Recently, targeted alpha therapy (TAT) is gaining grounds as a novel treatment for refractory cancer, particularly after an excellent treatment effect of 225Ac-PSMA-617 [1]. We have already proved the therapeutic efficacies of [211At]NaAt against differentiated thyroid cancer, 211At-labeled phenylalanine for glioma, and 225Ac-labeled fibroblast activation protein inhibitors (FAPI) against pancreatic cancer in preclinical studies [2,3,4]. For clinical translation, physicians initiated clinical trial is under preparation using [211At]NaAt in patients with differentiated thyroid cancer refractory to radio-iodine (131I) treatment. However, the TAT drugs which are successful in clinical application is still limited, and we need practical tools to evaluate the precise dose in the target and risk organs to define the most suitable dose for individual patients.

The absorbed dose (Gy) has generally been used as the primary index for predicting the therapeutic effects on tumor and unintended harmful effects on normal tissue, both in preclinical and clinical trials. In addition, higher relative biological effectiveness (RBE) must be considered in this prediction because α particles densely deposit their energies along their tracks and effectively induce cell killing compared to X-rays and β particles with the same dose. For simplicity, a fixed RBE value of 5 is recommended to use in the dosimetry of TAT [5]. However, actual values of RBE intrinsically depend on the absorbed dose. Thus, explicit consideration of the dose dependence of RBE in the design of TAT is desired in the same way as the carbon ion therapy [6]. In addition, the repair mechanism during the irradiation must also be considered because of a relatively lower dose rate of TAT in comparison to external radiotherapy. Therefore, the concept of the equieffective dose, EQDX(α/β), formalism was proposed to use in the TAT dosimetry [7], where EQDX represents the absorbed dose to give the same biological effect of the reference treatment, e.g., fractionated X-ray therapy [8]. The commonly used biological effective dose, BED [9], is a special case of EQDX(α/β). Using EQDX(α/β), the therapeutic and side effects of TAT can be predicted from the clinical data largely available from conventional external radiotherapy.

Dosimetry systems based on standardized phantoms such as OLINDA/EXM [10] and IDAC-Dose 2.1 [11] are widely used to estimate organ doses in nuclear medicine. However, they have some shortcomings when applied to the targeted radionuclide therapy (TRT) including TAT. For example, they cannot consider detailed anatomical differences of each patient and cannot calculate the heterogeneity of absorbed doses in the target tumor and normal tissues, which may influence tumor response and normal tissue toxicity. Therefore, several authors [12,13,14,15,16,17,18] developed 3-dimensional dosimetry systems by automatically creating patient-specific human phantoms and spatial distributions of radionuclides from CT and PET/SPECT images, respectively. These systems allow for a sophisticated design of TRT by calculating more detailed dosimetric quantities such as dose-mass histograms (DMH) in target tumor and normal tissues. In addition, some of them have a function of evaluating BED based on their calculated absorbed doses and dose rates. However, none of the existing system was capable of calculating EQDX(α/β) for TAT, considering the complex dose dependence of RBE.

Under these situations, we developed a patient-specific dosimetry system that can calculate EQDX(α/β) for TAT as well as other TRT, based on the Particle and Heavy Ion Transport code System (PHITS) [19] coupled with the microdosimetric kinetic model (MKM) [20]. The accuracy of RBE estimated by PHITS coupled with MKM was well verified for proton therapy [21], carbon-ion therapy [22], and boron neutron capture therapy (BNCT) [23]. In the system, a voxel phantom and a cumulative activity distribution map of a patient are automatically created in the PHITS input format from PET-CT images, respectively. After the PHITS simulation using these input files, EQDX(α/β) as well as the total absorbed dose and deposition energy in each voxel are estimated, considering the microscopic dose distribution and dose rate. In this study, the performance of the system was examined using the dynamic PET-CT data, and the results were compared with corresponding data obtained from OLINDA 2.0 [10].


Individual dosimetry system based on PHITS

Figure 1 shows the flowchart of our dosimetry system, which was developed as an extension of the radiotherapy package based on PHITS, so-called RT-PHITS. It can be divided into three processes: (1) conversion from PET-CT images to PHITS input files, (2) calculation of absorbed doses using PHITS, and (3) estimation of EQDX(α/β) based on the PHITS results coupled with MKM. EQDX(α/β) as well as total dose and deposition energy in each voxel are converted in DICOM RT-DOSE format. Thus, they can be imported to commercial DICOM software for further analysis. Details of each process are described below.

