Analysis of 70 - 300 MeV Proton Energy on Homogeneous and Inhomogeneous Phantoms using PHITS Monte Carlo Package

Proton therapy is a radiotherapy technique using proton particles for reach the target in a straight line and minimize damage to the surrounding tissue. Proton particles that penetrate the body will be deposited at a certain depth and produce a Bragg peak. This study aims to determine the percentage depth dose (PDD) produced by proton radiation in homogeneous and inhomogeneous phantoms. Homogeneous phantom contains water, bone, or lungs material, while inhomogeneous phantom consists of several materials, namely water, bone, and lungs. The interaction of phantom and proton radiation was simulated using the Monte Carlo-based PHITS software. The result indicate that the material density and the proton energy were influencing the dept of Bragg peak. For energy 70 MeV, the Bragg peak position for the water phantom, bone phantom, and lung phantom were 3.80 cm, 2.60 cm, and 15.8 cm. The increase of proton energy causes a deeper Bragg peak position.


Introduction
Proton radiation given to tissues will cause interactions in the form of the body's response to radiation exposure.The interaction that occurs can have an impact according to the dose of proton radiation received by the body.In general, the radiation given will trigger the process of water ionization that will react with DNA molecules so that it can cause rupture of the DNA structure and cause cell death [1][2][3].However, radiation exposure to healthy tissues can cause negative impacts, such as acute skin toxicity, central nervous system complications, oral dryness, and heart abnormalities due to radiation exposure.Radiation exposure to healthy tissues must be minimized so that cells in healthy tissues do not suffer serious damage [4].
Since its introduction in 1946, proton therapy has been widely utilized and has good prospects in the future [5][6][7][8].A proton beam consists of charged particles (protons) with a definite Bragg Peak depth range into the tissue.When the proton beam is radiated into tissue and penetrates it, these particles will slow down and deposit most of their energy near the end of their range (Bragg Peak).Research shows that protons can reduce about 50% of the irradiation dose to surrounding healthy tissue compared to photon beams [9][10][11][12][13].Thus, proton therapy is very superior to use in the aspect of reducing dose to healthy tissue and has been widely used to treat cancer around the world [5,14].
Dose distribution produced from many kinds of radiotherapy technique including proton therapy can be simulated with Monte Carlo simulation [15][16][17][18][19][20][21].Newpower et al. (2019) used two MC codes, TOPAS and MCNPX, to calculate the dose distribution in the water phantom and inhomogeneous phantoms of lung and bone that produce the same data [16].FLUKA Monte Carlo code also was used to predict the neutron contamination produced in proton therapy [18].In addition, FLUKA was used to verify and compare proton therapy doses generated by the new MC code, MonteRay, which is used to support proton therapy clinical activities at the Heidelberg Ion Beam Therapy center (HIT) [19].
In this study, the dose distribution generated by monoenergetic protons with energies of 70-300 MeV was analyzed by PHITS Monte Carlo package.In this study, an inhomogeneous phantom design consisting of water-bone-lung-bone-water material was conducted.

PHITS
The whole simulation process was carried out on PHITS software.PHITS is software used in particle transport computing.It can be run on Windows, Mac, Linux, and Unix.PHITS can be used to determine the distribution of particles such as neutrons, protons, photons, and electrons.The particle distribution is calculated using the "tally" track [22].PHITS can produce a variety of selectable output quantities, such as heat deposition, track length, energy absorption, which can be simulated using the "tally" estimator function.

Input File of Simulation
2.2.1.Parameters.Parameters are sections used to input the energy and number of particles used in the simulation.According to studies that have been done, the amount of proton energy for radiotherapy is generally in the range of 70 -250 MeV.In a study conducted by Sengbusch et al. (2009) found that the optimal proton energy that can be 100% absorbed by the body is 240 MeV, at 207 MeV energy there is 95% absorption, and 90% absorption at 198 MeV energy [23].In addition, in an experiment conducted by Beni et al. (2021) used 240 MeV energy.Based on the above studies, the proton energies used in this study are 70, 100, 150, 200, 250, and 300 MeV [24].

Source.
Source in PHITS is a section of defining the energy source used.The energy source comes from proton particles with energy variations of 70 -300 MeV.The proton source with point geometry is placed on the phantom surface on the z axis.

