-6 http://dx.doi.org/10.1016/j.apradiso.2015.06.019 ARI7012
To appear in: Applied Radiation and Isotopes Received date: 6 February 2015 Revised date: 16 May 2015 Accepted date: 15 June 2015 Cite this article as: R.L. Ramos, M.L. Sztejnberg Gonçalves-Carralves and F. Cantargi, Bioneutronics: Thermal scattering in organics tissues and its impact on BNCT dosimetry, Applied Radiation and Isotopes, http://dx.doi.org/10.1016/j.apradiso.2015.06.019 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 galley proof before it is published in its final citable 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.
Bioneutronics: Thermal Scattering in Organics Tissues and its Impact on BNCT Dosimetry R. L. Ramosa,∗, M.L. Sztejnberg Gon¸calves-Carralvesb , F. Cantargic a Instituto
Dan Beninson, Universidad Nacional de San Mart´ın, Av. General Paz 1499 (1650), San Mart´ın, Buenos Aires, Argentina b Comisi´ on Nacional de Energ´ıa At´ omica, Av. del Libertador 8250 (1429), Ciudad de Buenos Aires, Argentina c Comisi´ on Nacional de Energ´ıa At´ omica, Centro At´ omico Bariloche, Av. Bustillo 9500 (8500), Bariloche, R´ıo Negro, Argentina
Abstract Neutron transport calculation is a key factor in BNCT numerical dosimetry assessments where thermal neutron flux is intimately related to the neutron dose, specially, the therapeutic boron dose. In this work, numerical calculations in phantoms were performed to determine the importance of utilizing the appropriate thermal scattering treatment for different organic tissues. Two thermal treatments for the neutron scattering were included in the simulations: hydrogen bounded in bulk water and hydrogen bounded in a lipid like carbon chain (polyethylene). The results showed difference between both thermal treatments that can reach several percent points depending on the type of source and irradiated geometry. Keywords: Thermal Scattering, BNCT, dosimetry
1. Introduction The Boron Neutron Capture Therapy (BNCT) is a treatment for tumors which are based on the nuclear reaction that occurs when 10 B is irradiated with thermal neutrons [1]. In order to obtain appropriate outcomes, delivering high 5
enough doses to tumor and low enough doses to normal tissues is essential. In ∗ Corresponding
author Email address: [email protected] (R. L. Ramos)
Preprint submitted to Journal of LATEX Templates
June 16, 2015
consideration of planning the treatment, numerical dosimetry calculations must be performed. The results in BNCT numerical dosimetry depend on the nuclear data used in the particle transport calculations. Concerning neutron transport, the param10
eter that describes the interaction between neutrons and nuclei is called neutron cross section and it is related to the probability that a neutron interacts with a nucleus. In particular, the scattering cross section (σ) is related to the reaction in which the neutron remains free after the collision [2] . At neutron energies below several electron-volts, thermal motion of atoms and chemical binding states
15
alter neutron scattering cross section. In this case, the scattering cross section is called thermal scattering cross section [3] . Thermal scattering libraries contain the information of the the double differential thermal scattering cross section. This parameter for neutrons with incident energy E, secondary energy E 0 and scattering angle Ω on a material with bound scattering cross section σb and
20
mass number A at temperature T can be written as: d2 σ σb = S(α, β) dEdΩ 4πkT
r
E0 E
(1)
where S(α,β), the scattering law, is a function of the dimensionless change in momentum α, and the dimensionless change in energy β. The default treatment for thermal neutron scattering in many transport codes is the free gas treatment, which neglects the chemical binding between the 25
target nuclei. The existing thermal libraries normally correspond to standard materials at some temperatures. Figure 1 shows the thermal scattering cross section calculated for hydrogen in bulk water, for hydrogen in polyethylene and for hydrogen with the free gas treatment [4], [5]. In calculations for BNCT numerical dosimetry, scattering effect was studied for hydrogen [6], [7], and hy-
30
drogen bounded in bulk water has been typically taken into account to describe thermal scattering. Nevertheless, tissues are composed of other substances that also contain hydrogen and even the water content cannot be considered in bulk state for a large fraction of its distributions in tissues. This rise a very impor-
2
Thermal scattering cross section (barns)
100
H-polyethylene Free gas thermal treatment H-water
0.01
0.1
1
Energy (eV)
Figure 1: Thermal scattering cross section for hydrogen.
tant question for BNCT dosimetry: How correct is to use the thermal treatment 35
for H in bulk water for tissues compared to the utilization of a tissue specific treatment? This work presents the beginnings of a study, with the intention of achieving a more realistic bioneutronics approach and of evaluating the impact on organic tissues and, specifically, BNCT dosimetry.
