F L I N D E R S M E D I C A L C E N T R E , MEDICAL IMAGING DIVISION
Calculation
Calculation of
of radiation
radiation doses
doses and
and
restriction
restriction periods
periods for
for persons
persons coming
coming
into
-131 and
into contact
contact with
with II-131
and
In
-111 therapy
In-111
therapy patients
patients
John Cormack and Jane Shearer
Division of Medical Imaging
Flinders Medical Centre
South Australia
F L I N D E R S M E D I C A L C E N T R E , MEDICAL IMAGING DIVISION
Human Radioactive Sources
In-vivo radioactive sources are
harder to control than in-vitro
radioactive sources, and the
radiation dosimetry is more
complex.
Little Willie, full of glee
Put radium in his Grandma’s tea
Now he thinks it’s quite a lark
To see her glowing in the dark!
F L I N D E R S M E D I C A L C E N T R E , MEDICAL IMAGING DIVISION
Regulatory Requirements
In the USA the Nuclear Regulatory Commission (NRC)
has already published amendments to its regulations
pertaining to the release of radioactive patients which
will necessitate an estimate of exposure to other persons
to be made, in principle, for every patient.
In Australia, release criteria in most states will probably
be eventually based on the ARPANSA
“Recommendations for the Discharge of Patients
Undergoing Treatment with Radioactive Substances”
F L I N D E R S M E D I C A L C E N T R E , MEDICAL IMAGING DIVISION
Exposure Rate
Radiation Exposure from
Multiple Contact Periods
Time
F L I N D E R S M E D I C A L C E N T R E , MEDICAL IMAGING DIVISION
Calculation of Cumulative Exposure
 Total
  Initial
  Effective


 =
 ×

 Exposure  Exposure Rate  Exposure Time
E = E0′T
E = Total exposure
E0′ = Exposure rate at time zero (initial exposure rate)
T = Effective exposure time
F L I N D E R S M E D I C A L C E N T R E , MEDICAL IMAGING DIVISION
Calculation of Effective
Exposure Time
 Effective
  Sum over all exposure periods of


=

 Exposure Time  effective exposure time in each period




T = ∑  ∫ F (t)dt 

All exposure exposure

 period
periods
E ′(t) A(t)
F(t ) =
=
A0
E0′
F L I N D E R S M E D I C A L C E N T R E , MEDICAL IMAGING DIVISION
Radiation Exposure Pattern
Pattern Start
Pattern End
Administration
p
Delay
τ
Time
C1
C2
C3
C4
F L I N D E R S M E D I C A L C E N T R E , MEDICAL IMAGING DIVISION
Contact Delay (hrs)* = 0
60
42.8097804
404.677078
50
22
0
0
0
0
0
0
0
0
0.97298536
0.96815241
0.96334348
20.7542422
20.6511533
22
16
14
12
10
8
20
0
0
0
0
0
0
0
0
0.99997788
0.56730132
0.99997788
0.51170264
0.99997788
0.46155295
Time
Period (Hour of Day)
21.6510362
9.01391987
21.6510362
8.13050577
6
20.5485763
20.4465089
20.3449485
20.2438925
20.1433385
20.0432839
0.92112382
20
0
0
0
0
0
0
0
0
18
16
14
12
10
8
0
0
0
0
0
0
0
0
0.97298536
0.96815241
0.96334348
20.7542422
20.6511533
bcomp2
21.6510362
7.33367116
21.6510362
6.61493075
21.6510362
5.96663088
21.6510362
5.38186799
21.6510362
4.85441511
21.6510362
4.37865553
Time Period (Hour of Day)
0.99997788
0.18241324
6
4
2
bcomp1
Contact Delay (hrs)* = 0
1.5
4
0
0
0
0
1
0
0
0.5
0
0
0.567301320
0.51170264
0.46155295
9.01391987
8.13050577
20.5485763
20.4465089
20.3449485
20.2438925
20.1433385
20.0432839
0.92112382
2
7.33367116
20
6.61493075
5.96663088 10
5.38186799 0
4.85441511
4.37865553
0.18241324
t3
18
t2
0
30
0
Pattern #5
Partner or Spouse
40
F L I N D E R S M E D I C A L C E N T R E , MEDICAL IMAGING DIVISION
Phase Shifting Pattern
Ta
Administration
Reference Time
Tr
Delay
τ
Phase
Shift
φ
p
F L I N D E R S M E D I C A L C E N T R E , MEDICAL IMAGING DIVISION
I think you should
be more explicit
here in step two!
F L I N D E R S M E D I C A L C E N T R E , MEDICAL IMAGING DIVISION
Calculation of Effective Exposure Time
(Multi-exponential clearance, multiple exposure, single pattern phase locked)
n
T = ∑ ai
i =1
e
−λ iτ
λi
m
∑e
−λi θ j
j =1
(1 − e )
−λi C j
T = effective exposure time
C j = duration of jth period of contact
θ j = time lapse between start of contact pattern and jth period of contact
τ = time delay between administration and start of close contact pattern
m = number of periods of close contact
λ i = decay constant for ith component of decay
ai = fraction of decay occurring through ith component
F L I N D E R S M E D I C A L C E N T R E , MEDICAL IMAGING DIVISION
Calculation of Time Delay Required
to Limit Effective Exposure (and
hence Dose) to a Specified Value
(Inverse Calculations)
Analytical solution possible for single
exponential clearance
Numerical techniques must be used for
multi-exponential clearance
F L I N D E R S M E D I C A L C E N T R E , MEDICAL IMAGING DIVISION
Approximate Calculation
∞
D = kD& 0
ae
{
∫
− λ 1t
+ be
}dt
−λ 2t
ts
D is the total accumulated dose
D& 0 is the initial dose rate at 1 metre
λ1 and λ 2 are the two decay constants associated with the clearance
a and b are the proportions of each clearance component
t s is the time at which exposure starts
k is an exposure factor which relates the actual accumulated exposure from a given exposure
pattern to that received from continuous exposure at one metre
F L I N D E R S M E D I C A L C E N T R E , MEDICAL IMAGING DIVISION
Exposure Factor, k
Accumulated radiation dose from a given pattern of exposure
k=
Total dose resulting from exposure at 1 metre in the same time
D
k=
∞
D& 0
ae
{
∫
ts
− λ 1t
+ be
=
}dt
−λ 2t
D
a

