WSC Radioecology Research WSC Radioecology Research GroupGroup

A new methodology for the A new methodology for the assessment of radiation assessment of radiation

doses to biota under non-doses to biota under non-equilibrium conditionsequilibrium conditions

J. Vives i Batlle, R.C. Wilson, S.J. Watts, S.R. Jones,

P. McDonald and S. Vives-Lynch

EC PROTECT Workpackage 2 Workshop, Vienna, 27 - 29 June 2007

IntroductioIntroductionn

Interest in recent years regarding protection of non-human biota

Different approaches: Environment Agency R&D 128 FASSET/ERICA RESRAD - Biota, Eden, EPIC-DOSES3D, etc.

All have one common theme:

Assume equilibrium within the system they are modelling

Current work builds on previous work but takes it to the next stage:

Non-equilibrium conditions

ObjectivesObjectives

Model the retention behaviour observed for many organisms and radionuclides.

Express model rate constants as a function of known parameters from the

literature.

Ensure the model automatically reduces to the old CF-based approach in the

non-dynamic case.

Incorporate dosimetry compatible with FASSET and EA R&D 128

methodologies.

Encode the model in a simple spreadsheet which assesses for lists of

radionuclides and biota over time.

Model DesignModel Design

Environment

(seawater)

Slow phaseFast phase Organism

Fast Uptake

Slow Uptake

Fast Release

Slow Release

Rad

ioac

tive

de

cay

Rad

ioactive d

ecay

Multi-phasic Multi-phasic releaserelease

Some organisms have fast followed by slow release, represented by two biological half-lives

Typical biphasic retention curve, representing the depuration of 131I from L. littorea (Wilson et al., 2005).

Model optionsModel options Three cases are possible:

No biological half-lives known use instant equilibration with a CF (current method). One biological half-life known use simple dynamic 2-compartment model. Two biological half-lives known use fully dynamic 3-compartment model.

Flow diagramFlow diagramBiokineticdatabase

Water activity

Dosimetry database

Calculate initial conditions of the system

2 TB1/2 known?

Slope transition known

No

Yes

% retention known?

Calculate 2 rate constants from TB1/2s

At least 1 TB1/2 known?

No

No

Apply npn-dynamic model using CF

No

Yes

Calculate remaining rate constants for basic model

(2 components)

Yes

Calculate remaining rate constants for advanced model

(3 components)

Run a loop for series of regular time steps

Yes

Refresh initial conditions of new time step using solution

form previous step

Refresh initial conditions of new time step using solution

form previous step

Write results into the spreadsheet

Basic equationsBasic equations

33313232321313

22232123231212

11131213132121

)0();()()()()(

)0();()()()()(

)0();()()()()(

qtqtqkktqktqkdt

tdq

qtqtqkktqktqkdt

tdq

qtqtqkktqktqkdt

tdq

Basic equationsBasic equations General solution:

Involves Laplace transformation, algebraic manipulation and some substitutions (, , d’s and ƒ’s are functions of the rate constants).

3,2,1,

)()()(

22

iefdq

efdqf

tq tiiitiiiii

Model parameterisationModel parameterisation Initial conditions:

0;Aq 32W1 qqV

Approximation 1 (organism is a faster

accumulator than the medium):

Approximation (organism holds less activity than the medium):

k21 << k12 and k31 << k13

q1 >> q2 or q3

ConsequencesConsequences Biphasic release:

Simple formulae for all the model constants:

3

132

12

2lnk;

2lnk

TT

13

31

12

21

1t k

k

k

k

)(

)(lim tq

tq

V

mCF B

)(

;2ln

k ;2ln2ln

k;2ln

k

31

313

1

3221

212

unknownxk

Tx

TCF

V

m

TT

Calculation of "x"Calculation of "x" If we know the % retained at time

(f100):

If we know when the release curve closes in to slope of the final phase (factor f ):

213

31

100

221

k2ln

;100

11

2lnk 12

1213

TV

CFmk

ef

eeTV

CFm kkk

)(

13

12

12

132131

1

)(

13

121221

1312

1312

k

k

1

1k

;k

k

1

11kk

kk

kk

effk

kk

effV

CFm

Sensitivity analysisSensitivity analysis

Basis for the dosimetryBasis for the dosimetry Same as EA R&D 128 and FASSET

(aquatic)

i

extitotal

waterisurface

watersedimenti

surfacesedimentexternal

iitotal

orgiernal

water

solidentse

drysolidentse

DCCCf

fCf

fH

DCCCH

CfCfC

,

int,int

dimdim

22

)1(

i

= summation over all nuclides

Corg , Cwater and Csediment = nuclide concs.

