Internal dose assessment of ²¹⁰Po using biokinetic modeling and urinary excretion measurement

Abstract

The mysterious death of Mr. Alexander Litvinenko who was most possibly poisoned by Polonium-210 (²¹⁰Po) in November 2006 in London attracted the attention of the public to the kinetics, dosimetry and the risk of this high radiotoxic isotope in the human body. In the present paper, the urinary excretion of seven persons who were possibly exposed to traces of ²¹⁰Po was monitored. The values measured in the GSF Radioanalytical Laboratory are in the range of natural background concentration. To assess the effective dose received by those persons, the time-dependence of the organ equivalent dose and the effective dose after acute ingestion and inhalation of ²¹⁰Po were calculated using the biokinetic model for polonium (Po) recommended by the International Commission on Radiological Protection (ICRP) and the one recently published by Leggett and Eckerman (L&E). The daily urinary excretion to effective dose conversion factors for ingestion and inhalation were evaluated based on the ICRP and L&E models for members of the public. The ingestion (inhalation) effective dose per unit intake integrated over one day is 1.7 × 10⁻⁸ (1.4 × 10⁻⁷) Sv Bq⁻¹, 2.0 × 10⁻⁷ (9.6 × 10⁻⁷) Sv Bq⁻¹ over 10 days, 5.2 × 10⁻⁷ (2.0 × 10⁻⁶) Sv Bq⁻¹ over 30 days and 1.0 × 10⁻⁶ (3.0 × 10⁻⁶) Sv Bq⁻¹ over 100 days. The daily urinary excretions after acute ingestion (inhalation) of 1 Bq of ²¹⁰Po are 1.1 × 10⁻³ (1.0 × 10⁻⁴) on day 1, 2.0 × 10⁻³ (1.9 × 10⁻⁴) on day 10, 1.3 × 10⁻³ (1.7 × 10⁻⁴) on day 30 and 3.6 × 10⁻⁴ (8.3 × 10⁻⁵) Bq d⁻¹ on day 100, respectively. The resulting committed effective doses range from 2.1 × 10⁻³ to 1.7 × 10⁻² mSv by an assumption of ingestion and from 5.5 × 10⁻² to 4.5 × 10⁻¹ mSv by inhalation. For the case of Mr. Litvinenko, the mean organ absorbed dose as a function of time was calculated using both the above stated models. The red bone marrow, the kidneys and the liver were considered as the critical organs. Assuming a value of lethal absorbed dose of 5 Gy to the bone marrow, 6 Gy to the kidneys and 8 Gy to the liver, the amount of ²¹⁰Po which Mr. Litvinenko might have ingested is therefore estimated to range from 27 to 1,408 MBq, i.e 0.2–8.5 μg, depending on the modality of intake and on different assumptions about blood absorption.

Introduction

Polonium-210 (²¹⁰Po) is a natural radionuclide which decays to ²⁰⁶Pb, emitting alpha particles with energy of 5.3044 (100%) and 4.5166 MeV (0.00122%) [1]. The half-life of ²¹⁰Po is 138.376 days [1], which corresponds to a specific activity of 1.66 × 10¹⁴ Bq g⁻¹. High amounts of pure ²¹⁰Po activity can be produced by three ways: the activation of ²⁰⁹Bi (natural abundance 100%) with thermal neutrons (cross section σ = 0.034 barn), the separation from ²²²Rn daughter nuclides emanated from ²²⁶Ra, and the separation from Pb–Bi alloy coolants of some fast neutron reactors.