40
2. Methods The first step of this work consisted on an analysis on some basic aspects of the organic tissues of interest for BNCT. This included a revision of evaluated data and bibliographic material to understand elemental differences between bulk water and tissues and to determine properties of interest, specifically, the
45
diverse forms of atom binding in such tissues. In order to determine the impact of the thermal scattering cross section libraries in the numerical dosimetry, calculations of neutron flux and dose profiles
3
in phantoms of organic tissue were performed with the code MCNP6 [8]. Lipids were chosen in this first analysis as phantom material since their composition 50
and structure are similar to those of polyethilene, whose thermal scattering libraries are already available. Consequently, two thermal treatments were considered: hydrogen bounded in bulk water (typical treatment) and hydrogen bounded in a lipid like carbon chain (polyethylene). Two different geometries were selected: a cubic phantom of side of 60 cm with a beam source and three
55
spherical phantoms of radius 4.75 cm, 7.75 cm and 14.75 cm with a superficial source. Both model were created in order to represent the cases of: irradiation of a monodirectional external beam (cubic target) and irradiation in all the directions (spherical target) in a facility. In the case of the cubic phantom, thermal, epithermal, and fast neutron flux
60
profiles were calculated as well as profiles for boron, neutron, and photon doses. The profiles in the phantom were assessed on the beam axis, 8 cm off the beam axis, and radially from the beam axis at 2.5 cm depth. The tally considered for the calculations of neutron flux and boron dose was F4 and, for the doses by neutron and photon, F6 was used. In the case of the on axis profile, the
65
detectors were spherical MCNP cells of 0.25 cm radius and, in the other cases, the detectors were rings with 0.5 cm thickness and 8 cm radius. The simulations considered five source spectra: thermal (Maxwell spectrum centered at 2.53x10-8 MeV), epithermal (1/E spectrum between 4x10-7 and 1x10-2 MeV), fast (Watt spectrum with parameters a=0.956 MeV and b=2.29 MeV-1 ), JAERI’s[9] and
70
Petten’s[9] BNCT facilities. The last ones were selected in order to perform a simple dosimetry estimate with actual BNCT facility cases with largely differentiated spectra, having Petten’s a hardened epithermal spectrum and JAERI’s a softened one. In the case of spherical phantoms, radial profiles of thermal, epithermal, and
75
fast neutron flux, and boron, neutron, and photon dose were calculated. The detectors were spherical 0.5 cm radius shells. The simulations considered four sources: thermal (Maxwell spectrum centered at 2.53x10-8 MeV), epithermal (1/E spectrum between 4x10-7 and 1x10-2 MeV), fast (Watt spectrum with 4
parameters a=0.956 MeV and b=2.29 MeV-1 ), and a source from a fusion based 80
”thermal column like” irradiation facility [10]. The results were compared according to the following equation: relative dif erence(%) = |
φ(H − polyethylene) − φ(H − water) ∗ 100%| (2) φ(H − water)
where φ(H-polyethylene) is the flux or dose calculated considering the thermal treatment for hydrogen bounded in polyethylene and φ(H-water) is the flux or dose calculated considering the thermal treatment for hydrogen bounded in water.
85
3. Results and Discusions According to the bibliography, hydrogen, is present in organic tissues under different forms: bounded in bulk water, bounded in confined water, and bounded in biomolecules like proteins, lipids, DNA, etc. Regarding the importance of water around biomolecules, Michalarias et al [11] have showed that
90
at lower water concentrations, all of the water molecules are perturbed by the biomolecules and at concentrations of water above certain level, bulk water state can be detected, although the interfacial water continues to accumulate towards a saturation level. This transition point (where bulk water appears) is at about 30 g water/100 g for the membranes (Photosystem II) and about 50 g
95
water/100 g for the DNA, respectively. Table 1 shows average compositions of some human tissues according to their protein, lipid, and water contents.[12]. This clearly shows that, although water is a main carrier of hydrogen, the rest of the biomolecules provide also a large contribution of hydrogen. The tissue with a lower percentage of water is adipose tissue. In this tissue, lipids, mainly com-
100
posed of carbon chains, represent an 80 % of its weight[13]. Now, the scattering law for hydrogen will be different in each molecule and for different confinement conditions (clustered in between macromolecules). However, current thermal treatments used in calculations, neglects the presence of confined water and the fact that hydrogen is bound to molecules other than water. Even more,
5
105
no library was found that considers the thermal scattering treatment for such tissues. On the other hand, there are some libraries available for dosimetry calculations considering that treatment for lipid like carbon chains. This is the case of polyethylene. Consequently, an approach of the impact on dosimetry can be made for adipose tissue. Water (wt %)
Lipid (wt %)
Protein (wt %)
Adipose Tissue
15
80
5
Lung
78
1
17.7
Skin
61.5
10
28.5
Muscle
79
2.2
19.2
Liver
71
6.9
18
Table 1: Contribution of proteins, lipids, and water to human tissues.
