Gate/Geant4-based Monte Carlo simulation for calculation of dose distribution of 400 MeV/u carbon ion beam and fragments in water

NUCLEAR PHYSICS AND INTERDISCIPLINARY RESEARCH

Gate/Geant4-based Monte Carlo simulation for calculation of dose distribution of 400 MeV/u carbon ion beam and fragments in water

Hai-Feng Ou，

Bin Zhang，

Shu-Jun Zhao

Nuclear Science and Techniques

Vol.27, No.4

Article number 83

Published in print 20 Aug 2016

Available online 08 Jul 2016

DOI：10.1007/s41365-016-0097-3

55900

The applications of carbon ion beam in tumor therapy have attracted more attention in recent years. Monte Carlo simulation is an important approach to obtain accurate radiotherapy parameters. In this work, a 400 MeV/u carbon ion beam incident on water phantom was simulated with Gate/Geant4 tools. In methods, the authors set up a carbon ion beam source according to the experiment parameters of Haettner E, defined the geometries and materials, set up the physics processes, and designed the means of information collection. In results, the authors obtained the longitudinal dose distribution, the lateral dose distribution, and the relative uncertainty of dose. The dose contributions of all kinds of fragments were calculated detailedly, and compared with the Francis Z’s results. This work is helpful for people’s understanding of the dose distributions produced by carbon ion beam and fragments in water. The simulation method is also significative for radiotherapy treatment planning of carbon ion beam, and it is easy to extend. For obtaining a special result, we may change the particle energy, particle type, target material, target geometry, physics process, detector, etc.

Gatecarbon ion beamfragmentsdose distributionMonte Carlo simulation

1 INTRODUCTION

The applications of proton and heavy ion in tumor therapy have attracted more attention in developed countries. Worldwide, proton and carbon ion treatment devices have been undergoing fast development in recent years. The number of patients treated with proton and carbon ion radiotherapy has been gradually increasing.

In the clinic, the accuracy of radiotherapy treatment planning plays a very important role in radiotherapy quality^[1,2]. At present, Monte Carlo simulation is an important approach to obtain accurate radiotherapy parameters. Carbon ion has better biological effectiveness than proton^[3]. Water is considered as a kind of matter which is very approximate to body tissue, so we proposed a simulation that ion beam was incident on water phantom. Doing this work can help people to understand better the dose distribution of carbon ion beam and fragments in water.

In this work, the Geant4 and Gate were chosen as simulation tools. Geant4^[4,5] is a Monte Carlo simulation tool to simulate energetic particles through materials. It can be used in high energy physics, nuclear physics^[5], accelerator physics, medical physics^[7-10], and space science^[11]. The other tool, Gate^[12-16], an opensource software, is a toolbox based on Geant4. It is mainly used for numerical simulations in medical imaging and radiotherapy. Some articles^[17-19] have showed the applications of Gate in radiation therapy. We adopted the Gate6.2 and Geant4.9.5 in this work.

2 SIMULATION SCHEME

2.1 Carbon ion beam settings

In this work, the settings of carbon ion beam were consistent with the source parameters of Haettner E^[20] experiment. The energy of carbon ion was set to monoenergic 400 MeV/u. The beam was set to Gaussian distribution on the vertical and horizontal direction, and $δ_{x} = δ_{y} = 2.12 m m$ , of which the full width at half maximum(FWHM) was $5 m m$ . The angle scattering parameter of beam was $δ_{a n g} = 1 m r a d$ . The number of carbon ions used for this simulation was $1 \times 10^{5}$ .

2.2 Water phantom settings

As shown in Fig. 1, the water phantom of this simulation was a cuboid, of which the end surface was 20 cm×20 cm square, the length was 40 cm. The material parameter of water phantom was set to G4_WATER. Carbon ion beam was incident vertically on the center of left end surface. Carbon ion beam incident direction was marked as incident center line.

Fig. 1.

Schematic diagram of carbon ion beam incident on water phantom

2.3 Detector geometry

In this simulation, three kinds of detector geometries, thin slice A, thin slice B, and thin strip C, were used for collecting information in water phantom, of which the geometric sizes were 200mm×200mm×1mm, 0.5mm×200mm×400mm and 0.5mm×200mm×1mm, respectively. Specially, the thin strip C was in a slice A. A thin slice A can be divided into 400 thin strip C. The thin slice A was used for collecting the longitudinal dose information of water phantom. The thin slice B was used for collecting the lateral dose information of water phantom. The thin strip C was used for collecting the lateral dose information of thin slice A in different depth. The material parameters of three geometries were also set to G4_WATER. As shown in Fig. 1, the distance between the center of thin slice A and the incident point was set to $d$ .

