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Factors influencing the accuracy of beam range estimation in proton therapy using prompt gamma emission
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Institute of Physics and Engineering in Medicine Phys. Med. Biol. 59 (2014) 4427–4441
Physics in Medicine & Biology doi:10.1088/0031-9155/59/15/4427
Factors influencing the accuracy of beam range estimation in proton therapy using prompt gamma emission FMFC Janssen1, G Landry1,3, P Cambraia Lopes2, G Dedes3, J Smeets4, D R Schaart2, K Parodi3 and F Verhaegen1,5 1
Department of Radiation Oncology (MAASTRO), GROW-School for Oncology and Developmental Biology, Maastricht University Medical Center, Maastricht, The Netherlands 2 Faculty of Applied Sciences, Radiation Science and Technology Department, Delft University of Technology, Mekelweg 15, 2629 JB Delft, The Netherlands 3 Faculty of Physics, Division of Medical Physics, Ludwig-Maximilians-University Munich, Am Coulombwall 1, D-85748 Garching, Germany 4 Ion Beam Applications SA, Chemin du Cyclotron 3, B-1348 Louvain-la-Neuve, Belgium 5 Medical Physics Unit, Department of Oncology, McGill University, Montréal, QC H3G 1A4, Canada E-mail: [email protected] Received 10 January 2014, revised 17 April 2014 Accepted for publication 17 June 2014 Published 22 July 2014 Abstract
In-vivo imaging is a strategy to monitor the range of protons inside the patient during radiation treatment. A possible method of in-vivo imaging is detection of secondary ‘prompt’ gamma (PG) photons outside the body, which are produced by inelastic proton-nuclear interactions inside the patient. In this paper, important parameters influencing the relationship between the PG profile and percentage depth dose (PDD) in a uniform cylindrical phantom are explored. Monte Carlo simulations are performed with the new Geant4 based code TOPAS for mono-energetic proton pencil beams (range: 100–250 MeV) and an idealized PG detector. PG depth profiles are evaluated using the inflection point on a sigmoid fit in the fall-off region of the profile. A strong correlation between the inflection point and the proton range determined from the PDD is found for all conditions. Variations between 1.5 mm and 2.7 mm in the distance between the proton range and the inflection point are found when either the mass density, phantom diameter, or detector acceptance angle is changed. A change in cut-off energy of the detector could induce a range difference of maximum 4 mm. Applying time-of-flight discrimination during detection, changing the primary energy of the beam or changing the elemental 0031-9155/14/154427+15$33.00 © 2014 Institute of Physics and Engineering in Medicine Printed in the UK & the USA 4427
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composition of the tissue affects the accuracy of the range prediction by less than 1 mm. The results indicate that the PG signal is rather robust to many parameter variations, but millimetre accurate range monitoring requires all medium and detector properties to be carefully taken into account. Keywords: prompt gamma, proton therapy, beam range accuracy (Some figures may appear in colour only in the online journal) 1. Introduction Proton therapy is known for its theoretically superior radiation dose targeting compared to photons due to the low entrance dose and the sharp Bragg peak at the end of the proton range. However, the sharp dose gradients are also sensitive to range uncertainties (Lomax 2008), which can be substantial depending on the anatomical location. Due to these uncertainties, additional margins are necessary to ensure tumour coverage, thus reducing the advantages of protons over photons. Verifying the proton range with in-vivo measurements would provide additional information about the treatment and could lead to a reduction of margins (Paganetti 2012). In particle therapy, in-vivo imaging is challenging because the primary charged particles are completely stopped inside the patient. Fortunately, part of the secondary gamma radiation, created in non-elastic proton-nuclear reactions within the patient, can exit the body. In these nuclear interactions both positron emitters (PE) creating annihilation photons, as well as prompt gamma (PG) photons are created. These signals can be used for in-vivo monitoring (Bennett et al 1978; Stichelbaut and Jongen 2003; Min et al 2006). PG photons have the advantage to be emitted quasi-instantly (decay time smaller than 1 ns), and they are emitted from the point of creation. Moteabbed et al (2011) showed for representative proton plans at different heterogeneous treatment sites that, when taking the effects of detector acceptance and efficiency into account, PE is superior in terms of the amplitude of the detected signal, while PG has the major advantage of enabling online measurements with no washout effects. Previous studies demonstrated that PG imaging is a useful tool for range estimation (Min et al 2006; Polf et al 2009a, 2009b; Testa et al 2010; Biegun et al 2012). Moteabbed et al (2011) showed that the PG fall-off is closer located to the dose fall-off than the PE fall-off. Several PG studies to date have used Monte Carlo (MC) simulation codes. Significant differences in absolute production cross sections between different MC codes indicate that MC simulations are not yet sufficiently validated for absolute dose quantification with PG imaging or PE imaging, but the differences between models are under investigation (Verburg et al 2012; Seravalli et al 2012; Robert et al 2013). PG measurements with different types of detectors have been performed over the last few years, indicating the feasibility of PG imaging in homogenous targets (Min et al 2006; Polf et al 2009b; Testa et al 2010; Smeets et al 2012; Cambraia Lopes et al 2013; Verburg et al 2013). Additionally, the influence of tissue composition on the PG profile has been investigated. The PG signal depends on the elemental composition and the medium density (Polf et al 2009a, 2013). Polf et al (2009a) showed in a preliminary study that significant differences can be observed in the PG spectra for different tissue types. The use of specific PG emission lines to determine the density and composition of irradiated tumours and healthy tissues is also investigated (Polf et al 2009a; Verburg et al 2013).
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Dose deposition is mostly related to electromagnetic interactions along the proton path, while the PG profile is mainly a result of the nuclear interactions of the incoming protons. Therefore, no exact one-to-one relationship exists between the PG profile and the dose deposition. Therefore, a systematic analysis of uncertainties influencing the relation between PG profile and depth dose is necessary to be able to predict the range more accurately and understand the accuracy at which this can be achieved. In this work, TOPAS MC simulations are performed to quantify the uncertainties in range prediction in pencil beam scanning derived from prompt gamma profiles due to several factors. 2. Materials and methods The Geant4 based MC package TOPAS (Perl et al 2012) was used to investigate the correlation of proton range and the production of PG photons under different circumstances. A proton pencil beam is simulated incident on a cylinder with variable phantom parameters e.g. elemental composition, mass density and cylinder radius. The influence of these factors on the PG profile, as determined using an idealized detector, is analysed in a systematic way to study the accuracy of the proton range prediction. Additionally, the influence of different beam energies, detection acceptance angles and detector energy cut-offs is investigated. Section 2.1 summarises the physics settings of the code and section 2.2 illustrates the simulation setup for all calculations. The last section explains the extraction of parameters from the prompt gamma profile. 2.1. TOPAS and physics list
TOPAS (Perl et al 2012) is a MC simulation application, based on the Geant4 toolkit (Agostinelli et al 2003), which can be used to model proton beams with high complexity in a user friendly way. In this work, TOPAS version 1.0.b6 based on Geant4.9.6.b1 is used. The default physics list is selected, which is based on the recommendations of Jarlskog and Paganetti (2008) and which was thoroughly validated for proton beams in TOPAS (based on Geant4.9.4) (Perl et al 2012). Due to different versions of the code between the validation of Perl et al (2012) and this study, the PDD’s and lateral profiles calculated with the default physics list in this study are validated against other codes. No significant differences are observed. In the physics list, the default Geant4 opt3 electromagnetic standard package parameters are included. The binary cascade model is selected to handle the inelastic hadronic processes, which are based on a parameterization of the total inelastic hadronic cross-section of Wellisch and Axen (1996). To decrease simulation time by approximately a factor 2.5, the range cut-off for electrons is set to 1 m, causing direct energy deposition for all electrons at the origin of creation. The range cut only influences the gamma emission from bremsstrahlung (Yamaguchi et al 2012). However, in this study we only consider the PG profile of gamma photons above 1 MeV. Therefore, the PG profile remains uninfluenced. 2.2. Simulation setup and scored quantities
Figure 1 illustrates the global simulation setup. A mono-energetic Gaussian pencil beam (FWHM = 9 mm) is used to irradiate a 45 cm long homogeneous virtual cylinder (radius rcyl = 15 cm).
