Simulation of prompt gamma-ray emission during proton radiotherapy

Abstract

The measurement of prompt gamma rays emitted from proton-induced nuclear reactions has been proposed as a method to verify in vivo the range of a clinical proton radiotherapy beam. A good understanding of the prompt gamma-ray emission during proton therapy is key to develop a clinically feasible technique, as it can facilitate accurate simulations and uncertainty analysis of gamma detector designs. Also, the gamma production cross-sections may be incorporated as prior knowledge in the reconstruction of the proton range from the measurements. In this work, we performed simulations of proton-induced nuclear reactions with the main elements of human tissue, carbon-12, oxygen-16 and nitrogen-14, using the nuclear reaction models of the GEANT4 and MCNP6 Monte Carlo codes and the dedicated nuclear reaction codes TALYS and EMPIRE. For each code, we made an effort to optimize the input parameters and model selection. The results of the models were compared to available experimental data of discrete gamma line cross-sections. Overall, the dedicated nuclear reaction codes reproduced the experimental data more consistently, while the Monte Carlo codes showed larger discrepancies for a number of gamma lines. The model differences lead to a variation of the total gamma production near the end of the proton range by a factor of about 2. These results indicate a need for additional theoretical and experimental study of proton-induced gamma emission in human tissue.

1. Introduction

The main advantage of proton radiotherapy is the finite range of the protons in the patient. However, uncertainties in the proton range currently limit the ability to make full clinical use of the sharp distal falloff of the proton beam. In an ideal scenario, the incident protons are given such energy to position the end-of-range of the beam exactly on the distal edge of the clinical target volume, sparing all tissue downstream in the beam path. Range uncertainties, however, make necessary the use of additional margins to ensure tumour coverage. Also, if a tumour is located next to a critical organ, for safety reasons the lateral edge of the proton beam is placed on the tumour–organ interface instead of the sharper distal edge. Because of these limitations, it has been recognized that a means of verifying the proton range in vivo can facilitate better treatment designs, which could lead to reduced normal tissue complications or improved tumour control.

Although the primary protons stop inside the patient, a part of the secondary gamma radiation resulting from non-elastic nuclear interactions will escape the body and could potentially be used to establish the range of the beam. These gamma rays consist of prompt photons, which are emitted during the nuclear reactions, and delayed emission from the decay of unstable nuclear reaction products.

Initial clinical trials have been performed on the use of positron emission tomography (PET), which detects the photon pairs produced due to the decay of positron emitters such as ¹¹C and ¹⁵O and the subsequent annihilation of the positron (Knopf et al 2011). A coincidence measurement of these 511 keV photons enables tomographic reconstruction of the distribution of the positron emitters, which is correlated with the proton range. However, this technique is indirect and does not facilitate an immediate verification of the range of the protons. Because of the delay between the production of the reaction products and their decay, the PET scan needs to be performed over an extended period of time. This delay limits accuracy, as metabolism will result in a washout of the reaction products (Knopf et al 2011). Other issues include patient motion during the PET scan (Knopf et al 2011) and the uncertainty in the chemical composition of the tissue being irradiated, which affects the correlation between the positron emission and the proton range (Espana and Paganetti 2010).

The detection of prompt gamma rays has been proposed as an alternative method, which can provide a direct and potentially more precise proton range verification (Min et al 2006, Polf et al 2009, Testa et al 2010, Bom et al 2012). Since prompt gamma rays are emitted nearly instantaneous, treatment plan deviations could be determined prior to the actual treatment, by delivering only a small subset of the protons. Range errors could also be tracked continuously during treatment. Spectroscopy of the gamma emission may reduce uncertainties due to tissue composition, because the emitted gamma energies are unique to the nuclear structure of the reaction products.

The measurement and collimation of high-energy gamma rays is however challenging. Significant research and development is needed to determine the feasibility of this method and the potential detector designs for range verification. Simulation studies play an important role in these developments. Monte Carlo simulations in particular may be employed to design a complete simulation of both the radiation interactions as well as the geometry of the treatment hardware and patient anatomy. It is important to critically evaluate such simulations for each particular application under study. For dose calculations, the electromagnetic interactions of the protons are of primary importance, which are well known and can be reliably simulated. The simulation of prompt gamma-ray emission depends on detailed modelling of the hadronic interactions. These processes are not as well understood, and nuclear reaction models therefore rely to a high degree on phenomenology. Such models cannot be expected a priori to have good predictive power for all reaction channels. A recent study on the production of positron emitters during proton therapy showed large differences between various Monte Carlo codes (Seravalli et al 2012). Compared to the positron emitters, the production of prompt gamma rays depends on a far greater number of reaction channels.