2.4 Gate method

In Gate, all the things of simulation must be written in a script file with mac as suffix. The script file included the several aspects: source and particle management, defining geometry and material, setting up the physics, actor management. The source, particle, geometry and material have been described ahead A.

The physics processes of this simulation were set to default settings of particle radiotherapy in Gate. The settings were contained in two files. The first file, physicslist_EM_std.mac, included the standard Electromagnetic processes for leptons. The second, physicslist_HAD_std.mac, included the Electromagnetic processes for hadrons and Hadronic processes for hadrons.

Actors are the tools allowed to interact with the simulation, which are used for collecting information during simulating. In this work, DoseActors was used to record the particle dose distribution; PhaseSpaceActors was used to record the particle type, energy, and location. In addition, SecondaryProductionActors was used to record the secondary particles, and particleFilter was used to filter particles.

3 RESULTS AND DISCUSSION

3.1 Total dose of carbon ion beam

3.1.1 Longitudinal total dose of carbon ion beam

The incident carbon ions interacted with water, and produced a variety of fragments. These fragments included ionized electrons, photons, neutrons, and H, He, Li, Be, B, C, N, O, F, Ne elements (including their isotopes). Carbon ions and all fragments transfered in water and produced dose deposits, which formed the total dose of carbon ion beam. In this simulation, the Bragg peak position depth of 400 MeV/u carbon ion beam in water was 274.5 mm (corresponding to the depth value of the position of peak height 80%). This is consistent with the Haettner E’s experimental result $274.7 \pm 1.0$ mm^[20].

The dose distributions are shown in Fig. 2(a). In Fig. 2(a), the solid line is total dose distribution of carbon ion beam, the dashed line is dose distribution of primary ¹²C ion, and the dotted line is dose distribution of all fragments. The primary ¹²C ion dose has a minimum before the Bragg peak. Fragments dose reaches its maximum at 252mm depth before the Bragg peak. After the Bragg peak, the total dose line and fragments dose line are almost entirely overlapping. This is because the primary ¹²C ion contributes almost nothing after the Bragg peak, the tail of total dose is primarily due to the contribution of fragments.

Fig. 2.

(Color Online) (a)Relative dose distributions of carbon ion beam and fragments in water phantom (with the Bragg peak value of total dose as normalization factor) (b) Relative uncertainty distributions of total dose, primary ¹²C dose and fragments dose (c) Relative uncertainty distribution of primary ¹²C dose

Fig. 2(b) is the longitudinal distribution of relative uncertainty, where the solid line indicates total dose, the dashed line indicates primary ¹²C ion dose, and the dotted line indicates fragments dose. The relative uncertainty line of fragments dose has a minimum before the Bragg peak. After the Bragg peak, the relative uncertainty lines of total dose and fragments dose are almost overlapping. Fig. 2(c) shows the whole distribution of relative uncertainty of primary ¹²C ion dose.

3.1.2 Lateral total dose of carbon ion beam

The lateral dose distributions are shown in Fig. 3(a). In Fig. 3(a), the transverse coordinate 0 mm is the transverse center of water phantom. The solid line, the dashed line, and the dotted line represent total dose, primary ¹²C ion, and all fragments respectively. It can be seen that the lateral dose distribution curve of primary ¹²C ion, is narrower than the other two curves, which indicates the scattering of primary ¹²C ion is more inconspicuous than fragments during transmission. The lateral total dose and lateral fragments dose are almost overlapping when the absolute value of abscissa is greater than 5mm. The dashed line and dotted line intersect at a point where the lateral coordinate is approximately equal to ±1.6 mm. In the intersection point, the lateral dose of primary ¹²C ion and the lateral dose of fragments are equal. These dose distributions are consistent with spatial fragments distributions published by Matsufuji N^[21], Kusano Y^[22], and Braunn B^[23].

Fig. 3.

(Color Online) (a) Lateral relative dose distributions of carbon ion beam and fragments in water phantom (with lateral total dose maximum as normalization factor) (b) Relative uncertainty distributions of lateral total dose, lateral primary ¹²C dose and lateral fragments dose

Fig. 3(b) is the lateral distribution of relative uncertainty. The solid line, the dashed line, and the dotted line represent total dose, primary ¹²C ion and all fragments respectively. It can be seen from the graph that the solid line and dotted line are almost overlapping when the absolute value of abscissa is greater than 5mm, and the value of relative uncertainty is approximately equal to 0.01.

