In the study of a proton interaction with a water phantom, understanding the fundamental mechanisms behind energy loss is essential. Protons, as charged particles, primarily lose the energy through electromagnetic interactions, particularly ionization and excitation of atomic electrons.

When protons are injected in a water phantom, their energy loss can be calculated using the Bethe-Bloch equation, which is the standard formula for describing the ionization energy loss of charged particles in matter. According to PDG, the energy loss per unit length, dEdx, for a proton passing through a medium like water, follows the equation:

Where NA is Avogadro's number, re is the classical electron radius, me is the electron mass, c is the speed of light, Z and A are the atomic number and atomic mass of the medium (water), z is the charge of the proton, β is the proton's velocity relative to the speed of light, Tmax is the maximum kinetic energy transfer in a collision and I is the mean excitation potential of the medium[1].

This equation shows that as the proton slows down in the water, its energy loss increases, reaching a maximum near the end of its path, leading to the Bragg peak. This phenomenon is essential in proton therapy, where precise control of the proton beam allows for maximum energy deposition at the tumor site with minimal damage to surrounding healthy tissues. Figure 1 shows the stopping power of a proton in water. A graph in Fig. 1 was achieved by a calculation tool provided by International Commission on Radiation Units and Measurement [ICRT 90]. The conditions under which the data were obtained are as follows: Using the PSTAR program provided by ICRU 90, which calculates stopping power and range tables for protons in various materials, and setting the material to water, results similar to those shown in the Fig. 1 can be obtained. Energies are given in MeV, and be in the range from 1 keV to 10000 MeV. As shown in this Fig. 1, the stopping power value for the proton energy of 100 MeV simulated in this study is 7.289​MeV/cm2/g.

Figure 1. (Color online) Mass stopping power for a proton particle.

In addition to ionization, moving protons in water can also produce secondary particles, such as electrons from ionization and neutrons from nuclear interactions.

A proton beam therapy can be categorized as a part of the high energy radiation treatment to tumor in radiation therapy, particularly because of its precision in delivering a high dose of radiation to a tumor while sparing surrounding healthy tissues[2]. This precision is due to the Bragg peak, where the proton beam deposits its maximum energy just before it comes to a stop[3]. Proton therapy is especially beneficial for treating tumors located near critical structures in the body or in children, where minimizing damage to healthy tissue is crucial[4]. This study aims to evaluate the depth-dose distribution of a proton beam using simulations to understand their effectiveness better and explore potential improvements in clinical applications. Figure 2 shows the Bragg peak and Spread Out of Bragg Peak (SOBP) representation of a proton beam. A graph in Fig. 2 redrawn by the method based on Bortfeld & Schlegel (1996), who derived an analytical solution[5]. What we know about proton therapy is largely based upon simulation studies that investigate how interact with water phantom using Particle and Heavy Ion Transport code System (PHITS).

Figure 2. (Color online) The dose-depth curve of proton beam with a comparison of Bragg peak and SOBP.

PHITS is a powerful software used to simulate the movement of particles, such as neutrons, protons, and electrons, through different materials[6, 7]. Also, it is essential in areas like radiation protection, medical treatments involving radiation, and space exploration[6, 7]. PHITS helps medical physicists understand how radiation behaves in various environments, from shielding materials to human tissue[6, 7]. It’s particularly useful in designing protective barriers against radiation and calculating the safe and effective dose of radiation for patients in medical treatments[6, 7]. The software can also be used to study radiation in space, helping to protect astronauts during space missions. PHITS includes many models and data libraries that describe how particles interact with materials, and it offers tools to visualize the results of these simulations. Because of its reliability and versatility, PHITS is widely used in both scientific research and practical applications related to radiation. When a proton beam is directed into a water phantom, which is often used to simulate human tissue, several important physical processes occur. These processes can be outlined as follows:

• (i)

  Proton Incidence

  Protons are introduced into the water phantom with specific energy and direction. As charged particles, protons interact with the atoms in the water, gradually losing energy as they travel. In PHITS simulations, the user can define the proton’s initial energy, entry point, and angle to accurately model different experimental or therapeutic scenarios [6].

• (ii)

  Electromagnetic Interactions

  Protons primarily lose energy through electro-magnetic interactions with the electrons in water molecules. This can result in ionization, where electrons are ejected from atoms. These freed electrons, known as secondary particles, can further interact with the surrounding medium. As the proton slows down, its energy loss increases sharply, leading to the phenomenon known as the Bragg Peak and Energy Loss [7].

• (iii)

  Bragg Peak

  Initially, protons lose energy at a relatively slow rate, but upon reaching a specific depth, they experience a rapid increase in energy loss, forming the Bragg Peak. This peak is a critical feature in proton therapy, allowing for the precise deposition of energy at a target, such as a tumor, while minimizing damage to surrounding healthy tissue [6].

• (iv)

  Secondary Particle Production

  During the proton’s interaction with the water, secondary particles, including electrons from ionization events, are generated. Additionally, other secondary particles such as neutrons and gamma rays may be produced from proton-nucleus interactions. These secondary particles play a significant role in radiation therapy and radiation protection studies [8].

