131I dose coefficients for a reference population using age-specific models

Age-specific dose coefficients are required to assess internal exposure to the general public. This study utilizes reference age-specific biokinetic models of iodine to estimate the total number of nuclear disintegrations ã(r S,τ) occurring in source regions (r S) during the commitment time (τ). Age-specific S values are estimated for 35 target regions due to 131I present in 22 r S using data from 10 paediatric reference computational phantoms (representing five ages for both sexes) published recently by the International Commission of Radiation Protection (ICRP). Monte Carlo transport simulations are performed in FLUKA code. The estimated ã(r S,τ) and S values are then used to compute the committed tissue equivalent dose HT(τ) for 27 radiosensitive tissues and dose coefficients e(τ) for all five ages due to inhalation and ingestion of 131I. The derived ã(r S,τ) values in the thyroid source are observed to increase with age due to the increased retention of iodine in the thyroid. S values are found to decrease with age, mainly due to an increase in target masses. Generally, HT(τ) values are observed to decrease with age, indicating the predominant behaviour of S values over ã(r S,τ). On average, ingestion dose coefficients are 63% higher than for inhalation in all ages. The maximum contribution to dose coefficients is from the thyroid, accounting for 96% in the case of newborns and 98%–99% for all other ages. Furthermore, the estimated e(τ) values for the reference population are observed to be lower than previously published reference values from the ICRP. The estimated S, HT(τ) and e(τ) values can be used to improve estimations of internal doses to organs/whole body for members of the public in cases of 131I exposure. The estimated dose coefficients can also be interpolated for other ages to accurately evaluate the doses received by the general public during 131I therapy or during a radiological emergency.


Introduction
131 I, due to its small half-life (8.02 days) and high-energy beta-emission (maximum energy of 606 keV with a yield of 89%), is used in the treatment for hyperthyroidism caused by Graves' disease [1].Additionally, due to the presence of high-energy gamma radiation (energy of 364 keV with a yield of 82%), it is also used for thyroid/whole-body scintigraphy and other diagnostic purposes [2].Further, 131 I exposure to the public may occur via direct inhalation during radiological emergencies and/or via ingestion of fallout radiation through food, milk, etc. Assessment of internal dose is important during diagnostic and therapeutic use of radioiodine.Moreover, such assessments are also essential for public safety and regulatory compliance during radiological/nuclear emergencies [3].These factors make 131 I the most extensively studied and prominent internal contaminant in radiation protection.
Estimation of absorbed dose in a target region (r T ) due to emission from a source region (r S ) mainly requires two quantities: (1) ã(r S ,τ), which represents the time-integrated activity (or nuclear disintegration) in r S over a commitment time τ and (2) S(r T ←r S ), the mean absorbed energy in r T per unit disintegration in r S , also known as the S value [4].The estimation of ã(r S ,τ) involves solving biokinetic models of radionuclides.Furthermore, S values are computed based on the specific absorbed fractions (SAFs) derived from Monte Carlo simulations of absorbed fractions (AFs) in r T of computational phantoms due to emission from r S .S values can also be computed by directly simulating the energy deposition in r T due to complete decay of radionuclides in r S [5].
At present, the ã(r S ,τ) values of 131 I for the reference population [6] are based on the age-specific human respiratory tract model (HRTM) [7], the gastrointestinal tract (GI-tract) model [8] and the three-compartment systemic model of iodine [9].The reference SAF values are derived from age-specific Oak Ridge National Laboratory stylized mathematical phantoms [10][11][12].Based on these ã(r S ,τ) and SAF values, reference 131 I committed tissue equivalent doses, H T (τ), and dose coefficients, e(τ), have been provided in various International Commission of Radiation Protection (ICRP) publications [13,14].
Recently, a more comprehensive systemic model of iodine was published [15] that provides detailed retention and excretion rates for the redefined reference population [16].The age-specific human alimentary tract model (HATM) has also been updated for the reference population [17].In the revised HATM, all alimentary tract organs from the oral cavity to the rectosigmoid are included, with provisions for blood absorption from all these organs.Furthermore, mathematical stylized phantoms have been updated using 10 paediatric reference computational (PRC) phantoms [18], representing the reference population as per ICRP publication 89 [16].PRC phantoms have been developed by modifying the University of Florida and National Cancer Institute (UF/NCI) hybrid phantoms [19], and provide a more realistic representation of the human anatomy compared to stylized phantoms.Earlier studies have shown variations in effective doses due to photons, electron [20] and 18 F-FDG [21] estimated using a voxel-based model from those estimated using stylized phantoms.The UF/NCI and PRC phantoms have been used to compute SAF values for electrons and photons of various energies [22][23][24], which in turn are used to compute S values and organ doses for medical intake scenarios [24,25].These studies only focus on dose computation for medical protection pathways such as intravenous and oral administration, while leaving out the inhalation pathway required for radiological protection.
In this study, we estimated age-specific ã(r S ,τ) for the reference population in the case of 131 I inhalation and ingestion using the latest available biokinetic models.S values for 35 target regions are estimated due to 131 I distributed in 22 source regions for PRC phantoms by simulating the complete decay of 131 I in the FLUKA Monte Carlo simulation code.Using these ã(r S ,τ) and S values, age-specific H T (τ) and e(τ) are computed for the reference population.