In this work, we investigate the simulation of prompt gamma-ray emission during proton therapy, using the Monte Carlo codes GEANT4 and MCNP6 and the dedicated nuclear reaction codes TALYS and EMPIRE. Proton-induced nuclear reactions in the 1–200 MeV incident energy range on ¹²C, ¹⁶O and ¹⁴N were studied, which are the most abundant nuclides in human tissue. Of particular interest are the incident proton energies up to about 50 MeV, because of their impact on the gamma emission near the end-of-range of the proton beam. All simulation results are compared to experimental data reported in the literature and to evaluated nuclear data. The impact of the model differences on the simulation of proton range verification is also discussed.

2. Methods and materials

2.1. Prompt gamma-ray emission

Prompt gamma-ray emission due to proton-induced nuclear reactions is the result of a nucleus being brought into an excited state, which subsequently decays to the lower state accompanied by the emission of a photon. Above the particle-separation energies, this process competes with the emission of other ejectiles, such as neutrons, protons and alpha particles. If particle emission occurs, the residual nucleus may again be left in an excited state. Gamma emission therefore can originate from either the target nucleus or any of the reaction production created through fusion or fission.

The lower lying nuclear levels of most nuclei have clearly distinct quantum states and their properties are well established (Capote et al 2009). The cross-sections of certain transitions between these levels are sufficiently high to enable the discrete gamma emissions to be resolved from the background in a practical measurement. At high excitation energies, many close nuclear levels exist whose properties and decay modes are not completely known.

At lower incident proton energies, only a small number of excited levels can be reached and the gamma spectrum therefore consists of a small number of resolvable discrete lines. At higher energies, many nuclear reaction channels and gamma emissions are possible, most of which cannot be resolved and are also referred to as a quasi-continuum (Murphy et al 2009).

2.2. Nuclear reaction modelling

Current nuclear reactions codes divide the nuclear reaction process into three stages, for which different models are used (Herman et al 2007, NRG Petten 2012, Folger et al 2004).

• Direct reactions in which the proton interacts directly with only one or two nucleons of the target. These reactions are associated with short reaction times and high incident proton energies.

• Pre-equilibrium interactions which involve interactions with parts of the target nucleus before the target has reached statistical equilibrium.

• Compound reactions which take place after the energy of the proton is shared statistically among the target nucleons.

In the energy range of therapeutic protons, all three stages are of relevance. Near the end-of-range of the protons, the compound reaction stage is of main importance. At increasing proton energies, pre-equilibrium reactions and then direct reactions become dominant. Nuclear excitation and subsequent prompt gamma-ray emission can accompany the nuclear reactions in all stages.

Nuclear reaction models require tabulated nuclear levels schemes and branching ratios as input data. Most of the known lower lying levels are simulated as discrete levels. Above a certain cut-off energy, nuclear levels are simulated as a continuum based on a level density model.

2.3. ENDF/B-VII evaluated data

Evaluated data for proton-induced reactions are available in the ENDF/B-VII library (Chadwick 2012). These are generated using nuclear reaction models benchmarked to experimental data. Some small manual corrections to better fit experimental data may sometimes also be performed. Data for proton interactions are provided for energies up to 150 MeV and originate from the LA-150 evaluation, which was performed in the 1990s at Los Alamos National Laboratory (Chadwick et al 1999).

The evaluated data for ¹²C, ¹⁴N and ¹⁶O were produced by Chadwick and Young (1997), who specifically focused on their application for radiation transport simulation of particle therapy. Benchmarks to measured proton, neutron and alpha emissions are reported, but no mention is made of benchmarking to experimental data of discrete gamma lines. The evaluation was performed using the GNASH nuclear reaction code (Young et al 1992), and optical model parameters and level densities were analysed and fitted.

