Dose coefficients for members of the public

A dose coefficient is the committed dose per becquerel taken into the body: the equivalent dose to an organ or tissue, or the effective dose, received over the 50 years after an adult’s intake, or up to age 70 after a child’s. This page calculates them the way the ICRP does, from the ICRP’s biokinetic models (where the radionuclide goes in the body and how long it stays) and dosimetric models (how much of the energy emitted in one place is absorbed in another), for intakes by ingestion and inhalation (and, in the ICRP 103 system, direct uptake to blood) at the six reference ages of the ICRP’s publications for members of the public: 3 months, 1, 5, 10 and 15 years, and adults. Choose the system, the radionuclide, the route and the chemical form on the left. The button at the right end of the tabs gives the page the whole window, without the site’s header and footer; the kvot mark at the left of the tabs then goes to the home page, and the switch beside the button changes between light and dark. The page remembers the choice.

The two systems

The ICRP 60 system is the one of the ICRP’s 1990 Recommendations: the age-dependent models of Publications 56, 67, 69 and 71, whose dose coefficients Publication 72 tabulated and Publication 119 compiled. It is still the basis of many national regulations and of the IAEA Basic Safety Standards’ tables. The ICRP 103 system is the one of the 2007 Recommendations: new tissue weighting factors, voxel phantoms of reference persons of both sexes, the revised respiratory tract model of Publication 130, the alimentary tract model of Publication 100 and revised systemic models. For members of the public its coefficients are being published element by element: Part 1 (Publication 158, 2024) covers hydrogen to radium, Part 2 (the lanthanides and actinides) and Part 3 (35 more elements, beryllium to francium) were out for consultation as drafts when this page was made. The two systems give different numbers for the same intake, sometimes by a factor of several; the page tells you which one each result comes from.

The ICRP 60 system as calculated here

The ICRP calculated the Publication 72 coefficients with the software DCAL (Eckerman and Leggett, ORNL/TM-2001/190), which ORNL distributes with its data. This page reads DCAL’s own model and data files and reproduces its method:

• Respiratory tract: the ICRP 66 model, Types F, M and S and the gas and vapour classes, with DCAL’s age-dependent deposition fractions for members of the public (1 µm AMAD by default).
• Gastrointestinal tract: the ICRP 30 model (stomach, small intestine, upper and lower large intestine), absorption f₁ from the small intestine with its age-dependent values.
• Urinary bladder: emptied at 40, 32 and 12 d⁻¹ at 3 months, 1 year and from 5 years (Publication 67).
• Systemic models: the ones of Publications 56–71 as DCAL’s FGR-13 library holds them, with the transfer rates interpolated linearly in age, and the adult at 25 years for bone-seeking elements. Progeny follow the kinetics DCAL’s batch files give them: shared with the parent, or independent with the element-specific models for lead, radium, thorium and uranium chains, iodine from tellurium and noble gases.
• Dosimetry: specific effective energies from the Cristy–Eckerman phantoms (newborn, 1, 5, 10 and 15 years, adult), the ICRP 30 bone and walled-organ absorbed fractions, and the ICRP 66 absorbed fractions of the airways, interpolated in age between the phantoms.
• Effective dose: the tissue weighting factors of Publication 60 with the remainder of Publication 72 (mass-weighted, with the splitting rule).

The ICRP 103 system as calculated here

• Respiratory tract: the revised Human Respiratory Tract Model of Publication 130 (particle transport of its Fig. 2.4, dissolution and the bound state), with the deposition of Publication 158 Table A.1 for environmental exposure (1 µm AMAD by default), the absorption types and material-specific parameters of each element, and the parent’s absorption parameters for progeny formed in the lungs.
• Alimentary tract: the Human Alimentary Tract Model of Publication 100 with the age-specific transit rates of Publication 158 Table 2.10, absorption f_A from the small intestine; material cleared from the lungs is absorbed with f_r·f_A, and activity secreted from tissues with the highest reference f_A. An injection puts the activity into the systemic model’s blood at once.
• Systemic models: transcribed from each element’s section of Publication 158 and of the Part 2 and Part 3 drafts, with their age-specific transfer coefficients. The adult’s values apply from 20 years, from 25 years for the alkaline earths, lead and the actinides (Publication 158 para 13) and, as the ICRP’s own coefficients show, for yttrium, zirconium, niobium, hafnium, tantalum and francium. Mercury vapour absorbed from the lungs enters blood by the way it got there: dissolved as vapour to Plasma 0, the rest as Hg²⁺ to Plasma 1 (Part 3 draft paras 367–368).
• Dosimetry: the specific absorbed fractions of Publications 133 and 155 for the twelve reference individuals (newborn, 1, 5, 10 and 15 years, adult; male and female), with the radiations of Publication 107, interpolated in energy and in age as Publication 158 prescribes (PCHIP; a weighted linear interpolation in the first year).
• Effective dose: the tissue weighting factors of Publication 103 applied to the average of the male and female equivalent doses, the remainder the arithmetic mean of its thirteen tissues.