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Figure 1. (a) Global simulation setup of a solid cylinder, placed in air, with a cylindri-
cal detector around it. (b) Lateral view with a detector resolution of 1 mm along the beam penetration depth and detector acceptance angle θ for the 90° emitted photons.
The elemental composition of the cylinder is a mixture of oxygen, carbon, hydrogen and nitrogen, which are among the most abundant constituents of human soft tissue (International Commission on Radiation Units and Measurements (ICRU) 2000). The carbon and oxygen mass fractions are changed in different setups while the nitrogen and hydrogen concentrations are kept constant, as can be seen in table 1. The tissues in the table cover the range of possible carbon and oxygen concentrations for human tissues. Very high and low densities and varying nitrogen and hydrogen levels are not studied in this work. The chosen mass densities for nitrogen and hydrogen are representative for muscle tissue. For tissue number 2, the mass density and the primary energy of the beam are also changed. Tissue number 2 was chosen because it is most representative for soft tissue (male) (International Commission on Radiation Units and Measurements (ICRU) 1989). The mean excitation potential for the different tissues is determined with the Bragg additivity rule (Bragg and Kleeman 1905). Proton depth-dose curves along the beam axis are scored with a resolution of 0.5 mm in depth and the dose is laterally integrated over the full radius of the cylinder. PG distributions are scored in a cylindrical detector (rcyl = 30 cm), placed in air, with a resolution of 1 mm in depth and the gamma photons integrated over a full cylindrical ring. In a post-processing step, only the gamma photons in the detector above 1 MeV and with a detector acceptance angle of ±3° are selected. This angle is an average common value used in other studies (Cambraia Lopes et al 2012; Smeets et al 2012; Biegun et al 2012). Neutron interactions inside the detector are not taken into account, but impinging neutrons are scored. All simulations are performed with 107 primary protons. This is a rough average value for the number of protons per spot in a 2 Gy fraction scheme. For comparison, in a prostate spot-scanning treatment plan with primary energies between 145 MeV and 190 MeV the lowest (proximal) dose spots receive less than 107 protons while the highest (distal) dose spots receive more than 108 (Smeets et al 2012). 2.3. Extraction of parameters
The proton range is extracted from the scored PDD with a resolution of 0.5 mm. Between the dose points of the PDD, the curve is linearly interpolated to determine the proton range, which is defined in this study as the position of the 90% level of the distal dose fall-off according to Gall et al (1993). 4430
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Table 1. Overview of the different simulation setups. The mass fraction of hydrogen
(10.0 w/w%) and nitrogen (3.0 w/w%) is the same in all tissues.
Tissue Carbon Oxygen Excitation po- Mass density number concentration concentration tential (eV) (g/cm3) (w/w%) (w/w%)
Incident proton energy (MeV)
1 2 (a) 2 (b) 3 4 5
180 180 100, 145, 180, 215, 250 180 180 180
7.0 25.0 25.0 43.5 62.0 80.0
80.0 62.0 62.0 43.5 25.0 7.0
76.0 72.7 72.7 69.5 66.4 63.5
1.0 1.2, 1.1, 1.0, 0.9, 0.8 1.0 1.0 1.0 1.0
Normalization of the PG profiles is performed so as to limit the influence of noise on range estimation. The mean depth of the 10, not necessarily adjacent highest points, which we estimate corresponds to the position in depth of the maximum of the PG profile, is determined. The normalisation value is estimated by taking the maximum value of a second order polynomial fit of the 20 points of the PG profile located on either sides of the mean depth. To find a correlation between the PG profile and the proton range, the falloff region of the PG profile is fitted with the three-parameter sigmoid function: a + (1 − a)·erf [b(z – c)], which is a similar function as Henriquet et al (2012) used to fit the vertex distribution in their study of interaction vertex imaging for carbon ion therapy monitoring. After investigating several characteristics of this fit, the inflection point c extracted from the formula above, appeared to correlate best with the range and is therefore used to predict the proton range in this study. The fit is based on the points in the fall-off region, which are defined as the points between the depth of the normalisation point from the polynomial fit, and a point 7 cm deeper. This range definition includes the fall-off region of the PG profile for all cases in this study and results in a robust fit in this region. Figure 2 illustrates the fitting method. In this paper, the proton range minus the range from the inflection point c is noted as the Δ range. 3. Results 3.1. TOPAS validation for prompt gamma photons
The predicted PG emission with the default physics list in TOPAS is compared with Biegun et al (2012) in figure 3, showing differences in PG emission between two codes (Geant4 and MCNPX). Differences between TOPAS and Geant4.9.2.p02 occur due to different physics models in different Geant4 versions of the code. As can be seen in figure 3, the absolute PG emission values can vary up to a factor 3 between different codes and models. However, in this study the focus will not be on the absolute yields but on the differential effects. Therefore, these differences between codes are not further examined. 3.2. Precision of range prediction
In this study, the reproducibility of the inflection point, while simulating different numbers of primary protons, is investigated. The precision of the range determined from the PDD curve is also determined. Table 2 lists the precision of the inflection point and the range from the PDD for different numbers of primaries. The number of primaries mentioned in table 2 is simulated 4431
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110 range R90
100
PG emission (%)
90 80 70 inflection point c 60 50 40 PG profile sigmoid fit normalisation fit PDD
30 20 10 0 160
180
200 220 depth (mm)
240
260
Figure 2. PDD (green dash-dot line) and the PG profile (red dots), including the normalisation method (black dashed line) and the sigmoid fit (blue line), which ranges from the normalisation point to a point 7 cm deeper.
PG emission (particles\mm\incident proton)
−4
x 10
Geant4 9.2.p02 MCNPX 2.7.D TOPAS (Geant4 9.6.b01)
1.1 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0
20
40 60 80 100 120 140 depth in PMMA (mm)
Figure 3. Comparison of the PG emission between Geant4.9.2.p02, MCNPX 2.7.D
(Biegun et al 2012) and TOPAS (Geant4.9.6.b01) as a function of depth in a PMMA phantom, for a 100 MeV proton pencil beam with 2·107 primary protons. There is no cut-off applied on the electron range or the detector energy, and the detector acceptance angle is ±3°.
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Table 2. Precision of the inflection point and the range with N = 10.
Number of primaries
Mean inflection point c ± SD (mm) Range ± SD (mm)
108 107 106
216.96 ± 0.13 216.96 ± 0.51 216.45 ± 1.47
217.10 ± 0.00 217.10 ± 0.00 217.09 ± 0.01
ten batches with different random seeds, and the mean and standard deviation is determined from these batches. For the remainder of this study, 107 primary particles are simulated and the batch is always ten times repeated, to determine the mean and standard deviation. 3.3. Different primary energy
In beams with different energies, the Bragg peaks have different widths due to differences in range straggling, as can be seen in figure 4 (dashed curves). Also the height of the PG profile distal tail can be up to 10% different between the various proton energies. However, the slope of the PG profile remains constant, because this part is dominated by the detector acceptance angle. The combination of the widening of the Bragg peak, and the slope of the PG profile which remains constant, results in a slightly decreasing trend in Δ range towards higher energies, which can be seen in figure 5. This figure also shows that the precision of the range prediction decreases with increasing energy. 3.4. Influence of changes in phantom parameters 3.4.1. Changing carbon and oxygen concentration. The elemental composition of the phan-
tom influences the mean excitation potential and therefore also the proton range as well as the emitted prompt gamma spectrum. Figure 6 shows that the proton range increases with increasing oxygen levels and decreasing carbon levels, while the inflection point extracted from the PG profile increases to a slightly lesser extent. A change in the oxygen concentration from 7% to 80%, and consequently, a change from 80% to 7% in the carbon concentration, without changing the mass density, causes a range shift of less than 5 mm (figure 6(a)). At the same time, the Δ range (figure 6(b)) changes from −0.7 mm to 0.3 mm. 3.4.2. Mass density. The change in mass density of tissue #2 in the beam direction causes a
large shift in position of the Bragg peak (figure 7(a)), but the inflection point of the PG profile changes in a slightly different way with mass density, as can be seen in figure 7(b). The Δ range changes almost linearly with mass density and varies from +1.6 mm to −0.8 mm when increasing the density from 0.8 g cm−3 to 1.2 g cm−3. 3.4.3. Cylinder radius. In a real patient case, a tumor can be superficial or more deeply
located in the body, which might affect the PG signal. The effect of cylinder radius is studied by changing the radius from 15 cm to 2 cm. The difference in PG profile and the inflection point is shown in figure 8. The main differences can be observed in the shape of the plateau region and the height of the tail region. The contribution of gamma photons in the tail section is further investigated by studying the particle interactions. A distinction was made between gamma photons created 4433
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PG emission (%) - dose (%)
Phys. Med. Biol. 59 (2014) 4427
180 170 160 150 140 130 120 110 100 90 80 70 60 50 40 30 20 10 0 0
PDD 250 MeV PG profile 250 MeV fit 250 MeV PDD 100 MeV PG profile 100 MeV fit 100 MeV
50 100 150 200 250 300 350 400 depth (mm)
Figure 4. A comparison of the PG profiles for a 100 MeV (red circles) and 250 MeV (blue circles) proton beam, the PDDs for a 100 MeV (red dashed line) and 250 MeV (blue dashed line) proton beam, and the beam fit for both beams (red and blue solid lines).