In the published ENDF/B-VII data, prompt gamma-ray emission is only provided as an angle-integrated continuous spectrum with a relatively course energy resolution. Specific cross-sections for the discrete lines are not included. For proton energies up to 20 MeV, however, we were able to extract cross-sections for the main discrete lines from the continuous data. The total non-elastic cross-section and the total gamma production cross-section were also obtained.

2.4. Nuclear reaction simulations

The nuclear reaction simulations were performed using the nuclear reaction models of the Monte Carlo codes GEANT4 9.5 (Allison et al 2006) and MCNP6 beta 2 (Los Alamos National Laboratory 2012). Also, we used the dedicated nuclear reaction simulation codes TALYS 1.4 (NRG Petten 2012) and EMPIRE 3.1 (Herman et al 2007). We made effort to use the best available models and parameters, as discussed in this section. All simulations were performed with a 1 MeV energy resolution for the incident protons.

2.4.1. GEANT4.

GEANT4 generates nuclear reaction events on-the-fly using built-in nuclear reaction models. We used the binary cascade model, which performs an intranuclear cascade followed by a precompound and de-excitation model (Quesada et al 2011). This model has been recommended for proton therapy applications (Jarlskog and Paganetti 2008). Moreover, the alternative Bertini cascade was not suitable as it only provides a simple model for prompt gamma-ray emission that does not consider the discrete nuclear energy levels.

For incident protons with an energy below 45 MeV, the cascade is not used and the simulation starts with the precompound model. In the de-excitation model, Fermi break-up is activated by default for light nuclei; an evaporation model based on Weisskopf and Ewing (1940) theory is used for heavier nuclei. Gamma emission from the excited residual nuclei is handled by the photon evaporation model, which uses tabulated nuclear levels and branching ratios from the Evaluated Nuclear Structure Data File (Tuli 1996). A Fermi gas model is implemented for levels densities above the discrete tabulated data.

The standard GEANT4 physics lists relevant to proton therapy use a parametrization of the total non-elastic reaction cross-section by Wellisch and Axen (1996). Comparison with the ENDF/B-VII optical model analysis (Chadwick and Young 1997) for the nuclei considered, showed relatively large differences in the proton energy range up to about 20 MeV. The cross-sections of Tripathi et al (1999) for light systems were in better agreement and selected instead.

By default, Fermi break-up is activated for A < 17; therefore, the production of excited residuals for the reactions on carbon and nitrogen is fully simulated using this model. The initial compound system of p + ¹⁶O is however handled by the evaporation model followed by the Fermi break-up for residuals. Initial simulations showed this combination to strongly underestimate the excitation of the ¹⁶O residual nucleus. This may be a result of fact that the evaporation model does not consider the discrete levels of the nuclei, which leads to a mismatch with the photon evaporation model that does include the discrete levels. We therefore decided to activate Fermi break-up also for the complete oxygen reaction, and augmented the list of break-up products with the relevant nuclear levels. In addition, we removed the gamma energy corrections that are normally performed by GEANT4 to enforce per-event conservation of energy. Although such corrections are needed for certain applications, they result in unphysical gamma-emission energies, which is undesirable for the use case under study.

The calculations of gamma emission in GEANT4 are performed in the centre-of-mass frame, and a Lorentz boost to the lab frame is performed to simulate Doppler broadening. This boost was disabled in order to obtain the gamma energies in the centre-of-mass frame, which allows for the gamma emissions to be directly assigned to specific transitions.

To obtain cross-sections, a simple geometry was simulated in which mono-energetic protons pass through 50 μm of the target material. This range is sufficiently small to neglect proton energy loss and the possibility of multiple nuclear reactions. All secondary photons generated were scored directly when produced. This process was repeated for all incident proton energies with a total of 10⁹ histories simulated per energy. By scoring the results using narrow energy bins, the discrete gamma lines could be resolved.

2.4.2. MCNP6.

For the MCNP6 simulations, we used the default Bertini intranuclear cascade model followed by the multi-step pre-equilibrium and the evaporation model. Fermi break-up is used by default for light excited nuclei with A ⩽ 20 and an excitation below 44 MeV. MCNP6 includes a nuclear structure library by Prael (2000) and by default uses the Gilbert–Cameron–Cook–Ignatyuk level density model (Prael and Bozoian 1988).