• (v)

  Nuclear Interactions

  At high energies, protons can interact with the nuclei of water atoms, triggering nuclear reactions that can release secondary particles such as neutrons and gamma rays. PHITS is capable of simulating these nuclear interactions and the subsequent transport of secondary particles [6].

• (vi)

  Dose Distribution and Energy Deposition

  PHITS simulations can calculate the energy deposition profile of protons within the water phantom, which is critical for assessing radiation dose distribution. This information is particularly useful in proton therapy, where precise dose delivery to the target area is essential for treatment effectiveness [7].

• (vii)

  Analysis of Simulation Results

  Once the simulation is complete, PHITS provides detailed output on the proton’s trajectory, energy loss, and dose distribution. These results can be used to study the physical characteristics of proton interactions and optimize radiation therapy protocols or safety measures in radiation protection.

The simulation was executed using PHITS, a widely recognized tool for simulating the behavior of particles, including protons, as they pass through various materials[7, 9]. In our simulation setup, we defined a water phantom a model that mimics human tissue to study the deposition of energy by the proton beam. The simulation employed a 100 MeV proton beam directed at the water phantom. This simulation setting has already been previously studied[7, 9]. Precise definitions of materials and geometric configurations, including the sizes and boundaries of the simulated regions, were integral to this setup. The simulation tracked the spread of energy, focusing on both depth and lateral dose distributions and identified the peak deposition point (Bragg peak).

In this study, the geometrical configuration and material properties were carefully defined to accurately model the interaction environment. The geometry was specified within the [Surface] and [Cell] sections, where two rectangular parallelepipeds (rpp) were employed to delineate spatial boundaries. The first rpp, identified as surface 100, encompassed a smaller volume with boundaries set at -10 cm to 10 cm along the x, y, and z axes, ensuring that the volume of interest was centrally located within the simulation domain. The second rpp, labeled as surface 999, defined a larger enclosing volume with boundaries extending from -20 cm to 20 cm in all three dimensions, thereby encompassing the entire simulation space. A schematic drawing of simulation setting is shown in Fig. 3 and 4. Figure 3 shows setup for detector using PHITS and Fig. 4 shows the a schematic view on a water phantom.

Figure 3. (Color online) The illustration of geometries of a water phantom having a size of 20​×20​×20​cm3.

Figure 4. (Color online) Schematic view on a water phantom.

The source configuration, detailed under the [Source] section, employed a proton as the projectile. The initial position (r₀) of the proton beam was fixed at the origin, with the central coordinates for both the x-axis (x₀) and y-axis (y₀) set to 0.0000 cm. The z-position was specified from -20 to 20 cm, indicating a stationary starting point along the z-axis. The beam energy (e₀) was configured to 100.00 MeV, with the beam direction precisely aligned along the z-axis (cos(dir) = 1.0000) to ensure direct propagation through the simulation domain[10].

Different materials were assigned within these defined volumes in the [Cell] section. Cell 1, corresponding to surface 100, was filled with water (material 1000) at a density of -0.998207 g/cm³, simulating the water phantom[11]. In contrast, Cell 8 utilized air (material 2000) with a density of -0.001205 g/cm³, representing the surrounding environment outside the water volume but within surface 999. The region outside surface 999 was designated as Cell 9, which represented the external environment, effectively terminating the simulation space.

The simulation was controlled by parameters outlined in the [Parameters] section. The default control setting was maintained by setting the parameter to 0. The maximum number of cases was limited to 100, with the simulation divided into two batches (maxbch = 2). Event generation was enabled (e-mode = 1), and Electron Gamma Shower (EGS) mode was activated (negs = 1) to facilitate detailed tracking of particle interactions.

For dose calculation, the scoring, which refers to the process of collecting and recording physical quantities during the simulation, was configured under the [T - Deposit] section, with a focus on the depth-dose distribution. The mesh type for scoring was set to a cylindrical r-z coordinate system, with the center aligned at the origin (x₀ = 0.000000 cm, y₀ = 0.000000 cm). The radial mesh (r-mesh) extended linearly from r_min = 0.000000 cm to r_max = 1.000000 cm with only one point (nr = 1), while the axial mesh (z-mesh) extended linearly from z_min = 0.000000 cm to z_max = 10.000000 cm, divided into 200 points (nz = 200). The dose was computed as the total deposited energy along the z-axis and outputted in units of [MeV/source]. A user-defined multiplier of 2 was applied uniformly across all materials, and the results were saved to a file named dose.out for further analysis[7].

The simulation showed that a proton beam has a short tail effect, meaning that after the Bragg peak, there is minimal residual energy, reducing the risk of damage to tissues beyond the target. Additionally, the potential for using radioactive oxygen ion beams for in-beam PET imaging was discussed, which could enhance treatment by allowing real-time monitoring of the therapy[10, 12]. The results of the simulation provided a clear view of how the proton beam's dose is distributed at different depths within the water phantom. The key finding was the presence of a Bragg peak, where the dose sharply increases at a specific depth and then drops off quickly. This characteristic makes proton therapy highly effective for targeting tumors while sparing surrounding tissues[3, 13].