1.5
Δ range (mm)
1
0.5
0
-0.5
-1 80 100 120 140 160 180 200 220 240 260 proton energy (MeV) Figure 5. Difference in Δ range while changing the primary energy of the beam.
from neutron interactions, and gamma photons created from other interactions. As can be seen in figure 9, the tail section of the PG profile consists essentially of gamma photons created from neutron interactions with surrounding tissue. 4434
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219
carbon concentration (w/w %) 77 67 57 47 37 27 17 7 inflection point c proton range
218
0.5
217
Δ range (mm)
range (mm)
1
carbon concentration (w/w %) 77 67 57 47 37 27 17 7
216 215 214
0 -0.5 -1 -1.5
213 0 10 20 30 40 50 60 70 80 oxygen concentration (w/w %) (a)
-2 0 10 20 30 40 50 60 70 80 oxygen concentration (w/w %) (b)
Figure 6. (a) The proton range (red circles) and inflection point from the PG profile
(blue crosses) for five different phantoms with changing carbon and oxygen concentrations and constant nitrogen and hydrogen levels (table 1). (b) The difference in Δ range for the five tissues.
280
3 inflection point c proton range
2 Δ range (mm)
range (mm)
260 240 220 200
1 0 -1
180 0.8
0.9 1 1.1 density (g/cm3) (a)
-2
1.2
0.8
0.9 1 1.1 density (g/cm3) (b)
1.2
Figure 7. (a) The proton range (red circles) and inflection point from the PG profile
(blue crosses) for five phantoms with different mass densities. (b) The Δ range for different mass densities.
3.5. Effect of detector changes 3.5.1. Detector acceptance angle. In this work, a detector acceptance angle of 3° is used. However, this angle is system dependent. Therefore, a comparison with a smaller acceptance angle, but with a sufficiently high signal, e.g. ±0.7° was made in this study (Biegun et al 2012). The results are shown in figure 10. 4435
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120 c = 217.0 ± 0.5 mm
PG emission (%)
100 80 60 c = 215.5 ± 0.4 mm 40 20 0 0
PG profile, R = 2 cm fit, R = 2 cm PG profile, R = 15 cm fit, R = 15 cm 40
80 120 160 200 240 280 320 depth (mm)
Figure 8. A comparison of the PG profiles for a cylinder with a radius of 15 cm (red circles) and 2 cm (blue squares). The red and blue solid lines show the fit through the fall-off region of the curves.
120 110
all PG PG from n PG not from n
100 PG emission (%)
90 80 70 60 50 40 30 20 10 0 0
50 100 150 200 250 300 350 400 450 depth (mm)
Figure 9. PG profiles obtained from all interactions (red circles), interactions from
neutrons (green squares) and all interactions except interactions with neutrons (blue crosses).
The inflection point changes by 2.7 mm when the detector acceptance angle is changed from ±3° to ±0.7°. 3.5.2. Time-of-flight (TOF) selection. Testa et al (2008) proposed the concept of applying a
time-of-flight (TOF) window to decrease the background and improve PG imaging. Figure 11 4436
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120 110
θ = ± 3° fit θ = ± 3° θ = ± 0.7° fit θ = ± 0.7°
100 PG emission (%)
90 80 70 60 50 40
217.0 – 0.5 mm
214.3 – 0.9 mm
30 20 10 0 160 170 180 190 200 210 220 230 240 250 260 depth (mm) Figure 10. PG profiles obtained with a detector acceptance angle of ±3° (red) and ±0.7°
(blue).
shows the differences between a PG profile with or without a TOF window of 5 ns applied. This window was chosen because it was just large enough to include all ‘real’ PG photons in this setup. Applying a static TOF window of 5 ns reduces the background signal with approximately 12%. Only a minor change in inflection point is visible (figure 11) between the PG profile with TOF window applied (216.8 ± 0.5 mm) versus the PG profile without any TOF window applied (217.0 ± 0.5 mm). 3.5.3. Energy cut-off. The detector energy cut-off is changed from 1 MeV to 5 MeV for the two most extreme tissues (#1 and #5, table 1). The Δ range is also investigated for three different energy windows, because these windows might be of interest when measuring prompt gamma spectra from specific elements. As can be seen in figure 12, the cut-off energy and the energy windows result in a Δ range which varies from −3.2 mm to +1.7 mm, depending on the energy thresholds. Tissue #5 contains a carbon concentration of 80%. Consequently, the prompt gamma profile and the Δ range is strongly influenced when applying an energy threshold above 5 MeV since the spectral line of carbon (4.44 MeV) is not detected anymore.
4. Discussion Knowledge of all parameters influencing the PG profile is essential to develop a tool to accurately predict the proton range in all cases, in particular in real patient geometries. Discrepancies between the absolute PG emission simulated with TOPAS (Geant4.9.6.b01), MCNPX (version 2.7.D) and Geant4 (version 9.2.p02) indicate that the absolute emission values in the current models cannot be used for absolute in-vivo dose prediction without further study and validation. However, the range prediction might still be within the desired accuracy of 1–2 mm. The effect of different parameters on the shape of the PG profile, and consequently 4437
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120 TOF < 5ns fit TOF < 5ns no TOF fit no TOF
110 100 PG emission (%)
90 80 70 60
217.0 – 0.5 mm
50 40
216.8 – 0.5 mm
30 20 10 0 160 170 180 190 200 210 220 230 240 250 260 depth (mm) Figure 11. PG profiles obtained with (blue) and without (red) a static TOF window.
3 tissue #1 tissue #5
2
Δ range (mm)
1 0 −1 −2 −3 −4 −5
>1
>2
>3 >4 >5 3−5 4−6 4−7 cutoff energy (MeV)
Figure 12. The Δ range obtained for tissue #1 (red circles) and tissue #5 (blue crosses) when applying a cut-off energy ranging from 1 MeV to 5 MeV, or applying an energy window.
on the prediction of the proton range, has been investigated in this study. Real patient geometries and motion effects might induce much larger errors (Engelsman et al 2013), but these effects have not been studied in this paper.