The simulated geometry consisted of a sphere with a 50 μm radius, at the centre of which the primary protons were generated. A tally was activated on the surface to score the energy distribution of all photons passing through. The difference between MCNP6 and GEANT4 geometry was only for implementation reasons; for the proton energy range under study, both can be considered to represent an infinitely thin target. Similarly to the GEANT4 simulations, narrow energy bins were used, Doppler broadening was turned off, and mass–energy balancing was disabled.

It should be noted that MCNP6 also allows for the ENDF/B-VII data to be used, in which case no nuclear model calculations are performed, and the tabulated cross-sections are sampled and interpolated instead. The cross-section results will then be identical to the values that were obtained directly from the ENDF/B-VII database. Also, no detailed gamma spectra will be available.

2.4.3. TALYS.

The TALYS code is a modern dedicated nuclear reaction simulation code, which supports proton interaction with target nuclei A ⩾ 12 and a projectile energy up to 200 MeV. It features several models to determine the entire chain of possible nuclear reactions and their associated cross-sections.

The optical model calculations, which determine the reaction cross-section and transmission coefficients, are performed using the integrated ECIS-06 code. TALYS by default uses the Koning and Delaroche (2003) global optical model potential for proton-induced reactions, which was not designed for light nuclei. Therefore, the specific optical model potentials by Young (1995) were used when applicable (up to about 50 MeV), and the Madland global potential was used for higher energies (Madland 1997). The only exception is the p + ¹²C reaction above 10 MeV incident energy. In this energy range, Young uses a Gaussian form factor for the imaginary surface derivative potential, which is not supported by ECIS. We therefore used for these energies the Madland global potential and enabled the build-in TALYS feature to scale the total reaction cross-section and transmission coefficients to the universal parametrization of Tripathi (1997).

The default exciton pre-equilibrium model was used for the pre-equilibrium stage. The decay of the compound nucleus was simulated with a Hauser–Feshbach model (Hauser and Feshbach 1952). Levels densities above the discrete level region were calculated using the Fermi gas model.

TALYS includes a database of nuclear structure which is based on RIPL-3 (Capote et al 2009). The default database does not include deformation parameters for elements with Z < 10, which led to an underestimation of the direct contribution to the discrete levels at higher proton energies. Therefore, recommended parameters for carbon and oxygen were obtained from RIPL-3 and added into the database. The nuclear structure database was also adjusted to reflect the fact that several lower lying levels of the nuclei being studied decay only through alpha emission (Ajzenbergselove 1990, Tilley et al 1993).

2.4.4. EMPIRE.

The EMPIRE code (Herman et al 2007) is also dedicated to the simulation of nuclear reactions. The PCROSS exciton pre-equilibrium model was selected as this model is recommend by the authors for proton-induced reactions. Simulations of direct reactions were also activated.

EMPIRE provides the option to use any optical model potential from the RIPL-3 database (Capote et al 2009). The Young and Madland optical model potentials were used similarly to TALYS. For the p + ¹²C reactions above 10 MeV incident energy, the same ECIS limitation exists and we used the manual scaling option to scale the reaction cross-section to the published values obtained with the Young potential (Chadwick and Young 1997).

The discrete level and deformation parameter data originate from RIPL-3 and is mostly similar to the TALYS database. EMPIRE also implements the Hauser and Feshbach (1952) model to simulate the compound nucleus. The EMPIRE-specific level densities were used.

2.5. Experimental cross-sections

A literature search yielded a number of experimental studies of gamma emission during proton-induced reactions on ¹²C, ¹⁶O and ¹⁴N (Dyer et al 1981, Narayanaswamy et al 1981, Lang et al 1987, Kiener et al 1998, Belhout et al 2007, Benhabiles-Mezhoud et al 2011). Details of these studies are listed in table 1.

Table 1.

Available experimental cross-section data of gamma emission.