Materials and method
This section describes methods for determining the ã(r S ,τ) of 131 I in various r S of the reference population, as well as the incorporation of PRC phantoms in the Monte Carlo simulation code FLUKA.Additionally, methods for energy scoring and estimating S values, computations of age-specific H T (τ) and e(τ) values are also discussed.

Estimation of age-specific ã(r S ,τ)
The biokinetic compartmental model of any radionuclide is described by a system of first-order differential equations, which can be solved by transforming them into a matrix equation, as given in equation (1) [26]: where elements of column matrix A(t) represent activity in different compartments at time t, while R is a square matrix with diagonal elements given by r ii = − ∑ j λ ij − λ R and non-diagonal elements as r ij = λ ji .λ ij is the transfer rate from ith to jth compartment, λ R is the radioactive decay rate and A(0) represents the initial activity deposited in compartments.Equation (1) is integrated over a commitment time τ to obtain column matrix Ã(τ), whose elements represent time-integrated activity in various compartments (equation (2)): The commitment times are taken as (70-t) years for the reference population, with t being the age of the individual at intake.The complete inhalation model of iodine is shown in figure 1.This model is prepared for each individual age group (assuming same for males and females) by combining the HRTM [7], the HATM [17] and the iodine systemic model [15].For each age, an inhalation intake of 1 Bq of 131 I aerosol with an activity median aerodynamic diameter of 1 µm is assumed, with fast blood absorption.In the case of ingestion, respiratory tract compartments are excluded and unit activity is assumed to be directly deposited  in the oral cavity.The small intestine is assumed to be the only site of blood absorption, with a gut absorption factor of 0.99 for all ages [13].An in-house-developed octave program is utilized to solve these models and estimate Ã(τ).
Table 1 shows a list of the 22 source regions (r S ) and the corresponding biokinetic compartments of these regions.ã(r S ,τ) is calculated by adding the disintegration of related compartments obtained from the Ã(τ) matrix.

The Monte Carlo code and PRC phantoms
FLUKA code is utilized for radiation transport [27,28].Ten phantoms representing reference male and female individuals at 0 (newborn), 1, 5, 10 and 15 years of age are adapted into the simulation code.A FORTRAN program is employed to read the ASCII data files [18] for each phantom and convert them into voxel files that are compatible with the simulation code, incorporating information such as voxel resolution, tissue equivalent materials, etc. Input files for Monte Carlo simulations are created using FLAIR [29].Figure 2 shows the PRC female phantoms incorporated in the FLAIR geometry viewer.

Source sampling and energy scoring
In voxel phantoms, a tissue/organ is represented by tissue ids and r S /r T may comprise one or more tissue ids.Sampling of the uniform distribution for 131 I in r S is carried out using the SOURCE.F user routine.The isotropic emission of generated particles is achieved by randomly selecting azimuthal angles in the range [0, 2π] and the cosine of polar angle in the range [−1, 1], from a uniform distribution on a unit sphere.S values are estimated using a direct approach by estimating energy deposition in r T due to the complete radioactive emissions of 131 I in r S .As opposed to the conventional method of estimating SAF values for each particle and energy, this approach was used to reduce long computational times [5].Radioactive disintegration of 131 I is simulated by utilizing the 'HI-PROPert' and 'RADDECAY' cards of the FLUKA code.For each source, 5.0E 8  primaries are simulated to reduce the simulation error below 1% for most cases.The 'USRBIN' card of FLUKA is used to score energy deposition in the tissue ids of phantoms.Post processing of the 'USRBIN' output was carried out by writing a GNU Octave program, which provides the scored energy in region r T by adding deposited energies in corresponding tissue ids.The scored energy in region r T is the sum of products of energy, yield and AFs due to each particle ( , where φ (r T ← r S , E i ) is AF due to the ith particle with energy E i (GeV) and yield Y i .

