photon and photoneutron spectra produced in radiotherapy ... · al., 2009, hernandez-adame et al.,...
TRANSCRIPT
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XII International Symposium/XXII National Congress on Solid State Dosimetry
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Photon and photoneutron spectra produced in radiotherapy LINACs
H.R. Vega-Carrillo1, S.A. Martínez-Ovalle2, J.L. Benites-Rengifo3 and A.M. Lallena4
1Unidad Academica de Estudios Nucleares
Universidad Autónoma de Zacatecas C. Cipres 10, Fracc. La Peñuela 98068 Zacatecas, Zac. Mexico
2Grupo de Física Nuclear Aplicada y Simulación
Universidad Pedagógica y Tecnológica de Colombia Avenida Central del Norte Km.1. Vía Paipa
Tunja, Boyacá, Colombia
3Universidad Autonoma de Nayarit
Postgrado CBAP Xalisco, Nayarit, Mexico
4Dpto. de Física Atómica, Molecular y Nuclear
Universidad de Granada E-18071 Granada. SPAIN
e-mail: [email protected]
Abstract
A Monte Carlo calculation, using the MCNPX code, was carried out in order to estimate the photon and neutron spectra in two locations of two linacs operating at 15 and 18 MV. Detailed models of both linac heads were used in the calculations. Spectra were estimated below the flattening filter and at the isocenter. Neutron spectra show two components due to evaporation and knock-on neutrons. Lethargy spectra under the filter were compared to the spectra calculated from the function quoted by Tosi et al. that describes reasonably well neutron spectra beyond 1 MeV, though tends to underestimate the energy region between 10-6 and 1 MeV. Neutron and Bremsstrahlung spectra show the same features regardless of the linac voltage. The amount of photons and neutrons produced by the 15 MV linac is smaller than that found for the 18 MV linac. As expected, Bremsstrahlung spectra ends according to the voltage used to accelerate the electrons. Keywords: Neutron, photon, spectrum, LINAC, Monte Carlo
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Introduction
Worldwide, the number of cancer cases is growing. Nowadays cancer kills more
people than tuberculosis, HIV, and malaria combined. Developing countries, where
resources to prevent, diagnose and treat cancer are limited or nonexistent, are
worst hit by the cancer crisis (IAEA, 2010).
Cancer patients are treated by radiation alone or combined with surgery and/or
systemic therapy including chemical, immunological and genetic treatments.
Radiation can be applied as systemic radiotherapy, teletherapy, or brachytherapy.
In teletherapy a radiation beam is addressed to the patient aiming at killing cancer
cells, unaffecting the normal tissues around the tumor. Thus, the classical radiation
therapy, CRT, was improved to 3D-CRT, evolving to Intensity-Modulated Radiation
Therapy, IMRT. Changes included the multileaf collimator system, MLC, and
advanced optimization algorithms (Xu, Bednarz and Paganetti, 2008).
Despite there are several options for cancer treatment, radiotherapy with linacs is
the technique most commonly used, either with electron or photon beams
(Mesbahi et al., 2010).
A lower skin dose, a higher depth dose, a reduced scattered dose to healthy
tissues outside the tissue-target volume, and less rounded isodose curves, are
some of the advantages provided by the use of high-energy x-rays instead of low
energy photons (Brusa et al., 2008, Hashemi et al., 2007). However using high-
energy x-ray machines is a radiation protection issue because besides the
therapeutic beam, linacs produce neutrons that induce reactions in materials inside
the bunker, such as activation (Polaczek et al., 2010) and prompt -ray reactions.
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Neutrons deliver an undesirable dose to the patient, this dose can cause
secondary cancers.
Working above 8 MV, linacs produce neutrons regardless they operate with
electrons or x-rays. In case of electrons, neutrons are produced via virtual photon
reactions (e, e’n), while x-rays generate neutrons in (, n) nuclear reactions. Cross
sections for photoneutron production are roughly between 100 and 200 times
larger than for electro-neutron production, therefore studies have been focused in
photoneutrons (Martinez-Ovalle et al., 2011, Lin et al., 2001, McGinley 1998,
NCRP, 1984).
Photoneutrons are mainly induced in the high-Z materials on the linac head such
as the target, the flattening filter, the jaws, the MLC and the head shielding; also,
they are produced in the patient body and materials in the treatment hall whose
cross sections show the well known Giant Dipole Resonance (Hall et al., 1995,
IAEA, 2000)
Photoneutrons are produced when photons collide with a nucleus, its energy is
distributed among the nucleons and, eventually, a neutron near the nucleus
surface acquires enough energy to emerge as an evaporation neutron. These
neutrons are emitted isotropically. Another reaction occurring during photon-
nucleus reactions and that contributes also to the neutron productionis that in
which the photon gives out all its energy to a single neutron that is kicked-out from
the nucleus. These neutrons are mostly emitted in the direction of the incoming
photon and are known as knock-on neutrons. To describe the photoneutron
spectrum Tosi et al., (1991) derived the following expression:
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nmax SE
0 n
max
n
max
2
dESE
Eln
SE
Eln
T
Eexp
T
EEn (1)
Here, is the fraction of evaporation neutrons, T is the target nuclear temperature,
is the fraction of knock-on neutrons, Emax is the maximum energy of accelerated
electrons and Sn is the separation energy of neutrons in the target nucleus. For W,
= 0.8929, = 0.1071, T = 0.5 MeV, and Sn = 7.34 MeV. For the Bremsstrahlung
Cu target, Sn = 10.56 MeV and T = 1 MeV (Agosteo and Foglio, 1994, Agosteo et
al., 1995).