Target	Emit.	Eγ (MeV)	Transition	Study	Eproton (MeV)
12C	12C	4.44	2+ 4.44 → 0+ g.s.	Dyer (1981)	5–23
				Lang (1987)	40, 65, 85
				Lesko (1988)	9–50
				Belhout (2007)	5–25
	11C	2.00	${\frac{1}{2}}^{-}2.00\to {\frac{3}{2}}^{-}\text{g}.\text{s}.$	Lang (1987)	40, 65, 85
16O	16O	6.13	3− 6.13 → 0+ g.s.	Narayanaswamy (1981)	23.7, 44.6
				Dyer (1981)	5–23
				Lang (1987)	40, 65, 85
				Lesko (1988)	9–50
				Belhout (2007)	20.0, 22.5, 25.0
		6.92	2+ 6.92 → 0+ g.s.	Kiener (1998)	9–19
		7.12	1− 7.12 → 0+ g.s.	Kiener (1998)	9–19
		2.74	2− 8.87 → 3− 6.13	Lang (1987)	40, 65, 85
				Kiener (1998)	9–19
	12C	4.44	2+ 4.44 → 0+ g.s.	Dyer (1981)	14–23
				Lang (1987)	40
				Lesko (1988)	20–50
				Belhout (2007)	20.0, 22.5, 25.0
	15N	5.27	${\frac{5}{2}}^{+}5.27\to {\frac{1}{2}}^{-}\text{g}.\text{s}.$	Lang (1987)	40, 65, 85
				Lesko (1988)	30, 33, 40
14N	14N	1.64	1+ 3.95 → 0+ 2.31	Dyer (1981)	5–20
				Lesko (1988)	9–40
				Benhabiles (2011)	6–26
		2.31	0+ 2.31 → 1+ g.s.	Dyer (1981)	4–23
				Lang (1987)	40, 65, 85
				Lesko (1988)	9–40
				Benhabiles (2011)	6–26
		5.11	2− 5.11 → 1+ g.s.	Benhabiles (2011)	7–26
		0.73	3− 5.83 → 2− 5.11	Benhabiles (2011)	7–26
		3.38	1− 5.69 → 0+ 2.31	Benhabiles (2011)	7–14
		2.79	2− 5.10 → 0+ 2.31	Benhabiles (2011)	7–14
		3.89	1+ 6.20 → 0+ 2.31	Benhabiles (2011)	8–14

These cross-sections were reported by Dyer et al (1981), Narayanaswamy et al (1981), Lang et al (1987), Lesko et al (1988), Kiener et al (1998), Belhout et al (2007) and Benhabiles-Mezhoud et al (2011) (g.s. = ground state).

These studies were all performed in the context of gamma-ray astronomy, in which gamma lines are analysed to study nuclear reactions in the astrophysical environment. Most measurements used protons with energies up to 50 MeV, which is also the most important energy range for proton therapy range verification. All published experimental cross-sections describe the resolvable gamma lines resulting from transitions between the main lower lying discrete levels.

The angular distribution of gamma emission depends on the structure of the nuclear levels and the incident proton energy. To obtain a total angle-integrated cross-section, measurements at several angles were performed in these studies and a power function is fitted to the angular dependence. In this work, the angle-integrated cross-sections are compared.

The reported statistical and systematic errors were combined to obtain a total estimate of measurement error.

2.6. Proton Bragg curve simulations

The impact of the nuclear reaction model differences on prompt gamma-ray emission during proton therapy was assessed by simulating proton irradiation of soft tissue and lung tissue. Using GEANT4 9.5, the proton energy spectrum was determined as a function of depth in the tissue. These energy spectra were then convolved with the cross-section data obtained from the models, which allows for the impact of the cross-section differences to be analysed without introducing additional uncertainties due to other models.

The elemental compositions of the tissues as defined by the ICRP were used (ICRP 1975). The density of soft tissue was assumed to be 1.06 g cm⁻³, and the density of lung tissue was set to 0.30 g cm⁻³.

3. Results

3.1. Total non-elastic cross-sections

A comparison of the total non-elastic cross-sections as calculated by the models is shown in figure 1 along with experimental data (Bauhoff (1986) and references therein). Overall, with the previously discussed parameter adjustments, a reasonable agreement between the models and experiments was achieved. The experimental cross-sections for the p +¹² C reaction shows evidence of narrow resonances in the lower energy region. None of the simulations incorporate such details.

Figure 1.

Calculated total non-elastic cross-sections of the proton-induced reactions. Experimental data were obtained from the Bauhoff compilation (Bauhoff (1986) and references therein).