Material.
Materials are used to define 3-dimensional geometry.The materials used are written using the following format (Figure 1).Material numbers can use the format MAT[n] and Mn, the value of n can be specified up to 99,999.Writing elements using the chemical formula writing format, for example for water (H2O) it can be written H2O and can be followed by its mass meeting.The materials to be used are water phantoms, bone phantoms, lung phantoms and inhomogeneous phantoms.The inhomogeneous phantom is a phantom composed of water, bone, and lung materials.
Material composition is the composition of chemicals contained in the material.The material composition used in this research is adjusted to the actual material composition.Water is a material composed of hydrogen and oxygen.The lungs are an organ composed of many epithelial tissues.Some of the tissue composition consists of hydrogen, oxygen, carbon, and nitrogen.Bones are composed of hydrogen, oxygen, carbon, nitrogen, calcium, and phosphorus.The creation of a lattice or LAT cell is useful in the creation of repeating structures.Each unit on the lattice is part of the universe of a particular material.The format LAT=1 for a square, and LAT=2 for a hexagon.The placement of materials on the lattice can be filled using a matrix.The lattice created in this research is an arrangement of water, bones, and lungs.

Data Analysis
2.3.1.Lattice.out.This output displays the designed lattice shape which can be 2-dimensional or 3dimensional.The 2-dimensional lattice shape will show more details of the material position in the lattice.While the 3-dimensional form is a form of 3-dimensional visualization of the lattice arrangement made.
2.3.2.Deposit.out.Deposit.out is an output from PHITS that shows the deposition of proton energy in the material.This deposit.outoutput has units of Gy/source.This data shows the energy deposition at the depth of the phantom through which the protons pass.The data is processed to produce Percentage Depth Dose (PDD).The results of the PDD calculation are then visualized in the form of a graph.There is a Bragg peak on the graph that shows the maximum dose at a certain depth.

Homogeneous and Inhomogeneous Phantom
This research uses two types of phantoms: homogeneous phantoms and inhomogeneous phantoms (Figure 2).Homogeneous phantoms are phantoms composed of one type of material, such as water phantoms, bone phantoms, and lung phantoms.Inhomogeneous phantoms are phantoms composed of more than one material with different density.

PDD in water phantom.
The following Figure 3 is a graph of percentage depth dose (PDD) on a homogeneous phantom of water.Based on the graph below, it can be seen that the greater the proton energy, the greater the depth of the Bragg peak that can be reached.In addition, this graph shows that the protons deposit all their energy at the depth of the Bragg peak and the relative dose decreases drastically thereafter.The Bragg peak depths for each of the 70, 100, 150, 200, and 250 MeV energies in water are at depths of 3.80 cm, 7.60 cm, 15.6 cm, 25.8 cm, and 37.6 cm, respectively.These results are not much different from the research conducted by Jabbari and Seuntjens (2014) [25].Proton energies of 100, 150, and 200 MeV produce Bragg peak depths of 8.00 cm, 16.0 cm, and 26.0 cm.In addition, research conducted by Piersimoni et al. (2015) showed that protons with energies of 100 MeV and 149 MeV were deposited at a depth of 7.60 cm and 15.5 cm [26].

PDD in bone phantom.
Bone is an organ of the body that functions as a passive means of movement and protects other organs.When proton radiation is given to the body, the protons will hit the bones first before hitting other organs.The density of bone is greater than the density of water, which is 1.86 grams/cm 3 .This density indicates that bone has a denser structure compared to water.Figure 4 above shows that the greater the proton energy radiated to the bone, the deeper the Bragg peak position.Proton energies of 70, 100, 150, 200, 250, and 300 MeV produced maximum energy deposition in the bone at phantom depths of 2.60 cm; 5.00 cm; 10.6 cm; 17.4 cm; 25.6 cm; and 34.8 cm, respectively.

PDD in lung phantom.
The results of proton radiation on the lungs are different from proton radiation on water.This is because the lungs have a lower density than water, which is 0.28 gr/cm 3 .Figure 5 shows proton radiation with 70 MeV energy Bragg peak at a depth of 15.8 cm.Deposition of 100 MeV energy is at a depth of 30.0 cm.
Unlike the water phantom, the lung phantom is easier for protons to pass through due to its lower density.This resulted in the application of 150-300 MeV energy to the lung phantom depositing its energy at a position more than 40.0 cm deep, so the results of the 150-300 MeV energy deposition obtained were not displayed on the graph.The graph shows that the greater the energy of the proton source, the greater the depth of the Bragg peak.

