1 Introduction
Nowadays, hadron therapy is making immense contribution in the treatment of cancers. Hadrons have different dosimetric characteristics concerning photons and electrons in radiation therapy. In conventional radiotherapy, such as photon therapy, most of the photon’s energy deposits near the skin surface. However, in proton therapy, energy deposition increases proportionally reaching a maximum at the Bragg peak depth. The main benefits of proton therapy are the sharp lateral penumbra and fast dose fall at the end of the proton beam range [1-7]. It can target the tumors with high precision, reducing the damage to the healthy surrounding tissues and the risk of secondary cancers [8]. Proton therapy is used to treat cancers related to the central nervous system, eye, head and neck, lung, liver, and prostate. Targeting liver tumors must be carefully done because the radiations can damage other organs such as stomach, kidneys, and small intestine, as well as the heart, lungs, and spinal cord [9, 10]. Either a high dose to a small area or a low dose to a large area of these critical organs can lead to considerable debilitating consequences. Many studies have shown an increased rate of secondary cancer in healthy tissues around tumor areas due to radiation therapy. Proton therapy, owing to a low dose to the surrounding normal tissues, poses a low risk of radiation-induced secondary cancer [11]. After passing charged particles, like protons, through tissues, they slow down and lose their energy during atomic or nuclear interactions. The maximum interaction occurs at the end of the proton beam range because of maximum energy transfer and dose deposition in the target area [12]. The Bragg peaks are not wide enough to cover all the treatment targets. A Spread-Out Bragg Peak (SOBP) is generated using a set of beams with different energies, which delivers the dose to the whole treatment volume [13-15]. Beside Coulomb interactions of proton beam with atomic electrons and nuclear elastic scattering, passing of protons through the tissues lead to products of secondary particles, such as neutrons and photons [16, 17]. Owing to the long ranges of secondary particles, their energies can be deposited in the other organs [18, 19]. Generally, in hadron therapy, the secondary particles will be produced in the delivery system placed before they enter the patient’s body. The production of secondary particles depends on the geometry and materials of the proton beam delivery system. Another way to produce secondary particles is the interactions of incident particles with the patient’s body tissues [20]. Secondary particle dose due to the passive scattering method is greater than the pencil beam scanning method under similar treatment conditions [21]. The study of secondary neutrons in proton therapy has received significant attention in different areas of investigations [22]. Agosteo et al. estimated the dose of secondary particles in proton therapy systems by simulation. Their results indicated that the ratio of the dose of secondary particles in passive systems to the pencil beam scanning systems is approximately 10 [23]. Zheng et al. experimentally measured the contribution of secondary neutrons based on parameters such as aperture size, proton range, and proton scanning area for a uniform scanning system [24]. Brenner et al. calculated the secondary neutron dose using patient-specific aperture for 235 MeV proton beams in a passive scattering system [22]. In this study, the proton energy deposition in the liver tumor using Oak Ridge National Laboratory-Medical Internal Radiation Dose (ORNL-MIRD) phantom is calculated. The SOBP was created to extend the pristine narrow peaks to cover the target volume. The flux of secondary particles and two-dimensional dose distribution for protons, neutrons, and photons are determined. By using MCNPX 2.6, the total received doses of proton, photon, and neutron in non-involved organs are calculated.
2 Materials and methods
This section is divided into two parts. The first part introduces the Monte Carlo simulation of the human phantom, and the second part explains the dose calculations and SOBP construction to cover the liver tumor.
2.1 Monte Carlo simulation
A liver tumor in an ORNL-MIRD phantom was simulated. Monoenergetic proton pencil beams with 2 MeV steps were considered perpendicular to the phantom. Material compositions of the liver are presented in the International Commission on Radiation Units and Measurements (ICRU) report 44 [25]. Fig. 1 presents a schematic view of the simulated phantom. The elemental compositions of the liver and their fractions are listed in Table 1.
| Weight fraction | Element |
|---|---|
| 10.454 | H |
| 22.663 | C |
| 2.490 | N |
| 63.525 | O |
| 0.112 | Na |
| 0.013 | Mg |
| 0.030 | Si |
| 0.134 | P |
| 0.204 | S |
| 0.133 | Cl |
| 0.208 | K |
| 0.024 | Ca |
| 0.005 | Fe |
| 0.003 | Zn |
| 0.001 | Rb |
| 0.001 | Zr |
| 1.04 g/cm3 | Density |
In our simulation, a spherical shape tumor with 2 cm radius at a distance of - 14 cm to - 10 cm with a composition similar to that of the liver tissue has been considered (the negative value comes from the liver’s position in the ORNL-MIRD phantom). The proton beam is a circular disk of 2 cm in diameter in the direct irradiation. The source was placed at a distance of 1 cm from the phantom. Firstly, monoenergetic proton beam was used to calculate Bragg peaks for different energies. Next, the SOBP energies and their probabilities were used as particle beams to calculate the flux of secondary particles and their doses. The proton energy deposit was matched as a function of depth in rectangular voxels, each 1mm×1mm×1mm.