110
Figure 2 shows the normalized on axis thermal neutron flux profile in the cubic phantom calculated with five different source spectra (thermal, epithermal, fast, JAERI and Petten) and the thermal treatment for hydrogen bounded in water. Figure 3 shows the relative difference between the different thermal treatments, hydrogen bounded in water and hydrogen bounded in polyethylene,
115
for the thermal, JAERI’s, and Petten’s spectra. The largest impact of the thermal libraries was observed for the thermal source. The relative flux difference between both treatments reached values of 2% at 2.5 cm depth and about 9 % at 15 cm depth. In this case, the difference increased with the depth in phantom, what means larger transport paths, due to the fact that the whole
120
neutron population is thermal and, consequently, all of it suffers in multiple events the impact of the thermal scattering all along that path. Concerning the epithermal and fast sources, the relative differences in the thermal flux were under 2 %. The lower differences for these two cases were expected given that most of the transported neutrons are at energies high enough to be affected and
125
thermal neutrons only appear after the moderation of the former ones. In the
6
Thermal source, H-water Epithermal source, H-water Fast source, H-water JAERI source, H-water Petten source, H-water
Normalized Thermal Neutron Flux
1
0.5
0
0
10
5
15
Depth on axis (cm)
Figure 2: Normalized thermal neutron flux on the axis in the cubic phantom with thermal, epithermal, fast, JAERI and Petten sources.
case of JAERI’s spectrum, the relative differences reached values of 2 % at 2.5 cm depth and 4.5 % at 15 cm depth. In the case of Petten’s spectrum, the differences were under values of 3 %. The spectra from these two reactors lay between the spectra from the previous cases and, accordingly, the differences 130
too. Boron, neutron, and photon dose calculations were performed for JAERI’s and Petten’s spectra. Figure 4 shows the normalized on-axis boron dose profile in the cubic phantom extracted from the above mentioned calculations. Figure 5 shows the relative differences for each case in Figure 4. The differences in the
135
thermal flux between different thermal treatments (Figure 3) are directly reproduced in neutron dose calculations (Figure 5). Similar results were observed for photons dose. Flux and dose off-axis profiles showed differences according to both different thermal treatments that were similar to the results obtained for on-axis profiles.
7
Figure 3: Relative difference of thermal neutron flux on the axis in the cubic phantom with thermal, JAERI and Petten sources.
Figure 4: Normalized boron dose on the axis in the cubic phantom with JAERI and Petten sources.
8
Figure 5: Relative differences of boron dose on the axis in the cubic phantom with JAERI and Petten sources.
140
In the calculations of radial profiles at 2.5 cm depth (about the peak in the on-axis profile for epithermal spectrum), the differences in the thermal fluxes and doses were under 3 %. Figure 6 shows the normalized thermal neutron flux in the spherical 7.75 cm radius phantom calculated with the two thermal treatments and with four
145
different source spectra: thermal, epithermal, fast, and thermal from fusionbased facility. Figure 7 shows the relative differences for each case in Figure 6 . The largest differences with the thermal source were approximately 4 % near the center of the sphere, where the distance of neutron transport was largest. Concerning the fusion-based facility, epithermal and fast sources, the relative
150
differences in the thermal flux were under 2.5 %. As in the case of the cubic phantom, these differences in the thermal neutron flux impacted directly on dose calculations leading to differences similar to those in flux profiles. For simulations with the 14.75 cm radius spherical phantom, the highest values of the relative difference reached 10 % at the center of the sphere while in the
9
Figure 6: Normalized thermal neutron flux for the radial case in the spherical phantom of 7.75 cm with thermal, epithermal, fast and fusion facility sources.
155
first centimeters near the surface it was approximately 2 %.
Nevertheless,
differences up to approximately 2 % were also found in regions within 2 cm near the surface. These results show that the differences in the fluxes calculated with different thermal treatments increases when the transport distance increases as also showed with the cubic phantom. In the case of spherical phantom of 4.75 160
cm of radius, the highest values for the difference reached 2 % at the center of the sphere. One important remark is that the differences in the flux and doses found in this work between the utilization of thermal treatment for hydrogen bounded in bulk water and for hydrogen bounded in a tissue can be numerically significant.
165
Then, that difference was evaluated for one specific case (adipose tissue) and resulted in values around some to several percentage units. This type of difference was found in regions of low fluxes and doses as well as in regions of peak values, which could be associated to hot and cold spots, and target and organs at risks in the dosimetry. One must also consider that in neutron dosimetry, specially in
10
Figure 7: Relative difference of thermal neutron flux for the radial case in the spherical phantom of 7.75 cm with thermal, epithermal, fast and fusion reactor sources
170
BNCT, there are other variables with large uncertainties that would make the here reported values less relevant. Nevertheless, this study highlights the fact that a systematic non-negligible error might be involved when the appropriate tissue thermal treatment is not considered.
