Evaluation of relative biological effectiveness of 225Ac and its decay daughters with Monte Carlo track structure simulations

Ziyi Hu; Shuiyin Qu; Hongming Liu; Yunhao Zhang; Shuchang Yan; Ankang Hu; Rui Qiu; Zhen Wu; Hui Zhang; Junli Li

doi:10.1186/s40658-025-00765-0

. 2025 Jul 7;12:65. doi: 10.1186/s40658-025-00765-0

Evaluation of relative biological effectiveness of ²²⁵Ac and its decay daughters with Monte Carlo track structure simulations

Ziyi Hu ^1,², Shuiyin Qu ^1,², Hongming Liu ^1,², Yunhao Zhang ^1,², Shuchang Yan ^1,², Ankang Hu ^1,², Rui Qiu ^1,^2,^✉, Zhen Wu ³, Hui Zhang ^1,², Junli Li ^1,²

PMCID: PMC12234921 PMID: 40622666

Abstract

Background

²²⁵Ac is a radionuclide that can be utilized in targeted alpha therapy (TAT). To accurately assess the absorbed dose and radiation effects in TAT, it is necessary to calculate the relative biological effectiveness (RBE). This study aims to calculate the RBE of ²²⁵Ac and its decay daughters with a Monte Carlo method.

Methods

This study employed the NASIC program to perform microdosimetric simulations of ¹⁷⁷Lu, ²²⁵Ac and its decay daughters in a cell population. Absorbed doses and lineal energy spectra in the cell nucleus were obtained for eight different radionuclides, three different cells, and six radionuclide spatial distribution. The RBE was then calculated using a modified stochastic microdosimetric kinetic model (mSMKM).

Results

The results indicated that variations in radionuclide distribution had a greater impact on the absorbed dose in the cell nucleus. Taking ²²⁵Ac in V79 cells as an example, the maximum differences in RBE and absorbed dose due to different distributions were 10% and 80%, respectively. For V79 cells, with a uniform distribution of radionuclides within the cell, the RBE_M, i.e. RBE at zero dose, of ²²⁵Ac was 6.91 ± 0.04. In its decay chain, the RBE_M was 6.81 ± 0.04 for ²²¹Fr, 6.67 ± 0.02 for ²¹⁷At, 6.43 ± 0.05 for ²¹³Po, and 5.91 ± 0.09 for ²¹³Bi. The β-emitting radionuclides ²⁰⁹Tl and ²⁰⁹Pb had RBE close to 1.

Conclusions

RBE of each radionuclide in ²²⁵Ac decay chain was evaluated separately with a Monte Carlo track structure code. The RBE of ²²⁵Ac and its decay daughters was found to be influenced by absorbed dose, radionuclide distribution, and cell type. The intracellular distribution of radionuclides had influence on the magnitude of RBE, but was less significant than its impact on the absorbed dose. Additionally, there were differences in the RBE of each radionuclide in the ²²⁵Ac decay chain that could not be neglected. These findings contribute to the calculation of RBE-weighted doses and the assessment of biological effects in ²²⁵Ac-based TAT.

Supplementary Information

The online version contains supplementary material available at 10.1186/s40658-025-00765-0.

Keywords: Targeted alpha therapy, ²²⁵Ac, RBE, NASIC, Monte Carlo

Background

Prostate-specific membrane antigen (PSMA) labeled with the β-emitting radionuclide ¹⁷⁷Lu has shown promising results in targeted radionuclide therapy for metastatic castration-resistant prostate cancer (mCRPC) [1, 2]. α-emitting radionuclides, such as ²²⁵Ac, have also been employed in targeted therapy for mCRPC [3]. Compared to β particles, α particles have a shorter range, minimizing damage to surrounding healthy tissues when concentrated within the lesions. Additionally, the higher linear energy transfer (LET) of α particles leads to better cell killing. Clinical studies have also demonstrated that ²²⁵Ac-PSMA-617 can overcome resistance to ¹⁷⁷Lu-PSMA-617 and reduce hematologic toxicity [4]. ²²⁵Ac-PSMA-I&T has also been demonstrated to exhibit favorable antitumor efficacy in the treatment of mCRPC [5, 6]. As a result, targeted α therapy has emerged as an important research area [7]. Relative biological effectiveness (RBE) is used to describe the potency of charged particles in producing biological effects compared to low-LET reference radiation, such as γ-rays or β-rays. According to MIRD Pamphlet No. 21 [8], the absorbed dose to tumors or organs in radionuclide therapy should be weighted by RBE, and an empirical formula for calculating the RBE of α-particles was provided. In the study by Kratochwil et al., the RBE for α-particles was used to calculate the dose of ²²⁵Ac-PSMA-617, with a value of 5 [9]. However, the authors noted that this value may overestimate bone marrow toxicity while underestimating salivary gland toxicity.