The actual geometry and composition of the linac head are not always available.
For neutron transport studies around a linac using Monte Carlo methods, some
simplifications are usually assumed. Thus a point-like photoneutron source whose
energy distribution is given by Equation (1) is located at the centre of a 10 cm-thick
spherical shell, with 20 cm external radius, for W head, and 15 cm-thick spherical
shell for Pb head (Agosteo et al, 1995). According to the American Association of
Physics in Medicine (AAPM, 1986), the W head is preferred, because the Pb head
provides a dose enhancement of a factor 2.
This simple head model has been successfully used (Facure et al., 2005, Followill
et al., 2003) even with a thicker W sphere and different models for knock-on
photoneutrons (Barquero et al., 2005). In particular, it has been pointed out that the
results obtained using this simple model in Monte Carlo calculations show no
significant differences with those found for detailed geometries of the linac head
(Agosteo et al., 1995, Carinou, Kamenopoulou and Stamatelatos, 1999). On the
other hand, photoneutron features, such as thermal fluences, spectra, absorbed
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dose, and ambient dose equivalents have been investigated either using
experimental procedures or Monte Carlo calculations (Barquero et al., 2005, Kry et
al., 2009, Hernandez-Adame et al., 2011, Vega-Carrillo and Baltazar-Raigoza,
2011).
The aim of this work is to calculate, using Monte Carlo methods, the photon and
neutron spectra of two linac heads, and to compare the neutron spectra with the
analytical function of Tosi et al., (1991).
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Materials and methods
Spectra were calculated using the Monte Carlo code MCNPX code (Pelowitz,
2005). Detailed head models of the 15 MV Siemens Primus and the 18 MV Varian
Clinac 2100 C/D were used. Figures 1 and 2 show the geometry of the main
components of both linacs.
Figure 1. Target, compensator, flattening filter and jaws models for the 15 MV
Simens Primus linac
In the calculations an electron beam hits the 0.1 cm-diameter target. Electron
energies were sampled from a Gaussian distribution with a mean energy of 15.3
MeV and a standard deviation of 1.5 MeV. These values were fixed by comparing
the calculated percentage depth dose, PDD, with the experimentally measured in a
water phantom (Martinez-Ovalle et al., 2011). This procedure was also used for the
18 MV Varian Clinac 2100 C/D where a 18.3 MeV electron beam was used. Figure
3 shows the comparison between calculated and measured PDDs for both linacs.
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The geometry of both linacs included the shielding cover that was built up using Pb
and Fe.
Figure 2. 18 Varian Clinac 2100 C/D geometry model
Neutron spectra were tallied using point-like detectors located below the flattening
filter and at the isocentre. In order to reduce the computational time, calculations
were carried out in two steps. First a unidirectional electron beam was made to
collide with the target and the Bremsstrahlung spectrum was calculated in both
detectors, using the mode e/. Second, the x-ray spectrum obtained in the detector
located under the flattening filter was used as source term, in mode e//n, and the
photoneutron spectrum was estimated in both detectors.
For all calculations the amount of histories was large enough to have uncertainties
below 1%. Spectra were calculated using two energy arrays with 47 (MB) and 26
(FB) energy groups.
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In order to compare the Tosi’s function with the photoneutron spectra obtained
here, lethargy spectra, E E(E), were calculated. In the case of the Tosi’s function
the lethargy spectrum was obtained using equation 2.
Figure 3. Calculated and measured PDDs for the 15 MV Siemens Primus and the
18 MV Varian Clinac 2100 C/D linacs
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E E(E) = E n(E) , (2)
Here, n(E) is given by equation (1). For the spectra here calculated, that are
discrete, we used.
l
u
EE
E
Eln
EEE
(3)
In equation (3), Eu and El are the upper and lower energy bounds of the class
interval for each energy group.
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Results
As said above, photoneutron spectra in linacs include the contribution of
evaporation and knock-on neutrons, with a smaller contribution coming from (,nn)
and (,pn) reactions. In figure 4, the neutron spectra for the 15 MV LINAC, in the
detectors below the filter (in red) and at the isocenter (in blue) are shown.
Figure 4. 15 MV linac photoneutron spectra below the filter and at the isocenter
In the region between 0.1 and 10 MeV, two peaks with maxima around 0.3-0.5
MeV and 1.2-2 MeV are present. Neutrons whith energies between 1 eV and 1
MeV are the evaporation neutrons while knock-on neutrons appear above 1 MeV.