3.2. Discrete line of carbon-12

At lower proton energies, the gamma emission due to p + ¹²C reactions is dominated by the 4.44 MeV gamma emission. This emission corresponds to the ¹²C (p, p′)¹² C* ^4.439 reaction and also includes a small contribution of the ¹²C (p, 2p)¹¹ B* ^4.445 reaction. Because of the kinematic Doppler broadening, these two lines cannot be resolved from each other. Most levels above the 4.44 MeV state decay through alpha emission (Ajzenbergselove 1990).

The model results and experimental data are shown in figure 2. It is important to consider that, as shown by Kiener et al (1998), several narrow resonances exist at low incident energies. The models do not include such effects and aim to reproduce the general trend.

Figure 2.

Cross-section of 4.44 MeV gamma emission due to proton-induced reactions on ¹²C.

The TALYS simulations provide the best fit to the experimental data at higher proton energies. The other models underestimate the cross-sections in this energy region. For the lower incident energies, GEANT4 and MCNP6 seem to better fit the experimental data, although due to the resonances it is somewhat difficult to determine the trend in the measurements. The ENDF/B-VII results are similar to GEANT4.

3.3. Discrete lines of oxygen-16

The first three excited levels of ¹⁶O that can decay through gamma emission are at 6.13, 6.92 and 7.12 MeV (Tilley et al 1993). Gamma emission from these states to the ground state results in most gamma emission at lower incident proton energies, for which the simulation results and measurements are depicted in figure 3. The cross-sections for the important 6.13 MeV gamma line have been the subject of a large number of experimental studies. As the detailed measurements by Kiener et al (1998) show, various narrow resonances exist at low proton energies.

Figure 3.

Cross-section of 6.13, 6.92, 7.12 and 4.44 MeV gamma emission due to proton-induced reactions on ¹⁶O.

For the 6.13 MeV line, the TALYS and EMPIRE codes produce quite similar results, which mostly fit well to the experimental data, expect for an overestimation of the cross-section at the lowest proton energies. GEANT4 gives similar results up to 20 MeV. Above 20 MeV, the cross-section decreases rapidly to zero, which indicates the contribution of direct reactions to this discrete level is not simulated accurately. MCNP6 fits the data poorly, predicting almost no gamma production above 12 MeV. The proton separation energy of ¹⁶O is 12.13 MeV, which suggests a possible model deficiency in the competition between particle and gamma emission. The ENDF/B-VII data show an overall underestimation of the cross-section.

The experimental data show a narrow peak in the excitation function of the 6.92 MeV line, which is not reproduced by any of the models. The simulations of the 7.12 MeV gamma line follow the main trend in the experimental data, except for the MCNP6 results, which again show a large discrepancy at higher incident energies.

For incident proton energies above ~15 MeV, the ¹⁶O (p, p′α)¹² C reactions result in significant emission of 4.44 MeV gammas from the residual ¹²C nucleus, which is also shown in figure 3. This cross-section is quite well reproduced by TALYS, GEANT4 and MCNP6. EMPIRE underestimates the cross-section.

3.4. Discrete lines of nitrogen-14

Nitrogen-14 is the third most abundant element in the human body that results in gamma emission during proton therapy. It plays a more limited role, because the number of nitrogen atoms in most tissues is lower as compared to carbon and oxygen. Simulations on ¹⁴N can however also serve as an additional validation of the nuclear reaction models for light elements. Because of its role in astrophysics, experimental data are available for many of the discrete gamma lines.

The three most important gamma lines have energies of 2.31, 1.64 and 5.11 MeV (transitions listed in table 1), for which we show the models and data in figure 4. For all three lines, TALYS and EMPIRE reasonably reproduce the main trends, while MCNP6 and GEANT4 underestimate the the cross-sections.

Figure 4.

Cross-section of 2.31, 1.64 and 5.11 MeV gamma emission due to proton-induced reactions on ¹⁴N.

3.5. Gamma emission during proton therapy

The total gamma yield as a function of depth in tissue is shown in figure 5, for 150 MeV protons irradiating soft tissue and 70 MeV protons irradiating lung tissue. The difference near the end of the proton range is of the order of a factor of 2. Also, the slope of the fall-off of gamma emission differs. As compared to soft tissue, the lower density of lung tissue increases this difference relative to the depth.

Figure 5.

Simulated total gamma emission during irradiation of tissue. For reference, the energy deposited by the protons (Bragg curve) is also shown.

