^{137}Cs,

^{134}Cs, and

^{131}I

^{1}

^{*}

^{1}

^{2}

The authors have declared that no competing interests exist.

Analyzed the data: TS. Contributed reagents/materials/analysis tools: TS KM NH. Wrote the paper: TS NH.

The risk of internal exposure to ^{137}Cs, ^{134}Cs, and ^{131}I is of great public concern after the accident at the Fukushima-Daiichi nuclear power plant. The relative biological effectiveness (RBE, defined herein as effectiveness of internal exposure relative to the external exposure to γ-rays) is occasionally believed to be much greater than unity due to insufficient discussions on the difference of their microdosimetric profiles. We therefore performed a Monte Carlo particle transport simulation in ideally aligned cell systems to calculate the probability densities of absorbed doses in subcellular and intranuclear scales for internal exposures to electrons emitted from ^{137}Cs, ^{134}Cs, and ^{131}I, as well as the external exposure to 662 keV photons. The RBE due to the inhomogeneous radioactive isotope (RI) distribution in subcellular structures and the high ionization density around the particle trajectories was then derived from the calculated microdosimetric probability density. The RBE for the bystander effect was also estimated from the probability density, considering its non-linear dose response. The RBE due to the high ionization density and that for the bystander effect were very close to 1, because the microdosimetric probability densities were nearly identical between the internal exposures and the external exposure from the 662 keV photons. On the other hand, the RBE due to the RI inhomogeneity largely depended on the intranuclear RI concentration and cell size, but their maximum possible RBE was only 1.04 even under conservative assumptions. Thus, it can be concluded from the microdosimetric viewpoint that the risk from internal exposures to ^{137}Cs, ^{134}Cs, and ^{131}I should be nearly equivalent to that of external exposure to γ-rays at the same absorbed dose level, as suggested in the current recommendations of the International Commission on Radiological Protection.

The risk of internal radiation exposure is of great public concern after the accident at the Fukushima-Daiichi nuclear power plant

A number of studies have been carried out to estimate the RBE for the intake of α, low-energy β, and Auger-electron emitters ^{137}Cs, ^{134}Cs, and ^{131}I (major contributors to the internal exposure dose from the nuclear accident in Fukushima) was not extensively discussed. This is because these RIs emit relatively high energy electrons and photons, and because the scientific community considers that their RBE is 1. Nevertheless, the public occasionally believes that the risk from internal exposure is much greater than that from external exposure even for the intake of ^{137}Cs, ^{134}Cs, and ^{131}I, albeit no supportive scientific evidence. Such belief comes, at least in part, from the lack of a detailed analysis of the contribution of the track-structure and RI-inhomogeneity effects to the RBE for the intake of these RIs, except for the RI-inhomogeneity effect of ^{131}I ^{137}Cs are localized in cell nuclei

We therefore set out to quantitatively analyze the contribution of the track-structure and RI-inhomogeneity effects for the intake of ^{137}Cs, ^{134}Cs, and ^{131}I, and for this, a microdosimetric simulation was performed using the Particle and Heavy Ion Transport code System (PHITS) version 2.64

We performed Monte Carlo particle transport simulations in ideally aligned cell systems that were internally exposed to electrons emitted from ^{137}Cs, ^{134}Cs, and ^{131}I, using the PHITS code. Electrons emitted from ^{137m}Ba, which is a daughter isotope of ^{137}Cs with a half-life of 2.552 min, were also considered in the simulation of the intake of ^{137}Cs. Similar simulations were also performed for internal exposures to electrons from ^{3}H, α particles from ^{239}Pu, and 662 keV mono-energetic photons, which is the dominant γ-rays from ^{137}Cs (in strict sense, 662 keV photons are emitted from the decay of ^{137m}Ba). The last simulation condition also represented the external exposure to γ-rays, because the source location is not an important factor for photon exposure from the microdosimetric viewpoint. Thus, this condition served as the reference condition in this study, i.e., its RBE is equal to 1. The energy spectra of particles emitted from the RIs were taken from the International Commission of Radiological Protection (ICRP) Publication 107

The geometry of the simulations is shown in ^{3} of liquid water. They were placed in an 11×11×11 lattice structure, yielding 1,331 cells in the system. Cell nuclei were categorized into six groups according to the distance from their center to the origin of the cell system, _{C} and _{N}, respectively. The _{N} was changed from 3 to 7 µm in 1 µm steps, while _{C} was set to 1.5, 2, or 3 times larger than _{N}. For each cell system and RI source, the simulations were carried out four times by changing the RI localizations, where RIs were uniformly distributed in the cell nucleus, cytoplasm, extracellular space, or entire region of the central lattice.