As Hofmann et al. [10] pointed out in a review on the microdosimetry of α-emitting radionuclides, microdosimetric methods could be used to investigate the highly heterogeneous energy deposition of α-particles in the nucleus, and assess biological effects. The work of Li et al. [11] also demonstrated the necessity of conducting small-scale dosimetry and microdosimetry studies in radiopharmaceutical therapy with alpha-emitting radionuclides. Several studies have conducted the microdosimetric simulation of α-emitting radionuclides at the cellular scale. The MIRD committee developed the MIRDcell software [12, 13], which is used to calculate cellular doses and biological effects in the context of radionuclide therapy with an analytical calculation method [14] that has been validated against the Monte Carlo simulation results of EGS4. Lee et al. [15] investigated the impact of radionuclide internalization fractions on the dose to the nucleus, while Koniar et al. [16] calculated the intracellular dose distribution of ²²⁵Ac and its decay daughters based on varying radionuclide distribution within the cell. Sato et al. [17] extended the capabilities of PHITS to calculate doses for targeted alpha therapy (TAT) and employed a microdosimetric kinetic model (MKM) to compute dose-dependent RBE, thereby estimating EQDX(α/β). Rumiantcev et al. [18] simulated DNA damage and repair for ²²⁵Ac and ¹⁷⁷Lu, calculating the RBE of ²²⁵Ac relative to ¹⁷⁷Lu. It was the first simulation study estimating the RBE of ²²⁵Ac during ²²⁵Ac-PSMA therapy. However, in this work, it was assumed that all daughter nuclides decay at the same location and did not perform separate calculations for each nuclide. Previous research had shown that in TAT with ²²⁵Ac, the recoil energy from α-decay exceed the binding energy between the radionuclide and the targeting molecule [19], resulting in free decay daughters with distributions distinct from ²²⁵Ac. Free daughter radionuclides in-vivo may pose a risk to healthy tissues [20]. Therefore, it is necessary to calculate the absorbed dose and RBE for each decay daughters individually for a more accurate assessment of biological effects.

To the best of our knowledge, the RBE for each individual decay daughter in the ²²⁵Ac decay chain has not been calculated. Therefore, the primary focus of this study is evaluation of RBE for each individual radionuclide in ²²⁵Ac decay chain, using a validated track structure simulation Monte Carlo code (Nanodosimetry Monte Carlo Simulation Code, NASIC) [21–24] to perform event-by-event Monte Carlo simulations at the cellular scale. The RBE of ²²⁵Ac and its decay daughters was calculated based on a modified stochastic microdosimetric kinetic model (mSMKM) [25]. The results from this study can be further utilized to assess the biological dose in actual treatments, accounting for off-target effects and the redistribution of daughter nuclides. In contrast to the biological endpoint of DSBs employed in previous studies [18, 26, 27], this research assessed the RBE of ²²⁵Ac with the cell survival rate, another commonly utilized endpoint in radiobiological investigations [28–31]. DSBs describe radiation-induced damage to DNA and directly reflect the molecular mechanisms of radiation action. Their formation is closely related to the physical characteristics of energy deposition by radiation. However, a more complex repair model needs to be established to determine whether a cell undergoes death or mutation, as it cannot directly infer survival rates. On the other hand, cell survival rate as a biological endpoint directly quantifies the inhibition of the cell’s proliferative ability by radiation and can be used to further assess tumor control probability or the normal tissue complications probability. Moreover, RBE in this study was calculated based on irradiation experimental data from three different cell types. Compared to previous research with only one cell type, the influence of cellular radio-sensitivity on RBE was further considered. The study also investigated the effects of absorbed dose and radionuclide distribution on RBE in TAT. The findings of this study contribute to improving dose calculation and biological effect assessment in TAT.

Method

Microdosimetric quantities and stochastic microdosimetric kinetic model

The specific energy Inline graphic is defined as the ratio of the energy imparted to the mass in the sensitive volume [32, 33].

The lineal energy Inline graphic is defined as the ratio of the energy imparted by a single energy-deposition event to the mean chord length in the sensitive volume.

The frequency-mean specific energy Inline graphic and dose-mean specific energy are the first and second moments of the specific energy , respectively. is the probability density of the specific energy deposited in a single energy-deposition event.

The lineal energy spectrum is generally described using distributions of Inline graphic versus . is the probability density of the lineal energy deposited in a single energy-deposition event.

The stochastic microdosimetric kinetic model (SMKM) was developed by Sato et al. [34] based on the microdosimetric kinetic model (MKM) [35]. The model divided the nucleus into microscopic regions called domain and assumed that the cell died when lethal or sublethal lesions caused by radiation within a domain resulted in the domain’s death. The SMKM accounted for the stochastic nature of energy deposition in both the domain and the nucleus, enabling the prediction of cell survival fractions. Inaniwa [25] further developed a modified version of SMKM (mSMKM) and applied it to radiation therapy systems.

In the mSMKM, the cell survival fraction can be calculated using the specific energy in the domain and the nucleus.

In Eq. (6), Inline graphic and represent the survival fraction and absorbed dose, respectively. is the dose-mean specific energy in the cell nucleus, calculated according to Eq. (4). and are calculated according to Eqs. (7) and (8), respectively.

Inline graphic is the dose-mean specific energy in the domain, calculated according to Eq. (4). is the saturation-corrected dose-mean specific energy in the domain, calculated according to Eq. (9).

In the mSMKM, the parameters required to calculate the cell survival fraction are Inline graphic , , the saturation parameter , the domain radius , and the cell nucleus radius . These parameters are independent of radiation quality and are specific to the type of cells. In the work by Inaniwa et al. [25], these parameters were obtained by fitting using data of cell experimental in vitro. After identifying the cell type, substituting these parameters along with the mean specific energy calculated from Monte Carlo-simulated microdosimetric spectra into Eq. (6) yields the survival fraction corresponding to absorbed dose D.