2. 2 Construction of SOBP and dose calculation in different organs
The Bragg peak is not broad enough to cover the whole treatment volume. Therefore, an appropriate SOBP has to be created to obtain a homogenous depth dose profile. The SOBP was created by adding different Bragg curves and calculating appropriate weighting factors. The tumor treatment energy range was determined, and the weight of each pristine peak was calculated based on a set of solved linear equations [15]. The SOBP curve, in this study, is the sum of 16 Bragg curves. If these curves are denoted as P1 to P16, and the SOBP curve is Pm, then mathematically, the relationship between the SOBP curve and Bragg curves can be described as follows:
where A1 to A16 denote the weighting factors. In this study, proton, neutron, and photon fluencies were calculated on the surface of the liver tumor. To verify dose distribution in the tumor and surrounding healthy tissue, a two-dimensional dose distribution was created using mesh tally. Finally, the dose produced in proton and the secondary particles inside the different organs were determined.
3 Results and discussion
3.1 Depth dose and SOBP construction
For SOBP construction, the first step is to find a flat dose region in the treatment volume. To achieve this, after establishing peak depths in different energies, appropriate beam energies can be found that lead to approximate flat dose distribution in the desired volume. The range of proton beam energies and the Bragg peak positions are shown in Fig. 2. The minus sign for the depth values depicts the liver coordinates in the ORNL-MIRD phantom.
The calculated weighting factors corresponding to the different proton energies are listed in Table 2. The constructed SOBP based on the weighting factors listed in Table 2 is shown in Fig. 3.
| Energy (MeV) | Weighting factor | Energy (MeV) | Weighting factor |
|---|---|---|---|
| 120 | 1 | 104 | 0.108 |
| 118 | 0.387 | 102 | 0.098 |
| 116 | 0.270 | 100 | 0.0937 |
| 114 | 0.225 | 98 | 0.078 |
| 112 | 0.190 | 96 | 0.088 |
| 110 | 0.151 | 94 | 0.073 |
| 108 | 0.134 | 92 | 0.053 |
| 106 | 0.127 | 90 | 0.066 |
The characteristics of the constructed SOBP based on the beam parameters determined by ICRU (2007) [26] are described in Table 3.
| d'90 (cm) | DDF (cm) | m'90 (cm) | Target length (cm) | Beam parameters |
|---|---|---|---|---|
| 10.09 | 0.17 | 4.29 | 4.62 | Values |
The definition of these parameters is as follows:
1- The depth of penetration (d'90) is the depth along the beam profile axis to the distal 90% point of the maximum dose.
2- The distal dose fall-off (DDF) is the decreased dose interval from 80% to 20% of the maximum dose.
3- The SOBP length (m'90) is the interval between the distal and proximal 90% point of the maximum dose.
4- Target (or treatment) length is the distance between the DDF length from 90% proximal side of maximum dose value and twice the DDF length from the distal 50% of maximum dose value.
Fig. 4 shows the lateral dose profile in the middle depth of the SOBP. A larger lateral scattering creates a higher absorbed dose in healthy tissues around the liver tumor.
From Fig. 4, the values for full width at half maximum (FWHM) and the penumbra (80% – 20%) were determined to be approximately 4 and 0.14 cm, respectively. The penumbra is defined as the width length of the dose band lateral to the field edge when the dose decreases from 80% to 20% for a collimated scattered proton beam. This parameter depends on the design of the beam defining and collimating systems. Here, the sharp lateral penumbra of a proton beam is one of the major advantages [27].
3.2 Secondary neutrons and photons
Presence of non-primary particles is attributed to the interactions between the primary protons or that between the secondary particles. The flux curves of the secondary particles, such as neutrons and photons, calculated using Tally 2 on the surface of the tumor are shown in Fig. 5 and Fig. 6.
The neutron spectra depend on the energy of the primary beam and have relatively larger peaks at high-energy levels. Increasing the incident beam energy leads to higher energies for the neutron spectrum.
In the photon spectrum (Fig. 6), the highest peak appears at 4.44 MeV corresponding to the excited 12C nucleus [28].
3.3 Two-dimensional dose distribution
Two-dimensional (2D) dose distributions for neutrons and photons were plotted using mesh tally in MCNPX, and their results are depicted in Fig. 7 and Fig. 8. Figure 7(a) shows the isodose curves for neutrons. The unit of dose is ((Sv / h) / (particle / cm2/s)). Figure 7 (b) shows a projection of two-dimensional dose distribution (Fig. 7 (a)) as a function of depth.