In the PHITS simulations, all types of radiation were transported down to 1 keV, below which particles stop and deposit their entire energy at their location, except for positrons that cause pair production. This local approximation is adequate for our simulation because the ranges of 1 keV electrons and α particles are negligibly short compared to cell size. The probability density (PD) of the specific energy _{i}_{i}_{i}

The calculated PDs of _{i}_{i}

The mean number of cell nuclei categorized in group _{Gj}, can be calculated by_{i}_{i}_{1,Gj}(

_{1}(_{1}(

To determine the contribution from cell nuclei located outside the lattice structure, which were categorized into group 7, we assumed that the single-event PD of _{1,G7}(_{1,G6}(_{G7}, can be calculated from the ratio of the total to the mean deposition energies in the outer cell nuclei, which is written as_{out} is the total deposition energy outside the lattice structure, and _{N} and _{L} are the masses of a cell nucleus and a lattice, respectively. In this study, the value of _{out} was determined by the PHITS simulation. The single-event PD of _{1,ave}(

_{ave} is the mean number of the cell nuclei having z>0 per source emission. Namely,

Similarly, the dose PD as a function of _{ave}(_{i}_{Gj}(

where

For _{G7}(_{G6}(_{ave}(

To estimate the RBE, we assumed that radiation effects are only initiated by the ionization inside a cell nucleus; although there have been several lines of evidence that targeted cytoplasmic irradiation can induce biological effects ^{137}Cs, ^{134}Cs, and ^{131}I, which are expected to be higher under this assumption; when RIs are localized in cell nuclei, the higher cell-nucleus dose directly results in higher RBE values.

Under this assumption, the RBE for the RI-inhomogeneity effect can be defined as the ratio of the mean specific energy in a cell nucleus to that in a lattice. When RIs are uniformly distributed in each lattice and equilibrium between the incoming and outgoing particle energies is established, the mean specific energy in a cell nucleus and in a lattice,

and_{L} is the total energy deposited inside a lattice, which corresponds to the mean source energy emitted from the RIs. Note that this RBE is equal to 1 for external exposure as well as internal exposure for the intake of RIs without any microscopic localization tendency, i.e., those uniformly distributed in all subcellular structures.

It should also be mentioned that RIs are inhomogeneously distributed inside the human body not only on the microscopic scale of subcellular structures but also on the macroscopic scale of organs and tissues. However, the influence of the RI inhomogeneity on the macroscopic scale has already been taken into account in estimating the effective dose for internal exposure by introducing biokinetic models as well as the tissue weighting factor

In this study, the influence of the track-structure was represented by the mean quality factor based on the _{ave}, which can be calculated by

The RBE for the track-structure effect was then obtained from the ratio of _{ave} for internal exposure to the reference condition, which was represented by exposure to 662 keV photons as above.

It should be noted that the

The bystander effect is considered attributable to the inhomogeneity of absorbed dose on microscopic scales. Thus, it should be in close connection with the PDs of

The followings are the hypotheses adopted in our model:

A cell is affected by bystander effects (e.g., those manifested as gene mutations, chromosomal aberrations, and cell killing) when receiving a bystander signal.

Bystander signals are emitted from irradiated cells triggered with a probability depending on irradiation conditions, but their strength is independent of these conditions;

The probability that a cell is not triggered after irradiated with its nucleus specific energy

Bystander signals uniformly propagate over a certain distance;

All cells within the propagation distance can receive a bystander signal irrespective of whether they are directly irradiated or not; and

The fraction of cells receiving a bystander signal from a single signal-emitting cell is constant

Except for items 3 and 5, these hypotheses are similar to those adopted in Ref.