Other sources of uncertainties in
the simulation were not considered in this manuscript; some of them could be 175
related to variations in KERMA coefficients, material compositions, transport parameters [14]. Source modeling can also bring a significant amount of uncertainty if, for example, one considers the errors in measurements to characterize beams and adjust models [15]. These uncertainties might be around several percent units. Then, using the correct thermal scattering cross section, the total
180
uncertainty in calculations could be reduced. The cases studied showed differences between cross section for water and polyethylene, but these differences could be increased considering the appropriate thermal treatment for each organic tissue. There are still more uncertainties in the knowledge of what would happen with other tissues where hydrogen is bound to other type of molecules
11
185
and/or where water nano-confinement is relevant. The material presented in this section, shows the importance of using the correct library of thermal neutron scattering in the dosimetry calculations. This is encouraging to continue working on determining which tissues present these type of behavior and at what levels, and on building the basic bioneutronics
190
knowledge to develop the tools to include the appropriate thermal scattering treatment. In order to achieve this goal, a study is being developed that involves molecular dynamics of tissues, which can be different from the materials utilized so far. This can provide, through the utilization of specific tools such as GROMACS [16], the frequency spectrum which, afterwards, can be used to feed
195
the NJOY nuclear data processing system [17] to generate the scattering cross section libraries for each tissue in the correct format for dosimetry calculations.
4. Conclusions This study shows that there can be numerically significant differences between the utilization of thermal treatment for hydrogen bounded in bulk water 200
and hydrogen bounded in a tissue (lipid like carbon chain, in this specific case). Depending on the source, energy spectrum and flux distribution, the differences in fluxes and doses can reach significant values, around several percent units. With these values, thermal treatments choice would imply an important amount of systematic error in the dosimetry which can be comparable to other typically
205
found. These results have showed the importance of utilizing the appropriate thermal scattering treatment for each organic tissues in dosimetry calculations.
References [1] R. J. Barth, A critical assessment of boron neutron capture therapy: an overview, Neuro Oncology 62 (2003) 1–5. 210
[2] J. R. Lamarsh, Introduction to Nuclear Energy, 3rd Edition.
12
[3] G. L. Squires, Introduction to the theory of thermal neutron scattering, 1st Edition, Dover Publications, 1997. [4] J. R. Granada, J. Dawidowski, R. E. Mayer, V. H. Gillette, Thermal neutron cross section and transport properties of polyethylene, Nucl. Instrum. 215
Methods in Physics Res., 261 (1998) 573. [5] J. I. M´ arquez Dami´ an, J. R. Granada and D. C. Malaspina, CAB models for water: A new evaluation of the thermal neutron scattering laws for light and heavy water in ENDF-6 format, Annals of Nuclear Energy, 65 (2014) 280–289.
220
[6] S. A. Enger, P. Rosenschld, A. Rezaei and H. Lundqvist, Monte Carlo calculations of thermal neutron capture in gadolinium: A comparison of GEANT4 and MCNP with measurements, Med. Phys. 33 (2006) 337. [7] J. T. Goorley, W. Kiger Iii, R. Zamenhof, Reference dosimetry calculations for neutron capture therapy with comparison of analytical and voxel
225
models, Med. Phys. 29 (2002) 145. [8] T. Goorley, M. James, T. Booth, ... and T. Zukaitis, ”Initial MCNP 6 Release Overview”, LA-UR-11-07082, Los Alamos National Laboratory, also Nuclear Technology, 180, pg 298-315, 2012. [9] I. Auterinen, T. Sere, K. Anttila, A. Kosunen and S. Savolainen, Mea-
230
surement of free beam neutron spectra at eight BNCT facilities worldwide, Applied Radiation and Isotopes, 61 (2004) 1021–1026. [10] M. Sztejnberg and M. Miller, Controlled nuclear fusion for neutron generation: development in CNEA of a facility, Proceedings of AATN 2014, Argentine Association for Nuclear Technology, Buenos Aires, Argentina,
235
2014. [11] I. Michalarias, X. Gao, R. C. Ford and J. Lia, Recent progress on our understanding of water around biomolecules, Journal of Molecular Liquids, 117 (2005) 107–116. 13
[12] ICRU 44, Tissue subtitutes in radiation dosimetry and measurements, In240
ternational Comission on Radiation Units and Measurements, Betsheda, MD, 1989. [13] A. Blanco, Qu´ımica Biol´ogica, 6th Edition, El Ateneo, 1999. [14] A. Beceyro, R. Ramos and M. Sztejnberg, An´alisis de las diferentes formas de c´ alculo de perfiles de dosis en terapias por captura neutr´onica utilizando
245
MCNP, Tesis de la Carrera de Especializaci´on en Reactores Nucleares y su Ciclo de Combustible, Instituto Dan Beninson, UNSAM, (2014). [15] K.J. Riley, P.J. Binns, O.K. Harling, ... and H.R. Blaumann, Unifying dose specification between clinical BNCT centers in the Americas, M, Med. Phys. 35 (2008) 1295.
250
[16] D. Van Der Spoel, E. Lindahl, B. Hess, G. Groenhof, A. Mark and H. Berendsen, GROMACS: fast, flexible and free, Journal of computational chemistry , 26 (2005) 1701–1718. [17] R. E. MacFarlane and D. W. Muir, NJOY Nuclear Data Processing System, ´ Los Alamos National Laboratory, New Mexico, USA, 1994.
