Westlakes Radioecology Group

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Westlakes Radioecology Group
Dosimetric model for biota exposure to inhaled
Radon daughters
Jordi Vives i Batlle
ICRP Task Group Meeting, 30 June 2008
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Introduction

• This study presents a model based on
  allometrically derived respiration rates and
  target tissue masses, designed for calculating
  222Rn daughter dose rates to sensitive tissues
  and the whole body of terrestrial animals and
  plants.
• This work is designed as an improvement on the
  method developed by the EW EA, aimed at
  producing a conservative calculation without the
  need to develop a full respiratory model for
  radon in non-human biota.

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Basis for the model
Conceptual representation of irradiated
respiratory tissue
Simple respiratory model for 222Rn daughters
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Problem formulation

• We model the input of a constant flow of atoms
  into a compartment with continuous loss due to
  radioactive decay, with these two fluxes in
  equilibrium.
• It is assumed that the compartment is 100
  efficient at trapping the material, i.e. no
  particles escape by exhalation and decay is the
  only source of removal.
• The input flow I0i equals the specific activity ?
  breathing rate / decay constant (in order to
  convert disintegrations per unit time to
  particles).

i Index for the radionuclide 1 to 5 for 222Rn,
218Po, 214Pb, 214Bi and 214Po Ai Activity of
radionuclide i Bq m-3 A1 (secular
equilibrium) BR Breathing rate m3 s-1 tidal
volume (VT) ? breathing frequency (?R) ?i Decay
constant of radionuclide i s-1.
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Integration

• Simple differential equation

• Rate of energy per unit mass (dose rate)
  deposited in the lung by the each radon daughter
  i (i 2 5)

MT Mass of sensitive tissue ?T ? ST ? hT
m3 Ei? Total energy emitted by daughter
radionuclide i due to its own decay and the
(rapid) subsequent decay of its short-lived
daughters down to 210Pb J ej? Alpha decay
energy of emission of radionuclide k.
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Dose calculation

• Substitute, sum of all the dose rates for the
  short-lived daughters approximate and A1 Ai,
  i 2 5

• Where the sum is the potential
  ?-energy per Bq activity of the short-lived radon
  daughters in secular equilibrium and A1 is the
  activity of radon gas F ? EERn (equilibrium
  factor per equilibrium equivalent radon
  concentration). From here the DPUC is

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Allometry

• Allometric analysis is the comparison of a given
  structural or functional parameter (Y) as a
  function of body mass (M) across organisms of
  different species.
• Many biological parameters relate to metabolism
  and scale according to the Brody-Kleiber law

• Other parameters scale on the basis of surface
  exchange, like radiation flux and heat transfer

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Example of DPUC allometry

• Examples of DPUC (? ?) dependency with respect
  to area/volume. Internal irradiation 125I, 137Cs
  and 210Po (left), and external irradiation 14C,
  63Ni and 230Th (right).

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Allometric formulas for dose

• Simple power functions for DPUCs in ?Gy per Bq h
  m-3

FU Unit conversion factor (3.6 ? 109 ?Gy h-1 per
Gy s-1) BR Gross extrapolation to the bronchial
epithelium (airway generations 1 - 8) TB Full
tracheobronchial epithelium (generations 1 - 15)
L Full lung WB Whole body ABR(ALM), BBR(BLM)
Base and exponent of the allometric formulae for
breathing rate lung mass STBRM and SBRM
surface area of the tracheobronchial tree or the
bronchial epithelium Rwfa Radiation weighting
factor for ?-energy (default 20).
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Parameterisation
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Basis for the dosimetry

• applicable to all radionuclides whose
  concentration is referenced to air - that is, 3H,
  14C, 32P, 35S, 41Ar, 85Kr and 222Rn

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Model validation
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Model validation

• Good agreement with McDonald ad Laverock.
  Additional comparison with rat DPUCs for the
  tracheobronchial tree by is problematic as
  reported sources they use a full respiratory
  model
• Predicting significant fractions of the radon
  daughters removed by the nasal passages.
• Including lung clearance processes, resulting in
  transport from the alveolar region to the
  bronchial area, with associated decay included in
  transit.
• The models consider atmospheres with various
  assumptions of equilibrium resulting in varying
  particle size, F lt 1 and fP values.
• As a result, ours is a conservative approximation.

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Eggs

• For the purposes of this exercise the maximising
  assumption was made that the breathing rate for
  eggs is equal to the breathing rate of a bird
  having the same mass as the egg.
• Consequently, using our standard equation for the
  breathing rate is an extremely conservative
  assumption, because it is likely that the pores
  of the egg shell will trap a substantial
  component of the unattached and attached
  fractions of the radon aerosol before they reach
  the animal.
• This assumption does not lead to unusually high
  doses for eggs compared with other organisms.