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Table 3. Summary of uncertainties
Effect
Investigated range
Uncertainty (mm)
Primary energy C–O concentration Mass density Cylinder radius Detector acceptance angle TOF selection
100–250 MeV max 1 C: 7–80 w/w% O: 80–7 w/w% max 1 −3 0.8–1.2 g cm max 2.4 2 cm versus 15 cm 1.5 ±0.7º vs ±3º 2.7 No selection versus static 0.2 window 5 ns Detector energy cut-offEnergy 1–5, 3–5, 4–6, 4–7 MeV max 4.9 window
Table 3 shows an overview of the range uncertainties induced by different effects in the uniform, cylindrical phantom setup simulated in this work. A change in elemental compositions (oxygen 7%–80%, carbon 80%–7%) influences the Δ range, because the absolute value of the PG profile up to the Bragg peak is up to twice as high for the tissues with the highest oxygen levels, compared to the tissues with the lowest oxygen content (Polf et al 2013). However, this influence on the Δ range is less than 1 mm. Changing the mass density from 0.8 g cm−3 to 1.2 g cm−3 changes Δ range by approximately 2.4 mm, because the PDD scales with mass density while the PG profile does not scale to the same extent. The PG profile cannot simply be scaled with mass density, because the falloff region of the PG profile is convolved with the detector resolution, which in this study is determined by the simulated acceptance angle of the detector (figure 10). When changing the primary energy of the beam, the energy loss of the protons in the distal part of their track is similar and therefore a similar shape of the PG fall-off region might be expected. However, in beams with higher energies, more range and energy straggling occurs at the end of the track, and more neutrons and gamma photons from proton-nuclear interactions are produced. In this study these effects appear to affect the range prediction by approximately 1 mm. As can be seen in figure 8, the radius of the cylinder influences the amount of gamma photons created from interactions with neutrons. As a consequence, the amount of background radiation can be very different when the phantom size is changed. This may result in a difference of approximately 1.5 mm in range prediction when changing the radius from 2 cm towards 15 cm. Detector properties, such as the acceptance angle or the energy cut-off, may have a large influence on the shape of the fall-off of the measured PG profile. For example, in this study a change in detector acceptance angle from ±0.7° to ±3.0° resulted in a difference in the position of the inflection point of 2.7 mm. A change in cut-off energy or energy window could induce a maximum Δ range difference of 4.9 mm. 5. Conclusions The accuracy of the proton range prediction from the PG profile is investigated in a simulated uniform cylindrical phantom under several circumstances. It has been found that the uncertainty, based on the inflection point of a sigmoid fit of the PG profile, is small and approximately 1–2 mm for most of the investigated effects, like changes in proton primary energy, phantom properties or changes in the TOF background rejection. This indicates that the PG profile fitting method presented here to extract the range is a robust method. Changes in detector acceptance angle or in cut-off energy might induce slightly larger errors (max. 4 mm), but
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the detector properties are well-known in practice and can be calibrated before treatment. Uncertainties in a real patient geometry need to be further investigated. Acknowledgments This study was carried out under the European collaboration ENVISION (Envision 2010), which focuses on improving the quality assurance tools for hadrontherapy and the development of novel imaging modalities. This project was supported by work package 5 of the ENVISION group. The authors are also grateful to the developers of TOPAS, and especially to Dr Joseph Perl (SLAC, Stanford, USA) for frequent improvements to TOPAS when needed. We also would like to thank Dr Enrica Seravalli for her input at the beginning of this study, and Mark Podesta for setting up the environment to run the simulations on a cluster of computers. References Agostinelli S et al 2003 Geant4—a simulation toolkit Nucl. Instrum. Methods Phys. Res. Sect. A: Accelerat., Spectromet. Detect. Assoc. Equip. 506 250–303 Bennett G, Archambeau J, Archambeau B, Meltzer J and Wingate C 1978 Visualization and transport of positron emission from proton activation in vivo Science 200 1151–3 Biegun A K et al 2012 Time-of-flight neutron rejection to improve prompt gamma imaging for proton range verification: a simulation study Phys. Med. Biol. 57 6429–44 Bragg W H and Kleeman R 1905 On the α particles of radium, and their loss of range in passing through various atoms and molecules Phil. Mag. 10 318–40 Cambraia Lopes P et al 2013 First performance tests of digital SiPMs in prompt gamma imaging with a knife-edge slit camera for proton range verification IEEE Nuclear Science Symposium and Medical Imaging Conference (NSS-MIC) (Seoul, Korea, Oct–Nov 2013) Cambraia Lopes P, Pinto M, Simões H, Biegun A and Parodi K 2012 Optimization of collimator designs for real-time proton range verification by measuring prompt gamma rays IEEE Nuclear Science Symposium and Medical Imaging Conference Record (NSS/MIC) (Anaheim, CA, Oct–Nov 2012) Engelsman M, Schwarz M and Dong L 2013 Physics controversies in proton therapy Semin. Radiat. Oncol. 23 88–96 Envision 2010 http://envision.web.cern.ch/ENVISION/ Gall K P et al 1993 State of the art? New proton medical facilities for the Massachusetts General Hospital and the University of California Davis Medical Center Nucl. Instrum. Methods Phys. Res. B 79 881–4 Henriquet P et al 2012 Interaction vertex imaging (IVI) for carbon ion therapy monitoring: a feasibility study Phys. Med. Biol. 57 4655–69 International Commission on Radiation Units and Measurements (ICRU) 1989 Tissue substitutes in radiation dosimetry and measurement ICRU (Bethesda, MD: ICRU) International Commission on Radiation Units and Measurements (ICRU) 2000 Photon, Electron, Proton and Neutron Interaction Data for Body Tissues ICRU (Bethesda, MD: ICRU Publications) Jarlskog C Z and Paganetti H 2008 Physics settings for using the Geant4 toolkit in proton therapy IEEE Trans. Nucl. Sci. 55 1018–25 Lomax A J 2008 Intensity modulated proton therapy and its sensitivity to treatment uncertainties 1: the potential effects of calculational uncertainties Phys. Med. Biol. 53 1027–42 Min C-H, Kim C H, Youn M-Y and Kim J-W 2006 Prompt gamma measurements for locating the dose falloff region in the proton therapy Appl. Phys. Lett. 89 183517 Moteabbed M, Espana S and Paganetti H 2011 Monte Carlo patient study on the comparison of prompt gamma and PET imaging for range verification in proton therapy Phys. Med. Biol. 56 1063–82 Paganetti H 2012 Range uncertainties in proton therapy and the role of Monte Carlo simulations Phys. Med. Biol. 57 R99–117 Perl J, Shin J, Schumann J, Faddegon B and Paganetti H 2012 TOPAS: an innovative proton Monte Carlo platform for research and clinical applications Med. Phys. 39 6818–37
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Polf J C, Panthi R, Mackin D S, McCleskey M, Saastamoinen A, Roeder B T and Beddar S 2013 Measurement of characteristic prompt gamma rays emitted from oxygen and carbon in tissueequivalent samples during proton beam irradiation Phys. Med. Biol. 58 5821–31 Polf J C, Peterson S, Ciangaru G, Gillin M and Beddar S 2009a Prompt gamma-ray emission from biological tissues during proton irradiation: a preliminary study Phys. Med. Biol. 54 731–43 Polf J C, Peterson S, McCleskey M, Roeder B T, Spiridon A, Beddar S and Trache L 2009b Measurement and calculation of characteristic prompt gamma ray spectra emitted during proton irradiation Phys. Med. Biol. 54 N519–27 Robert C et al 2013 Distributions of secondary particles in proton and carbon-ion therapy: a comparison between GATE/Geant4 and FLUKA Monte Carlo codes Phys. Med. Biol. 58 2879–99 Seravalli E et al 2012 Monte Carlo calculations of positron emitter yields in proton radiotherapy Phys. Med. Biol. 57 1659–73 Smeets J et al 2012 Prompt gamma imaging with a slit camera for real-time range control in proton therapy Phys. Med. Biol. 57 3371–405 Stichelbaut F and Jongen Y 2003 Verification of the proton beam position in the patient by the detection of prompt gamma-rays emission 39th Meeting of the Particle Therapy Co-Operative Group (San Francisco, CA 2003) Testa E, Bajard M, Chevallier M, Dauvergne D, Le Foulher F, Poizat J-C, Ray C and Testa M 2008 Monitoring the Bragg peak location of 73 MeV/u carbon ions by means of prompt gamma-ray meausurements Appl. Phys. Lett. 93 093506 Testa M et al 2010 Real-time monitoring of the Bragg-peak position in ion therapy by means of single photon detection Radiat. Environ. Biophys. 49 337–43 Verburg J M, Riley K, Bortfeld T and Seco J 2013 Energy- and time-resolved detection of prompt gamma-rays for proton range verification Phys. Med. Biol. 58 L37–49 Verburg J M, Shih H A and Seco J 2012 Simulation of prompt gamma-ray emission during proton radiotherapy Phys. Med. Biol. 57 5459–72 Wellisch H P and Axen D 1996 Total reaction cross section calculations in proton-nucleus scattering Phys. Rev. C 54 1329–32 Yamaguchi M et al 2012 Beam range estimation by measuring bremsstrahlung Phys. Med. Biol. 57 2843–56
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Factors influencing the accuracy of beam range estimation in proton therapy using prompt gamma emission