14
PII: DOI: Reference:
S0969-8043(15)30064-6 http://dx.doi.org/10.1016/j.apradiso.2015.06.019 ARI7012
To appear in: Applied Radiation and Isotopes Received date: 6 February 2015 Revised date: 16 May 2015 Accepted date: 15 June 2015 Cite this article as: R.L. Ramos, M.L. Sztejnberg Gonçalves-Carralves and F. Cantargi, Bioneutronics: Thermal scattering in organics tissues and its impact on BNCT dosimetry, Applied Radiation and Isotopes, http://dx.doi.org/10.1016/j.apradiso.2015.06.019 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 galley proof before it is published in its final citable 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.
Bioneutronics: Thermal Scattering in Organics Tissues and its Impact on BNCT Dosimetry R. L. Ramosa,∗, M.L. Sztejnberg Gon¸calves-Carralvesb , F. Cantargic a Instituto
Dan Beninson, Universidad Nacional de San Mart´ın, Av. General Paz 1499 (1650), San Mart´ın, Buenos Aires, Argentina b Comisi´ on Nacional de Energ´ıa At´ omica, Av. del Libertador 8250 (1429), Ciudad de Buenos Aires, Argentina c Comisi´ on Nacional de Energ´ıa At´ omica, Centro At´ omico Bariloche, Av. Bustillo 9500 (8500), Bariloche, R´ıo Negro, Argentina
Abstract Neutron transport calculation is a key factor in BNCT numerical dosimetry assessments where thermal neutron flux is intimately related to the neutron dose, specially, the therapeutic boron dose. In this work, numerical calculations in phantoms were performed to determine the importance of utilizing the appropriate thermal scattering treatment for different organic tissues. Two thermal treatments for the neutron scattering were included in the simulations: hydrogen bounded in bulk water and hydrogen bounded in a lipid like carbon chain (polyethylene). The results showed difference between both thermal treatments that can reach several percent points depending on the type of source and irradiated geometry. Keywords: Thermal Scattering, BNCT, dosimetry
1. Introduction The Boron Neutron Capture Therapy (BNCT) is a treatment for tumors which are based on the nuclear reaction that occurs when 10 B is irradiated with thermal neutrons [1]. In order to obtain appropriate outcomes, delivering high 5
enough doses to tumor and low enough doses to normal tissues is essential. In ∗ Corresponding
author Email address: [email protected] (R. L. Ramos)
Preprint submitted to Journal of LATEX Templates
June 16, 2015
consideration of planning the treatment, numerical dosimetry calculations must be performed. The results in BNCT numerical dosimetry depend on the nuclear data used in the particle transport calculations. Concerning neutron transport, the param10
eter that describes the interaction between neutrons and nuclei is called neutron cross section and it is related to the probability that a neutron interacts with a nucleus. In particular, the scattering cross section (σ) is related to the reaction in which the neutron remains free after the collision [2] . At neutron energies below several electron-volts, thermal motion of atoms and chemical binding states
15
alter neutron scattering cross section. In this case, the scattering cross section is called thermal scattering cross section [3] . Thermal scattering libraries contain the information of the the double differential thermal scattering cross section. This parameter for neutrons with incident energy E, secondary energy E 0 and scattering angle Ω on a material with bound scattering cross section σb and
20
mass number A at temperature T can be written as: d2 σ σb = S(α, β) dEdΩ 4πkT
r
E0 E
(1)
where S(α,β), the scattering law, is a function of the dimensionless change in momentum α, and the dimensionless change in energy β. The default treatment for thermal neutron scattering in many transport codes is the free gas treatment, which neglects the chemical binding between the 25
target nuclei. The existing thermal libraries normally correspond to standard materials at some temperatures. Figure 1 shows the thermal scattering cross section calculated for hydrogen in bulk water, for hydrogen in polyethylene and for hydrogen with the free gas treatment [4], [5]. In calculations for BNCT numerical dosimetry, scattering effect was studied for hydrogen [6], [7], and hy-
30
drogen bounded in bulk water has been typically taken into account to describe thermal scattering. Nevertheless, tissues are composed of other substances that also contain hydrogen and even the water content cannot be considered in bulk state for a large fraction of its distributions in tissues. This rise a very impor-
2
Thermal scattering cross section (barns)
100
H-polyethylene Free gas thermal treatment H-water
0.01
0.1
1
Energy (eV)
Figure 1: Thermal scattering cross section for hydrogen.
tant question for BNCT dosimetry: How correct is to use the thermal treatment 35
for H in bulk water for tissues compared to the utilization of a tissue specific treatment? This work presents the beginnings of a study, with the intention of achieving a more realistic bioneutronics approach and of evaluating the impact on organic tissues and, specifically, BNCT dosimetry.
