WSC Radioecology Research Group
A new methodology for the
assessment of radiation doses
to biota under non-equilibrium
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
Introduction
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
Objectives

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 Design
Fast
Release
Slow
Release
Fast
Uptake
Fast phase
Slow
Uptake
Organism
Slow phase
Radioactive decay
Radioactive decay
Environment
(seawater)
Multi-phasic release
Some organisms have fast followed by slow release,
represented by two biological half-lives
0.2
0
-0.2
-0.4
Ln (C/C0)

Phase 1
-0.6
-0.8
-1
Phase 2
-1.2
-1.4
-1.6
-1.8
0
50
100
150
200
250
Time (h)
Typical biphasic retention curve, representing the depuration of
131I from L. littorea (Wilson et al., 2005).
300
Model 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 diagram
Water
activity
Biokinetic
database
Dosimetry
database
Calculate initial conditions of the system
No
Yes
2 TB1/2 known?
No
At least 1 TB1/2
known?
Calculate 2 rate constants
from TB1/2s
Yes
No
% retention
known?
Yes
Calculate remaining rate
constants for advanced model
(3 components)
No
Slope transition
known
Yes
Calculate remaining rate
constants for basic model
(2 components)
Apply npn-dynamic model
using CF
Run a loop for series of regular time steps
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 equations
dq1 (t )
 k12q2 (t )  k13q3 (t )  (k 21  k31 )q1 (t ); q1 (t  0)  q1
dt
dq2 (t )
 k 21q1 (t )  k 23q3 (t )  (k12  k32 )q2 (t ); q2 (t  0)  q2
dt
dq3 (t )
 k31q1 (t )  k32q2 (t )  (k 23  k13 )q3 (t ); q3 (t  0)  q3
dt
Basic equations

General solution:
qi (t ) 

fi

q 

i



 di  f i t qi 2  di  f i t
e 
e , i  1,2,3
 (   )
 (   )
2
Involves Laplace transformation, algebraic
manipulation and some substitutions (, ,
d’s and ƒ’s are functions of the rate
constants).
Model parameterisation

Initial conditions:
V
q1  A W ; q2  q3  0


Approximation 1 (organism is a faster
accumulator than the medium):
k21 << k12 and k31 << k13

Approximation (organism holds less activity
than the medium):
q1 >> q2 or q3
Consequences

Biphasic release:
ln 2
ln 2
k12 
  ; k13 

T2
T3
m
qB (t ) k 21 k 31
CF  lim t 


V
q1 (t ) k12 k13

Simple formulae for all the model
constants:
1

 ln 2
 
 ln 2
 m
ln 2
ln 2
k12 
  ; k 21  
    CF  
   x ; k13 
 ;
T2
T3
 T2
  V
 T3
 
k31  x (unknown)
Calculation of "x"

If we know the % retained at time  (f100):
k 21 

CFm  ln 2
1

   1   k13
V  T2
 e  k12
 e
k31 

CFm  ln 2

    k 21
V  T3


 f100
 k12  

e

 ;
 100

If we know when the release curve closes
in to slope of the final phase (factor f ):
CFm 
1
k 21  k12
1


V  1 f
k 21k13  1
k31 
k12  1  f
1

k12  ( k12  k13 ) 
 f 
e
 ;
k13 



k12  ( k12  k13 ) 
 f 
e

k13 


Sensitivity analysis
Basis for the dosimetry

Same as EA R&D 128 and FASSET (aquatic)

= summation over all nuclides
i
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
ext
DCCtotal
,i and DCCtotal,i = DCCs
in Gy h–1 per Bq kg-1
C
se diment
 f solidC
se diment
dry
 (1  f solid )
C
water
fsediment , fsurface and fwater = fractions of time in
different media

int
H int ernal   Ciorg DCCtotal
,i
i
water


f
f




C
surface
surface
sediment
ext
i

Ci

H external    f sediment 
  f water 
 DCCtotal,i
2 
2   
i 

Model inputs
Biokinetic Parameters

Current data defaults from literature

User can edit with site-specific data
Model Outputs

Reference organisms

Nuclides

Phytoplankton

99Tc

Zooplankton

125I, 129I

Macrophyte

134Cs

Winkle

238Pu, 239Pu

Benthic mollusc

241Am

Small benthic crustacean

Large benthic crustacean

Pelagic fish

Benthic fish
&
&
131I
137Cs
&
Weighted and un-weighted external and
internal doses and activity concentrations
within biota produced
241Pu
Validation


129I
activity in winkles:
comparison with
model by Vives i Batlle
et al. (2006)
99Tc
activity in
lobsters:
comparison with
model by Olsen and
Vives i Batlle (2003)
Results - Long term assessment
Annual time steps
1.00E+01
Total weighted dose rate (µGy h-1)
Benthic
mollusc
1.00E+00
1.00E-01
1.00E-02
1.00E-03
Large benthic crustacean
Dynamic model
Equilibrium model
1.00E-04
1950
1960
1970
1980
1990
2000
Time (year)
Pu benthic mollusc - TB1/2 = 474 days
Tc large benthic crustacean - TB1/2 = 56.8 & 114 days
Results - Short term assessment
Daily time steps
(a) Macrophyte
7
Dynamic model
Weighted dose rate (µGy h-1)
6
Equilibrium model
5
4
3
2
1
Date
Tc in macrophytes - TB1/2 = 1.5 & 128 days
99
28
/0
8
/1
9
99
20
/0
5
/1
9
99
09
/0
2
/1
9
98
01
/1
1
/1
9
98
24
/0
7
/1
9
98
15
/0
4
/1
9
98
05
/0
1
/1
9
97
27
/0
9
/1
9
97
/1
9
/0
6
19
11
/0
3
/1
9
97
0
Results - Short term assessment
Daily time steps
(b) Winkle
0.8
Dynamic model
Weighted dose rate (µGy h-1)
0.7
Equilibrium model
0.6
0.5
0.4
0.3
0.2
0.1
Date
Tc in winkles - TB1/2 = 142 days
99
28
/0
8
/1
9
99
20
/0
5
/1
9
99
09
/0
2
/1
9
98
01
/1
1
/1
9
98
24
/0
7
/1
9
98
15
/0
4
/1
9
98
05
/0
1
/1
9
97
27
/0
9
/1
9
97
/1
9
/0
6
19
11
/0
3
/1
9
97
0
Time-integrated doses
Test
Time period
Sellafield discharges 1952 - 2005
(short-term test)
(50 y)
Organism
Winkle
Benthic fish
Benthic Crust.
(long-term test)

TB1/2 (d) % difference
137
0.86
64.7
0.00
0.00
99
Cs
137
Cs
56.8, 114
-1.48
239
Pu
474
8.63
Jul 1997 – Jun 1999 Macrophyte
99
Tc
1.5, 128
-7.1
(700 d)
Winkle
99
142
-16.6
25 Jan - 7 Mar 1998 Winkle
99
1.5, 128
-37.1
(40 d)
99
142
-78.3
Benthic mollusc
Seawater at Drigg
Nuclide
Macrophyte
Tc
Tc
Tc
Tc
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.
Conclusions

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
References



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.
Acknowledgements
The authors would like to thank the
Nuclear Decommissioning Authority
(NDA), UK, for funding this project.