Calculation methodology
S values are computed using target tissue masses from ICRP publication 143 [18].However, for self-irradiation cases, blood mass in target regions is included based on the information provided in ICRP publications 89 and 143 [16,18].

Computation of S values
For each phantom, S values are estimated for 35 r T , namely, active marrow (AM), breast, colon walls (right, left, rectosigmoid), bronchi basal cells, bronchi secretory cells, bronchiolar secretory cells, alveolar interstitial, stomach wall, adrenals, basal cells of extra thoracic region 1 and 2, gall bladder wall, heart wall, kidneys, lymph nodes (thoracic, extra thoracic and systemic), muscles, oral mucosa, pancreas, prostate/uterus, small intestine wall, spleen, thymus, testes/ovaries, bladder wall, oesophagus, liver, bone surface, brain, salivary gland, and skin.S values [mGy (Bq s) −1 ] to r T due to emission from r S are calculated using equation (3), where factor 1.602 × 10 −7 is used to convert the energy unit from GeV to mJ and m(r T ) is the mass of r T in kg.Special cases of skeletal tissues, blood and other tissues are discussed in the following subsections.

S values for skeletal tissue
The skeletal target tissues of interest are the AM and the endosteal tissue layer or bone surface (TM 50 ).For each phantom, 22 bone sites were identified as skeletal target tissues r T' and fractional masses of AM and TM 50 for these bones are considered in S value calculations using equation (4), where f rT ′ is mass fraction of AM or TM 50 in site r T ′ .The fractional masses of AM and TM 50 for the target bone sites are taken from ICRP publication 143 [18].

S values due to blood
In voxel phantoms, only blood vessels and the content of the heart are segmented, while tissue blood content is not segmented.To obtain S values for a region r T due to whole body blood (or source region 'Blood'), S values due to segmented vessels, heart content and blood contained in tissues are added.The S value for a region r T due to tissue blood content is calculated using equation (5), where S(r T ←r S ′ ) is S value to region r T due to blood-containing tissues r S ′ and f rS ′ is the fraction of total body blood assigned to it [18].
To obtain the S value for a region r T due to source 'Other tissues' , S values due to r S ′ are estimated and added according to equation (6), where m r S ′ is mass of r S ′ and m Other is the total mass of these tissues, as given in ICRP publication 143 [18].

Tissue equivalent doses and dose coefficients
H T (τ) values to 27 radiosensitive tissues, T, including stomach wall, breast, gonads, urinary bladder wall, oesophagus, liver, thyroid, brain, salivary gland, skin, AM, endosteum layer, lungs, colon wall and remainder tissues (adrenal, gall bladder wall, heart wall, muscle, oral mucosa, pancreas, prostate/uterus, small intestine wall, spleen, thymus, kidneys, extra-thoracic regions and lymph nodes) are estimated for each PRC phantom and for both intake cases.In most cases, where T has a single r T , the H T (τ) values are computed using equation ( 7), where summation is taken over all r S of the biokinetic model.For T comprising more than one r T , such as the extra thoracic region, lungs, colon and lymph nodes, the H T (τ) values are estimated using equation ( 8), where f (r T , T) is the fractional weight of the target region r T of tissue T, as defined in ICRP publication 133 [4].For a given age, the dose coefficient e (τ ) is estimated using equation ( 9), where superscripts M and F are for male and female, respectively, and w T is the tissue weighting factor for T, as given in ICRP publication 133 [4].

Results and discussion
Age-specific ã(r S ,τ) values for 131 I for inhalation and ingestion cases are included in the supplementary data.
The data also include a comprehensive list of 131 I S values for 35 r T due to 22 r S for each PRC phantom.S values due to 27 sub tissues considered for source 'Other tissues' are also provided.Moreover, the H T (τ) values for 27 radiosensitive target tissues are also listed for each PRC phantom and both intake cases.In this section, a general discussion is presented about the estimated quantities, including the trends followed by ã(r S ,τ), S, H T (τ) and e(τ) values, considering various factors such as age, gender, phantom size, and possible reasons for these observed trends.