Fig. 1
figure 1

Flowchart of the individual dosimetry system based on PHITS

Conversion from PET-CT images to PHITS input files

Firstly, the patient-specific voxel phantom in the PHITS input format is created from his/her CT image using the CT2PHITS module, which was formerly called DICOM2PHITS [19]. Then, we adopted the correlation between CT numbers (Hounsfield Unit) and tissue parameters proposed by Schneider et al. [24] in this conversion, though users can define their own formula to represent the correlation in our system. The tallies for scoring the absorbed doses in Gy and deposition energies in MeV are also generated during this process. The resolutions of the created voxel phantom and mesh tallies are the same as the CT image.

A new module of RT-PHITS named PET2PHITS was developed in this study to create the maps of the cumulative activities as well as biological decay constants of the radionuclides based on the PET images. There are two types of patient-specific dosimetry systems; one is to create time-dependent activity maps and execute the particle transport simulations for each time step, and the other is to create a cumulative activity map and execute a single particle transport simulation. Using the former method, dynamical dose evaluation is possible by fitting the calculated doses for each time step. However, it is very time-consuming because the Monte Carlo simulation needs to be continued until sufficiently small statistical uncertainties of the calculated doses in each voxel and time step are obtained to achieve the meaningful fitting. We therefore adopted the latter method; our system determines the cumulative activities and the biological decay constants of the radionuclides by fitting the dynamic PET images. Then, the dose rates are estimated under the assumption that they are proportional to the sum of the physical and biological decay constants of nearby voxels. The detail procedures for determining the cumulative activities and the biological decay constants are shown in Appendix A.

Calculation of absorbed doses using PHITS

Using the input files created from CT and PET images, PHITS simulation is performed to calculate the absorbed doses in the patient. In this study, PHITS version 3.20 was employed, and the EGS5 mode [25] was used for the photon, electron, and positron transport. The fluences of the source particles including the contributions from daughter nuclides are determined from the RI source generation function in PHITS, based on ICRP Publication 107 [26]. The absorbed doses due to the ionization induced by α and β± particles (referred to α and β doses, respectively) were separately calculated in the simulation. Note that the kerma approximation was not adopted, and thus, the photon doses were categorized as their secondary particle doses, i.e., β dose.

Before performing the particle transport simulation inside the patient body, another PHITS simulation must be performed to calculate the dose probability densities (PD) of lineal energy, d(y), in water for α and β doses, which are to be provided to MKM for the RBE estimation. The definition of the fundamental microdosimetric quantities such as lineal energy y is described in Appendix B. This simulation is required once for each radionuclide because it is not specific at each patient. The microdosimetric function of PHITS [27] is utilized for this calculation because the site size of y needed to be evaluated for MKM is too small (less than 1 μm) to be handled with the condensed history method employed in EGS5. Note that the microdosimetric function was developed by fitting the results of track-structure simulation. Thus, it can analytically determine the PD of y down to the nanometer scales, considering the dispersion of deposition energies from the production of δ-rays. Figure 2 shows examples of the calculated PD of y for α and β doses of 211At.

Fig. 2
figure 2

Calculated dose PD of y, yd(y), for rd = 0.282 μm for the α and β doses of 211At

Estimation of EQDX(α/β)

EQDX(α/β) is defined as the total absorbed dose delivered by the reference treatment plan (fraction size X) leading to the same biological effect as a test treatment plan [8]. Assuming that the biological effectiveness is proportional to the cell surviving fraction following a linear-quadratic (LQ) relationship, EQDX(α/β) for a test treatment with the surviving fraction S can be calculated by

$$ \mathrm{EQDX}\left(\frac{\alpha }{\beta}\right)=\frac{-\ln (S)}{\alpha +\beta X}, $$

where α and β are the LQ parameters for the reference treatment. Based on MKM with the extensions of the saturation correction due to the overkill effect [28] and the dose rate effect [29], the cell surviving fraction in any radiation field with an absorbed dose D can be estimated by

$$ S(D)=\exp \left[-\left({\alpha}_0+\beta {z}_{1\mathrm{D}}^{\ast}\right)D- G\beta {D}^2\right], $$