40
2. Methods The first step of this work consisted on an analysis on some basic aspects of the organic tissues of interest for BNCT. This included a revision of evaluated data and bibliographic material to understand elemental differences between bulk water and tissues and to determine properties of interest, specifically, the
45
diverse forms of atom binding in such tissues. In order to determine the impact of the thermal scattering cross section libraries in the numerical dosimetry, calculations of neutron flux and dose profiles
3
in phantoms of organic tissue were performed with the code MCNP6 [8]. Lipids were chosen in this first analysis as phantom material since their composition 50
and structure are similar to those of polyethilene, whose thermal scattering libraries are already available. Consequently, two thermal treatments were considered: hydrogen bounded in bulk water (typical treatment) and hydrogen bounded in a lipid like carbon chain (polyethylene). Two different geometries were selected: a cubic phantom of side of 60 cm with a beam source and three
55
spherical phantoms of radius 4.75 cm, 7.75 cm and 14.75 cm with a superficial source. Both model were created in order to represent the cases of: irradiation of a monodirectional external beam (cubic target) and irradiation in all the directions (spherical target) in a facility. In the case of the cubic phantom, thermal, epithermal, and fast neutron flux
60
profiles were calculated as well as profiles for boron, neutron, and photon doses. The profiles in the phantom were assessed on the beam axis, 8 cm off the beam axis, and radially from the beam axis at 2.5 cm depth. The tally considered for the calculations of neutron flux and boron dose was F4 and, for the doses by neutron and photon, F6 was used. In the case of the on axis profile, the
65
detectors were spherical MCNP cells of 0.25 cm radius and, in the other cases, the detectors were rings with 0.5 cm thickness and 8 cm radius. The simulations considered five source spectra: thermal (Maxwell spectrum centered at 2.53x10-8 MeV), epithermal (1/E spectrum between 4x10-7 and 1x10-2 MeV), fast (Watt spectrum with parameters a=0.956 MeV and b=2.29 MeV-1 ), JAERI’s[9] and
70
Petten’s[9] BNCT facilities. The last ones were selected in order to perform a simple dosimetry estimate with actual BNCT facility cases with largely differentiated spectra, having Petten’s a hardened epithermal spectrum and JAERI’s a softened one. In the case of spherical phantoms, radial profiles of thermal, epithermal, and
75
fast neutron flux, and boron, neutron, and photon dose were calculated. The detectors were spherical 0.5 cm radius shells. The simulations considered four sources: thermal (Maxwell spectrum centered at 2.53x10-8 MeV), epithermal (1/E spectrum between 4x10-7 and 1x10-2 MeV), fast (Watt spectrum with 4
parameters a=0.956 MeV and b=2.29 MeV-1 ), and a source from a fusion based 80
”thermal column like” irradiation facility [10]. The results were compared according to the following equation: relative dif erence(%) = |
φ(H − polyethylene) − φ(H − water) ∗ 100%| (2) φ(H − water)
where φ(H-polyethylene) is the flux or dose calculated considering the thermal treatment for hydrogen bounded in polyethylene and φ(H-water) is the flux or dose calculated considering the thermal treatment for hydrogen bounded in water.
85
3. Results and Discusions According to the bibliography, hydrogen, is present in organic tissues under different forms: bounded in bulk water, bounded in confined water, and bounded in biomolecules like proteins, lipids, DNA, etc. Regarding the importance of water around biomolecules, Michalarias et al [11] have showed that
90
at lower water concentrations, all of the water molecules are perturbed by the biomolecules and at concentrations of water above certain level, bulk water state can be detected, although the interfacial water continues to accumulate towards a saturation level. This transition point (where bulk water appears) is at about 30 g water/100 g for the membranes (Photosystem II) and about 50 g
95
water/100 g for the DNA, respectively. Table 1 shows average compositions of some human tissues according to their protein, lipid, and water contents.[12]. This clearly shows that, although water is a main carrier of hydrogen, the rest of the biomolecules provide also a large contribution of hydrogen. The tissue with a lower percentage of water is adipose tissue. In this tissue, lipids, mainly com-
100
posed of carbon chains, represent an 80 % of its weight[13]. Now, the scattering law for hydrogen will be different in each molecule and for different confinement conditions (clustered in between macromolecules). However, current thermal treatments used in calculations, neglects the presence of confined water and the fact that hydrogen is bound to molecules other than water. Even more,
5
105
no library was found that considers the thermal scattering treatment for such tissues. On the other hand, there are some libraries available for dosimetry calculations considering that treatment for lipid like carbon chains. This is the case of polyethylene. Consequently, an approach of the impact on dosimetry can be made for adipose tissue. Water (wt %)
Lipid (wt %)
Protein (wt %)
Adipose Tissue
15
80
5
Lung
78
1
17.7
Skin
61.5
10
28.5
Muscle
79
2.2
19.2
Liver
71
6.9
18
Table 1: Contribution of proteins, lipids, and water to human tissues.