Dependency of ã(r S ,τ) values on various factors 3.1.1. Dependence on age
Except for inhalation at 15 years, ã(r S ,τ) values in the thyroid are found to increase with age (figure 3).This is due to an increase in the biological half-life (T 1/2 = 0.693/λ Thyroid2→Blood2 ) of iodine with age, resulting in an increase in the overall residence time of iodine in the thyroid.Decreased ã(r S ,τ) for inhalation at 15 years is due to the lowest fractional activity deposition in the respiratory tract in comparison to other age groups.Apart from in the thyroid, fractional ã(r S ,τ) for a region w.r.t.total ã(r S ,τ) in all sources generally decreases with age.For example, percentage ã(r S ,τ) in the ET 1 region for inhalation cases are 14.25, 13.24, 11.58, 11.38 and 9.73% from newborn to 15 years, respectively.Similarly, percentage ã(r S ,τ) in the liver region for ingestion cases are 4.85, 3.82, 2.31, 1.61 and 1.36% from newborn to 15 years, respectively.Percentage ã(r S ,τ) in urinary bladder content (UBC) is found to increase with age in both cases due to a decreasing clearance rate (λ UBC→urine ) from UBC to urine.

Dependence on route of intake
Ingestion ã(r S ,τ) in the thyroid is observed to be ∼63% higher (average for all ages) than from inhalation.This difference can be attributed to two main factors.Firstly, for inhalation, only a fraction of intake is initially deposited, with fractional deposition ranging from 0.60 for newborns to 0.46 for 15 year olds.In contrast, for ingestion, complete deposition of activity occurs in the oral cavity.Secondly, there is additional clearance from the ET 1 region to the environment for inhalation, whereas no such clearance exists for ingestion.Similarly, ã(r S ,τ) for ingestion is found to be higher than inhalation for other source regions.

Dependency of S values on various factors
It should be emphasized that for a specific source-target combination, S values depend on the energy absorbed in r T as well as on its mass.Furthermore, the absorbed energy in r T depends on the solid angle subtended by r S on r T , which roughly depends on the size and shape of these regions and the mean distance between them.Attenuation due to intermediate organs also contributes to absorbed energy.Dependency of S values on other physiological factors of PRC phantoms is described in the following subsections.

Variation for self-irradiation
Figure 4 illustrates the self-irradiation S values for different sources of male PRC phantoms.In general, self-irradiation S values exhibit an inverse relationship with source masses.For instance, the breast of a newborn male has the highest S value of 7.89 × 10 −08 mGy (Bq s) −1 with the lowest mass of 0.36 g, while the muscle has the lowest S value of 4.02 × 10 −11 mGy (Bq s) −1 , with the highest mass of 822.26 g.Furthermore, since organ masses generally increase with age, the S value for a given source tends to decrease with age.An exception where organ mass decreases with age is the adrenals of newborn and 1 year old male phantoms.As a result, the S value for the adrenals of a 1 year old male is higher than that of a newborn male.Similar effects of organ masses on self-irradiation S values are also observed for PRC female phantoms.

Variation with age of phantom
Since organ masses and mean distances between organs increase with increasing age, S values for a given r S -r T combination are found to decrease with age. Figure 5 depicts age-specific S values for the brain targets of female PRC phantoms, due to thyroid and liver sources, respectively.The S value due to the thyroid for the brain of a newborn female is about 10 times higher than those for a 15 year old female, due to lower brain mass and relative distance between the source and target in newborn compared to 15 year olds.Similarly, S value due to the liver for the brain of newborn female is about 15 times higher than for 15 years old female.

Variation with gender
Except for 15 year old phantoms, voxel characteristics such as resolution, total number of voxels, etc, are the same for male and female counterparts of PRC phantoms of a given age.This makes the male and female PRC phantoms almost identical up to the age of 10 years, with the main difference being in the sex organs and the positions of nearby organs.As a result, S values are generally the same for male and female phantoms of any age.Observable variations in S values are seen for sex organs, lymph nodes, urinary bladder, etc. S values for the urinary bladder wall due to the thyroid are 1.79 × 10 −14 mGy (Bq s) −1 and 1.87 × 10 −14 mGy (Bq s) −1 for 5 year old male and female phantoms, respectively.
Significant variations in S values are observed between the male and female counterparts of 15 year old phantoms due to differences in body characteristics such as height, weight, organ mass, size, etc. figures 6(a)-(d) illustrate S values for various r T in 15 year old male and female phantoms due to thyroid, liver, AI and urinary bladder content, respectively.While there is very little difference in the self-irradiation S values, with thyroid and liver S values being 1.18 and 3.48% higher for females than for male phantoms, respectively, comparable variations are seen for cross-firing S values.In general, S values for females are observed to be higher than those for males due to lower organ masses and smaller inter-organ distances.The most substantial difference is observed for the gonads (testes/ovaries), where the S values for female are 93.79,68.78, 84.46 and 62.12% higher than those for male due to thyroid, liver, AI and UBC sources, respectively.