²¹⁰Po is a decay daughter of ²¹⁰Pb in ²³⁸U decay chain of the uranium series; it occurs in the uranium ores and exists ubiquitously in the environment. According to the United Nations Scientific Committee on the Effects of Atomic Radiation (UNSCEAR) [2], the concentration of ²¹⁰Po in air is reported to be from 10 to 80 μBq m⁻³ with a reference value of 50 μBq m⁻³; the annual intake of the public ranges from 18 Bq in South America to 220 Bq in Asia with a reference value of 58 Bq. Through inhalation and diet ²¹⁰Po is accumulated in the human body, its concentration in human tissues is 200 mBq kg⁻¹ in lungs, 600 mBq kg⁻¹ in liver, 600 mBq kg⁻¹ in kidneys, 100 mBq kg⁻¹ in muscle and other tissues, and 2,400 mBq kg⁻¹ in bone. However, these body contents are reference values, they vary between individuals. The presence of ²¹⁰Po in tobacco greatly increases the intake of this radionuclide by smokers. Recently, Desideri et al. [3] reported that in Italy smokers who smoke 20 cigarettes per day inhale, on average, 79.5 mBq of ²¹⁰Po daily; those smokers concomitantly inhale the same amount of radioactivity from ²¹⁰Pb. The measured ²¹⁰Po concentration in lung parenchyma of smokers is about three times that of non-smokers [4]. Hill reported a higher content of ²¹⁰Po in kidneys, liver, lungs, and gonads for smokers compared to non-smokers [5].

With regard to daily excretion, Glöbel et al. [6] reported in 1966 the measurements in one German subject to be in the range of 40.7–351.5 mBq in feces and 2.2–37 mBq in urine. Naumann et al. [7] reported daily urinary excretion ranging from 2.8 (detection limit of 2 mBq l⁻¹ with urinary excretion of 1.4 l d⁻¹) to 9.9 mBq d⁻¹ in Berlin area. Dalheimer et al. [8] recently reported a daily urinary excretion median value of 3.5 mBq d⁻¹ for non-smokers and 6.6 mBq d⁻¹ for smokers. In Brazil, the reported values of ²¹⁰Po excretion in urine were 5.2 mBq l⁻¹ for non-smokers and 9.8 mBq l⁻¹ for smokers [9, 10]. In Saudi Arabia, the measured values range from 1.5 to 10 mBq l⁻¹ for non-smokers and 3.3 to 15.9 mBq l⁻¹ for smokers [11].

According to the model recommended by the International Commission on Radiological Protection (ICRP), about 10–50% of ingested ²¹⁰Po is absorbed by the intestine and flows into the bloodstream and mostly deposits in the liver, kidneys, spleen, red bone marrow and other tissues [12]. To distinguish between ingestion of the organic and inorganic forms of polonium, ICRP recommended an f ₁ value of 0.1 for workers and 0.5 for members of the public [12]. For intake by inhalation, ICRP recommended an f ₁ value of 0.1 for workers and members of the public inhaling the material of Type F (fast absorption into blood) and M (moderate absorption into blood) [13, 14], an f ₁ value of 0.01 was used for members of the public inhaling the material of Type S (slow absorption into blood) [14]. The effective dose coefficients of ²¹⁰Po for adult members of the public recommended by ICRP are 1.2 × 10⁻⁶ Sv Bq⁻¹ for ingestion calculated with an f ₁ value of 0.5, and 3.3 × 10⁻⁶ Sv Bq⁻¹ for inhalation assuming a material of Type M with an f ₁ value of 0.1 [14].

As reported in the media, Mr. Alexander Litvinenko died 23 days (the 23rd of November 2006 was included) after he was possibly poisoned by ²¹⁰Po. In this context, the organ absorbed doses in the days following, say from days 1 to 30, after acute intake of ²¹⁰Po are important for intake lethal dose estimation. The equivalent dose and effective dose coefficients are needed for the effective dose and the risk assessments of other probably contaminated members of the public.

In the present work, the daily urinary and fecal excretions, the time-dependence of the equivalent dose and the effective dose from 1 to 1,000 days after acute ingestion and inhalation of 1 Bq of ²¹⁰Po were calculated using the biokinetic model for polonium recommended by ICRP [12] and the model recently developed by Leggett and Eckerman (L&E) [15]. These modeled excretions and dose coefficients can be used for the estimate of intake and the risk assessment, provided that the ²¹⁰Po urinary or other excreta data are available from the people who were potentially contaminated in this ²¹⁰Po accident. The GSF Radioanalytical Laboratory measured urine samples of seven German subjects who were suspected to have been exposed to traces of ²¹⁰Po in the aftermath of the poisoning of Mr. Litvinenko. Those measured results and the calculated conversion factors of the daily urinary excretion to effective dose are applied to assess the effective dose for those persons. In order to estimate the possible intake of ²¹⁰Po and organ dose for Mr. Litvinenko, the mean organ absorbed dose was calculated applying the two above-mentioned models. The results obtained using ICRP and L&E models are compared and critically discussed.