In the second and third hypotheses, the fraction of signal-emitting cells in the radiation field having the mean absorbed dose _{S}(_{ave}(_{ave}(

_{k}_{,ave}(_{1,ave}(_{k}_{-1,ave}(

Using _{1,ave}(_{k}_{,ave}(

Let _{0} be the number of cells within the distance in which the bystander signals can propagate, and _{A}(

According to Ref. _{B}(

It should be noted that this bystander probability does not represent the fraction of cells that actually respond to the bystander signal. For example, the actual fraction of cells inactivated after receiving a cell-killing bystander signal is supposed to be 10∼20%, because the survival fraction of bystander cells is generally saturated around 80∼90%, even for high-dose irradiation _{B}(

_{1,Gj}(^{137}Cs localized inside the cell nucleus. It should be mentioned that the PD of _{N} = 3 µm, _{C} = 4.5 µm) and largest (_{N} = 7 µm, _{C} = 21 µm) cells. It can be found from _{1,G7}(_{1,G6}(

These data represent the exposure to electrons emitted from ^{137}Cs localized inside the cell nucleus. Panels A and B show the data for the smallest and largest cell sizes, respectively.

_{ave}_{1,ave}(^{137}Cs localized in either the cell nucleus, cytoplasm, or extracellular space for the median cell size (_{N} = 5 µm, _{C} = 10 µm). The PDs agreed well with one another except for the very low specific energy region, where the PDs become larger when ^{137}Cs was localized in the cell nucleus. This is because low-energy β-rays and Auger electrons can deposit their energy inside a cell nucleus only when they are generated inside or very close to the nucleus. The RBE for the RI inhomogeneity is attributed to this difference, as discussed later.

Data represent the exposure to electrons emitted from ^{137}Cs localized inside the cell nucleus, cytoplasm, and extracellular space, respectively, for a median cell size (_{N} = 5 µm, _{C} = 10 µm).

_{1,ave}(_{ave}(^{137}Cs, ^{134}Cs, and ^{131}I, agreed well with one another, and were similar to those for 662 keV photons. Conversely, the PDs for α emitter ^{239}Pu and low-energy β emitter ^{3}H were shifted to higher ^{239}Pu. This verifies that the absorbed dose distributions in subcellular and intranuclear scales are inhomogeneous for the intake of α and low-energy β emitters, when compared to high-energy β emitters producing the same mean absorbed dose. The difference in _{1,ave}(_{ave}(

Data are for the median cell size (_{N} = 5 µm, _{C} = 10 µm).

Data are for the median cell size (_{N} = 5 µm, _{C} = 10 µm).

^{3}H and ^{239}Pu due to the shorter range of the emitted particles (low-energy β and α particles, respectively). The RBE for ^{134}Cs was slightly higher than that for ^{137}Cs and ^{131}I because of its lower mean energy of the emitted β-rays.

The upper, middle, and lower panels are for the cases that RIs are localized in cell nucleus, cytoplasm, and extracellular space, respectively.

On the other hand, the RBE was less than or close to 1 when the RIs were localized in the cytoplasm or extracellular space because lower energy particles cannot reach the cell nucleus from such extranuclear compartments. Moreover, the RBE was nearly zero for ^{3}H localized in the extracellular space, thereby indicating that the β-rays emitted from ^{3}H can deposit their energy inside the nucleus only when ^{3}H is incorporated into the cell. The RBE was occasionally greater than 1 for ^{239}Pu localized in the cytoplasm because some of the emitted α particles create a Bragg peak inside the cell nucleus. It should be noted that the RBE was always equal to 1 when RIs were uniformly distributed inside a lattice, although this was not shown in the figure.

_{ave}(^{137}Cs, ^{134}Cs, and ^{131}I, and those for ^{3}H and ^{239}Pu were slightly and much larger than 1, respectively.

RI | Mean RBE | SD | P-value |

^{137}Cs |
1.00 | 0.014 | 0.40 |

^{134}Cs |
1.02 | 0.036 | 0.028 |

^{131}I |
1.02 | 0.016 | 0.035 |

^{3}H |
1.49 | 0.000 | 0.000 |

^{239}Pu |
37.0 | 0.26 | 0.000 |

It should be mentioned that the average quality factors, _{ave}, were smaller than the data given in _{ave} for the reference condition (662 keV photon exposure). This is because the reference radiation of the _{ave} for each internal exposure and the reference condition are also given in ^{137}Cs, the p-values were smaller than the significance level; p<0.05. This result indicates that their RBE values are greater than 1 in statistically significant.

Our bystander model contains four free parameters: _{0}, and

As examples, the bystander probabilities for exposure to electrons from ^{137}Cs, α particles from ^{239}Pu, and 662 keV photons are shown in _{0} = 100,000 and _{0} = 10,000 and ^{−2} to investigate the dependence of the RBE on the threshold specific energy. These data were similar irrespective of whether the RIs were uniformly distributed inside a lattice or had a microscopic localization tendency.

