Radionuclide therapy is a kind of inner radiation therapy method. In this method, the specified radionuclide fused in the radiotherapy drug is implanted into the body. Then, the radionuclide contained in the radiotherapy drug could be largely deposited into the target region of the patient. With the decay of the radionuclide, the emitters can be used to destroy the target cell.

Based on their emitters, radionuclides can be divided into α-emitting radionuclides, β-emitting radionuclides, γ-emitting radionuclides, and multiple radionuclides. Among these radionuclides, α-emitter radionuclides are considered as an ideal candidate in more cases because of the following reasons:

• α-Emitters have higher energy compared with beta emitters and gamma emitters.

• α-Emitters have shorter range, normally limited in the region of a single or several target cells, which may reduce radiation damage to the surrounding normal cells.

• α-Emitters have higher linear energy transform values, which may lead to a more energy deposition in a unit region of the target cell.

• α-Emitters have higher relative biological effect values, which cause more biological damage to the target cell.

• α-Emitters have lower oxygen enhancement ratio in radiobiology, which can destroy target cells under the same dose deposition in a region.

Therefore, α-emitting radionuclides are mostly considered in radionuclide therapy.

At present, several α-emitting radionuclides are being applied or developed in clinical radiotherapy. The main radionuclides include Bi-212, Bi-213, At-211, and Ac-225. Here in evaluating the therapeutic effect of radionuclides, the dose distribution in the cellular level is a micro-interaction that cannot be detected by devices. Thus, the Monte Carlo method is used to calculate the dose distribution induced from α-emitting radionuclides[1-3].

In this study, PHITS (Particle and Heavy Ion Transport code System, version 3.27), which is a widely used Monte Carlo simulation tool in heavy ion radiotherapy, is used to simulate the interaction of the emitters with cellular structures and to calculate the dose of emitters in concern volumes.

The geometrical structures of target cells are shown in Fig. 1, in which the radius of the target cell is 6 µm, and the radius of the nucleus is 3 µm. The four nuclei of the target cell are defined as the target regions (regions of 102, 104, 106, and 108). The destruction of a cell is primarily dependent on the damage of the nucleus; therefore, the dose deposited in the four nuclei is calculated in simulation. In addition, the materials of all target cells are assigned to water[4, 5].

Figure 1. (Color online) Geometric illustration of cells. The 102, 104, 106, and 108 regions are the nucleus of the target cells, and the 101, 103, 105, and 107 regions are the cytoplasm of the target cells.

For simulation, the characteristics of α-particles emitted from Bi-212, Bi-213, At-211, and Ac-225 are summarized in Table 1. In addition, the positions of radionuclides are defined on two situations: the surface of target cell and the cytoplasm of target cell. Moreover, the number of radionuclides (decay) is defined to 10000.

Table 1 Characteristics of α-emitting radionuclides in this investigation.

Radionuclides	Bi-212	Bi-213	At-211	Ac-225
Energy of main α-emitters (MeV)*	6.1	8.5	5.9	5.82 6.34 7.07 5.86 8.35
Half-life	60.6 min	45.6 min	7.21 h	10 days

* The emitter spectrum of each radionuclide is included in the PHITS tool and is automatically applied in the simulations.

In this study, the calculation results have the output of three parts: the dose distribution in four target regions, the track distribution of emitters, and the dose deposition values in four target regions. They are divided into two situations: the radionuclides located outside of the four target cells and the radionuclides located inside of the cytoplasm of a target cell.

1. Radionuclides Located Outside of Target Cells

The distribution of dose and tracks of α-emitter and its induced secondary particle are shown in Fig. 2, which includes four sub-figures for four radionuclides. In addition, the dose deposition values in the 102, 104, 106, and 108 regions are calculated and summarized in Table 2.

Table 2 Dose (in the unit of Gy) deposition values in the target regions.