Microdosimetric simulations in NASIC and mSMKM parameter fitting

NASIC is a nanodosimetric Monte Carlo simulation program developed and validated by Li et al. [21, 24]. In this study, its physics module was extended to enable microdosimetric simulation. Since NASIC’s physics module employed an event-by-event Monte Carlo simulation, which differed from the approach used by Inaniwa et al. [25], the mSMKM parameters were re-fitted accordingly. The cell nucleus radius Inline graphic of 8.1 μm used by Inaniwa et al. was directly measured with a light microscope, and thus, the same value was adopted in this study.

This study utilized the physics module of NASIC, which can simulate the transport process of particles in liquid water step by step. In this module, photon interactions, including the photoelectric effect, Compton scattering, and pair production, are defined based on the Livermore physics model. It also defines the elastic scattering, excitation, ionization, vibrational excitation, and capture of electrons with liquid water; multiple scattering, ionization, bremsstrahlung, and annihilation of positrons; excitation, ionization, charge decrease, and charge increase of protons, hydrogen atoms, α-particles, α + particles, and helium atoms with liquid water; ionization of heavy charged particles; and radioactive decay of radionuclides is modeled using the process of G4RadioactiveDecayPhysics() [36]. The cutoff energy for electrons was set to 11 eV, while no cutoff energy was applied to other particles. The inelastic scattering of electrons, protons and hydrogen atoms in liquid water is based on cross-sections calculated using the dielectric response theory, employing experimental optical data and the dielectric function methods [24, 37]. Other physical processes are modeled using cross-section data from Geant4-DNA [38]. Three concentric spheres with radii of 8.1 μm, 9.9 μm, and 10 μm were established in NASIC, representing the boundaries of the cell nucleus, cytoplasm, and cell membrane, respectively, with water used as the cell material. Similar to the microdosimetric simulation method used by Kyriakou et al. [39, 40], the location of the domain was randomly sampled in the cell nucleus. Lineal energy and specific energy in the domains were scored for each event. Figure 1 shows a schematic of the microdosimetric simulation. Since the domain radius Inline graphic was unknown, it was set vary between 2.0 and 5.0 μm, with a step size of 0.1 μm, and microdosimetric simulations were performed for each .

Fig. 1 — Schematic of the microdosimetric simulation. The red dots represent the particle track

To determine the parameters of mSMKM, aside from Inline graphic , experimental data for three cell types were used from the particle irradiation data ensemble (PIDE) [41] for fitting: V79 cells [42–55], HSG cells [56], and Renca cells [57]. V79 are Chinese hamster cells (a normal cell), irradiated with ¹H (3.44–37.8 keV/µm) and ⁴He (6.0–201 keV/µm); HSG are human salivary gland cells (a tumor cell), irradiated with ³He (18.5–71 keV/µm) and ¹²C (22.5–493 keV/µm); Renca are mouse renal carcinoma cells (a tumor cell), irradiated with ⁴He (4.78–26.52 keV/µm). The particle type and energies used in the microdosimetric simulations were set according to the experimental conditions for each cell type, and the predicted cell survival fractions were calculated using Eq. (6). Fitting was performed using the least squares method, with the root mean square error (RMSE) of the survival fraction as the objective function, as shown in Eq. (10). Parameter optimization was performed using the fmincon() in MATLAB. The number of experimental data for V79 cells, HSG cells, and Renca cells were 215, 134, and 44, respectively.

In our simulations, the type and energy of primary particles were maintained identical to that utilized in the cellular experiments. While our simulations could not fully reproduce the exact cellular environments from the original experiments, we applied monoenergetic planar sources with uniform irradiation on cell surfaces to approximate the exposure conditions in petri dishes.

Microdosimetric simulations of ²²⁵Ac and its decay daughters

To simulate particle interactions in a 3D geometry and better approximate real treatment conditions, cells were arranged in a 15 × 15 × 15 body-centered cubic lattice, as show in Fig. 2. To investigate the impact of radionuclide distribution on the absorbed dose and RBE in the cell nucleus, the locations of the radionuclides were set in various regions: uniformly distributed in the nucleus, in the cytoplasm, in the whole cell, outside the cell, both inside and outside the cell, and bound to membrane. ²²⁵Ac and its decay daughters were set to undergo a single decay event. Figure 3 shows the decay chain of ²²⁵Ac. To calculate the RBE, ¹⁷⁷Lu was also simulated as the reference radiation, as the clinical application of ¹⁷⁷Lu-labeled PSMA had already been well established.

Fig. 2 — Schematic of 3D cell arrangement

The simulation used NASIC’s default physical list, where the cutoff energy of the electrons was set to 11 eV. In addition to lineal energy and specific energy in the domain, energy deposits in the whole nucleus were also scored. A total of 48 simulation conditions were set up, considering 8 different radionuclides and 6 different radionuclide distributions. In each simulation, 10 thousand particles were transported without variance reduction technique. All the setting of simulations are listed in Table 1. Each condition was repeated 10 times for independent microdosimetric spectrum analyses to calculate the uncertainty.

Table 1.

