Analysis of Bragg Curve Parameters and Lateral Straggle for Proton and Carbon Beams
Fatih Ekinci, Erkan Bostanci, Ozlem Dagli, Mehmet Serdar Guzel
1 Analysis of Bragg Curve Parameters and Lateral Straggle for Proton and Carbon Beams
Fatih EKİNCİ , Erkan BOSTANCI , Özlem DAĞLI and Mehmet Serdar GÜZEL [email protected], [email protected], [email protected], [email protected] down, the possibility of ionization of the atoms in the environment increases and the maximum LET is transferred to the depth where the ionization events are maximum. All this process loss is represented by the Bragg curve [5-6]. The Bragg curve, calculated using the Bethe-Bloch equation, shows that this decrease in the energy of the particle increases along the way and reaches the maximum energy loss at the end of the range. It appears that the absorbed dose decreases sharply after the peak due to the very small number of particles reaching the back of this peak. Bragg curve; It consists of the Bragg peak, plateau, FWHM (Full Width at Half Maximum), entrance zone and Penumbra [7-8]. Heavily charged particles do not travel in a straight line through the target. There are deviations in their direction due to ionization and collisions in atomic scale. Lateral straggle is a measure of the amount of scatter from the direction of each ion within the target. Lateral straggle occurs mostly at the Bragg peak [8-9]. This concept determines which particle should be used in the treatment of tumors close to critical tissues in hadron therapy. To the best of the authors’ knowledge, it was observed that there is a gap in the comparison of the lateral straggle profiles of protons and carbon ions used in heavy ion therapy. The goal of our study is to find out which of these two particles works better. In this sense, Bragg curve parameters were compared as well as the values of lateral straggle. Thus, effort was made in order to determine which particle will be preferred in tumor treatment close to critical points where lateral straggle is very important. In this study, the Bragg curves of protons with 80, 100, 120 and 140 MeV energies and carbon bundles with 1.6, 2.4 and 3.0 GeV energies in water were obtained using the TRIM Monte Carlo (MC) simulation software and compared with the literature. After the results, were observed to be compatible with the literature, the Bragg curve parameters and lateral straggle of proton and carbon beams in the water phantom were calculated and compared with each other. The rest of the paper is structured as follows: Section 2 describes the approach used in the study, followed by Section 3 where the findings are analyzed. A thorough discussion is presented in Section 4 and finally the paper is concluded in Section 5. 2. Methods MC method is a statistical simulation technique developed for solving mathematical problems where finding an analytical solution is hard. Simulation systems developed on this technique follow the traces of each particle traveling through matter step by step, based on the assumption that the quantities describing particle interactions have certain probability distributions. Quantities such as flux, energy loss and absorbed dose are recorded for many particles and average values for these distributions are computed [10]. TRIM (TRansport of Ions in Matter) simulation software developed using MC technique has the ability to calculate all interactions of ions within the target. The type, energy, target phantom type and shape, parameter to be calculated, particle and probability number of ions can be selected from the TRIM screen. The program records all calculation fields and can view as required [8]. As with photon radiotherapy, the most important problem for hadron therapy is whether the desired dose can be administered to the patient. For this, before the patient is treated, an attempt is made to determine and calibrate the correct dose using the water phantom [11]. Water is the most important medium used in medical physics. Reliability of stopping power calculations for water and accurate calculation of dose distribution mean reliable treatment doses for patients. This is due to the fact that the main component of the human body is considered water. In hadron therapy applications, as in photon radiotherapy, dose distribution is controlled by tissue equivalent phantoms (such as water phantoms). In this respect, the shape and design of the phantom structure to be used are important. There are phantom types used for different body planning in literature [12]. In this study, a cylindrical water phantom was employed.
3. Findings In order to test the accuracy of the calculations in order to find the appropriate doses of protons and carbon beams in the water phantom, the Bragg curves of 80,100, 120 and 140 MeV energy proton beams and 1.6, 2.4 and 3.0 GeV energy carbon beams normalized to the maximum dose in the water phantom were compared with the literature [ 13-23]. By comparison, an average difference of 3.37% for the two particles was observed is generally not significant and is within acceptable limits (<5%) in medical physics. The deviations above the acceptable difference are within acceptable limits in the literature considering the inhomogeneity effects and Monte Carlo-based probabilities. The energies of the protons and carbon beams were chosen at energies that would have the same Bragg peak positions. According to the Bethe–Bloch equation, the penetration depth (R) of particles with the same kinetic energy is the ratio of the mass number (A) to square of the atomic number (Z); namely R ∼ A/Z . Therefore, one can expect different range values for Protons (A = Z = 1) and carbon particles (A = 12, Z = 6) [24]. Looking at the Bragg curves of these particles in the water phantom (Table 1 and Figure 1), carbon bundles require 12 times more energy for achieving the same range. The input LET was realized as an average of 0.0716 eV / A in the proton beam and an average of 1.6260 eV/A in the carbon beam. As the energy increased, the input LET decreased within two particles. The Bragg peak amplitude (Table 1) was found to be an average of 12.4772 eV/A in the carbon beam and 0.3563 eV/A in the proton. The carbon particle Bragg peak transferred an average of 35 times more LET. The average FWHM value (Figures 1 and 2) was found to be 1.5 cm in the proton and 0.48 cm in the carbon. In penumbra value, the proton was found to be about 0.8 cm, while it was found to be about 0.32 cm in carbon. Table 1.
Bragg peak positions, peak amplitudes and percentage differences of protons and carbon beams
Energy Proton Energy Carbon (MeV) Bragg peak (cm) Peak Amplitude (eV/A) (MeV/u) Bragg peak (cm) Peak Amplitude (eV/A)
80 5.2 0.4130 150 5.3 11.62910 100 7.6 0.3877 183 7.5 12.67340 120 10.4 0.3291 217 10.1 13.41200 140 13.6 0.2953 258 13.6 12.19430
Figure 1.
Bragg curves for proton and carbon beams
LET ( e V / A ) z, cm Proton
80 MeV
100 MeV
120 MeV140 MeV
LET ( e V / A ) z, cm Carbon
150 MeV/u183 MeV/u
217 MeV/u
283 MeV/u Figure 2.
FWHM for proton and carbon beams Lateral straggle (Table 2) was realized as an average of 1.878 mm in the proton and 0.558 mm in carbon. As the energy increased, the lateral straggle increased by 0.470 mm, i.e. i.e.
Table 2.
Lateral straggle difference for proton and carbon beams
Energy (GeV/u) Proton (mm) Energy (GeV/u) Carbon (mm) Difference, mm Difference, %
80 1.01 150 0.33 0.68 67 100 1.55 183 0.49 1.06 68 120 2.17 217 0.61 1.56 72 140 2.78 250 0.80 1.98 71
Mean difference 1.32 70
Figure 3.
Change in the lateral straggle vs energy in water phantom 4. Discussion The physical and radiobiological properties of heavy ions provide a superior dose distribution compared to photon radiotherapy, thus minimizing the dose delivered to normal tissues. Thus, the risk of secondary cancer is significantly reduced [25]. In photon radiotherapy, there are risks from side effects due to the high input dose and a non-zero output dose. In contrast, proton therapy has a significantly lower input dose and little output dose, which reduces damage to healthy tissue N o r m a li ze d LET z, cm
Proton-Carbon
C-183 MeV/uP-100 MeV/uC-258 MeV/uP-140 MeV/u y = 0,0297x - 1,384R² = 0,9991 y = 0.0046x - 0.3603R² = 0.9929 L a t e r a l S t r a gg l e ( mm ) Energy (MeV)