110
Figure 2 shows the normalized on axis thermal neutron flux profile in the cubic phantom calculated with five different source spectra (thermal, epithermal, fast, JAERI and Petten) and the thermal treatment for hydrogen bounded in water. Figure 3 shows the relative difference between the different thermal treatments, hydrogen bounded in water and hydrogen bounded in polyethylene,
115
for the thermal, JAERI’s, and Petten’s spectra. The largest impact of the thermal libraries was observed for the thermal source. The relative flux difference between both treatments reached values of 2% at 2.5 cm depth and about 9 % at 15 cm depth. In this case, the difference increased with the depth in phantom, what means larger transport paths, due to the fact that the whole
120
neutron population is thermal and, consequently, all of it suffers in multiple events the impact of the thermal scattering all along that path. Concerning the epithermal and fast sources, the relative differences in the thermal flux were under 2 %. The lower differences for these two cases were expected given that most of the transported neutrons are at energies high enough to be affected and
125
thermal neutrons only appear after the moderation of the former ones. In the
6
Thermal source, H-water Epithermal source, H-water Fast source, H-water JAERI source, H-water Petten source, H-water
Normalized Thermal Neutron Flux
1
0.5
0
0
10
5
15
Depth on axis (cm)
Figure 2: Normalized thermal neutron flux on the axis in the cubic phantom with thermal, epithermal, fast, JAERI and Petten sources.
case of JAERI’s spectrum, the relative differences reached values of 2 % at 2.5 cm depth and 4.5 % at 15 cm depth. In the case of Petten’s spectrum, the differences were under values of 3 %. The spectra from these two reactors lay between the spectra from the previous cases and, accordingly, the differences 130
too. Boron, neutron, and photon dose calculations were performed for JAERI’s and Petten’s spectra. Figure 4 shows the normalized on-axis boron dose profile in the cubic phantom extracted from the above mentioned calculations. Figure 5 shows the relative differences for each case in Figure 4. The differences in the
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thermal flux between different thermal treatments (Figure 3) are directly reproduced in neutron dose calculations (Figure 5). Similar results were observed for photons dose. Flux and dose off-axis profiles showed differences according to both different thermal treatments that were similar to the results obtained for on-axis profiles.
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Figure 3: Relative difference of thermal neutron flux on the axis in the cubic phantom with thermal, JAERI and Petten sources.
Figure 4: Normalized boron dose on the axis in the cubic phantom with JAERI and Petten sources.
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Figure 5: Relative differences of boron dose on the axis in the cubic phantom with JAERI and Petten sources.
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In the calculations of radial profiles at 2.5 cm depth (about the peak in the on-axis profile for epithermal spectrum), the differences in the thermal fluxes and doses were under 3 %. Figure 6 shows the normalized thermal neutron flux in the spherical 7.75 cm radius phantom calculated with the two thermal treatments and with four
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different source spectra: thermal, epithermal, fast, and thermal from fusionbased facility. Figure 7 shows the relative differences for each case in Figure 6 . The largest differences with the thermal source were approximately 4 % near the center of the sphere, where the distance of neutron transport was largest. Concerning the fusion-based facility, epithermal and fast sources, the relative
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differences in the thermal flux were under 2.5 %. As in the case of the cubic phantom, these differences in the thermal neutron flux impacted directly on dose calculations leading to differences similar to those in flux profiles. For simulations with the 14.75 cm radius spherical phantom, the highest values of the relative difference reached 10 % at the center of the sphere while in the
9
Figure 6: Normalized thermal neutron flux for the radial case in the spherical phantom of 7.75 cm with thermal, epithermal, fast and fusion facility sources.
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first centimeters near the surface it was approximately 2 %.
Nevertheless,
differences up to approximately 2 % were also found in regions within 2 cm near the surface. These results show that the differences in the fluxes calculated with different thermal treatments increases when the transport distance increases as also showed with the cubic phantom. In the case of spherical phantom of 4.75 160
cm of radius, the highest values for the difference reached 2 % at the center of the sphere. One important remark is that the differences in the flux and doses found in this work between the utilization of thermal treatment for hydrogen bounded in bulk water and for hydrogen bounded in a tissue can be numerically significant.
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Then, that difference was evaluated for one specific case (adipose tissue) and resulted in values around some to several percentage units. This type of difference was found in regions of low fluxes and doses as well as in regions of peak values, which could be associated to hot and cold spots, and target and organs at risks in the dosimetry. One must also consider that in neutron dosimetry, specially in
10
Figure 7: Relative difference of thermal neutron flux for the radial case in the spherical phantom of 7.75 cm with thermal, epithermal, fast and fusion reactor sources
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BNCT, there are other variables with large uncertainties that would make the here reported values less relevant. Nevertheless, this study highlights the fact that a systematic non-negligible error might be involved when the appropriate tissue thermal treatment is not considered.