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Institute of Physics and Engineering in Medicine Phys. Med. Biol. 59 (2014) 4427–4441
Physics in Medicine & Biology doi:10.1088/0031-9155/59/15/4427
Factors influencing the accuracy of beam range estimation in proton therapy using prompt gamma emission FMFC Janssen1, G Landry1,3, P Cambraia Lopes2, G Dedes3, J Smeets4, D R Schaart2, K Parodi3 and F Verhaegen1,5 1
Department of Radiation Oncology (MAASTRO), GROW-School for Oncology and Developmental Biology, Maastricht University Medical Center, Maastricht, The Netherlands 2 Faculty of Applied Sciences, Radiation Science and Technology Department, Delft University of Technology, Mekelweg 15, 2629 JB Delft, The Netherlands 3 Faculty of Physics, Division of Medical Physics, Ludwig-Maximilians-University Munich, Am Coulombwall 1, D-85748 Garching, Germany 4 Ion Beam Applications SA, Chemin du Cyclotron 3, B-1348 Louvain-la-Neuve, Belgium 5 Medical Physics Unit, Department of Oncology, McGill University, Montréal, QC H3G 1A4, Canada E-mail: [email protected] Received 10 January 2014, revised 17 April 2014 Accepted for publication 17 June 2014 Published 22 July 2014 Abstract
In-vivo imaging is a strategy to monitor the range of protons inside the patient during radiation treatment. A possible method of in-vivo imaging is detection of secondary ‘prompt’ gamma (PG) photons outside the body, which are produced by inelastic proton-nuclear interactions inside the patient. In this paper, important parameters influencing the relationship between the PG profile and percentage depth dose (PDD) in a uniform cylindrical phantom are explored. Monte Carlo simulations are performed with the new Geant4 based code TOPAS for mono-energetic proton pencil beams (range: 100–250 MeV) and an idealized PG detector. PG depth profiles are evaluated using the inflection point on a sigmoid fit in the fall-off region of the profile. A strong correlation between the inflection point and the proton range determined from the PDD is found for all conditions. Variations between 1.5 mm and 2.7 mm in the distance between the proton range and the inflection point are found when either the mass density, phantom diameter, or detector acceptance angle is changed. A change in cut-off energy of the detector could induce a range difference of maximum 4 mm. Applying time-of-flight discrimination during detection, changing the primary energy of the beam or changing the elemental 0031-9155/14/154427+15$33.00 © 2014 Institute of Physics and Engineering in Medicine Printed in the UK & the USA 4427
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composition of the tissue affects the accuracy of the range prediction by less than 1 mm. The results indicate that the PG signal is rather robust to many parameter variations, but millimetre accurate range monitoring requires all medium and detector properties to be carefully taken into account. Keywords: prompt gamma, proton therapy, beam range accuracy (Some figures may appear in colour only in the online journal) 1. Introduction Proton therapy is known for its theoretically superior radiation dose targeting compared to photons due to the low entrance dose and the sharp Bragg peak at the end of the proton range. However, the sharp dose gradients are also sensitive to range uncertainties (Lomax 2008), which can be substantial depending on the anatomical location. Due to these uncertainties, additional margins are necessary to ensure tumour coverage, thus reducing the advantages of protons over photons. Verifying the proton range with in-vivo measurements would provide additional information about the treatment and could lead to a reduction of margins (Paganetti 2012). In particle therapy, in-vivo imaging is challenging because the primary charged particles are completely stopped inside the patient. Fortunately, part of the secondary gamma radiation, created in non-elastic proton-nuclear reactions within the patient, can exit the body. In these nuclear interactions both positron emitters (PE) creating annihilation photons, as well as prompt gamma (PG) photons are created. These signals can be used for in-vivo monitoring (Bennett et al 1978; Stichelbaut and Jongen 2003; Min et al 2006). PG photons have the advantage to be emitted quasi-instantly (decay time smaller than 1 ns), and they are emitted from the point of creation. Moteabbed et al (2011) showed for representative proton plans at different heterogeneous treatment sites that, when taking the effects of detector acceptance and efficiency into account, PE is superior in terms of the amplitude of the detected signal, while PG has the major advantage of enabling online measurements with no washout effects. Previous studies demonstrated that PG imaging is a useful tool for range estimation (Min et al 2006; Polf et al 2009a, 2009b; Testa et al 2010; Biegun et al 2012). Moteabbed et al (2011) showed that the PG fall-off is closer located to the dose fall-off than the PE fall-off. Several PG studies to date have used Monte Carlo (MC) simulation codes. Significant differences in absolute production cross sections between different MC codes indicate that MC simulations are not yet sufficiently validated for absolute dose quantification with PG imaging or PE imaging, but the differences between models are under investigation (Verburg et al 2012; Seravalli et al 2012; Robert et al 2013). PG measurements with different types of detectors have been performed over the last few years, indicating the feasibility of PG imaging in homogenous targets (Min et al 2006; Polf et al 2009b; Testa et al 2010; Smeets et al 2012; Cambraia Lopes et al 2013; Verburg et al 2013). Additionally, the influence of tissue composition on the PG profile has been investigated. The PG signal depends on the elemental composition and the medium density (Polf et al 2009a, 2013). Polf et al (2009a) showed in a preliminary study that significant differences can be observed in the PG spectra for different tissue types. The use of specific PG emission lines to determine the density and composition of irradiated tumours and healthy tissues is also investigated (Polf et al 2009a; Verburg et al 2013).
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Dose deposition is mostly related to electromagnetic interactions along the proton path, while the PG profile is mainly a result of the nuclear interactions of the incoming protons. Therefore, no exact one-to-one relationship exists between the PG profile and the dose deposition. Therefore, a systematic analysis of uncertainties influencing the relation between PG profile and depth dose is necessary to be able to predict the range more accurately and understand the accuracy at which this can be achieved. In this work, TOPAS MC simulations are performed to quantify the uncertainties in range prediction in pencil beam scanning derived from prompt gamma profiles due to several factors. 2. Materials and methods The Geant4 based MC package TOPAS (Perl et al 2012) was used to investigate the correlation of proton range and the production of PG photons under different circumstances. A proton pencil beam is simulated incident on a cylinder with variable phantom parameters e.g. elemental composition, mass density and cylinder radius. The influence of these factors on the PG profile, as determined using an idealized detector, is analysed in a systematic way to study the accuracy of the proton range prediction. Additionally, the influence of different beam energies, detection acceptance angles and detector energy cut-offs is investigated. Section 2.1 summarises the physics settings of the code and section 2.2 illustrates the simulation setup for all calculations. The last section explains the extraction of parameters from the prompt gamma profile. 2.1. TOPAS and physics list
TOPAS (Perl et al 2012) is a MC simulation application, based on the Geant4 toolkit (Agostinelli et al 2003), which can be used to model proton beams with high complexity in a user friendly way. In this work, TOPAS version 1.0.b6 based on Geant4.9.6.b1 is used. The default physics list is selected, which is based on the recommendations of Jarlskog and Paganetti (2008) and which was thoroughly validated for proton beams in TOPAS (based on Geant4.9.4) (Perl et al 2012). Due to different versions of the code between the validation of Perl et al (2012) and this study, the PDD’s and lateral profiles calculated with the default physics list in this study are validated against other codes. No significant differences are observed. In the physics list, the default Geant4 opt3 electromagnetic standard package parameters are included. The binary cascade model is selected to handle the inelastic hadronic processes, which are based on a parameterization of the total inelastic hadronic cross-section of Wellisch and Axen (1996). To decrease simulation time by approximately a factor 2.5, the range cut-off for electrons is set to 1 m, causing direct energy deposition for all electrons at the origin of creation. The range cut only influences the gamma emission from bremsstrahlung (Yamaguchi et al 2012). However, in this study we only consider the PG profile of gamma photons above 1 MeV. Therefore, the PG profile remains uninfluenced. 2.2. Simulation setup and scored quantities
Figure 1 illustrates the global simulation setup. A mono-energetic Gaussian pencil beam (FWHM = 9 mm) is used to irradiate a 45 cm long homogeneous virtual cylinder (radius rcyl = 15 cm).