Materials and methods

Experimental measurement of urinary excretion of ²¹⁰Po

Seven persons (5 male and 2 female) aged from 23 to 48 years from Germany provided their 24-h-urine samples in December 2006. Among those persons only one was a smoker. Information on the suspected day of exposure to ²¹⁰Po was also acquired. Samples were measured between 6 and 12 days after the possible exposure. The complete 24-h-urine samples were transferred into appropriate glass beakers. The sampling containers were washed twice with 20 ml 9 M HCl. The washing solutions were added to the samples. About 160 mBq ²⁰⁸Po yield tracer and 1 g ascorbic acid per liter urine were added. Polonium was deposited onto copper discs (20 h, 20°C). The urine was discarded and the discs were rinsed with water and isopropanole. The polonium isotopes were determined by alpha spectrometry with Canberra PIPS detectors in vacuum chambers. The spectra were evaluated with Eurisys Interwinner Software. The analytical procedure was last validated by participating in the IAEA proficiency test IAEA-CU-2007-09 on the determination of ²¹⁰Po in water.

Biokinetic model of ²¹⁰Po

The ICRP and L&E systemic biokinetic models of polonium [12, 15], coupled with the gastrointestinal tract model of ICRP Publication 30 [16] and the respiratory tract model of ICRP Publication 66 [17], were used to calculate the retentions of ²¹⁰Po in organs or tissues after incorporation. In the ICRP model, a fraction of 30, 10, 5, 10, and 45% of polonium entering into the systemic circulation is deposited in the liver, kidneys, spleen, red marrow and the rest of the body, respectively. It is retained in those organs with a half-life of 50 days. A ratio of 1:2 between the urinary and fecal excretions is assumed for systemic polonium [12]. Recently, an improved, physiologically realistic systemic biokinetic model for polonium in humans was constructed by Leggett and Eckerman based on the data identified to most likely represent the typical behavior of polonium in laboratory animals and human subjects [15]. In contrast to the current ICRP model, the new proposed model enables one to predict the excretion of polonium in human hair and sweat. In addition, a compartment representing the bone surface was integrated into the model of polonium. The urinary excretion pathway is more physiologically realistic than the current ICRP model. Therefore, the new model is expected to provide a more reliable estimation of the intake and the effective dose from the measured urinary excretion data.

Dose calculation of ²¹⁰Po after ingestion and inhalation

The average organ absorbed dose, D _T , in an organ or a tissue T, due to nuclear transformations, U _S , of a radionuclide in various source organs S, is calculated applying the methodology developed by the Medical Internal Radiation Dose (MIRD) Committee [18]: $D_{T} = {\sum\limits_s { \ifmmode\expandafter\tilde\else\expandafter\sim \fi{A}_{S} \times S{\left( {T \leftarrow S} \right)}} },$ where $\ifmmode\expandafter\tilde\else\expandafter\sim \fi{A}_{S}$ is the time-integrated, or cumulated activity, and is equal to the number of transformations U _S in S; S(T ← S) is the absorbed dose in T per unit cumulated activity in S. The equivalent dose, H _T , is given by summing the product of U _S and the specific effective energy [SEE(T ← S)] over all source organs, S [19]. In the values of the specific effective energy each type of radiation is weighted by a given radiation weighting factor, which accounts for the different effectiveness in inducing late effects.

The U _S of the radionuclide in the source organ or tissue was obtained by integrating the retention function, which was modeled by the SAAM II program (University of Washington, Seattle, WA). The values of S(T ← S) and SEE(T ← S) were calculated by using the SEECAL program [20]. The effective dose, E, was calculated by the sum of the product of the equivalent dose, H _T and the corresponding tissue weighting factor, w _T , over 12 organs and tissues (T) and the product between the equivalent dose of the so called remainder tissue, H _rem, and its weighting factor, w _rem [19, 21]. The equivalent dose of the colon, H _colon, was calculated as 0.57 × H _ULI + 0.43 × H _LLI, where H _ULI and H _LLI are the equivalent doses in the walls of the upper large intestine (ULI) and the lower large intestine (LLI), respectively [19]. The dose of thymus is taken as a surrogate for the oesophagus, in absence of a dosimetric model for the oesophagus [12]. For the lungs, the apportionment factors for target cells in different lung regions recommended by ICRP were used [17].