The discrete gamma emission at 4.44 and 6.13 MeV, which dominates at low incident proton energies, is plotted in figure 6. The gamma line of 6.13 MeV originates from the p + ¹⁶O reaction. The line of 4.44 MeV corresponds to the decay of the first excited level of ¹²C, which is due to several reactions, such as ¹²C(p, p′)¹²C*, ¹⁴N (p, 2pn)¹² C* and ¹⁶O (p, pα)¹² C*. As can be seen in the figure, the correspondence to the dose delivered of the specific discrete gamma lines is more strongly impacted by the model differences.

Figure 6.

Simulated 4.44 and 6.13 MeV gamma emission during irradiation of ICRP soft tissue with 150 MeV protons. For reference, the energy deposited by the protons (Bragg curve) is also shown.

4. Discussion and conclusions

Prompt gamma-ray emission during proton therapy is dominated by proton-induced nuclear reactions on ¹²C, ¹⁶O and ¹⁴N. Knowledge of these reactions is key to an accurate simulation of potential proton therapy range verification methods employing prompt gamma rays. In this study, we found considerable differences in the prediction of the prompt gamma emission due to these elements, comparing the nuclear reaction models of GEANT4, MCNP6, TALYS and EMPIRE, and the evaluated ENDF/B-VII cross-sections.

The model estimates of the total gamma emission during proton irradiation of soft tissue and lung tissue, differed by a factor of about 2 near the end-of-range of the protons. At higher incident proton energies, the models agreed within ~25%. If specific discrete gamma lines are considered, the models variations can be larger. The dedicated nuclear reaction codes reproduced the general trends of experimental data more consistently as compared to the Monte Carlo codes. The GEANT4 and MCNP6 models showed a number of larger discrepancies. In particular, the important 6.13 MeV gamma emission due the ¹⁶O (p, p′)¹⁶ O* ^6.13 reaction is not simulated accurately at higher energies, where the direct reaction processes are of importance.

The evaluated ENDF/B-VII data include only a continuous gamma spectrum with a limited energy resolution. The main gamma line cross-sections that we could extract from these data showed uncertainties similar to some of the other models.

These findings are important to consider in the design of simulations of prompt gamma-ray detection systems. Because experimental data are limited, a complete simulation of prompt gamma-ray detection needs to rely on phenomenological nuclear reaction models. Practical detectors used in clinically realistic scenarios will likely have to deal with low count rates; therefore, the model uncertainties may lead to sub-optimal design choices. The cross-section uncertainties can also affect the reconstruction of the proton range from the detected gamma radiation. The impact of the model uncertainly will depend on the extend in depth in which the gamma production is analysed as well as the gamma energy range considered. In addition, accurate cross-sections are important to study the sensitivity of a particular technique to factors, such as the elemental composition of the tissue being irradiated.

This work may also be used to guide the choice of simulation models and parameters. It is important to note that for each code, several model adjustments were required to obtain reasonable simulations. We recommend to critically assess the nuclear reaction model used and to consider the uncertainties when interpreting the results. If specific resolvable gamma lines are considered, the use of a direct parametrization of experimental data would currently be advisable.

Our results indicate a clear need for additional theoretical and experimental studies of the nuclear reactions of relevance to proton therapy. An updated cross-section evaluation based on the most recent experiment data, and with additional focus on the production of prompt gamma rays and positron emitters, would certainly be desirable. Improved input parameters for the nuclear reaction models most likely can improve the agreement between models and measurements and result in a better predictive power of the models for gamma lines for which no experimental data are currently available. In general, the differences between the models exceeded the reported uncertainties in the available experimental data, which shows room for model improvement even based on current data.

A number of other issues should be noted. We analysed angle-integrated cross-sections, but prompt gamma-ray emission in general is not isotropic. Depending on the quantum properties of the excited nuclear level, various angular dependences are possible. Each gamma line has a different double differential cross-section, which also depends on the proton energy. Also, the Doppler broadening due to nuclear reaction kinematics is a factor that is specific to each nuclear reaction.

To summarize, we have shown that nuclear reaction simulations of prompt gamma-ray emission during proton therapy are subject to considerable uncertainties. Even with our attempts to identify the best models and parameters available, the difference in the total gamma production near the end-of-range of the protons was approximately a factor of 2. These uncertainties should be considered when simulations are performed for the design of gamma detection and proton range reconstruction methods.