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Figure 1. (a) Global simulation setup of a solid cylinder, placed in air, with a cylindri-
cal detector around it. (b) Lateral view with a detector resolution of 1 mm along the beam penetration depth and detector acceptance angle θ for the 90° emitted photons.
The elemental composition of the cylinder is a mixture of oxygen, carbon, hydrogen and nitrogen, which are among the most abundant constituents of human soft tissue (International Commission on Radiation Units and Measurements (ICRU) 2000). The carbon and oxygen mass fractions are changed in different setups while the nitrogen and hydrogen concentrations are kept constant, as can be seen in table 1. The tissues in the table cover the range of possible carbon and oxygen concentrations for human tissues. Very high and low densities and varying nitrogen and hydrogen levels are not studied in this work. The chosen mass densities for nitrogen and hydrogen are representative for muscle tissue. For tissue number 2, the mass density and the primary energy of the beam are also changed. Tissue number 2 was chosen because it is most representative for soft tissue (male) (International Commission on Radiation Units and Measurements (ICRU) 1989). The mean excitation potential for the different tissues is determined with the Bragg additivity rule (Bragg and Kleeman 1905). Proton depth-dose curves along the beam axis are scored with a resolution of 0.5 mm in depth and the dose is laterally integrated over the full radius of the cylinder. PG distributions are scored in a cylindrical detector (rcyl = 30 cm), placed in air, with a resolution of 1 mm in depth and the gamma photons integrated over a full cylindrical ring. In a post-processing step, only the gamma photons in the detector above 1 MeV and with a detector acceptance angle of ±3° are selected. This angle is an average common value used in other studies (Cambraia Lopes et al 2012; Smeets et al 2012; Biegun et al 2012). Neutron interactions inside the detector are not taken into account, but impinging neutrons are scored. All simulations are performed with 107 primary protons. This is a rough average value for the number of protons per spot in a 2 Gy fraction scheme. For comparison, in a prostate spot-scanning treatment plan with primary energies between 145 MeV and 190 MeV the lowest (proximal) dose spots receive less than 107 protons while the highest (distal) dose spots receive more than 108 (Smeets et al 2012). 2.3. Extraction of parameters
The proton range is extracted from the scored PDD with a resolution of 0.5 mm. Between the dose points of the PDD, the curve is linearly interpolated to determine the proton range, which is defined in this study as the position of the 90% level of the distal dose fall-off according to Gall et al (1993). 4430
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Table 1. Overview of the different simulation setups. The mass fraction of hydrogen
(10.0 w/w%) and nitrogen (3.0 w/w%) is the same in all tissues.
Tissue Carbon Oxygen Excitation po- Mass density number concentration concentration tential (eV) (g/cm3) (w/w%) (w/w%)
Incident proton energy (MeV)
1 2 (a) 2 (b) 3 4 5
180 180 100, 145, 180, 215, 250 180 180 180
7.0 25.0 25.0 43.5 62.0 80.0
80.0 62.0 62.0 43.5 25.0 7.0
76.0 72.7 72.7 69.5 66.4 63.5
1.0 1.2, 1.1, 1.0, 0.9, 0.8 1.0 1.0 1.0 1.0
Normalization of the PG profiles is performed so as to limit the influence of noise on range estimation. The mean depth of the 10, not necessarily adjacent highest points, which we estimate corresponds to the position in depth of the maximum of the PG profile, is determined. The normalisation value is estimated by taking the maximum value of a second order polynomial fit of the 20 points of the PG profile located on either sides of the mean depth. To find a correlation between the PG profile and the proton range, the falloff region of the PG profile is fitted with the three-parameter sigmoid function: a + (1 − a)·erf [b(z – c)], which is a similar function as Henriquet et al (2012) used to fit the vertex distribution in their study of interaction vertex imaging for carbon ion therapy monitoring. After investigating several characteristics of this fit, the inflection point c extracted from the formula above, appeared to correlate best with the range and is therefore used to predict the proton range in this study. The fit is based on the points in the fall-off region, which are defined as the points between the depth of the normalisation point from the polynomial fit, and a point 7 cm deeper. This range definition includes the fall-off region of the PG profile for all cases in this study and results in a robust fit in this region. Figure 2 illustrates the fitting method. In this paper, the proton range minus the range from the inflection point c is noted as the Δ range. 3. Results 3.1. TOPAS validation for prompt gamma photons
The predicted PG emission with the default physics list in TOPAS is compared with Biegun et al (2012) in figure 3, showing differences in PG emission between two codes (Geant4 and MCNPX). Differences between TOPAS and Geant4.9.2.p02 occur due to different physics models in different Geant4 versions of the code. As can be seen in figure 3, the absolute PG emission values can vary up to a factor 3 between different codes and models. However, in this study the focus will not be on the absolute yields but on the differential effects. Therefore, these differences between codes are not further examined. 3.2. Precision of range prediction
In this study, the reproducibility of the inflection point, while simulating different numbers of primary protons, is investigated. The precision of the range determined from the PDD curve is also determined. Table 2 lists the precision of the inflection point and the range from the PDD for different numbers of primaries. The number of primaries mentioned in table 2 is simulated 4431
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110 range R90
100
PG emission (%)
90 80 70 inflection point c 60 50 40 PG profile sigmoid fit normalisation fit PDD
30 20 10 0 160
180
200 220 depth (mm)
240
260
Figure 2. PDD (green dash-dot line) and the PG profile (red dots), including the normalisation method (black dashed line) and the sigmoid fit (blue line), which ranges from the normalisation point to a point 7 cm deeper.
PG emission (particles\mm\incident proton)
−4
x 10
Geant4 9.2.p02 MCNPX 2.7.D TOPAS (Geant4 9.6.b01)
1.1 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0
20
40 60 80 100 120 140 depth in PMMA (mm)
Figure 3. Comparison of the PG emission between Geant4.9.2.p02, MCNPX 2.7.D
(Biegun et al 2012) and TOPAS (Geant4.9.6.b01) as a function of depth in a PMMA phantom, for a 100 MeV proton pencil beam with 2·107 primary protons. There is no cut-off applied on the electron range or the detector energy, and the detector acceptance angle is ±3°.
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Table 2. Precision of the inflection point and the range with N = 10.
Number of primaries
Mean inflection point c ± SD (mm) Range ± SD (mm)
108 107 106
216.96 ± 0.13 216.96 ± 0.51 216.45 ± 1.47
217.10 ± 0.00 217.10 ± 0.00 217.09 ± 0.01
ten batches with different random seeds, and the mean and standard deviation is determined from these batches. For the remainder of this study, 107 primary particles are simulated and the batch is always ten times repeated, to determine the mean and standard deviation. 3.3. Different primary energy
In beams with different energies, the Bragg peaks have different widths due to differences in range straggling, as can be seen in figure 4 (dashed curves). Also the height of the PG profile distal tail can be up to 10% different between the various proton energies. However, the slope of the PG profile remains constant, because this part is dominated by the detector acceptance angle. The combination of the widening of the Bragg peak, and the slope of the PG profile which remains constant, results in a slightly decreasing trend in Δ range towards higher energies, which can be seen in figure 5. This figure also shows that the precision of the range prediction decreases with increasing energy. 3.4. Influence of changes in phantom parameters 3.4.1. Changing carbon and oxygen concentration. The elemental composition of the phan-
tom influences the mean excitation potential and therefore also the proton range as well as the emitted prompt gamma spectrum. Figure 6 shows that the proton range increases with increasing oxygen levels and decreasing carbon levels, while the inflection point extracted from the PG profile increases to a slightly lesser extent. A change in the oxygen concentration from 7% to 80%, and consequently, a change from 80% to 7% in the carbon concentration, without changing the mass density, causes a range shift of less than 5 mm (figure 6(a)). At the same time, the Δ range (figure 6(b)) changes from −0.7 mm to 0.3 mm. 3.4.2. Mass density. The change in mass density of tissue #2 in the beam direction causes a
large shift in position of the Bragg peak (figure 7(a)), but the inflection point of the PG profile changes in a slightly different way with mass density, as can be seen in figure 7(b). The Δ range changes almost linearly with mass density and varies from +1.6 mm to −0.8 mm when increasing the density from 0.8 g cm−3 to 1.2 g cm−3. 3.4.3. Cylinder radius. In a real patient case, a tumor can be superficial or more deeply
located in the body, which might affect the PG signal. The effect of cylinder radius is studied by changing the radius from 15 cm to 2 cm. The difference in PG profile and the inflection point is shown in figure 8. The main differences can be observed in the shape of the plateau region and the height of the tail region. The contribution of gamma photons in the tail section is further investigated by studying the particle interactions. A distinction was made between gamma photons created 4433
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PG emission (%) - dose (%)
Phys. Med. Biol. 59 (2014) 4427
180 170 160 150 140 130 120 110 100 90 80 70 60 50 40 30 20 10 0 0
PDD 250 MeV PG profile 250 MeV fit 250 MeV PDD 100 MeV PG profile 100 MeV fit 100 MeV
50 100 150 200 250 300 350 400 depth (mm)
Figure 4. A comparison of the PG profiles for a 100 MeV (red circles) and 250 MeV (blue circles) proton beam, the PDDs for a 100 MeV (red dashed line) and 250 MeV (blue dashed line) proton beam, and the beam fit for both beams (red and blue solid lines).