Region	Ac-225	At-211	Bi-212	Bi-213
102	15.572	3.546	3.054	2.259
104	15.523	3.506	3.032	2.200
106	15.623	3.502	3.052	2.281
108	15.286	3.537	3.003	2.258

Figure 2. (Color online) Distributions of dose (left figures) and track (right figures) for selected radionuclides.

Analyzing the simulation results, α-emitters from the decay of Ac-225 are found to deposit more dose to the nucleus of four target cells. Therefore, destroying the power of target cells of Ac-225 is more than that of other radionuclides, when the concentration of radionuclides in the target region is similar.

For the other three radionuclides, At-211 and Bi-212 show the same dose deposition values as the target regions. Bi-213 induces the lowest dose deposition values in the four target regions.

2. Radionuclides Located at the Cytoplasm of a Target Cell

The distribution of dose and tracks of α-emitter and its induced secondary particle are shown in Fig. 3, which include four sub-figures for the results of four radionuclides. In addition, the dose deposition values in the 102, 104, 106, and 108 regions are calculated and summarized in Table 3.

Table 3 Dose (in the unit of Gy) deposition values in four target regions.

Region	Ac-225	At-211	Bi-212	Bi-213
102	18.300	10.059	9.590	6.092
104	5.748	3.532	3.092	2.043
106	2.340	1.276	1.200	0.976
108	1.615	1.059	1.050	0.860

Figure 3. (Color online) Distribution of dose (left figures) and track (right figures) for selected radionuclides.

Analyzing the simulation results, the α-emitters from the decay of Ac-225 are found to deposit more dose to the four target regions when the radionuclides are located in one of the four target cells.

For the other three radionuclides, At-211 and Bi-212 also show the same dose deposition values as the target regions, and Bi-213 induces the lowest dose deposition value in the four target regions in the four radionuclides.

Notably, the dose deposition in the target cell that contains the radionuclides is higher than that in the other three target cells because the α-emitters from the above radionuclides have a shorter range. Consequently, these α-emitters can hardly penetrate the local target cell and directly deposit dose to the other three target cells.

3. Comparison Analysis for Specified Radionuclides

For better comparison of the dose deposition results induced from four radionuclides, the dose deposition values in four target regions are shown in Figs. 4 and 5 based on the positions of radionuclides.

Figure 4. (Color online) Comparison of dose depositions of specified radionuclides, which are located outside of target cells.

Figure 5. (Color online) Comparison of dose depositions of specified radionuclides, which are located at the cytoplasm of target cells.

When the radionuclides are located outside of target cells, Ac-225 induced the highest dose deposition value among the other radionuclides. For the other three radionuclides, the dose deposition value of At-211 is high. In addition, Bi-212 induced more dose deposition than Bi-213. Here, the radionuclides are located at the center of four target cells; therefore, the dose deposited in the four target regions is similar.

When the radionuclides are located at the cytoplasm of a target cell, the dose value of Ac-225 remains the highest. In addition, enhancing the distance of radionuclides and target cells, the dose deposition values are reduced. Moreover, the difference in dose values in a specified target region is reduced for four radionuclides.

In this study, based on the Monte Carlo method, the dose distribution of four kinds of radionuclides for radiotherapy is calculated and analyzed. Based on the evaluation results, Ac-225 shows a better dose deposition value in target regions, indicating that the α-emitters from the decay of Ac-225 may effectively and efficiently destroy the target cells, when the number of radionuclides in target cells is similar.

On the contrary, half-life is an important concern for radiotherapy centers, which cannot produce the radionuclides on site. Therefore, Ac-225 shows another benefit because of its eligible half-life. It allows the radiotherapy center to have longer time to receive the radionuclide drug from the production site. However, for other radionuclides, a local system that is used to produce radionuclides and drug is necessary.

The physical dose distribution of Ac-225 for the main candidates of radionuclides is remarkable; thus, it can be considered on more efficient radionuclides to destroy tumor cells outside of the target region.

This work was supported by the grant of NRF-2017R1D1A1B03036042 and the Rare Isotope Science Project of Institute for Basic Science funded by Ministry of Science and ICT and NRF of Korea (2013M7A1A1075764).