Results and discussion

Firstly, the measured ²¹⁰Po urinary excretion is presented. Secondly, the time-dependent organ equivalent dose, effective dose, organ absorbed dose and daily excretion in urine and in feces, in hair and sweat after acute ingestion and inhalation of ²¹⁰Po are shown. The average values of body content and daily excretion of ²¹⁰Po for the normal unexposed public are estimated. Finally, the effective doses for the possibly contaminated seven subjects are predicted. The amount of ²¹⁰Po Mr. Litvinenko probably ingested are estimated and discussed based on different assumptions.

Measured ²¹⁰Po urinary excretion

Figure 1 shows one alpha spectrum of the samples. The ²⁰⁸Po tracer contained some ²⁰⁹Po impurities. However, this did not interfere with the determination of ²¹⁰Po. In Table 1, the ²¹⁰Po activities (±1 combined standard uncertainty) of seven 24-h-urine samples are shown. Daily urinary excretion ranged from 3.3 to 26.4 mBq d⁻¹, with a mean value of 11.3 mBq d⁻¹. All these values are in the range of natural levels, and below the reported level of 30 mBq d⁻¹ set by the Health Protection Agency (HPA) [22].

Fig. 1

Alpha spectrum of ^208/209/210Po isolated from one 24-h-urine sample. ²⁰⁹Po is an impurity of the ²⁰⁸Po tracer

Table 1 ^{21 0}Po activities (±1 combined standard uncertainty) of the 24-h-urine samples and the estimate of effective dose for the possible contaminated persons

²¹⁰Po organ equivalent dose and effective dose after acute intake

The equivalent and effective doses per unit intake for members of the public and for workers after acute ingestion and inhalation using both the ICRP and L&E models are presented in Fig. 2. The time-dependent equivalent and effective doses incline to a constant value after 300 days of acute intake. The effective dose coefficient for inhalation is generally higher than for ingestion. The organ equivalent doses of public are higher than that of workers because the f ₁ value of 0.5 recommended for the members of the public is higher than the value of 0.1 for workers.

Fig. 2

Time-dependence of organ equivalent dose and effective dose coefficient after acute ingestion and inhalation for members of the public and the workers by using the systemic models recommended by ICRP [12] and the model developed recently by Leggett and Eckerman (L&E) [15], combining the gastrointestinal tract and the human respiratory tract models [16, 17]. The line legend symbols, which are shown in the figure, are applicable for the others. The title of “ICRP Public/Workers Ingestion/Inhalation” represents the ICRP model for members of the public/the workers by ingestion/inhalation

By inhalation, the total deposition of inhaled aerosols in the whole respiratory tract for workers is 1.7 times higher than that of the public. However, for workers, about 74% of the total inhaled aerosols are assumed to be deposited in the extrathoracic (ET) region, which gives less contribution to the resulting dose coefficient, in comparison to the public, for which only 32% is assumed to be deposited in ET region. The deposition in the alveolar–interstitial (AI) region of the lungs for public is two times higher than that for the workers [17]. Therefore, the dose coefficient of the lungs is higher for the public. This higher equivalent dose in lungs makes a slightly higher effective dose for the public.

For most organs, e.g. kidneys, liver, red marrow and spleen, the organ equivalent dose calculated using the ICRP model is generally higher than that by the L&E model. By inhalation, the lung doses are the main contribution to the effective dose and they are almost identical between the two models. Anyway, the effective doses by the two models show a smaller discrepancy than the change in organ equivalent doses. For members of the public, the effective dose coefficients range from 1.7 × 10⁻⁸ Sv Bq⁻¹ on the first day, 2.0 × 10⁻⁷ Sv Bq⁻¹ on the 10th day, 5.2 × 10⁻⁷ Sv Bq⁻¹ on the 30th day, to a constant value of 1.2 × 10⁻⁶ Sv Bq⁻¹ in the later days for acute ingestion; and 1.4 × 10⁻⁷, 9.6 × 10⁻⁷, 2.0 × 10⁻⁶, 3.3 × 10⁻⁶ Sv Bq⁻¹ for acute inhalation on the same mentioned days with the ICRP model, respectively.