15 MV
Neutron energy [ MeV ]
10-6 10-5 10-4 10-3 10-2 10-1 100 101
E(E
)
[
cm
-2 -
MeV
-1
]
10-15
10-14
10-13
10-12
10-11
10-10
10-9
10-8
10-7
Filter
Isocenter
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The upper energy in these spectra is 6 MeV. In figure 5 the corresponding spectra
for the 18 MV linac are plotted. They show the same features as those found for
the 15 MV linac, except that in this case the upper energy is 9 MeV. Also, a larger
amount of neutrons per photon are produced in this case.
18 MV
Energy [ MeV ]
10-6 10-5 10-4 10-3 10-2 10-1 100 101
E(E
)
[
cm
-2 -
MeV
-1
]
10-15
10-14
10-13
10-12
10-11
10-10
10-9
10-8
10-7
10-6
Filter
Isocenter
Figure 5. 18 MV linac photoneutron spectra below the filter and at the isocenter
For both linacs, the difference between the spectra below the flattening filter and at
the isocenter is mainly due to the distance between both detectors’ locations.
In figure 6, the lethargy spectrum calculated with the function of Tosi et al. is
compared to those obtained in our simulations. Both MB and FB spectra are
shown.
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Figure 6. Photoneutron lethargy spectra below the flattening filter for the 15 MV
linac. The spectra obtained from the function of Tosi et al. is shown in
red. The MB and FB Monte Carlo results are shown in blue and black,
respectively
The Tosi et al spectrum shows evaporation neutrons from 1 eV up to 4 MeV, with a
maximum for 1 MeV; the small tail above 4 MeV corresponds to knock-on
neutrons. Both Monte Carlo spectra have the maximum shifted towards slightly
lower energies having a larger contribution for all energies below that of the
maximum.
15 MV
Energy [ MeV ]
10-6 10-5 10-4 10-3 10-2 10-1 100 101 102
E
E(E
)
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
Tosi et al., function
Monte Carlo MB
Monte Carlo FB
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In figure 7, the results found for the 18 MV linac are shown. Similar features, as
those for 15 MV linac, are noticed; however differences are larger in this case in
agreement with the findings of Huang et al. (2005).
18 MV
Energy [ MeV ]
10-6 10-5 10-4 10-3 10-2 10-1 100 101 102
E
E(E
)
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
Tosi et al., function
Monte Carlo MB
Monte Carlo FB
Figure 7. Same as figure 6 but for the 18 MV linac
In figure 8 the photon spectra for 15 and 18 MV linacs calculated below the
flattening filter and at the isocentre are shown. For both linacs the Bremsstrahlung
spectra estimated under the flattening filter have a peak near 0.5 MeV and a
continuous energy spectrum up to the incident electron energy (Patil et al., 2011).
As the electrons colliding with the target are slowed down producing heat and
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Bremsstrahlung x-rays that are continuous. Due to the distance between the target
and the isocenter, the number of photons that reach the isocenter is strongly
reduced and this effect is most visible in case of the lower energy photons.
Regardless of the linac voltage, the photon maximum energy at the isocenter is
approximately 1.5 MeV. Spectra at this position are into agreement with spectra
reported in literature (Patil et al., 2011, Sheikh-Bagheri and Rogers, 2002).
Energy [ MeV ]
0 5 10 15 20
Ph
oto
n f
lue
nc
e
[
c
m-2
]
10-9
10-8
10-7
10-6
10-5
10-4
10-3
18 MV by the filter
15 MV by the filter
18 MV at the IC
15 MV at the IC
Figure 8. Photon spectra below the filter and at the isocenter for both linacs
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Conclusions
Detailed models of 15 MV Siemens Primus and 18 MV Varian Clinac 2100C/D
heads were used to estimate the photon and neutron spectra below the flattening
filter and at the isocenter. The spectra were calculated using the Monte Carlo code
MCNPX. The features of the incident electron beam were tuned by comparing the
PDDs calculated with the measured ones.
For both linacs, and for both locations, neutron spectra has the same features: they
present two peaks around 0.3-0.5 MeV and 1.2-2 MeV. Evaporation neutrons
appear between 1 eV and 1 MeV, whilst knock-on neutrons are beyond 1 MeV.
Spectra at the isocenter are reduced with respect to those below the filter mainly
due to the distance between both locations.
Neutron lethargy spectra were compared with those obtained from the function of
Tosi et al. that has its maximum at 1 MeV. In both linacs, the agreement is
reasonable above 1 MeV, though the spectra found for the function of Tosi et al.
underestimate the Monte Carlo spectra below this energy.
For both linacs, Bremsstrahlung spectra calculated below the flattening filter have a
peak near 0.5 MeV and a continuous spectra that, as expected, end at the
maximum electron energy. At the isocenter, Bremsstrahlung spectra have the
maximum between 1 and 2 MeV, regardless the accelerating voltage. The 15 MV-
linac continuous spectrum is smaller than the 18 MV spectrum.
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