It can be noted that the neutrons deposit most of their energies outside the tumor (less than -14 cm). Fig. 8 (a) presents the isodose curves for photons. Fig. 8 (b) shows the projection of two-dimensional dose distribution (Fig. 8 (a)) as a function of depth.
Fig. 8 shows that the photon dose is approximately concentrated inside the tumor and some parts of them are in the healthy tissue. The photon dose peaks are at the edge of the tumor (-14 cm) and some of their parts deposit their energies in the normal tissue.
3.4 Determination of proton, neutron, and photon doses in different organs
The deposited dose in the tumor and other non-involved organs of the body were calculated using F6 tally and the results are summarized in Table 4.
| Organ name | Proton×10-10 | Neutron×10-14 | Photon×10-14 | |
|---|---|---|---|---|
| 1 | Tumor | 1.49 | 1.88 | 1.06 |
| 2 | Liver | 4.06 × 10-2 | 2.94 × 10-1 | 1.4 × 10-1 |
| 3 | Rib cage | 3.68 × 10-3 | 3.18 × 10-2 | 2.03 × 10-2 |
| 4 | Trunk skin | 1.54 × 10-3 | 1.5 × 10-2 | 1.27 × 10-2 |
| 5 | Trunk | 4.13 × 10-4 | 1.68 × 10-2 | 9.29 × 10-3 |
| 6 | Gall bladder | 8.5 × 10-5 | 3.09 × 10-1 | 8.89 × 10-2 |
| 7 | Heart & contents | 4.84 × 10-5 | 1.82 × 10-1 | 9.25 × 10-2 |
| 8 | Kidney | 2.32 × 10-5 | 8.48 × 10-2 | 3.07 × 10-2 |
| 9 | Stomach | 2.23 × 10-5 | 7.89 × 10-2 | 2.2 × 10-2 |
| 10 | Adrenals | 2.26 × 10-5 | 7.43 × 10-2 | 2.4 × 10-2 |
| 11 | Pancreas | 2.09 × 10-5 | 6.95 × 10-2 | 1.98 × 10-2 |
| 12 | Right lung | 5.39 × 10-6 | 2.07 × 10-2 | 1.69 × 10-2 |
| 13 | Left lung | 3.62 × 10-6 | 1.22 × 10-2 | 5.43 × 10-3 |
| 14 | Breasts | 2.28 × 10-6 | 8.43 × 10-3 | 7.46 × 10-3 |
| 15 | Brain | 8.23 × 10-8 | 3.38 × 10-4 | 6.99 × 10-4 |
The results show that some of the organs that are far from the target, such as the brain, will receive a small amount of the dose. The ratios of the dose in the different organs were calculated based on the dose delivered to the tumor and are shown in Fig. 9.
The normal tissue of the liver received a dose that was more than the other organs, although this ratio was just 0.01 of the delivered dose to the tumor. Fig. 9 shows that the dose due to the protons in the other organs is more than the neutron and photon doses.
4 Conclusion
In proton therapy, a large amount of the dose is delivered inside the tumor, while the surrounding healthy organs are preserved. In this study, a typical liver tumor in a human ORNL-MIRD phantom was used. To cover the tumor volume, an SOBP was created by using optimized weighting factors and the best proton energy interval was 90 MeV – 120 MeV for the complete coverage of the liver tumor. The flux curves of the secondary particles (neutron and photon) were calculated on the tumor surface. With increased incident beam energy, higher energies were seen in the neutron spectrum. The photon flux due to the particle interactions had a range up to 10 MeV and for neutron flux, this range was up to 100 MeV. There were certain peaks in the photon flux histograms, which corresponded to excited nuclei such as C. In 2D dose distributions for different particles, neutron dose value was more than the photon dose value, and the maximum dose of the neutron was in the healthy tissue. The total absorbed dose due to the proton, photon, and neutron was calculated in the tumor and 14 non-involved organs. Most of the organs were under radiation exposure, and the organs such as the heart and pancreas, which are closer to the liver, received a higher dose than the others. The ratios for gall bladder, heart, kidney, stomach, pancreas, and right lung were approximately 2.34 ×10 -5, 5.1 ×10 -5, 2.18 ×10 -5, 2.01×10 -5, and 16 ×10 -6, and approximately 0.01 for the healthy tissue of liver. The ratios for the organs far from the liver were quite small, for example, in the brain, the ratio was 1.25 ×10 -7. The results indicated that the dose of particles in the non-involved organs, in liver proton therapy, was minimal.
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