Progeny

A radionuclide’s dose coefficient includes the dose from its radioactive progeny formed in the body after the intake. How the progeny move is where the two systems, and this page, need most care.

In the ICRP 60 system the progeny follow what DCAL’s batch files for Publication 72 give them: the parent’s model (shared kinetics) for most chains, element-specific models for the chains of lead, radium, thorium and uranium, iodine from tellurium and noble gases (independent kinetics), as Publications 67, 69 and 71 describe.

In the ICRP 103 system Publication 158 (section 2.5) gives the general rules: in the respiratory tract every member keeps the parent’s absorption parameters, but noble gases escape at 100 d⁻¹; progeny formed in the alimentary tract are absorbed with their own reference f_A (after an inhalation of particles, times the parent’s f_r; after a gas or vapour, their own f_A alone, as the ICRP’s coefficients for ruthenium tetroxide have it); isotopes of the parent’s element share its model. How a progeny of another element moves once it is formed in the body is set by the parent element’s section of the OIR series (Publications 134, 137, 141 and 151, “Treatment of radioactive progeny”), the same for every chain that element heads, and this page carries those sections’ models:

• chains of lead, bismuth and polonium (Publication 137 section 9.2.3.3): lead and bismuth with red marrow, spleen, skin, testes and ovaries added to their models, polonium entering blood at Plasma 2, and models of their own for thallium, gold and mercury;
• chains of radium, thorium and uranium (sections 13.2.3.3, 14.2.3.3 and 15.3.3): the lead-chain models with trabecular and cortical marrow; radium, thorium, uranium, actinium and neptunium with added spleen, skin, marrow and gonads; protactinium with thorium’s model; francium and astatine decay where they are formed;
• the other actinides (Publication 141 section 18.2.10): each element’s model with skin and spleen added, plutonium without its fast blood compartment;
• caesium, barium, the lanthanides, tellurium, antimony, iodine, strontium, yttrium, zirconium, niobium, molybdenum, ruthenium, iridium, iron, cobalt, zinc, calcium and sulphur: their sections’ models, among them those for scandium, manganese, gallium, rubidium, rhodium, osmium, platinum and rhenium as progeny, and the model of ^137mBa formed from ¹³⁷Cs (with Publication 158 para 450 for children);
• nickel, selenium and silver (Publication 151 sections 15, 20 and 25): cobalt formed from nickel; arsenic, bromine and krypton from selenium; rhodium, palladium, cadmium and indium from silver, with the adult characteristic models of Publication 151 at every age (which reproduces the annex of Publication 158), extended by the parent’s tissues as its Annex B describes;
• the elements of Part 3 (Publication 151, the section of each): magnesium, silicon, chlorine, potassium, titanium, chromium, manganese, gallium, germanium, arsenic, bromine, rubidium, rhodium, palladium, cadmium, indium, tin, hafnium, tantalum, tungsten, rhenium, osmium, platinum, gold, mercury, thallium, astatine and francium as parents, each progeny with its own model and the tissues and rates the section adds; argon formed from chlorine leaves tissue with a half-time of 15 minutes. Polonium formed from astatine enters blood at Plasma 1, not at Plasma 2 as in lead chains: the Part 3 draft’s ²¹⁰At coefficients need it (with Plasma 2 they come out 7–12 % lower).

A progeny formed in a compartment that its model also has (the same tissue, of the same name) is in that compartment, but the unspecific soft-tissue pools (ST0–ST2) of another element’s model are not its own, except in radium chains and those that share their models: there thorium and radium formed in the pools of a progeny’s model take their own pools of the same name, though not in those of the chain’s parent (the ICRP’s coefficients for ²²⁷Ra, ²²⁸Ra, ²³¹Pa and ²²⁸Ac follow the one, those for ²²⁹Th and ²³²Th the other), and thorium formed in radium’s bone volume, exchangeable or not, returns to blood at the bone turnover rate. Formed anywhere else it moves to its own blood at the rate the section gives: 1000 d⁻¹ from blood, a rate of its own model from soft tissue, the bone turnover rate from bone volume. Noble gases formed in the body follow the OIR series’ generic model: to blood at 100 d⁻¹ from bone surface, 1.5 or 0.36 d⁻¹ from bone volume, with a half-time of 30, 20 or 15 minutes from soft tissue (radon, xenon, krypton), exhaled at 1000 d⁻¹. Activity secreted into the alimentary tract is reabsorbed with the element’s highest reference f_A, for polonium 0.1, the value the ICRP’s own calculations used. Where a section changes a model by shares of its flows (the spleen’s share of the soft tissue, say), the same shares are applied to the children’s models.