Setup of Monte Carlo simulation

Radionuclide	Radionuclide distributions: Uniformly distributed	Number of transported particles
²²⁵Ac, ²²¹Fr, ²¹⁷At, ²¹³Po, ²¹³Bi, ²⁰⁹Tl, ²⁰⁹Pb, and ¹⁷⁷Lu	1) in the nucleus,	10 thousand per condition
	2) in the cytoplasm,
	3) in the whole cell,
	4) outside the cell,
	5) both inside and outside the cell,
	6) bound to membrane

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Evaluation of RBE of ²²⁵Ac and its decay daughters

RBE is defined as the ratio of the absorbed dose of a reference radiation to the investigated radiation required to produce the same biological effect. In this study, the cell survival fraction was considered as a measure of the biological effect, and ¹⁷⁷Lu was used as the reference radiation for calculating the RBE of ²²⁵Ac and its decay daughters. The relationship between the surviving fraction S and the absorbed dose D was in Eq. (6).

The ‘intrinsic’ RBE refers to the RBE at zero dose, independent of absorbed dose, and is denoted as RBE_M [58].

Results

Parameters of mSMKM

Table 2 presents the parameters of mSMKM and RMSE for the V79, HSG, and Renca cells. The parameters calculated in this study differ slightly from those reported by Inaniwa [25], primarily due to the use of different Monte Carlo simulation programs. Figure 4 shows the predicted survival curves and experimental data for the three cell types. It can be observed that the mSMKM provides a good prediction of cell survival following radiation exposure.

Table 2.

Parameters of mSMKM and RMSE for the three cell types

	V79	HSG	Renca
	0.127	0.183	0.019
	0.014	0.051	0.019
	144.7	66.1	66.0
	0.23	0.28	0.26
	8.1	8.1	8.1
RMSE	0.31	0.23	0.03

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Fig. 4 — Survival curve of three cell types. Dots represent experimental data, and lines represent predicted survival fractions. A for V79 cells, B for HSG cells, C for Renca cells

Absorbed dose of cell nucleus

Table 3 shows the average absorbed dose to the cell nucleus per single decay for ¹⁷⁷Lu, ²²⁵Ac, and its decay daughters, distributed in different locations. As evident from the table, the dose per decay from alpha-emitting radionuclides in the ²²⁵Ac decay chain is two orders of magnitude higher than that from beta-emitting radionuclides, with ²¹³Bi, undergoing both beta and alpha decay, falling in between. The radionuclide distribution has a significant effect on the absorbed dose to the cell nucleus. For instance, for ²²⁵Ac, the dose when distributed within the nucleus is roughly double that of a uniform distribution.

Table 3.

Dose in nucleus per decay of ²²⁵Ac decay chain and ¹⁷⁷Lu from different source distributions

	Dose in nucleus (Gy/decay)
	Nucleus	Cytoplasm	Whole cell	Outside the cell	Inside and outside the cell	Bound to membrane
²²⁵Ac	1.08E-01 ± 1.78E-03	9.08E-02 ± 1.73E-03	9.97E-02 ± 1.76E-03	5.99E-02 ± 1.44E-03	7.37E-02 ± 1.56E-03	8.56E-02 ± 1.70E-03
²²¹Fr	1.14E-01 ± 1.86E-03	9.63E-02 ± 1.78E-03	1.06E-01 ± 1.81E-03	6.63E-02 ± 1.49E-03	7.81E-02 ± 1.58E-03	9.19E-02 ± 1.74E-03
²¹⁷At	1.20E-01 ± 1.85E-03	1.03E-01 ± 1.78E-03	1.12E-01 ± 1.81E-03	8.27E-02 ± 1.58E-03	8.58E-02 ± 1.63E-03	1.01E-01 ± 1.79E-03
²¹³Po	1.29E-01 ± 1.85E-03	1.14E-01 ± 1.81E-03	1.23E-01 ± 1.84E-03	8.27E-02 ± 1.58E-03	9.81E-02 ± 1.69E-03	1.14E-01 ± 1.83E-03
²¹³Bi	4.85E-03 ± 3.47E-04	4.37E-03 ± 3.34E-04	4.60E-03 ± 3.44E-04	3.27E-03 ± 2.88E-04	3.86E-03 ± 3.11E-04	4.50E-03 ± 3.40E-04
²⁰⁹Tl	8.02E-04 ± 1.45E-05	7.09E-04 ± 1.30E-05	7.54E-04 ± 1.40E-05	5.17E-04 ± 1.08E-05	6.02E-04 ± 1.19E-05	6.95E-04 ± 1.29E-05
²⁰⁹Pb	9.65E-04 ± 1.51E-05	8.41E-04 ± 1.41E-05	9.07E-04 ± 1.46E-05	6.56E-04 ± 1.25E-05	7.29E-04 ± 1.31E-05	8.44E-04 ± 1.42E-05
¹⁷⁷Lu	1.25E-03 ± 1.96E-05	1.03E-03 ± 1.71E-05	1.12E-03 ± 1.83E-05	7.35E-04 ± 1.46E-05	8.81E-04 ± 1.59E-05	1.02E-03 ± 1.72E-05

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Lineal energy spectra of ²²⁵Ac and its decay daughters

Figure 5 shows the lineal energy spectra in the nucleus for ²²⁵Ac distributed in different locations, with the sensitive region being the domain. To validate the accuracy of the lineal energy spectra, the spectra of ²²⁵Ac were simulated under the same conditions using Geant4-DNA [38]. It was found that the results showed minimal differences from the NASIC simulations. The results are presented in Fig. 5.