where α0 is the linear coefficient of the surviving fraction with the limit of LET → 0, G is the correction factor due to the dose rate effect, and \( {z}_{1\mathrm{D}}^{\ast } \) is the saturation-corrected dose-mean specific energy, deduced by

$$ {z}_{1\mathrm{D}}^{\ast }=\frac{1}{\pi {r}_{\mathrm{d}}^2}{y}^{\ast }=\frac{1}{\pi {r}_{\mathrm{d}}^2}{y}_0^2\int \frac{\left[1-\exp \left(-{y}^2/{y}_0^2\right)\right]d(y)}{y}\mathrm{d}y, $$

where y* is the saturation-corrected lineal energy, rd is the radius of a subcellular structure referred to as domain, y0 is a so-called saturation parameter that indicates the lineal energy above which the saturation correction due to the overkill effect becomes very important, and d(y) is the dose probability density in domain. d(y) in each voxel can be determined from its α and β doses, Dα and Dβ, respectively, as written by

$$ d(y)=\frac{D_{\alpha }{d}_{\alpha }(y)+{D}_{\beta }{d}_{\beta }(y)}{D_{\alpha }+{D}_{\beta }}, $$

where dα(y) and dβ(y) are their dose PD for each radionuclide precalculated by PHITS using the microdosimetric function. More detailed descriptions about the features of MKM are given in Appendix B in addition to the definition of fundamental microdosimetric quantities.

Assuming that the dose rates of TRT are expressed as a mono-exponential function with a decay constant of λphy + λbio, where λphy and λbio are the physical and biological decay constants, respectively, the value of G can be calculated using [13]

$$ G=\frac{\lambda_{\mathrm{phy}}+{\lambda}_{\mathrm{bio}}}{\mu +{\lambda}_{\mathrm{phy}}+{\lambda}_{\mathrm{bio}}}, $$

where μ is the recovery rate constant. The parameters α, β, μ, α0, rd, and y0 depend on the cell line. Among them, α0, rd, and y0 are specific to MKM, and their determination requires the experimental data of cell surviving fractions for various ion irradiations, which are generally not available. Thus, we fixed rd and y0 to 0.282 μm and 93.4 keV/μm, respectively, which were evaluated from the surviving fractions of the HSG cell irradiated by various radiations including He ions [30, 31], and calculated α0 from α and \( {z}_{1\mathrm{D}}^{\ast } \) for the reference radiation, \( {z}_{1\mathrm{D},\mathrm{ref}}^{\ast } \), using the equation of \( {\alpha}_0=\alpha -\beta {z}_{1\mathrm{D},\mathrm{ref}}^{\ast } \). Then, the user input parameters to our dosimetry system are α, β, and μ, which can be obtained from the measured surviving fractions of the reference radiation, as well as the fraction size X. Referring to our previous works [23, 30], we set α = 0.251 Gy−1, β = 0.0615 Gy−2, μ = 1.5 h−1, and X =2 Gy in the test simulations performed in this study. Consequently, EQDX(α/β) calculated in this study can be expressed as EQD2(4.08), where 4.08 is the α/β ratio, i.e., 0.251/0.0615.

EQDX(α/β) in a certain voxel can be simply calculated from Eq. 1 by substituting the surviving fraction in the voxel obtained from Eq. 2. In contrast, special care should be taken when EQDX(α/β) in a certain volume of interest (VOI) consisting of multiple voxels such as tumor and normal tissue is calculated because of the non-linear relationship between the EQDX(α/β) and the surviving fraction. In such cases, the mean surviving fraction in VOI, SVOI, is given by

$$ {S}_{\mathrm{VOI}}=\frac{\sum_i{S}_i\left({D}_i\right){m}_i}{\sum_i{m}_i}, $$

where Si, Di, and mi are the surviving fraction, dose, and mass, respectively, of voxel i made up of VOI. EQDX(α/β) in VOI can be obtained from Eq. 1 by supplying SVOI to S in similar to the concept of the equivalent uniform dose (EUD) [32]. DMH in VOI is the key quantity in this evaluation, which can be also calculated from our dosimetry system. These calculations are performed by a newly developed module of RT-PHITS named PHITS2TRTDOSE.