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Insects

• Respiration in insects is mainly a diffusion and
  convection process through a network of
  tracheolae.
• This differs from a scaled-down version of the
  mammal lung but is still a fractal network of
  tubes and so the Brody-Kleiber Law should still
  apply.

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Insects

• Metabolic rates of all animals scale
  approximately the ¾ power of mass (Brody-Kleiber
  Law).
• Allometric formulae optimised to fit the more
  complex organisms tend to over-predict breathing
  rates for the simpler organisms.
• Consequently, using the same equations for the
  whole size range of animals including
  invertebrates (e.g. insects) is possibly a
  justifiable conservative assumption.

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Plants breathing rate

• CO2 enters, while water and O2 exit through a
  leafs stomata.

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Plants breathing rate

• The rate of resource use in plants A x M¾,
  though isometric respiration rates have also been
  suggested.
• We calculated a breathing rate relationship for
  plants from whole plant respiration
• Use resp. rate (net CO2 efflux in nmol CO2 s-1)
  1.19 ? M1.02 from Reich et al. (2005).
• Apply conversion factor of 2.5 ? 103 mols of air
  per mols of CO2
• Apply a generic wet dry mass ratio of 5 and a
  molar volume of 22.4 l STP.
• This is the largest potential source of
  uncertainty in this calculation.

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Plants geometry

• Ellipsoid with axes L, a, a

• Equivalent cylinder radius

• The target tissue is the space between the two
  interlocking cylinders of radii R and R hT and
  length L, with mass

• Where M is the total mass of the organism.

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DPUC calculation

• DPUC to target tissue (?Gy per Bq s m-3)

• Where
• DPa Potential ?-energy factor 5.54 ? 10-9 J
  Bq-1
• APL Allometric base for breathing rate in
  plants, 1.95 ? 10-4 m3 s-1
• a Minor axis of the ellipsoid representing the
  plant in m
• hT Depth of sensitive tissue 5.5 ? 10-5 m
• FU Unit conversion factor (3.6 ? 109 ?Gy h-1
  per Gy s-1)
• Rwfa Radiation weighting factor for ?-energy
  (default 20).

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DPUC calculation

• DPUC to whole plant (?Gy per Bq s m-3)

• Assumes that assume that the whole plant is a
  surface exchanging gases with the atmosphere.
• Give doses a factor of lt 5 of what would have
  been obtained using the allometric formulae for
  animals.
• A dose model representing gas exchange through
  plant stomatae is the next logical developmental
  step.

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Weighted 222Rn daughter DPUCs (internal ?
irradiation)
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Weighted 222Rn daughter DPUCs (external
irradiation)
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Practical calculation for the EA

• Extend method to report to all the feature
  species used by the EW EA for habitats
  assessments.
• Calculate dose rates for 1 Bq m-3 of 222Rn in
  equilibrium with its short-lived daughters
• Derive an "effective total" DPUC by factorising,
  as part of the external dose component
• concentration factors
• air density
• occupancy factors
• Both internal and external components of dose
  expressed as a linear function of the 222Rn
  activity concentration.
• Apply the scaling method from the EW EA SP1A
  report - power function fittings between DPUC and
  area/volume for different radionuclides.

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Practical calculation for the EA
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Conclusions

• Radon dosimetry now codified into new DPUCs for
  internal ?-irradiation arising from exposure of
  animals and plants to short-lived 222Rn
  daughters.
• The 222Rn DPUCs can be used to produce an
  assessment in the normal way, using atmospheric
  radionuclide versions of the standard EA RD 128
  formula for terrestrial ecosystems.
• The main exposure pathway is identified to be
  exposure of the target tissues of the respiratory
  system to ? radiation arising from 222Rn
  daughters.

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Conclusions (2)

• Target tissue dose rates calculated by a
  process-based respiratory model are, in all
  likelihood, lower by a factor of 5.5 7.5.
• An additional layer of conservatism is the
  overestimation of breathing rates by allometry in
  the smaller organisms, estimated to be within a
  factor of 2.
• As a result, the tracheo-bronchial doses
  estimated in this assessment are likely to be
  conservative by an order of magnitude.

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Perspectives for further work

• Additional investigation of the dosimetry for
  insects and plants - especially allometry
  aspects.
• Review of evidence for dose rates that would
  cause stochastic effects in the lung and more
  detailed lung modelling.
• Consideration could also be given to how to
  extend the dose assessment for 226Ra in soil to
  include 222Rn emissions in that environment.
• Consider also the development of a similar
  approach to calculate thoron doses.

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Thank you!