Fig. 5 — Lineal energy spectra in the nucleus for ²²⁵Ac distributed in different locations, with =0.23 μm

Inline graphic — Lineal energy spectra in the nucleus for ²²⁵Ac distributed in different locations, with =0.23 μm

Figure 6 shows the lineal energy spectra for ²²⁵Ac, its decay daughters, and ¹⁷⁷Lu, with the radionuclides uniformly distributed in the whole cell. For alpha-emitting radionuclides such as ²²⁵Ac, ²²¹Fr, ²¹⁷At, and ²¹³Po, the lineal energy is higher, resulting in spectra shifted to the right. In contrast, for beta-emitting radionuclides, ²⁰⁹Tl, ²⁰⁹Pb, and ¹⁷⁷Lu, the lineal energy is lower, causing their spectra to shift to the left. As for ²¹³Bi, which undergoes both alpha decay (2%) and beta decay (98%), its lineal energy spectrum is spread across both the high and low lineal energy regions.

Fig. 6 — Lineal energy spectra for ²²⁵Ac, its decay daughters, and ¹⁷⁷Lu, with radionuclides uniformly distributed in the cell, =0.23 μm

RBE of ²²⁵Ac and its decay daughters

Figure 7 shows the RBE-Dose curves for ²²⁵Ac distributed in different locations within three cell types. Figure 8 shows the RBE-Dose curves for ²²⁵Ac and its decay daughters uniformly distributed within the three cell types. For the same radionuclide, the differences in RBE due to distribution location are small. As shown in Supplemental Tables S1 to S3, the differences in the saturation-corrected dose-mean specific energy, Inline graphic , for the same radionuclide are also minor, leading to similarly small differences in RBE calculated by mSMKM. Among the radionuclides in the ²²⁵Ac decay chain, the RBE is comparable for those with the same type of decay, while radionuclides with different decay mode show variation. Beta-emitting radionuclides, such as ²⁰⁹Tl and ²⁰⁹Pb, consistently exhibit RBE values close to 1. In contrast, ²¹³Bi, which undergoes both beta and alpha decay, has an RBE greater than 1 but lower than other pure alpha emitters. As shown in Fig. 8, the RBE of ²²⁵Ac and its decay daughters also varies between different cell types. For example, with ²²⁵Ac uniformly distributed within the cell, the RBE_M for V79, HSG, and Renca cells are 6.91 ± 0.04, 6.78 ± 0.05, and 9.76 ± 0.14, respectively. Table 4 lists the RBE_M and uncertainty for three cell types.

Fig. 7 — RBE-Dose (Dose of Ac-225) curves for ²²⁵Ac distributed in different locations. A for V79 cells, B for HSG cells, C for Renca cells

Fig. 8 — RBE-Dose (Dose of investigated radiation) curves for ²²⁵Ac and its decay daughters, with radionuclides uniformly distributed in the whole cell: A for V79 cells, B for HSG cells, C for Renca cells

Table 4.

Inline graphic for ²²⁵Ac and its decay daughters in V79, HSG and Renca cells

		RBE_M
		Nucleus	Cytoplasm	Whole cell	Outside the cell	Inside and outside the cell	Bound to membrane
V79	²²⁵Ac	6.63 ± 0.04	7.10 ± 0.04	6.91 ± 0.04	7.30 ± 0.05	7.23 ± 0.06	7.03 ± 0.05
	²²¹Fr	6.54 ± 0.04	6.98 ± 0.04	6.81 ± 0.04	7.23 ± 0.03	7.10 ± 0.03	6.97 ± 0.04
	²¹⁷At	6.39 ± 0.03	6.88 ± 0.03	6.67 ± 0.02	7.05 ± 0.04	7.00 ± 0.05	6.80 ± 0.03
	²¹³Po	6.07 ± 0.03	6.58 ± 0.03	6.43 ± 0.05	6.79 ± 0.04	6.71 ± 0.04	6.49 ± 0.04
	²¹³Bi	5.77 ± 0.12	5.84 ± 0.11	5.91 ± 0.09	5.90 ± 0.07	5.83 ± 0.10	6.42 ± 0.08
	²⁰⁹Tl	0.99 ± 0.01	1.00 ± 0.01	0.99 ± 0.01	1.00 ± 0.01	1.00 ± 0.01	1.03 ± 0.01
	²⁰⁹Pb	0.95 ± 0.01	0.98 ± 0.01	0.97 ± 0.01	0.98 ± 0.01	0.97 ± 0.01	1.02 ± 0.01
HSG	²²⁵Ac	6.54 ± 0.06	6.94 ± 0.03	6.78 ± 0.05	6.95 ± 0.06	6.82 ± 0.04	6.57 ± 0.05
	²²¹Fr	6.57 ± 0.06	7.02 ± 0.04	6.75 ± 0.03	7.09 ± 0.05	6.90 ± 0.05	6.58 ± 0.05
	²¹⁷At	6.52 ± 0.05	7.02 ± 0.03	6.84 ± 0.06	7.09 ± 0.06	6.95 ± 0.05	6.63 ± 0.04
	²¹³Po	6.41 ± 0.05	6.93 ± 0.04	6.69 ± 0.05	7.09 ± 0.04	6.94 ± 0.04	6.54 ± 0.04
	²¹³Bi	5.83 ± 0.10	5.96 ± 0.09	5.75 ± 0.13	6.04 ± 0.11	5.82 ± 0.12	6.28 ± 0.13
	²⁰⁹Tl	0.98 ± 0.01	1.00 ± 0.01	1.00 ± 0.01	0.99 ± 0.01	0.99 ± 0.01	1.02 ± 0.01
	²⁰⁹Pb	0.94 ± 0.01	0.98 ± 0.01	0.95 ± 0.01	1.00 ± 0.01	0.97 ± 0.01	0.96 ± 0.01
Renca	²²⁵Ac	9.60 ± 0.13	10.35 ± 0.11	9.76 ± 0.14	10.20 ± 0.18	10.09 ± 0.21	9.75 ± 0.15
	²²¹Fr	9.54 ± 0.11	10.45 ± 0.11	9.77 ± 0.14	10.44 ± 0.18	10.12 ± 0.19	9.83 ± 0.16
	²¹⁷At	9.67 ± 0.14	10.61 ± 0.11	9.94 ± 0.12	10.49 ± 0.17	10.28 ± 0.22	10.01 ± 0.19
	²¹³Po	9.64 ± 0.13	10.69 ± 0.11	9.87 ± 0.14	10.65 ± 0.20	10.33 ± 0.21	10.03 ± 0.19
	²¹³Bi	8.36 ± 0.11	9.06 ± 0.22	8.70 ± 0.11	8.78 ± 0.21	8.70 ± 0.21	9.54 ± 0.15
	²⁰⁹Tl	1.00 ± 0.02	0.99 ± 0.02	0.94 ± 0.03	0.99 ± 0.02	0.99 ± 0.02	1.09 ± 0.03
	²⁰⁹Pb	0.88 ± 0.01	0.96 ± 0.01	0.89 ± 0.02	0.95 ± 0.03	0.91 ± 0.03	1.02 ± 0.02