A progeny that its parent’s section does not name (yttrium from zirconium, say) falls back to simpler rules: in a compartment its model also has, it is there; formed in bone volume it leaves at the parent’s rates; elsewhere it returns to its blood at the rate of its own model’s intermediate soft tissue.

When progeny of other elements emit a tenth or more of a chain’s energy, the Coefficients tab says so: those results rest on these rules, and can differ from the ICRP’s by more than its rounding (see below).

How the calculation is done

Each intake becomes one system of linear differential equations: the activity of every chain member in every compartment, with transfer rates interpolated linearly in age between the reference ages (the rates change as the child grows), and decay feeding each member’s progeny. The equivalent dose to each target region is the activity in each source region times its dose per transformation (SEE in the ICRP 60 system, S in the ICRP 103 system), integrated over the commitment period; the dose per transformation also changes with age: between the reference phantoms linearly (ICRP 60), or by a monotone cubic spline (PCHIP) through the six reference ages (ICRP 103), with in both a weighted interpolation in the first year that follows the growth curves of Publication 89. Between two reference ages it is therefore one polynomial in age for every source and target, and the integrator carries, for each group of compartments that share a source region, the integral of their activity weighted by each of its basis functions (four for the cubic, in Bernstein form; two for a straight line): the doses to all targets follow from these exactly, at the end of each stretch. The integrator is a variable-order backward differentiation method (NDF) with the exact sparse Jacobian, restarted wherever a rate table has a corner; it crosses the commitment period in one to two thousand steps however stiff the system (rates from 10⁻⁵ to 4·10⁴ d⁻¹) and however long the chain (a few hundred compartments for the actinide series). Specific absorbed fractions are interpolated in energy as each publication says (linearly for the ICRP 60 photon SAFs, as DCAL; PCHIP for the ICRP 103 SAFs), beta particles enter through their spectra.

The integrals keep the system small: for ²²⁶Ra by ingestion, 1,782 equations with 5,622 coefficients. The ages at intake are separate integrations and run in parallel, each in a worker of its own, as many at a time as the device has cores to spare; so do the inhalations behind radon at home. Before a run, the foot of the settings sums up the model Calculate will solve — the nuclides the cut-off keeps, the compartments, transfers and equations, and the number of integrations — and the Model and Decay chain tabs show it. Results stay on their tabs when a setting is changed, marked as not of the current settings until Calculate runs again.

After a calculation the Model tab can show where the activity is and where the dose comes from. Under Show, Activity in the body fills each box of the drawing, as a bucket, to its share of the chosen member’s activity in the whole body at a time after intake, and Effective dose to its share of the committed effective dose received up to that time, or of its rate then, from the activity in the box: the member’s, or the whole chain’s. The time is one of the calculation’s output times, ten to a decade from about a minute and a half after intake, for one of its ages at intake; Run through moves it to the last. Each compartment’s dose is its own, not a share of its source region’s: with a time series the integrator keeps the integrals of every compartment apart (otherwise those of a member in a source region together), which takes a tenth to a quarter longer. The drawing has one box for each part of the gut’s contents and for the bladder’s, whichever copy of the alimentary tract the activity is in; with the whole chain, a nuclide counts in the box of the same name, or, where it was formed in a compartment of another member’s model, in that compartment’s box. What the drawing has no box for — the respiratory tract, the mouth and the oesophagus, and the compartments a progeny is given where it is formed in a part of another member’s model that its own model lacks — is listed under the slider with its share.

Checking it

Batch calculations

The Batch tab calculates many coefficients at once, for one system and one route: the radionuclides typed or pasted into its field (names such as Cs-137 or cs137, separated by commas, spaces or lines; an element’s symbol stands for all its nuclides in the system), or chosen from the list that Choose from the list opens — the system’s radionuclides to the left, narrowed by a search, an element, a half-life range, a decay mode and whether the route has forms for them, and the chosen ones to the right, moved with the buttons (the selected ones, or all that are shown), by double-clicking or with Enter. Each is calculated in all its chemical and physical forms for the route or in its default one, for inhalation at each aerosol size ticked (a gas or vapour has no aerosol size and is calculated once), at each age at intake ticked, with the tab’s own decay chain cut-off (ICRP 103 system) and tolerance. The count above the button says how many calculations that is. They run in the page’s workers, as many at a time as the device has cores to spare, after any single calculation started meanwhile; the bar shows how far the batch has come and about how long is left, and Stop ends it, keeping what is done. A calculation that fails is noted in its row and the batch goes on.