Comparison of Homogeneous Phantom PDDs
Materials with different densities will produce different Bragg peak positions.Density indicates how tight and strong the bonds between particles are.A lower density will be easier for any particle including protons to pass through than a higher density.The higher the density means that the material has a denser particle arrangement so that more energy is needed for protons to pass through.
Figure 6 show that bone has a lower maximum PDD depth/Bragg peak than water and lung.This shows that the smaller the density of the material, the greater the depth of the Bragg peak that can be reached by protons.Density shows the density of a material, so the greater the density of the material, the denser the constituent electrons.This causes protons passing through a material with a larger density to produce a Bragg peak at a shallower depth.Research conducted by Jabbari and Seuntjens (2014) showed that 100 MeV-energized protons given to water, bones, and lungs will reach maximum depths at a depth of 8.00 cm, 5.00 cm, and 27.0 cm [25].These values are not much different from the simulation results obtained in Figure 6.
In addition, the Bragg curve also explains the energy loss rate or Linear Energy Transfer (LET).LET is the amount of energy transferred by protons to the material they pass through per unit distance.
The energy loss is characterized primarily by the square of the nuclear charge, Z, the inverse square of the projectile velocity, and density and atomic number of materials expressed in Bethe-Bloch formula.This gives the Bragg Curve its familiar shape, peaking at very low energies, just before the projectile stops.The Bragg curve obtained in this study shows the characteristics of this energy loss rate or LET.

Simulation in Inhomogeneous Phantom
The shape of the inhomogeneous phantom is made to resemble the actual human body.This inhomogeneous phantom is composed of water, bone, and lung materials with the thickness of each material being 3.00 cm of water; 1.00 cm of bone; and 7.00 cm of lung.The thickness of each material is set according to the actual situation.Figure 7 shows that the dose produced by 70 MeV proton energy radiation on the inhomogeneous phantom increases at a depth of 3.51 cm or at the bone material.After the protons pass through the bones, the relative dose of the protons will rise again when passing through the lungs because the density of the lungs is smaller than that of the bones.Energy of 100 MeV produces a Bragg peak in the lung material at a depth of 11.90 cm.
The maximum dose produced by protons with energies of 150-300 MeV in an inhomogeneous phantom is not maximally deposited in the phantom.This is known from the graph above which shows that at a depth of 15 cm the dose still continues to increase.Figure 7 above also shows that the greater the energy given, the greater the relative dose received by the phantom.This can be seen from the relative doses generated at the border of water and bone when irradiated with 150, 200, 250, and 300 MeV energized protons of 23.9%; 32.4%; 36.4%; and 38.6%, respectively.

Relative error and Simulation time
PHITS records the simulation time and the amount of error that occurs during the simulation.Error data from the simulation is used to determine the accuracy of the simulation results.The amount of uncertainty/error that can be tolerated in proton radiation simulations is 3.5% [27].Table 1 shows the relative error obtained from the simulation results is below 3.5% which is still below the error allowed in Monte Carlo simulation.The smaller the source energy used, the greater the error value obtained.The highest average error is 2.91% in the inhomogeneous phantom simulation with 70 MeV energy.This is because at a certain depth the proton particles have run out of energy, so the protons do not reach the maximum depth of the phantom.As a result, the error generated at the depth that is not passed by the proton becomes large.The simulation time shows the time required for running the simulation starting from the particles being produced until all the particles die.The table above shows that the greater the energy applied to the phantom, the longer the time required.This is because greater energy causes proton particles and secondary particles produced to live longer.Inhomogeneous phantoms have a faster simulation time than homogeneous phantoms.Based on the table above, a large energy of more than equal to 200 MeV in a homogeneous phantom will take more than 10 hours of simulation time.

Conclusion
The use of proton radiation for radiotherapy can produce maximum energy deposition on the target according to the simulations that have been carried out.Proton with its energy can penetrate the material with a straight trajectory and almost does not cause scattering.The results showed that 70 MeV energy will produce Bragg peaks on water phantoms (ρ=1 gram/cm 3 ), bone phantoms (ρ=1.86 gram/cm 3 ), and lung phantoms (ρ=0.28 gram/cm 3 ) at a depth of 3.80 cm; 2.60 cm; and 15.8 cm, respectively.The greater the density, the shallower the depth of the Bragg peak reached.The water phantoms irradiated by protons with energies of 70, 100, 150, 200, and 250 MeV produced Bragg peaks at depths of 3.80 cm; 7.60 cm; 15.6 cm; 25.8 cm; and 37.6 cm, respectively, while the depth of the Bragg peak of 300 MeV energy exceeded the depth of the phantoms.This shows that the greater the energy given, the deeper the Bragg peak depth achieved.The increase and decrease of PDD in inhomogeneous phantoms are due to differences in the density of the constituent materials.

Figure 2 .
Figure 2. Homogeneous phantom filled with water and inhomogeneous phantom filled with water-bone-lung-bone-water.

Figure 3 .
Figure 3. Percent depth dose of water phantom.

Figure 4 .
Figure 4. Percent depth dose of bone phantom.

Figure 5 .
Figure 5. Percent depth dose of lung phantom.

Table 1 .
Relative error and simulation time.