Panels A and B show the results for the reactive (_{0} = 100,000 and _{0} = 10,000 and

Nearly perfect agreements between the bystander probabilities for the exposures to electrons from ^{137}Cs and 662 keV photons were observed in ^{134}Cs and ^{131}I also agreed with the photon data, although not shown in the graph. These agreements were attributed to the fact that their radiation fields characterized by _{1,ave}(^{137}Cs, ^{134}Cs, and ^{131}I should be very close to 1 irrespective of the calculation conditions.

Conversely, the bystander probability for the exposure to α particles from ^{239}Pu was significantly higher than that for the electron and photon exposures at the same absorbed dose. This tendency can be explained by the probability of cell nuclei having the specific energy over _{ave}(>^{239}Pu is generally >1, and depends on both the model parameters and mean absorbed dose in a complicated manner.

Data are for exposure to electrons from ^{137}Cs, α particles from ^{239}Pu, and 662 keV photons with mean absorbed dose

It is evident from the above analyses that the RI-inhomogeneity effect is the dominant factor in determining the RBE for internal exposure to ^{137}Cs, ^{134}Cs, and ^{131}I. In this subsection, their maximum possible RBE was estimated considering the realistic RI localization tendency. ^{137}Cs, ^{134}Cs, and ^{131}I as a function of the RI fraction in cell nuclei. In this calculation, the rest of RIs was assumed to be uniformly distributed in the cytoplasm and extracellular space. These data were for the largest cell size (_{N} = 7 µm, _{C} = 21 µm), which yielded the highest RBE as shown in

Data are for exposure to electrons emitted from ^{137}Cs, ^{134}Cs, and ^{131}I, and for the largest cell size (_{N} = 7 µm, _{C} = 21 µm).

According to an animal study in Ref. ^{137}Cs were localized inside the cell nuclei. If the maximum fraction of ^{137}Cs and ^{134}Cs in nuclei of human cells is also 21%, then the maximum possible RBE for exposure to electrons from those RI will be ∼1.1 and ∼1.2, respectively. This estimate is quite conservative because cell-nucleus mass adopted in this calculation was very small – only 2% of the total weight. Thus, intranuclear cesium concentration is approximately 10 times higher than that in the other structures. This value is quite high compared to the results obtained with the yeast ^{137}Cs and ^{134}Cs, respectively, on the basis of the specific absorbed fractions calculated using the ICRP/ICRU adult male reference phantom ^{137}Cs and ^{134}Cs including the photon contribution were approximately 1.04 and 1.03, respectively.

For the exposure to ^{131}I, there is no evidence that thyroid cell nucleus accumulates iodine, although its subcellular distribution has not been thoroughly revealed. In addition, the extracellular space such as lumen and blood contains a non-trivial portion of iodine ^{131}I was much smaller than that in thyroid, which accounted for ∼98% of the effective dose. Thus, the assumption that iodine is uniformly distributed inside the cell nuclei probably yields an adequate estimate of the RBE due to the intake of ^{131}I. Even if the intranuclear iodine concentration is twice as high as that of the entire system, the RBE would only be 1.02.

The PDs of specific energy inside cell nuclei and dose PDs of the lineal energy for a site diameter of 1 µm for internal exposure to ^{137}Cs, ^{134}Cs, and ^{131}I, as well as external exposure to 662 keV photons, were calculated by performing Monte Carlo particle transport simulations with PHITS. The RBEs for the RI-inhomogeneity, track-structure, and bystander effects were then derived from the calculated PDs. The RBEs for the track-structure and bystander effects were very close to 1, owing to the nearly identical PDs between the internal exposure and the external exposure to 662 keV photons. On the other hand, the RBEs for the RI-inhomogeneity effect largely depended on the intranuclear RI concentration and cell size. However, their maximum possible RBE was only 1.04 even under conservative assumptions. Therefore, it can be concluded from the microdosimetric viewpoint that the risk from internal exposure to these RIs should be nearly equivalent to that from external exposure to γ-rays at the same absorbed dose level, as suggested in the current ICRP recommendations

We wish to thank Dr. R. Leggett of Oak Ridge National Laboratory, and Drs. A. Endo, F. Takahashi, K. Sato, and R. Watanabe of JAEA for their advice on this work.

_{R}). ICRP Publication 92.