²¹⁰Po mean organ absorbed dose after acute intake

In order to assess deterministic effects of exposure to ²¹⁰Po, organ absorbed dose was also calculated. The time-dependence of the organ absorbed dose after acute intake of ²¹⁰Po is shown in Fig. 3. Because ²¹⁰Po is an alpha emitter (negligible contribution to dose from gamma ray), the organ absorbed doses are 20 times smaller than the corresponding values of the organ equivalent dose since a radiation weighting factor of 20 for alpha particles is applied in calculating the organ equivalent dose. The highest organ absorbed doses are in the kidneys after intake for ingestion, and in the lungs after inhalation. Doses to members of the public are generally higher than for workers; the L&E model gives lower estimates than the ICRP model. The dose absorbed by the red marrow per unit ingestion (inhalation), calculated using the ICRP model for members of the public, is 1.5 × 10⁻³ (1.4 × 10⁻⁴) Gy MBq⁻¹ at 1 day after incorporation, 2.2 × 10⁻² (2.1 × 10⁻³) Gy MBq⁻¹ at 10 days, 5.7 × 10⁻² (6.0 × 10⁻³) Gy MBq⁻¹ at 30 days, and 1.1 × 10⁻¹ (1.5 × 10⁻²) Gy MBq⁻¹ at 100 days, respectively.

Fig. 3

Time-dependence of mean organ absorbed dose after acute ingestion and inhalation for members of the public and the workers by using the systemic models recommended by ICRP [12] and the model developed recently by Leggett and Eckerman (L&E) [15], combining the gastrointestinal tract and the human respiratory tract models [16, 17]. The line legend symbols, which are shown in the figure, are applicable for the others. The title of “ICRP Public/Workers Ingestion/Inhalation” represents the ICRP model for members of the public/the workers by ingestion/inhalation

²¹⁰Po daily excretion in urine and in feces after acute intake

The predicted daily excretions in urine and in feces, by using both models, are shown in Fig. 4. The lower intestinal absorption, assumed for the workers, results in a higher value in their fecal excretions. For both the public and the workers, the daily urinary and fecal excretions by ingestion are much higher than that by inhalation. By means of the L&E model, the excretion of ²¹⁰Po in human hair and sweat could be used to estimate the intake and the level of ²¹⁰Po in the human body, provided that the measured amount of ²¹⁰Po in hair is available. However, it is not obvious to assess the intake and level of ²¹⁰Po in the body from hair measurements because their results are highly dependent on modality of sample collection and because the model does not discriminate between excretion into sweat and hair. In the first few days after incorporation, the amount of ²¹⁰Po excreted in urine is markedly higher than that in hair and sweat (of a factor up to 25 times). This factor is predicted to be smaller at later times, reaching about the value of 1 approximately 100 days after intake.

Fig. 4

Daily urinary and fecal excretions for members of the public and the workers after acute ingestion and inhalation of 1 Bq of ²¹⁰Po by using the systemic models recommended by ICRP [12] and the model developed recently by Leggett and Eckerman [15], coupled with the gastrointestinal tract and the human respiratory tract models [16, 17]

By using the ICRP model, the predicted daily urinary excretions of ²¹⁰Po for members of the public are 1.1 × 10⁻³ Bq d⁻¹ on the first day, 2.0 × 10⁻³ Bq d⁻¹ on the 10th day, 1.3 × 10⁻³ Bq d⁻¹ on the 30th day and 3.6 × 10⁻⁴ Bq d⁻¹ on the 100th day after acute ingestion of 1 Bq of ²¹⁰Po; and 1.0 × 10⁻⁴, 1.9 × 10⁻⁴, 1.7 × 10⁻⁴ and 8.3 × 10⁻⁵ Bq d⁻¹ on same mentioned days after acute inhalation, respectively.