3.1.3 Lateral total dose in water slices

Four detector slices, such as slice A of Fig. 1, were arranged at the longitudinal direction 25 mm, 150 mm, 274 mm, and 300 mm depth of water phantom, respectively. These were used to collect the lateral dose information of carbon ion beam at the four different depths.

The simulation results are shown in Fig. 4. It can be seen from Fig. 4(a) and Fig. 4(b) that the lateral dose line at 25 mm depth is narrow and high, and the relative dose at the center (0 mm abscissa position) is about 3.03. That is to say that the dose of incident center line at 25 mm depth is 3 times of lateral total dose maximum of carbon ion beam. In addition, the lateral dose line at 25mm depth is the steepest descent when it extends from center to both sides. The other three lines of 150 mm, 274 mm, and 300 mm depth are rising in turn when they extend from center to both sides. This is just because of particle scattering during transmission.

Fig. 4.

(Color Online)Lateral dose distributions of carbon ion beam in different depth of water phantom (with the lateral total dose maximum of carbon ion beam as normalization factor) (a) The vertical axis is logarithmic. (b) The vertical axis is linear.

More detector slices were arranged to collect detailed information of dose distribution at different depths. The dose distribution of incident center line is shown in Fig. 5. The relative doses of incident center line at 5mm, 25mm, 100mm, 150mm, 225mm, 274mm, and 300mm depth are 3.03, 2.90, 1.65, 0.92, 0.52, 1.22, and 0.03 respectively.

Fig. 5.

Dose distribution of incident center line in water phantom (with the lateral total dose maximum of carbon ion beam as normalization factor)

3.2 Dose of fragments

3.2.1 Longitudinal dose of fragments

In this simulation, a variety of fragments were considered. These fragments included electrons, photons, neutrons, and H-, He-, Li-, Be-, B-, C-, N-, O-, F-, Ne elements (including their isotopes). As shown in Fig. 6, each fragment forms its own dose distribution in water phantom. The thick solid line indicates total dose distribution of all fragments. Others indicate the dose distributions of H-, He-, Li-, Be-, B-, C isotopes (except ¹²C) and electron respectively. Because the doses formed by N-, O-, F-, Ne isotopes and γ are so small, their dose curves are not shown in Fig. 6. From Table 1, we know the dose contribution of N-, O-, F-, Ne isotopes and γ in the range (1-400 mm) are between 0.1% to 0.00025%. These values are really very small.

Dose contributions of all kinds of fragments in the water phantom

Fragments	Dose contribution（%）
	This work			Francis
	1-400mm	1-275mm	276-400mm	1 to unknown mm
¹²C	58.39776	65.85672	0.83115	64^a
H	8.73729	6.86052	23.22173	14^b
He	9.22231	5.11578	40.91557	13^c
Li	2.19841	1.41168	8.27021	1.7
Be	2.46668	1.78520	7.72622	1.3
B	5.81482	4.83029	13.41321	4.2
C（except ¹²C）	5.08843	5.73208	0.12090	-
N	0.10605	0.10560	0.10947	-
O	0.09918	0.09320	0.14529	-
F	0.00243	0.00245	0.00227	-
Ne	0.00055	0.00058	0.00030	-
γ	0.00025	0.00026	0.00017	-
e^-	7.82327	8.16501	5.18574	-
Neutron	0	0	0	-

Francis Z data description:^a: Carbon element dose, contains all the C isotopes dose.^b: Contains only the ¹H(proton) dose.^c: Contains only ⁴He(α) dose.

Fig. 6.

(Color Online)Dose distributions of all kinds of fragments in water phantom (with the Bragg peak value of total dose as normalization factor)

As can be seen from Fig. 6, the dose curves of H-, He-, Li-, Be-, B isotopes reach their peaks nearby the Bragg peak position. The dose curve of C isotopes (except ¹²C) reaches its peak at 252 mm depth, and the dose curve of all fragments reaches its peak at 252 mm depth.

Electron dose curve is also very special. It begins to fall sharply at about 250 mm depth, and becomes relatively flat again after the Bragg peak. It also can be seen from Fig. 6 that the doses of H, He, B, C, and e^- maintain a relatively high level before the Bragg peak, while the doses of Li, and Be are relatively low. After the Bragg peak the dose of He isotopes remains high level, while the dose of B isotopes falls steeply.