Dynamic PET-CT acquisition and analysis

This study was approved by the institutional review board, and written informed consents were obtained from all participants. The performance of the system was examined using the dynamic PET-CT data of four healthy volunteers after injecting 18F-labeled NKO-035 with 221.6 ± 3.8 MBq, which is a specific substrate of L-type amino acid transporter-1 (LAT1). The dynamic PET data were acquired in nine frames (total scan duration: 90 min) with low-dose CT scan. All images were depicted by OSIRIX (Newton Graphics, Inc., Sapporo, Japan). Details of the data acquisition procedures were described in Appendix C. In the dose estimation, NKO-035 was assumed to be labeled with not only 18F but also 211At, 131I, and 177Lu with the same distribution in the body. Volume of interest was placed in major organs on dynamic PET images using PMOD software (PMOD Technologies Ltd., Zurich, Switzerland) with reference to CT images. The residence times in major organs and tissues were estimated for each patient based on their dynamic PET data using the method described in Appendix A. Supplying those data into OLINDA 2.0, the organ doses were calculated and compared with the corresponding data obtained from our dosimetry system by Bland-Altman analysis.


Figure 3 shows the coronal view of CT and PET scans for a volunteer after injecting 18F-NKO-035, and the corresponding deposition energy, absorbed dose, and EQD2(4.08) maps, where 4.08 is the α/β ratio. The history number of the PHITS simulation was set to 300 million so that the statistical uncertainties are very small. The deposition energy map seems to be a blurred image of the PET data particularly around the high-activity organs such as kidney and bladder because annihilation γ-rays deposit their energies rather far from the source location. In contrast, the dose and EQD2(4.08) maps exhibit higher values even at low activity regions such as the lungs. This is because the dose and EQDX(α/β) are closely related to the activity per mass (and not volume) and consequently tend to be higher at low-density regions. The relative distributions of the dose and EQD2(4.08) are similar to each other, though the absolute values of EQD2(4.08) are approximately 74% of the corresponding dose as discussed later.

Fig. 3
figure 3

Representative CT and PET images (90 min average) of a volunteer after the injection of NKO-035 labeled with 18F and the corresponding deposition energy, absorbed dose, and EQD2(4.08) maps obtained from RT-PHITS

Table 1 summarises the absorbed doses in the brain, lung, liver, spleen, pancreas, and kidney obtained from RT-PHITS and OLINDA 2.0. It constitutes the mean values and standard deviations of the four volunteers after injection of NKO-035 virtually labeled with 1 MBq of 18F, 211At, 131I, or 177Lu. The mean organ doses for four volunteers calculated by RT-PHITS agree with the corresponding OLINDA data mostly within 20%. Figure 4 shows the Bland-Altman plot between the mean and percent difference of the organ doses calculated by RT-PHTIS and OLINDA 2.0 for each volunteer, radioisotope, and organ. It is evident that data are scattered randomly with respect to the mean organ doses.

Table 1 Absorbed doses (μGy) in the brain, lung, liver, spleen, pancreas, and kidney obtained from RT-PHITS and OLINDA 2.0. The data are the mean value and standard deviation (S.D.) of the four volunteers with the injection of NKO-035 virtually labeled with 1 MBq of 18F, 211At, 131I, or 177Lu
Fig. 4
figure 4

Bland-Altman plot between the mean and percent difference of the organ doses calculated by RT-PHITS and OLINDA 2.0 for each volunteer, radioisotope, and organ. The percent differences were obtained from (DRT-PHITSDOLINDA)/Dmean, where DRT-PHITS and DOLINDA are organ doses calculated by RT-PHITS and OLINDA 2.0, respectively, while Dmean is the mean value of the two doses


We have developed an individual dosimetry system, including the function for calculating EQDX(α/β), based on PHITS coupled with the microdosimetric kinetic model. The agreements between the calculated doses obtained from RT-PHITS and OLINDA 2.0 are quite satisfactorily, confirming the reliability of our developed system. In addition, no apparent trend is observed in the Bland-Altman plot drawn in Fig. 4, suggesting that the discrepancies between RT-PHITS and OLINDA results are predominantly attributed to random issues such as anatomical differences between each volunteer and the standardized phantom adopted in OLINDA 2.0. For example, data with the percent difference out of ± 1.96 S.D. are for organs whose masses differ from those of the standardized phantom by more than 30%.