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Discussion

This study conducted microdosimetric simulations to assess the absorbed dose and biological effects of ²²⁵Ac and its decay daughters in 3D cell populations. Six different radionuclide distributions were considered. As shown in Table 3, the location of radionuclide distribution within the cell model significantly affects the absorbed dose to the nucleus. Internalizing radionuclides into the cell increases the nuclear dose, which is consistent with previous findings [15, 16]. In TAT of ²²⁵Ac, the recoil energy from alpha decay exceeds the binding energy between the radionuclide and targeting molecules [19], leading to different distributions of the free radionuclides compared to ²²⁵Ac. Therefore, the impact of redistribution of daughter radionuclides in the ²²⁵Ac decay chain on dose to target or normal tissue cells is non-negligible, especially for longer-lived alpha emitters like ²¹³Bi (with half-life 45.6 min).

The lineal energy spectra and RBE for different radionuclide distributions are shown in Figs. 5 and 7, respectively. It can be observed that the differences in the lineal energy spectra due to varying radionuclide distributions are little. This is also reflected in Supplemental Tables S1 to S3, where the saturation-corrected dose-mean specific energy, Inline graphic , shows little sensitivity to the radionuclide distribution, resulting in only minor changes in RBE (Fig. 7). Similarly, Rumiantcev et al. [18] found that the cell shape and radionuclide distribution position have small impact on RBE. This could be attributed to the range of alpha particles in the ²²⁵Ac decay chain, which is approximately 40 to 80 μm in cells [15], several times larger than the diameter of a cell. In the 3D cell populations, the lineal energy spectra are averaged across all cell nuclei, making them largely unaffected by changes in radionuclide distribution. Furthermore, the study by Tamborino et al. [59] also demonstrated that for ¹⁷⁷Lu, variations in its distribution position have small impact on the energy distribution of electrons within the cell nucleus. This finding could potentially be extended to ²²⁵Ac and its decay daughters. It can be observed from Tables 3 and 4 that the influence of radionuclide distribution on absorbed dose was significantly greater than its effect on RBE. For example, in V79 cells exposed to ²²⁵Ac, the maximum difference in RBE_M across different distributions is only 10%, which is significantly smaller compared to the 80% difference in absorbed dose.

Due to the differences in the metabolic processes of the various radionuclides in the ²²⁵Ac decay chain in vivo [20], it is necessary to calculate the dose for each radionuclide individually when assessing the dose to tumors or organs. Consequently, this study performed separate microdosimetric simulations and RBE calculations for each radionuclide to facilitate accurate RBE-weighted dose calculations for different radionuclides. Figure 8 presents the RBE-dose curves for various radionuclides of three cell types. Taking V79 cells as an example, the RBE_M of radionuclides emitting alpha particles ranges from 6.91 ± 0.04 for ²²⁵Ac to 5.91 ± 0.09 for ²¹³Bi, with a 17% difference. This variation cannot be overlooked when calculating RBE-weighted doses, particularly in cases where the distribution of progeny radionuclides differs from that of ²²⁵Ac.

The RBE also varies between different cell types; for instance, for uniformly distributed ²²⁵Ac, the RBE_M of V79, HSG, and Renca cells are 6.91 ± 0.04, 6.78 ± 0.05, and 9.76 ± 0.14, respectively, with a maximum difference of 44%. This variation reflects the differences in radio-sensitivity among cell types, which is a critical factor when calculating the biological dose to tumors or normal tissues in clinical applications.