in Bq kg–1 or Bq m–3

= density of sea water

fsolid = solids fraction of wet sediment (0.4).

int,itotalDCC and

extitotalDCC , = DCCs

in Gy h–1 per Bq kg-1

fsediment , fsurface and fwater = fractions of time in

different media

Model inputsModel inputs

Biokinetic Biokinetic ParametersParameters

Current data defaults from literature

User can edit with site-specific data

Model OutputsModel Outputs Reference organisms

Phytoplankton

Zooplankton

Macrophyte

Winkle

Benthic mollusc

Small benthic crustacean

Large benthic crustacean

Pelagic fish

Benthic fish

Nuclides 99Tc

125I, 129I & 131I

134Cs & 137Cs

238Pu, 239Pu & 241Pu

241Am

Weighted and un-weighted external and internal doses and activity concentrations

within biota produced

ValidationValidation 99Tc activity in lobsters: comparison with

model by Olsen and Vives i Batlle (2003)

129I activity in winkles: comparison with model by Vives i Batlle et al. (2006)

Results - Results - Long term Long term assessmentassessment

Pu benthic mollusc - TB1/2 = 474 days

Tc large benthic crustacean - TB1/2 = 56.8 & 114 days

1.00E-04

1.00E-03

1.00E-02

1.00E-01

1.00E+00

1.00E+01

1950 1960 1970 1980 1990 2000

Time (year)

Tot

al w

eigh

ted

dose

rat

e (µ

Gy

h-1

)

Large benthic crustacean

Equilibrium model

Benthic mollusc

Dynamic model

Annual time steps

Results - Results - Short term Short term assessmentassessment

Tc in macrophytes - TB1/2 = 1.5 & 128 days

(a) Macrophyte

0

1

2

3

4

5

6

7

Date

Wei

ghte

d do

se ra

te (µ

Gy

h-1

)

Dynamic model

Equilibrium model

Daily time steps

Results - Results - Short term Short term assessmentassessment

Tc in winkles - TB1/2 = 142 days

Daily time steps(b) Winkle

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Date

Wei

gh

ted

do

se ra

te (

µG

y h-1

)

Dynamic model

Equilibrium model

Time-integrated dosesTime-integrated doses

differences between the integrated dose rates obtained from the two approaches increase with slowness of response of the organism to an input of radioactivity, due to the smoothing effect of the dynamic method.

Test Time period Organism Nuclide TB1/2 (d) % difference

Sellafield discharges 1952 - 2005 Winkle 137Cs 0.86 0.00

(short-term test) (50 y) Benthic fish 137Cs 64.7 0.00

Benthic Crust. 99Tc 56.8, 114 -1.48

Benthic mollusc 239Pu 474 8.63

Seawater at Drigg Jul 1997 – Jun 1999 Macrophyte 99Tc 1.5, 128 -7.1

(long-term test) (700 d) Winkle 99Tc 142 -16.6

25 Jan - 7 Mar 1998 Winkle 99Tc 1.5, 128 -37.1

(40 d) Macrophyte 99Tc 142 -78.3

ConclusionsConclusions

Successfully production of a dynamic model that makes

assessments to biota more realistic

Simple, user-friendly spreadsheet format similar to R&D 128

Model is rigorously tested and validated against CF and

dynamic research models

Can be edited with site-specific data

Expandable for extra nuclides and organisms

ReferencesReferences

Vives i Batlle, J., Wilson, R.C., Watts, S.J., Jones, S.R., McDonald, P. and Vives-Lynch, S. Dynamic model for the assessment of radiological exposure to marine biota. J. Environ. Radioactivity (submitted).

Vives i Batlle, J., Wilson, R. C., McDonald, P., and Parker, T. G. (2006) A biokinetic model for the uptake and release of radioiodine by the edible periwinkle Littorina littorea. In: P.P. Povinec, J.A. Sanchez-Cabeza (Eds): Radionuclides in the Environment, Volume 8. Elsevier, pp. 449 – 462.

Olsen, Y.S. and Vives i Batlle, J. (2003). A model for the bioaccumulation of 99Tc in lobsters (Homarus gammarus) from the West Cumbrian coast. J.

Environ. Radioactivity 67(3): 219-233.

AcknowledgementsAcknowledgements

The authors would like to thank the Nuclear Decommissioning Authority (NDA), UK, for funding this project.