Figure 5 shows the activity dependency of the calculated dose and EQD2(4.08) in the kidney for a volunteer after injecting NKO-035 labeled with 211At or 18F. The calculated doses are directly proportional to the injection activity because the biokinetics of the radionuclides are assumed to be independent of their activity in this calculation. In contrast, EQD2(4.08) complicatedly depend on the injection activity. For 211At, they are higher and lower than the corresponding dose at lower and higher activities, respectively, and vice versa for 18F.

Fig. 5
figure 5

Activity dependences of the calculated dose and EQD2(4.08) in the kidney for volunteer 1 with the injection of NKO-035 labeled with 211At or 18F

In order to clarify these complicated relationships, we calculated EQD2(4.08) without considering the dose heterogeneity by simply averaging EQD2(4.08) in the kidney, and those without considering the dose-rate effect by setting the recovery rate constant μ = 0. Figure 6 shows the ratios of each EQD2(4.08) to the corresponding absorbed dose as a function of the injection activity. It is evident from the graph that ignoring the dose heterogeneity results in the increase of EQD2(4.08) particularly when injecting 211At with higher activities. This tendency can be explained due to the following. Firstly, the surviving fractions at high-dose irradiation are predominantly determined from those of cells having relatively smaller doses as discussed in our previous paper [33]. Lastly, the dose heterogeneity is relatively large for the injection of 211At in comparison to 18F, as shown in Fig. 7. Therefore, the consideration of the dose heterogeneity in a target volume is indispensable in the clinical design of TAT. The ignorance of the dose-rate effect also results in the increase of EQD2(4.08), but its influence is not so significant and is limited only at higher activities. This is because the dose rates are not very low in the studied cases owing to rather short half-lives of 211At and 18F, and the dose-rate effect reduces the coefficient of the quadratic term as expressed in Eq. 2, which is important only at high-dose irradiation. Note that the ratio of EQD2(4.08) to dose at lower activities becomes closer to 5.5 and 0.74 for 211At and 18F, respectively, which correspond to RBE at the limit of D → 0, RBEM, multiplied with α/(α+βX).

Fig. 6
figure 6

Activity dependences of the ratios of EQD2(4.08) to the corresponding dose for the kidney. The data for EQD2(4.08) calculated without considering the dose heterogeneity or the dose-rate effect are also plotted

Fig. 7
figure 7

Dose mass histogram (DMH) in the kidney for volunteer 1 with the injection of NKO-035 labeled with 211At or 18F. The mean doses were adjusted to 1 Gy for both DMH

It should be mentioned that the model parameters used in these test calculations were determined from the surviving fractions of cells irradiated with external radiations, which might be inappropriate to be used for representing the surviving fraction of TAT because the absorbed doses are heterogeneously distributed in a microscopic scale due to the heterogeneity of radionuclides among each cell compartment [34] and organ microstructure [35]. Thus, the evaluation of the reliable model parameters is the key issue for introducing RT-PHITS in the preclinical study of TAT. For precisely calculating the doses in organs with fine structure such as stomach wall, implementation of tetrahedral-mesh phantoms in RT-PHITS is ongoing by introducing the technology developed by another PHITS-based internal dosimetry tool PARaDIM [36]. Reduction of the computational time is also desirable before the practical use of RT-PHITS in the clinic because PET-CT data of patients are generally confidential and not able to be transferred to a high-performance computer that is publicly accessible. Currently, the conventional organ dose calculation using RT-PHITS costs less than a few CPU hours, but the precise estimation of EQDX requires at least 100 CPU hours because the statistical uncertainties in each voxel must be very small in the calculation.


As an extension of RT-PHITS, we developed an individual dosimetry system dedicated to nuclear medicine particularly to TAT based on PHITS coupled with the microdosimetric kinetic model. It calculates not only absorbed doses but also EQDX(α/β) from the PET-CT images, considering the dose dependence of RBE, the dose-rate effect, and the dose heterogeneity. With these functionalities, RT-PHITS enables us to predict the therapeutic and side effects of TAT based on the clinical data largely available from conventional external radiotherapy. RT-PHITS including the modules developed in this study has been implemented in the latest version of PHITS, which is freely available upon the request to Japan Atomic Energy Agency.