In the work by Rumiantcev et al. [18], the reported RBE at zero dose for ²²⁵Ac in cells with different geometric shapes ranged from 9.33 to 10.84. Their study used as well an event-by-event Monte Carlo simulation; however, the biological endpoint in their research was the yield of radiation-induced double-strand breaks (DSBs), whereas our study focuses on cell survival fraction. Additionally, in their work, it was assumed no translocation of decay products, allowing them to calculate the total RBE for the entire ²²⁵Ac decay chain. In contrast, this study calculated the RBE for each radionuclide individually, which may account for the differences in results. Ruigrok et al. [60] conducted clonogenic survival assays and measured an RBE of 4.2 for ²²⁵Ac-PSMA-I&T relative to ¹⁷⁷Lu-PSMA-I&T. The RBE for ²²⁵Ac, calculated using the empirical formula provided in MIRD pamphlet No. 21 [8], was approximately 6.1. Compared to these studies, the results of our work further highlight the differences in RBE across cells with varying radiation sensitivities.

The results of this study can be used for the dose assessment of ²²⁵Ac TAT. Once the absorbed dose for a tumor or organ has been determined using nuclear medicine imaging or other methods, the appropriate cell type can be selected based on the radio-sensitivity of the organ. Based on the pharmacokinetic model of α-emitting radiopharmaceuticals, the total number of decays for each radionuclide within the region of interest can be calculated. By applying the weighting method proposed by Zaider et al. [61] using the computational results from this study, the radiobiological parameters and RBE of the mixed radiation field within the region of interest can be determined, enabling the determination of the RBE-weighted dose.

It is important to note that due to the lack of experimental data on ²²⁵Ac or ¹⁷⁷Lu directly irradiation of cells, the mSMKM parameters in this study were fitted using data from experiments with monoenergetic radiation, with the assumption that the results from in vitro cell experiments can be extrapolated to in vivo scenarios. Additionally, the cell model used in this study is relatively simple. While cell morphology and radionuclide distribution have minimal impact on RBE, the absorbed dose to the cell nucleus depends on the cell shape. In actual TAT, radionuclides remain in tumors or organs for several weeks, whereas the mSMKM does not account for the simultaneous occurrence of radiation damage and repair. Therefore, our RBE calculation method could be improved by incorporating more detailed modeling of cell morphology and repair processes.

Conclusions

This study conducted microdosimetric simulations of each individual decay daughters in the ²²⁵Ac decay chain in 3D cell populations with a track structure Monte Carlo code and calculated their RBE. The results showed that the RBE of ²²⁵Ac and its decay daughters was influenced by the absorbed dose, radionuclide distribution, and cell type. The intracellular distribution of radionuclides affected the RBE, though its influence was less pronounced than its impact on absorbed dose. Furthermore, notable variations in the RBE of different radionuclides within the ²²⁵Ac decay chain were observed and should not be disregarded. The RBE calculated in this study provided valuable insights for calculating RBE-weighted doses and assessing biological effects in ²²⁵Ac TAT.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary Material 1^{(42.1KB, docx)}

Acknowledgements

Not applicable.

Abbreviations

TAT: Targeted alpha therapy
PSMA: Prostate-specific membrane antigen
mCRPC: Metastatic castration-resistant prostate cancer
RBE: Relative biological effectiveness
mSMKM: Modified stochastic microdosimetric kinetic model
NASIC: Nanodosimetry Monte Carlo Simulation Code

Author contributions

R. Q. (Corresponding Author) conceived the presented research work and prepared the manuscript. Z.H. and S.Q. designed the study, conducted the data analysis, and wrote manuscript. H.L., J.L. and Y.Z. contributed to the simulation and processing. A.H. and S.Y. contributed to the writing and revision. Z.W. and H.Z. contributed to the design of simulation and the interpretation of the data.

Funding

This work was supported by the National Natural Science Foundation of China (Grant No. U2167209), the National Natural Science Foundation of China (Grant No. 12375312), and the National Natural Science Foundation of China (Grant No. U23B2067).

Data availability

The datasets used and analyzed during the current study are available from the corresponding author on reasonable request.

Declarations

Ethics approval and consent to participate

Not applicable.

Consent for publication

Not applicable.

Competing interests

The authors declare that they have no competing interests.

Footnotes

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

Supplementary Material 1^{(42.1KB, docx)}

Data Availability Statement

The datasets used and analyzed during the current study are available from the corresponding author on reasonable request.

[CR1] 1.Kratochwil C, Fendler WP, Eiber M, Baum R, Bozkurt MF, Czernin J, et al. EANM procedure guidelines for radionuclide therapy with 177Lu-labelled PSMA-ligands (177Lu-PSMA-RLT). Eur J Nucl Med Mol Imaging. 2019;46(12):2536–44. [DOI] [PubMed] [Google Scholar]

[CR2] 2.Thang SP, Violet J, Sandhu S, Iravani A, Akhurst T, Kong G, et al. Poor outcomes for patients with metastatic Castration-resistant prostate Cancer with low prostate-specific membrane antigen (PSMA) expression deemed ineligible for 177Lu-labelled PSMA radioligand therapy. Eur Urol Oncol. 2019;2(6):670–6. [DOI] [PubMed] [Google Scholar]

[CR3] 3.Hooijman EL, Radchenko V, Ling SW, Konijnenberg M, Brabander T, KOOLEN, S L W, et al. Implementing Ac-225 labelled radiopharmaceuticals: practical considerations and (pre-)clinical perspectives. EJNMMI Radiopharm Chem. 2024;9(1):9. [DOI] [PMC free article] [PubMed] [Google Scholar]