Other sources of uncertainties in
the simulation were not considered in this manuscript; some of them could be 175
related to variations in KERMA coefficients, material compositions, transport parameters [14]. Source modeling can also bring a significant amount of uncertainty if, for example, one considers the errors in measurements to characterize beams and adjust models [15]. These uncertainties might be around several percent units. Then, using the correct thermal scattering cross section, the total
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uncertainty in calculations could be reduced. The cases studied showed differences between cross section for water and polyethylene, but these differences could be increased considering the appropriate thermal treatment for each organic tissue. There are still more uncertainties in the knowledge of what would happen with other tissues where hydrogen is bound to other type of molecules
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and/or where water nano-confinement is relevant. The material presented in this section, shows the importance of using the correct library of thermal neutron scattering in the dosimetry calculations. This is encouraging to continue working on determining which tissues present these type of behavior and at what levels, and on building the basic bioneutronics
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knowledge to develop the tools to include the appropriate thermal scattering treatment. In order to achieve this goal, a study is being developed that involves molecular dynamics of tissues, which can be different from the materials utilized so far. This can provide, through the utilization of specific tools such as GROMACS [16], the frequency spectrum which, afterwards, can be used to feed
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the NJOY nuclear data processing system [17] to generate the scattering cross section libraries for each tissue in the correct format for dosimetry calculations.
4. Conclusions This study shows that there can be numerically significant differences between the utilization of thermal treatment for hydrogen bounded in bulk water 200
and hydrogen bounded in a tissue (lipid like carbon chain, in this specific case). Depending on the source, energy spectrum and flux distribution, the differences in fluxes and doses can reach significant values, around several percent units. With these values, thermal treatments choice would imply an important amount of systematic error in the dosimetry which can be comparable to other typically
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found. These results have showed the importance of utilizing the appropriate thermal scattering treatment for each organic tissues in dosimetry calculations.
References [1] R. J. Barth, A critical assessment of boron neutron capture therapy: an overview, Neuro Oncology 62 (2003) 1–5. 210
[2] J. R. Lamarsh, Introduction to Nuclear Energy, 3rd Edition.
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[3] G. L. Squires, Introduction to the theory of thermal neutron scattering, 1st Edition, Dover Publications, 1997. [4] J. R. Granada, J. Dawidowski, R. E. Mayer, V. H. Gillette, Thermal neutron cross section and transport properties of polyethylene, Nucl. Instrum. 215
Methods in Physics Res., 261 (1998) 573. [5] J. I. M´ arquez Dami´ an, J. R. Granada and D. C. Malaspina, CAB models for water: A new evaluation of the thermal neutron scattering laws for light and heavy water in ENDF-6 format, Annals of Nuclear Energy, 65 (2014) 280–289.
220
[6] S. A. Enger, P. Rosenschld, A. Rezaei and H. Lundqvist, Monte Carlo calculations of thermal neutron capture in gadolinium: A comparison of GEANT4 and MCNP with measurements, Med. Phys. 33 (2006) 337. [7] J. T. Goorley, W. Kiger Iii, R. Zamenhof, Reference dosimetry calculations for neutron capture therapy with comparison of analytical and voxel
225
models, Med. Phys. 29 (2002) 145. [8] T. Goorley, M. James, T. Booth, ... and T. Zukaitis, ”Initial MCNP 6 Release Overview”, LA-UR-11-07082, Los Alamos National Laboratory, also Nuclear Technology, 180, pg 298-315, 2012. [9] I. Auterinen, T. Sere, K. Anttila, A. Kosunen and S. Savolainen, Mea-
230
surement of free beam neutron spectra at eight BNCT facilities worldwide, Applied Radiation and Isotopes, 61 (2004) 1021–1026. [10] M. Sztejnberg and M. Miller, Controlled nuclear fusion for neutron generation: development in CNEA of a facility, Proceedings of AATN 2014, Argentine Association for Nuclear Technology, Buenos Aires, Argentina,
235
2014. [11] I. Michalarias, X. Gao, R. C. Ford and J. Lia, Recent progress on our understanding of water around biomolecules, Journal of Molecular Liquids, 117 (2005) 107–116. 13
[12] ICRU 44, Tissue subtitutes in radiation dosimetry and measurements, In240
ternational Comission on Radiation Units and Measurements, Betsheda, MD, 1989. [13] A. Blanco, Qu´ımica Biol´ogica, 6th Edition, El Ateneo, 1999. [14] A. Beceyro, R. Ramos and M. Sztejnberg, An´alisis de las diferentes formas de c´ alculo de perfiles de dosis en terapias por captura neutr´onica utilizando
245
MCNP, Tesis de la Carrera de Especializaci´on en Reactores Nucleares y su Ciclo de Combustible, Instituto Dan Beninson, UNSAM, (2014). [15] K.J. Riley, P.J. Binns, O.K. Harling, ... and H.R. Blaumann, Unifying dose specification between clinical BNCT centers in the Americas, M, Med. Phys. 35 (2008) 1295.
250
[16] D. Van Der Spoel, E. Lindahl, B. Hess, G. Groenhof, A. Mark and H. Berendsen, GROMACS: fast, flexible and free, Journal of computational chemistry , 26 (2005) 1701–1718. [17] R. E. MacFarlane and D. W. Muir, NJOY Nuclear Data Processing System, ´ Los Alamos National Laboratory, New Mexico, USA, 1994.
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