The simulation results provide an insightful depiction of the linear energy transfer (LET) and the Bragg Peak curve, essential elements in understanding a proton beam therapy. The plot illustrates the dose distribution of the proton beam at varying depths within a water phantom, with the x-axis representing the position of a water phantom as simulated in PHITS[7].

Key observations from the plot reveal that the dose exhibits a pronounced peak at a specific depth within the phantom, a phenomenon known as the Bragg Peak[2]. This peak is a characteristic feature of proton therapy, where the maximum energy deposition occurs just before the particles come to rest, resulting in a highly localized dose at the tumor site while sparing surrounding healthy tissues[4]. The detailed analysis of this depth-dose relationship is critical for optimizing the therapeutic efficacy of a proton beam treatments[3]. As a consequence of this simulation, The Bragg peak and LET value are well shown in Fig. 5. Figure 5 shows the Bragg Peak values for 100 MeV proton in a water phantom and has no scatter radiation tail in the case of a proton beam. The bragg peak shows 30MeV/cm3/source at a depth of 16.9 cm. The simulated LET values exhibit a gradual rise in the entrance region of the phantom, starting as low as 0.25​keV/μm for proton, followed by a sharp increase, reaching up to 131​keV/μm. From this Fig. 5, we can conclude that a 100 MeV proton exhibits minimal changes in LET, indicating that it is suitable for tumors with a size of at least 2 cm or larger. The reason for mentioning a tumor size of 2 cm is that the LET changes significantly about 2 cm beyond the Bragg peak maximum point. LET is related to Relative Biological Effectiveness (RBE). RBE is a way to measure how much damage different types of radiation can cause compared to x-rays, given the same amount of radiation exposure. If the radiation has a high LET, which means it gives off a large amount of energy quickly, it will generally cause more damage, showing a high RBE.

Figure 5. (Color online) The simulation results show the depth along the LET and Bragg peak curve, with the x-axis indicating the position of a water phantom in PHITS.

Percent Depth Dose (PDD), LET, and RBE are closely related. As a proton beam travels through a water phantom, the PDD increases with depth, reaching a maximum at the Bragg peak. At this point, the LET also peaks, as the protons slow down and release energy more densely. This high LET leads to an increase in RBE, meaning that the biological damage is greater at the depth where the energy is concentrated. Therefore, the RBE increases near the Bragg peak, where both PDD and LET are high, making proton therapy highly effective for targeting tumors at specific depths. This allows for a concentrated delivery of energy to the tumor while minimizing damage to surrounding healthy tissues. The provided data also indicates that a 100 MeV proton beam is suitable for tumors of at least 2 cm in size, as the LET changes significantly about 2 cm beyond the Bragg peak.

A proton beam therapy is confirmed as a highly effective method for delivering precise radiation doses to tumors, particularly in challenging cases like pediatric cancers or tumors near critical structures[4, 14]. The simulation results demonstrate the advantages of a proton beam, especially its ability to concentrate energy at the tumor site while minimizing exposure to healthy tissue[2]. This study also highlights the potential for integrating imaging techniques like in-beam PET to further improve the accuracy and effectiveness of proton therapy. This research supports the continued development and application of a proton beam in radiation therapy, with an emphasis on its unique clinical benefits[3].

The simulation study shows the unique behavior of different radiation types based on their LET properties[10, 11]. High LET radiation, such as a proton beam, tends to deposit a substantial amount of energy within a small area, leading to a higher potential for biological damage when concentrated in specific regions of human tissue[11]. This characteristic is particularly important in medical treatments like proton therapy, where precise energy delivery is essential for effectively targeting tumors while minimizing harm to adjacent healthy tissues[4].

In this PHITS simulation, the interaction between a proton beam and a water phantom is carefully modeled by accurately setting the source parameters, material properties, and geometric boundaries[7, 9]. The simulation demonstrates how the proton beam's dose is distributed within the phantom, which is crucial for understanding how energy is delivered to a tumor site in proton therapy. This knowledge is key for optimizing treatment plans to achieve maximum therapeutic benefit while reducing exposure to surrounding tissues[3, 13]. Additionally, the insights gained from this simulation are valuable for enhancing radiation protection strategies and improving the design and accuracy of detectors used in a proton beam applications, thereby contributing to advancements in both medical treatment and safety measures[10]. We conclude that PHITS is applicable to a simulation tool with proton therapy. We compared the measured the depth-dose distribution 100 MeV proton beam injected on a water phantom using TOPAS between with dosimetric data. The results compared to the data show a difference of about 1 cm in depth. This is because the position of the injected protons are different.This comparison not only clarity the simulation but also ensures that the Bragg peak result from the simulation accurately represents the real proton interactions within the given energy range.

Furthermore, the research indicates that charged particle therapy, such as proton therapy, can offer significant clinical advantages, especially in cases where conventional radiation therapy might pose risks to surrounding healthy tissues[14]. Historical data and ongoing research underscore the importance of a proton beam in advancing radiation therapy techniques[15]. The cost-effectiveness of proton therapy, when compared to X-ray radiation therapy, also plays a crucial role in its adoption and further development[16].

This work was supported by the grant of NRF-2021R1F1A1061174.