²¹⁰Po dose conversion factor of daily urinary excretion to effective dose

To enable an easy calculation of the effective dose for the persons whose urinary excretion were measured, the daily urinary excretion to effective dose conversion factor were calculated based on the ICRP and L&E models. They are tabulated in Table 2. There are two kinds of conversion factors presented in Table 2, namely, E/U and E’/U, where E is the effective dose coefficient, as defined and recommended by ICRP; E’ is the effective dose by the time T after intakes. In the earlier days, the factor E/U is larger than E’/U, however, after 300 days from intake, those two factors reach the same value. For example, if one has inhaled 1 Bq of ²¹⁰Po, according to the ICRP model for members of the public, the resulting effective dose E’ is 1.4 × 10⁻⁷ by T = 1 day, 2.0 × 10⁻⁶ by T = 30 days and 3.3 × 10⁻⁶ Sv Bq⁻¹ by T = 50 years. The effective dose E’ released at the time of urine collection can be estimated. It represents approximately the lower limits of dose released by ²¹⁰Po in the earlier days. Since measurements were generally conducted few days after sampling, the results of the activity measurements in urine needed to be corrected for radioactive decay in order to obtain the actual activity value at the day of urine collection.

Table 2 Daily urinary excretion to effective dose conversion factor (mSv per mBq d^{− 1}) for adult members of the public

²¹⁰Po body content and urinary and fecal excretion for normal unexposed people

According to the average concentration of ²¹⁰Po in the foodstuffs and in the air reported by UNSCEAR [2], the normal unexposed person ingests 0.16 Bq and inhales 1 mBq of ²¹⁰Po each day. Applying the ICRP model for members of the public, the content of ²¹⁰Po in human body is predicted to be about 1.1 Bq. It is estimated that about 4 mBq in urine and 0.15 Bq in feces could be found daily. These results are in excellent agreement with the experimental values reported in the literature [6–11, 22, 23].

Internal dose assessment for the monitored subjects

Although the measured excreted activities were comparable to the natural levels, and below the threshold set by the HPA to identify individuals probably exposed to ²¹⁰Po from the London incident [22], effective doses were nonetheless calculated under the pessimistic assumption that the measured activities were actually due to an acute intake on the day of suspected exposure to ²¹⁰Po. In Table 1 the values of committed effective dose E (over 50 years) and E′ (till the day of sample collection) are presented as estimated from the results of the measurements in urine. The intakes of inhalation and ingestion were assumed separately. As samples were collected only few days after the suspected exposure, the estimate of the effective dose E′ is much lower than the value of E. Considering the values of E as conservative estimates of the exposures of the monitored subjects, it can be seen that the resulting effective doses range from 2.1 × 10⁻³ to 1.7 × 10⁻² mSv by ingestion, and from 5.5 × 10⁻² to 4.5 × 10⁻¹ mSv by inhalation. Even under the very restrictive and pessimistic assumptions used for these evaluations, the dose received would be considered to represent the natural background radiation dose contributed from ²¹⁰Po.

Estimating ²¹⁰Po intake for Mr. Alexander Litvinenko

As reported in the media, Mr. Litvinenko was most possibly poisoned on 1 November 2006 and died 23 days later on 23 November at 21:21 o’clock. From the available information, it is possible to assume that polonium was administered orally, and that multiple organ failure, probably connected with bone marrow syndrome, was responsible for the death of Mr. Litvinenko.

As Harrison et al. [24] pointed out, animal studies showed that multiple organ damages were the cause of deaths within few weeks from intake of ²¹⁰Po. The results of the biokinetic modeling presented above indicated that kidneys, liver and red marrow could be the critical organs, being among the organs with the highest absorbed dose coefficients. According to the data presented by Harrison et al. [24], the lethal dose LD₅₀ may be estimated as about 3–4 Gy for the bone marrow syndrome, 6 Gy for acute kidneys damage and 8 Gy for acute liver damage. An LD₁₀₀ of 5 Gy for red marrow syndrome is also given. Those values were calculated for internal irradiation from ²¹⁰Po, taking into account relative biological effectiveness (RBE) of alpha particles and dose protraction. The absorbed dose of 5 Gy to red marrow, 6 Gy to kidneys and 8 Gy to liver were applied as a basis on the organ lethal dose in this work to estimate the possible intake of ²¹⁰Po by Mr. Litvinenko.