3.2.2 Lateral dose of fragments

The lateral dose distributions of the various fragments in water phantom are shown in Fig.7. It can be seen from Fig. 7 that the lateral dose curves of H and He decline relatively flat when they extend from center to both sides. This indicates that the scattering of H and He is obvious. The lateral dose curves of downmost N and O decline steeply when they extend from center to both sides. This indicates that the scattering of N and O is not obvious. Other fragments, such as Li, Be, B and C, their scattering characteristics are between H and He and N and O. It suggests that the element with greater atomic number is more difficult to scatter.

Fig. 7.

(Color Online)Lateral dose distributions of the various fragments in water phantom (with the lateral total dose maximum of carbon ion beam as normalization factor). The solid line shows the lateral total dose distribution of all fragments, the others show respectively the lateral dose distributions of H, He, Li, Be, B, C, N, O, e^-. Since the doses of F, Ne and γ are very small, their curves aren’t shown in figure.

In Fig. 7, the electron is not in line with the above law. The lateral dose curve is not flat when it extends from center to both sides. This is because the electron is affected mainly by the ionization interaction, and the electron dose distribution is affected by the comprehensive distribution of carbon ions and fragments.

3.3 Dose contributions of fragments

The dose contributions of all kinds of fragments in water phantom are shown in TABLE 1.

The right column of TABLE 1 shows the data obtained by Francis Z^[24]. Francis Z gave the dose contributions of C (¹²C and all other C isotopes), ¹H, ⁴He, Li, Be, and B. The dose contributions of other elements or particles weren’t listed in his article. He only gave that the sum of dose contributions of other elements and particles was not more than 1.7%.

In this work, the dose contribution of carbon element (¹²C and all other C isotopes) in the range (1-400 mm) is 63.5%. It is similar with the Francis Z’s result 64%. Comparing the data of this study and Francis Z, we find that the differences of dose contributions of Li, Be and B are unobvious. While the differences of dose contributions of H, He and e^- are obvious. In addition, we can see that the dose contributions of N, O, F, Ne, and γ are very tiny. Especially, the neutron dose contribution is zero. This is because in Geant4 neutral particles almost do not deposit any dose directly but mostly indirectly.

In TABLE 1, we also list the dose contributions of various fragments in the range (1-275mm) and range (276-400mm). Comparing the data of these two ranges, we can see that some change hugely, while others change slightly.

The dose contributions of some fragments of this work are consistent with the Francis Z’s^[24], while others have the differences. In our opinions, the reasons which lead to the differences include the following four aspects: simulation tools, physics processes, calculated particles, and phantom size.

In simulation tools, this work used the Gate6.2/Geant4.9.5.1, while Francis Z used the Geant4.9.5.

In physics processes, this work used the default physics settings of Gate. The first settings file, physicslist_EM_std.mac, included the standard electromagnetic processes for leptons. The second file, physicslist_HAD_std.mac, included the electromagnetic processes for hadrons and Hadronic processes for hadrons. While in Francis Z’s work, ions interactions are taken into account using the inelastic processes, e.g. ionizations, and the fragmentation process is simulated according to the quantum molecular dynamics (QMD) model.

In calculated particles, this work included γ, e^-, neutron, and H-, He-, Li-, Be-, B-, C-, N-, O-, F-, Ne isotopes. While Francis Z calculated the H-, He-, Li-, Be-, B-, C isotopes, and whether the dose contribution of e^- was considered in his study can’t be judged.

In phantom size, the dimension of water phantom in this simulation was 20cm×20cm×40cm. While Francis Z. didn’t describe the special size of water phantom in his calculation; he only said it was an infinite water phantom.

4 SUMMARY

As mentioned above, a 400 MeV/u carbon ion beam incident on water phantom was simulated with Gate/Geant4 tools. The carbon ion beam source was set up according to the experiment parameters of Haettner E. The geometries, materials, physics processes and detectors were defined or designed respectively.

In this work, the authors obtained the longitudinal total dose distribution, the lateral total dose distribution, and the relative uncertainty of total dose. In a similar way, the longitudinal dose distribution- and the lateral dose distribution of fragments were shown. The dose contributions of all kinds of fragments were calculated detailedly, and compared with the Francis Z’s results.

This work is helpful for people’s understanding of the dose distributions produced by carbon ion beam and fragments in water. The simulation method is also significative for radiotherapy treatment planning of carbon ion beam, and it is easy to extend. For obtaining a special result, we may change the particle energy, particle type, target material, target geometry, physics process, detector, etc.

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