Under the bar is what the table shows, which calculates nothing again when changed: the committed effective dose, and if chosen the committed equivalent doses of the tissues weighted in it, of the remainder’s tissues and of the others, in the ICRP 103 system for each sex as well; a row for each radionuclide, form and aerosol size with the ages as columns, or a row for each age as well; and the digits. Save as CSV and Save as Excel write the whole table, six significant figures in CSV and the full values in Excel, the workbook with a second sheet of the settings.

Risk coefficients

The Risk tab recalculates the ICRP’s detriment-adjusted nominal risk coefficients from the inputs its recommendations give, tissue by tissue, beside the values it printed:

• ICRP 103 system (Publication 103 Table 1 and Annex A): for each tissue the nominal risk R, lifetime cases per 10 000 persons per Sv, is adjusted for lethality k and for the quality of life of those who survive, R (k + q (1 − k)) with q = q_min + (1 − q_min) k, and weighted by the relative cancer-free life lost l. Summed, this gives 5.7 × 10⁻² Sv⁻¹ for the whole population and 4.2 × 10⁻² Sv⁻¹ for adults; Table 1 lists the heritable part before the life-lost weighting (para A 164).
• ICRP 60 system (Publication 60 Table 3 and Annex B): for each organ the probability of fatal cancer F, with non-fatal cancers weighted by their lethality, F (2 − k), times the relative length of life lost l / l̄, plus severe hereditary effects: 7.3 × 10⁻² Sv⁻¹ for the whole population and 5.6 × 10⁻² Sv⁻¹ for workers, the basis of its tissue weighting factors.

The nominal risks themselves come from risk models fitted to the atomic bomb survivors and carried to other populations with life tables and age weights that the publications do not give, so the calculation starts from them; the tab shows for each tissue where its value comes from (the mix of excess relative and excess absolute risk models, or another study) and the tissue weighting factor its relative detriment led to.

Once a dose coefficient is calculated, the tab also gives its nominal detriment per becquerel, two ways: the committed effective dose times the total coefficient (5.7 × 10⁻² Sv⁻¹, or 7.3 in the ICRP 60 system), and tissue by tissue, each tissue’s detriment per sievert times its committed equivalent dose. They agree when the dose is spread through the body and part when it gathers in a few tissues (iodine in the thyroid gives about half), because the weighting factors are rounded and grouped detriments. Both are nominal values for protection purposes: the coefficients are averages over the sexes and the ages at exposure, and the ICRP does not recommend them, or effective dose, for the risk of an individual (Publication 103 paras 155–161, A 164).

Radon and thoron at home

For radon (²²²Rn) and thoron (²²⁰Rn) indoors the ICRP gives doses per exposure, not per becquerel taken in: most of the dose comes from the short-lived progeny the air carries, as tiny unattached clusters or attached to the aerosol, and is reckoned from their potential alpha energy concentration times the time spent in it (mJ h m⁻³; 1 WLM = 3.54 mJ h m⁻³), or from the gas concentration through the equilibrium factor F. The Radon at home tab calculates them as Publication 158 does (Section 32, Annex C), with the method of Publication 137 (Annex A):

• each progeny nuclide (²¹⁸Po, ²¹⁴Pb, ²¹⁴Bi; ²¹²Pb, ²¹²Bi) in each mode of the home aerosol — unattached, nucleation and accumulation — is an inhalation calculated by this page’s engine, with the regional deposition of Table C.1, the absorption of Table 32.1 and the element’s systemic model;
• per mode they are combined per unit potential alpha energy with the progeny’s activity ratios and the breathing rate at home of each age (Table 32.3), and the modes weighted by the unattached fraction f_p and the nucleation share f_pn (Table 32.2), which you can change;
• the gas itself adds its own dose per exposure, from the radon model (Annex C para C 18).

Against Publication 158 the radon progeny agree within 1 % at every age (Table 32.7), the gas within 3 % (Table C.7) and each nuclide and mode within the rounding of Table C.8. Thoron progeny come out 2–5 % higher than Table 32.8: Table C.1 gives the deposition of the 200 nm accumulation mode for radon progeny’s spread (σ_g 2.0), not for thoron progeny’s narrower one (1.8). The tab also shows the coefficients the ICRP recommends for every age, 3 mSv per mJ h m⁻³ for radon and 1 for thoron (paras 532–537), and an annual dose for a concentration and the hours spent at home.

Data and where they come from

What it does not do

• Intakes by the embryo and fetus, and by infants through breast milk (Publications 88 and 95).
• Wounds as such (the NCRP wound model), and occupational exposure (the OIR series for workers). Direct uptake to blood is calculated in the ICRP 103 system (route Injection).
• Radon and thoron in workplaces, mines and caves (Publication 137), and actinon (²¹⁹Rn); homes are on the Radon at home tab.
• Argon, krypton and xenon, which the ICRP treats as external exposure to the gas around the body rather than as intakes.

References