The organ absorbed dose coefficients were calculated for day 23 after ingestion (the day of 23 November was included as full day in the calculations) in the present work. The resulting dose coefficients are 4.6 × 10⁻² (1.8 × 10⁻²) Gy MBq⁻¹ for red bone marrow, 2.2 × 10⁻¹ (1.3 × 10⁻¹) Gy MBq⁻¹ for kidneys, 1.1 × 10⁻¹ (8.5 × 10⁻²) Gy MBq⁻¹ for liver with ICRP (L&E) model, assuming an f ₁ value of 0.5; and 9.2 × 10⁻³ (3.6 × 10⁻³) Gy MBq⁻¹ for red bone marrow, 4.4 × 10⁻² (2.6 × 10⁻²) Gy Bq⁻¹ for kidneys, 2.3 × 10⁻² (1.7 × 10⁻²) Gy MBq⁻¹ for liver assuming an f ₁ value of 0.1.

The estimation of possible intake of ²¹⁰Po is summarized in Table 3. Both of the ICRP and L&E models were used. According to different f ₁ values of 0.5 and 0.1, the estimated amounts of ²¹⁰Po range from 27 to 1,408 MBq, corresponding to 0.2 to 8.5 μg. Moreover, the organ absorbed doses, calculated after an incorporation of estimated amount of ²¹⁰Po assuming the red bone marrow as a critical organ with an absorbed dose of 5 Gy, are presented in Table 4. In their paper, Harrison et al. [24] concluded that 0.1–0.3 GBq or more absorbed to blood of an adult male is likely to be fatal within 1 month. This range would correspond to an intake of 200–600 MBq assuming 50% absorption to blood and to 1–3 GBq assuming 10% absorption to blood, respectively. These values are consistent with the estimates obtained in the present work.

Table 3 Possible incorporation of ²¹⁰Po estimated for Mr. Alexander Litvinenko using the biokinetic models of ICRP [12] and L&E [15] with the assumption of different damaged organ and the lethal absorbed dose

Table 4 Estimated incorporation and organ absorbed doses based on different assumptions of lethal red bone marrow dose of 5 Gy with f ₁ values of 50 and 10% for blood absorption

Conclusions

In this work, the time-dependent organ equivalent dose, effective dose and daily excretion in urine and in feces after an acute intake of ²¹⁰Po are calculated by applying the models of polonium recommended by ICRP and the new model developed recently by Leggett and Eckerman. The conversion factors from the daily urinary excretion to the effective dose were evaluated. Moreover, the 24-h-urine samples of seven persons who were possibly contaminated were measured in the GSF Radioanalytical Laboratory. Their measured excretions resulted within the natural level of the excretion rate of ²¹⁰Po, and below the threshold limit value of 30 mBq d⁻¹ recommended by the HPA to identify individuals probably exposed to ²¹⁰Po from the London incident. The effective dose was estimated for those seven persons using their measured urinary excretion and the calculated conversion factors. They were in the range of 2.1 × 10⁻³ to 1.7 × 10⁻² mSv assuming an intake by ingestion, and 5.5 × 10⁻² to 4.5 × 10⁻¹ mSv by inhalation. They are much lower than the mean effective dose of 2.4 mSv to the population in the federal republic of Germany during the year 2005 [25]. From the fact that the measured results were within the natural level of the excretion rate of ²¹⁰Po, it is concluded that no additional ²¹⁰Po intake can be detected. Thus, no excess health effects related to the toxicity of ²¹⁰Po are expected for those monitored subjects besides the background exposure to the natural level of ²¹⁰Po. In addition, the time-dependent mean organ absorbed dose was calculated with the ICRP and L&E models. Based on these calculated organ absorbed doses, and different assumptions on lethal absorbed doses for red bone marrow, kidneys, liver, and on blood absorption, the minimum estimated amount of ²¹⁰Po which led to the death of Mr. Alexander Litvinenko in November 2006 in London is estimated to range from 27 to 1,408 MBq, about 0.2 to 8.5 μg, if only ²¹⁰Po was used as a poison.