1.5
Δ range (mm)
1
0.5
0
-0.5
-1 80 100 120 140 160 180 200 220 240 260 proton energy (MeV) Figure 5. Difference in Δ range while changing the primary energy of the beam.
from neutron interactions, and gamma photons created from other interactions. As can be seen in figure 9, the tail section of the PG profile consists essentially of gamma photons created from neutron interactions with surrounding tissue. 4434
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219
carbon concentration (w/w %) 77 67 57 47 37 27 17 7 inflection point c proton range
218
0.5
217
Δ range (mm)
range (mm)
1
carbon concentration (w/w %) 77 67 57 47 37 27 17 7
216 215 214
0 -0.5 -1 -1.5
213 0 10 20 30 40 50 60 70 80 oxygen concentration (w/w %) (a)
-2 0 10 20 30 40 50 60 70 80 oxygen concentration (w/w %) (b)
Figure 6. (a) The proton range (red circles) and inflection point from the PG profile
(blue crosses) for five different phantoms with changing carbon and oxygen concentrations and constant nitrogen and hydrogen levels (table 1). (b) The difference in Δ range for the five tissues.
280
3 inflection point c proton range
2 Δ range (mm)
range (mm)
260 240 220 200
1 0 -1
180 0.8
0.9 1 1.1 density (g/cm3) (a)
-2
1.2
0.8
0.9 1 1.1 density (g/cm3) (b)
1.2
Figure 7. (a) The proton range (red circles) and inflection point from the PG profile
(blue crosses) for five phantoms with different mass densities. (b) The Δ range for different mass densities.
3.5. Effect of detector changes 3.5.1. Detector acceptance angle. In this work, a detector acceptance angle of 3° is used. However, this angle is system dependent. Therefore, a comparison with a smaller acceptance angle, but with a sufficiently high signal, e.g. ±0.7° was made in this study (Biegun et al 2012). The results are shown in figure 10. 4435
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120 c = 217.0 ± 0.5 mm
PG emission (%)
100 80 60 c = 215.5 ± 0.4 mm 40 20 0 0
PG profile, R = 2 cm fit, R = 2 cm PG profile, R = 15 cm fit, R = 15 cm 40
80 120 160 200 240 280 320 depth (mm)
Figure 8. A comparison of the PG profiles for a cylinder with a radius of 15 cm (red circles) and 2 cm (blue squares). The red and blue solid lines show the fit through the fall-off region of the curves.
120 110
all PG PG from n PG not from n
100 PG emission (%)
90 80 70 60 50 40 30 20 10 0 0
50 100 150 200 250 300 350 400 450 depth (mm)
Figure 9. PG profiles obtained from all interactions (red circles), interactions from
neutrons (green squares) and all interactions except interactions with neutrons (blue crosses).
The inflection point changes by 2.7 mm when the detector acceptance angle is changed from ±3° to ±0.7°. 3.5.2. Time-of-flight (TOF) selection. Testa et al (2008) proposed the concept of applying a
time-of-flight (TOF) window to decrease the background and improve PG imaging. Figure 11 4436
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120 110
θ = ± 3° fit θ = ± 3° θ = ± 0.7° fit θ = ± 0.7°
100 PG emission (%)
90 80 70 60 50 40
217.0 – 0.5 mm
214.3 – 0.9 mm
30 20 10 0 160 170 180 190 200 210 220 230 240 250 260 depth (mm) Figure 10. PG profiles obtained with a detector acceptance angle of ±3° (red) and ±0.7°
(blue).
shows the differences between a PG profile with or without a TOF window of 5 ns applied. This window was chosen because it was just large enough to include all ‘real’ PG photons in this setup. Applying a static TOF window of 5 ns reduces the background signal with approximately 12%. Only a minor change in inflection point is visible (figure 11) between the PG profile with TOF window applied (216.8 ± 0.5 mm) versus the PG profile without any TOF window applied (217.0 ± 0.5 mm). 3.5.3. Energy cut-off. The detector energy cut-off is changed from 1 MeV to 5 MeV for the two most extreme tissues (#1 and #5, table 1). The Δ range is also investigated for three different energy windows, because these windows might be of interest when measuring prompt gamma spectra from specific elements. As can be seen in figure 12, the cut-off energy and the energy windows result in a Δ range which varies from −3.2 mm to +1.7 mm, depending on the energy thresholds. Tissue #5 contains a carbon concentration of 80%. Consequently, the prompt gamma profile and the Δ range is strongly influenced when applying an energy threshold above 5 MeV since the spectral line of carbon (4.44 MeV) is not detected anymore.
4. Discussion Knowledge of all parameters influencing the PG profile is essential to develop a tool to accurately predict the proton range in all cases, in particular in real patient geometries. Discrepancies between the absolute PG emission simulated with TOPAS (Geant4.9.6.b01), MCNPX (version 2.7.D) and Geant4 (version 9.2.p02) indicate that the absolute emission values in the current models cannot be used for absolute in-vivo dose prediction without further study and validation. However, the range prediction might still be within the desired accuracy of 1–2 mm. The effect of different parameters on the shape of the PG profile, and consequently 4437
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120 TOF < 5ns fit TOF < 5ns no TOF fit no TOF
110 100 PG emission (%)
90 80 70 60
217.0 – 0.5 mm
50 40
216.8 – 0.5 mm
30 20 10 0 160 170 180 190 200 210 220 230 240 250 260 depth (mm) Figure 11. PG profiles obtained with (blue) and without (red) a static TOF window.
3 tissue #1 tissue #5
2
Δ range (mm)
1 0 −1 −2 −3 −4 −5
>1
>2
>3 >4 >5 3−5 4−6 4−7 cutoff energy (MeV)
Figure 12. The Δ range obtained for tissue #1 (red circles) and tissue #5 (blue crosses) when applying a cut-off energy ranging from 1 MeV to 5 MeV, or applying an energy window.
on the prediction of the proton range, has been investigated in this study. Real patient geometries and motion effects might induce much larger errors (Engelsman et al 2013), but these effects have not been studied in this paper.