Committed tissue equivalent doses
For a given intake scenario, the H T (τ) values for most tissues in both male and female PRC phantoms up to 10 years are found to be the same, as they have similar S and ã(r S ,τ) values.However, variations are seen in sex organs (testes/ovaries and prostate/uterus), lymph nodes and urinary bladder wall.For example, in the case of ingestion, H T (τ) values for gonads (testes/ovaries) are 7.1 × 10 −10 Sv Bq −1 and 1.2 × 10 −9 Sv Bq −1 for newborn males and females, respectively.Similarly, in the case of inhalation, H T (τ) values for the prostate/uterus are 4.4 × 10 −9 Sv Bq −1 and 1.9 × 10 −9 Sv Bq −1 for 5 year old males and females, respectively.
Large variations in H T (τ) values are observed for 15 year old PRC phantoms due to variations in the S values.Generally, H T (τ) values for 15 year old females are higher than their male counterparts, except for breast, lungs, colon, muscles, gall bladder wall and uterus/prostate.Overall, for all tissues, the sex-averaged H T (τ) values are found to decrease with age, primarily due to a decrease in S values.The maximum H T (τ) values are obtained for the thyroid for a given age and intake case.

Age-specific dose coefficients
Table 2 provides age-specific e(τ) of 131 I for inhalation and ingestion.It is observed that ingestion e(τ) values are about 63% higher than inhalation e(τ) values.The maximum contribution to dose is from the thyroid, which accounts for about 96% of the doses for newborns and 98%-99% for all other ages.The next contributor to the dose is breast tissue, which accounts for about (1.79, 0.32, 0.21, 0.24 and 0.10% from newborns to 15 years) followed by the remaining tissues and stomach wall.Furthermore, the dose coefficients decrease with age for both intake cases.Compared to newborns, the inhalation e(τ) values for 1,   Figure 7 illustrates a comparison between the estimated e(τ) values for PRC phantoms and the available reference values from previous ICRP publications [13,14].It is observed that the estimated e(τ) values for PRC phantoms are slightly lower than previous reference values.Specifically, for newborn to 15 year old PRC phantoms, the average ratios of estimated e(τ) values to earlier values are approximately 0.78, 0.67, 0.74, 0.69 and 0.74 for both intake routes.This decrease in estimated e(τ) can be attributed to two factors: (i) lower equivalent dose for the thyroid due to its higher mass (including blood mass) in PRC phantoms than in stylized phantoms [14,16] and (ii) the lower thyroid w T value (0.04) used in our calculations than (0.05) used in the ICRP publication values [4,13].

Conclusion
This study provides updated values of ã(r S ,τ), S, H T (τ) and e(τ) for a reference population in terms of inhalation and ingestion of 131 I.These findings will contribute to enhance the accuracy of dose estimations for members of the public in cases of radioiodine intake for medical purposes or radiological emergency scenarios.

Figure 1 .
Figure 1.Iodine inhalation biokinetic model with latest alimentary tract and systemic models.Arrows indicate the transfer of activity between compartments.

Figure 2 .
Figure 2. FLAIR view of paediatric reference computational female phantoms (newborn to 15 years).

Figure 4 .
Figure 4. Self-irradiation S values for PRC male phantoms.

Figure 5 .
Figure 5. S values to brain of female PRC phantoms due to 131 I exposure from thyroid and liver sources.

Figure 6 .
Figure 6.S values for various target regions of 15 year old male (15 M) and female (15 F) PRC phantoms due to 131 I in (a) thyroid, (b) liver, (c) AI and (d) UBC.

Figure 7 .
Figure 7.Comparison of estimated age-specific 131 I dose coefficients with previous reference values from ICRP publications.

Table 1 .
Iodine inhalation biokinetic compartments and derived source regions.

Table 2 .
131I dose coefficients for the reference population.