[CR4] 4.Kratochwil C, Bruchertseifer F, Giesel FL, Weis M, Verburg FA, Mottaghy F, et al. 225Ac-PSMA-617 for PSMA-Targeted alpha-Radiation therapy of metastatic Castration-Resistant prostate Cancer. J Nucl Med. 2016;57(12):1941–4. [DOI] [PubMed] [Google Scholar]

[CR5] 5.Zacherl MJ, Gildehaus FJ, Mittlmeier L, Böning G, Gosewisch A, Wenter V, et al. First clinical results for PSMA-Targeted α-Therapy using (225)Ac-PSMA-I&T in Advanced-mCRPC patients. J Nucl Med. 2021;62(5):669–74. [DOI] [PubMed] [Google Scholar]

[CR6] 6.Hooijman EL, Chalashkan Y, Ling SW, Kahyargil FF, Segbers M, Bruchertseifer F et al. Development of [(225)Ac]Ac-PSMA-I&T for targeted alpha therapy according to GMP guidelines for treatment of mCRPC. Pharmaceutics, 2021;13(5). [DOI] [PMC free article] [PubMed]

[CR7] 7.Tronchin S, Forster JC, Hickson K, Bezak E. Dosimetry in targeted alpha therapy. A systematic review: current findings and what is needed. Phys Med Biol, 2022;67(9). [DOI] [PubMed]

[CR8] 8.Sgouros G, Roeske JC, Mcdevitt MR, Palm S, Allen BJ, Fisher DR et al. MIRD Pamphlet No. 22 (abridged): radiobiology and dosimetry of alpha-particle emitters for targeted radionuclide therapy. J Nucl Med, 2010;51(2):311– 28. [DOI] [PMC free article] [PubMed]

[CR9] 9.Kratochwil C, Bruchertseifer F, Rathke H, Bronzel M, Apostolidis C, Weichert W, et al. Targeted alpha-Therapy of metastatic Castration-Resistant prostate Cancer with (225)Ac-PSMA-617: dosimetry estimate and empiric dose finding. J Nucl Med. 2017;58(10):1624–31. [DOI] [PubMed] [Google Scholar]

[CR10] 10.Hofmann W, Li WB, Friedland W, Miller BW, Madas B, Bardiès M, et al. Internal microdosimetry of alpha-emitting radionuclides. Radiat Environ Biophys. 2020;59(1):29–62. [DOI] [PMC free article] [PubMed] [Google Scholar]

[CR11] 11.Li WB, Bouvier-Capely C, Saldarriaga Vargas C, Andersson M, Madas B. Heterogeneity of dose distribution in normal tissues in case of radiopharmaceutical therapy with alpha-emitting radionuclides. Radiat Environ Biophys. 2022;61(4):579–96. [DOI] [PMC free article] [PubMed] [Google Scholar]

[CR12] 12.Vaziri B, Wu H, Dhawan AP, Du P, Howell RW, Committee SM. Mird pamphlet 25: MIRDcell V2.0 software tool for dosimetric analysis of biologic response of multicellular populations. J Nucl Med. 2014;55(9):1557–64. [DOI] [PubMed] [Google Scholar]

[CR13] 13.Katugampola S, Wang J, Rosen A, Howell RW, Committee SM. Mird pamphlet 27: MIRDcell V3, a revised software tool for multicellular dosimetry and bioeffect modeling. J Nucl Med. 2022;63(9):1441–9. [DOI] [PMC free article] [PubMed] [Google Scholar]

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PERMALINK

Evaluation of relative biological effectiveness of 225Ac and its decay daughters with Monte Carlo track structure simulations

Ziyi Hu

Shuiyin Qu

Hongming Liu

Yunhao Zhang

Shuchang Yan

Ankang Hu

Rui Qiu

Zhen Wu

Hui Zhang

Junli Li

Abstract

Background

Methods

Results

Conclusions

Supplementary Information

Background

Method

Microdosimetric quantities and stochastic microdosimetric kinetic model

Microdosimetric simulations in NASIC and mSMKM parameter fitting

Fig. 1.

Microdosimetric simulations of 225Ac and its decay daughters

Fig. 2.

Fig. 3.

Table 1.

Evaluation of RBE of 225Ac and its decay daughters

Results

Parameters of mSMKM

Table 2.

Fig. 4.

Absorbed dose of cell nucleus

Table 3.

Lineal energy spectra of 225Ac and its decay daughters

Fig. 5.

Fig. 6.

RBE of 225Ac and its decay daughters

Fig. 7.

Fig. 8.

Table 4.

Discussion

Conclusions

Electronic supplementary material

Acknowledgements

Abbreviations

Author contributions

Funding

Data availability

Declarations

Ethics approval and consent to participate

Consent for publication

Competing interests

Footnotes

References

Associated Data

Supplementary Materials

Data Availability Statement

ACTIONS

PERMALINK

RESOURCES

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Evaluation of relative biological effectiveness of ²²⁵Ac and its decay daughters with Monte Carlo track structure simulations

Microdosimetric simulations of ²²⁵Ac and its decay daughters

Evaluation of RBE of ²²⁵Ac and its decay daughters

Lineal energy spectra of ²²⁵Ac and its decay daughters

RBE of ²²⁵Ac and its decay daughters