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Table 3. Summary of uncertainties
Effect
Investigated range
Uncertainty (mm)
Primary energy C–O concentration Mass density Cylinder radius Detector acceptance angle TOF selection
100–250 MeV max 1 C: 7–80 w/w% O: 80–7 w/w% max 1 −3 0.8–1.2 g cm max 2.4 2 cm versus 15 cm 1.5 ±0.7º vs ±3º 2.7 No selection versus static 0.2 window 5 ns Detector energy cut-offEnergy 1–5, 3–5, 4–6, 4–7 MeV max 4.9 window
Table 3 shows an overview of the range uncertainties induced by different effects in the uniform, cylindrical phantom setup simulated in this work. A change in elemental compositions (oxygen 7%–80%, carbon 80%–7%) influences the Δ range, because the absolute value of the PG profile up to the Bragg peak is up to twice as high for the tissues with the highest oxygen levels, compared to the tissues with the lowest oxygen content (Polf et al 2013). However, this influence on the Δ range is less than 1 mm. Changing the mass density from 0.8 g cm−3 to 1.2 g cm−3 changes Δ range by approximately 2.4 mm, because the PDD scales with mass density while the PG profile does not scale to the same extent. The PG profile cannot simply be scaled with mass density, because the falloff region of the PG profile is convolved with the detector resolution, which in this study is determined by the simulated acceptance angle of the detector (figure 10). When changing the primary energy of the beam, the energy loss of the protons in the distal part of their track is similar and therefore a similar shape of the PG fall-off region might be expected. However, in beams with higher energies, more range and energy straggling occurs at the end of the track, and more neutrons and gamma photons from proton-nuclear interactions are produced. In this study these effects appear to affect the range prediction by approximately 1 mm. As can be seen in figure 8, the radius of the cylinder influences the amount of gamma photons created from interactions with neutrons. As a consequence, the amount of background radiation can be very different when the phantom size is changed. This may result in a difference of approximately 1.5 mm in range prediction when changing the radius from 2 cm towards 15 cm. Detector properties, such as the acceptance angle or the energy cut-off, may have a large influence on the shape of the fall-off of the measured PG profile. For example, in this study a change in detector acceptance angle from ±0.7° to ±3.0° resulted in a difference in the position of the inflection point of 2.7 mm. A change in cut-off energy or energy window could induce a maximum Δ range difference of 4.9 mm. 5. Conclusions The accuracy of the proton range prediction from the PG profile is investigated in a simulated uniform cylindrical phantom under several circumstances. It has been found that the uncertainty, based on the inflection point of a sigmoid fit of the PG profile, is small and approximately 1–2 mm for most of the investigated effects, like changes in proton primary energy, phantom properties or changes in the TOF background rejection. This indicates that the PG profile fitting method presented here to extract the range is a robust method. Changes in detector acceptance angle or in cut-off energy might induce slightly larger errors (max. 4 mm), but
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the detector properties are well-known in practice and can be calibrated before treatment. Uncertainties in a real patient geometry need to be further investigated. Acknowledgments This study was carried out under the European collaboration ENVISION (Envision 2010), which focuses on improving the quality assurance tools for hadrontherapy and the development of novel imaging modalities. This project was supported by work package 5 of the ENVISION group. The authors are also grateful to the developers of TOPAS, and especially to Dr Joseph Perl (SLAC, Stanford, USA) for frequent improvements to TOPAS when needed. We also would like to thank Dr Enrica Seravalli for her input at the beginning of this study, and Mark Podesta for setting up the environment to run the simulations on a cluster of computers. References Agostinelli S et al 2003 Geant4—a simulation toolkit Nucl. Instrum. Methods Phys. Res. Sect. A: Accelerat., Spectromet. Detect. Assoc. Equip. 506 250–303 Bennett G, Archambeau J, Archambeau B, Meltzer J and Wingate C 1978 Visualization and transport of positron emission from proton activation in vivo Science 200 1151–3 Biegun A K et al 2012 Time-of-flight neutron rejection to improve prompt gamma imaging for proton range verification: a simulation study Phys. Med. Biol. 57 6429–44 Bragg W H and Kleeman R 1905 On the α particles of radium, and their loss of range in passing through various atoms and molecules Phil. Mag. 10 318–40 Cambraia Lopes P et al 2013 First performance tests of digital SiPMs in prompt gamma imaging with a knife-edge slit camera for proton range verification IEEE Nuclear Science Symposium and Medical Imaging Conference (NSS-MIC) (Seoul, Korea, Oct–Nov 2013) Cambraia Lopes P, Pinto M, Simões H, Biegun A and Parodi K 2012 Optimization of collimator designs for real-time proton range verification by measuring prompt gamma rays IEEE Nuclear Science Symposium and Medical Imaging Conference Record (NSS/MIC) (Anaheim, CA, Oct–Nov 2012) Engelsman M, Schwarz M and Dong L 2013 Physics controversies in proton therapy Semin. Radiat. Oncol. 23 88–96 Envision 2010 http://envision.web.cern.ch/ENVISION/ Gall K P et al 1993 State of the art? New proton medical facilities for the Massachusetts General Hospital and the University of California Davis Medical Center Nucl. Instrum. Methods Phys. Res. B 79 881–4 Henriquet P et al 2012 Interaction vertex imaging (IVI) for carbon ion therapy monitoring: a feasibility study Phys. Med. Biol. 57 4655–69 International Commission on Radiation Units and Measurements (ICRU) 1989 Tissue substitutes in radiation dosimetry and measurement ICRU (Bethesda, MD: ICRU) International Commission on Radiation Units and Measurements (ICRU) 2000 Photon, Electron, Proton and Neutron Interaction Data for Body Tissues ICRU (Bethesda, MD: ICRU Publications) Jarlskog C Z and Paganetti H 2008 Physics settings for using the Geant4 toolkit in proton therapy IEEE Trans. Nucl. Sci. 55 1018–25 Lomax A J 2008 Intensity modulated proton therapy and its sensitivity to treatment uncertainties 1: the potential effects of calculational uncertainties Phys. Med. Biol. 53 1027–42 Min C-H, Kim C H, Youn M-Y and Kim J-W 2006 Prompt gamma measurements for locating the dose falloff region in the proton therapy Appl. Phys. Lett. 89 183517 Moteabbed M, Espana S and Paganetti H 2011 Monte Carlo patient study on the comparison of prompt gamma and PET imaging for range verification in proton therapy Phys. Med. Biol. 56 1063–82 Paganetti H 2012 Range uncertainties in proton therapy and the role of Monte Carlo simulations Phys. Med. Biol. 57 R99–117 Perl J, Shin J, Schumann J, Faddegon B and Paganetti H 2012 TOPAS: an innovative proton Monte Carlo platform for research and clinical applications Med. Phys. 39 6818–37
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Polf J C, Panthi R, Mackin D S, McCleskey M, Saastamoinen A, Roeder B T and Beddar S 2013 Measurement of characteristic prompt gamma rays emitted from oxygen and carbon in tissueequivalent samples during proton beam irradiation Phys. Med. Biol. 58 5821–31 Polf J C, Peterson S, Ciangaru G, Gillin M and Beddar S 2009a Prompt gamma-ray emission from biological tissues during proton irradiation: a preliminary study Phys. Med. Biol. 54 731–43 Polf J C, Peterson S, McCleskey M, Roeder B T, Spiridon A, Beddar S and Trache L 2009b Measurement and calculation of characteristic prompt gamma ray spectra emitted during proton irradiation Phys. Med. Biol. 54 N519–27 Robert C et al 2013 Distributions of secondary particles in proton and carbon-ion therapy: a comparison between GATE/Geant4 and FLUKA Monte Carlo codes Phys. Med. Biol. 58 2879–99 Seravalli E et al 2012 Monte Carlo calculations of positron emitter yields in proton radiotherapy Phys. Med. Biol. 57 1659–73 Smeets J et al 2012 Prompt gamma imaging with a slit camera for real-time range control in proton therapy Phys. Med. Biol. 57 3371–405 Stichelbaut F and Jongen Y 2003 Verification of the proton beam position in the patient by the detection of prompt gamma-rays emission 39th Meeting of the Particle Therapy Co-Operative Group (San Francisco, CA 2003) Testa E, Bajard M, Chevallier M, Dauvergne D, Le Foulher F, Poizat J-C, Ray C and Testa M 2008 Monitoring the Bragg peak location of 73 MeV/u carbon ions by means of prompt gamma-ray meausurements Appl. Phys. Lett. 93 093506 Testa M et al 2010 Real-time monitoring of the Bragg-peak position in ion therapy by means of single photon detection Radiat. Environ. Biophys. 49 337–43 Verburg J M, Riley K, Bortfeld T and Seco J 2013 Energy- and time-resolved detection of prompt gamma-rays for proton range verification Phys. Med. Biol. 58 L37–49 Verburg J M, Shih H A and Seco J 2012 Simulation of prompt gamma-ray emission during proton radiotherapy Phys. Med. Biol. 57 5459–72 Wellisch H P and Axen D 1996 Total reaction cross section calculations in proton-nucleus scattering Phys. Rev. C 54 1329–32 Yamaguchi M et al 2012 Beam range estimation by measuring bremsstrahlung Phys. Med. Biol. 57 2843–56
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