b
D& 0  e − λ 1ts + e − λ 2ts 
λ1

λ2
F L I N D E R S M E D I C A L C E N T R E , MEDICAL IMAGING DIVISION
Exposure Factor, k - Note
Note that for exposure patterns where there are periods of exposure at
distances less than 1 metre, the exposure factor may have a value
exceeding 1. It should not be confused with occupancy factor.
Note also that the exposure factor, k , is not a constant for a given
exposure pattern, and will, in fact, vary with the start time of the exposure
ts as well as the clearance rate of the radionuclide from the body;
however, this variation is small for radioactive materials which have an
overall clearance rate which is slow compared with the period of the
exposure pattern.
For I-131 and In-111 therapy, therefore, an averaged exposure factor for
each pattern can be utilized, allowing the approximate equation to be used
in estimating accumulated doses
F L I N D E R S M E D I C A L C E N T R E , MEDICAL IMAGING DIVISION
Standard Exposure Patterns
Exposure
Pattern
Activity
1
Public transport travel
2
Return to work not involving prolonged close contact with others
3
Return to work involving prolonged close contact with others
4
Close contact with adult friends and family/carers
5
Close contact with pregnant women
6
Caring for infants (demanding or sick)
7
Caring for infants (normal )
8
Close contact with 2-5 year old children
9
Close contact with 5-15 year old children
10
Sleeping with spouse or partner, or a child
11
Work with radiosensitive materials
F L I N D E R S M E D I C A L C E N T R E , MEDICAL IMAGING DIVISION
Calculated exposure factors for various
clearance rates and patterns of exposure
Exposure
Pattern
1
2
3
4
5
6
7
8
9
10
11
In-111
I-131 iodide I-131 iodide I-131 iodide I-131 iodide octrocide
Ablation Ablation - fast Euthyroid
Thyrotoxic
"Normal"
slow
Patients
clearance
patients
clearance rate
clearance
0.68
0.35
0.65
1.26
0.98
5.26
1.73
2.95
1.33
4.86
0.35
0.67
0.36
0.68
1.28
1.01
5.36
1.75
2.89
1.30
4.69
0.36
0.62
0.42
0.77
1.33
1.09
5.69
1.80
2.71
1.20
4.15
0.42
0.68
0.34
0.64
1.26
0.98
5.24
1.73
2.96
1.33
4.89
0.34
0.67
0.36
0.66
1.27
1.00
5.31
1.74
2.91
1.31
4.76
0.36
Mean
CV(%)
0.66
0.37
0.68
1.28
1.01
5.37
1.75
2.89
1.29
4.67
0.37
3.8
8.3
7.9
2.4
4.5
3.4
1.8
3.5
4.1
6.5
8.3
F L I N D E R S M E D I C A L C E N T R E , MEDICAL IMAGING DIVISION
Calculated
restriction times using approximate and
rigorous models
Calculated Restriction (hours)
Exposure
Pattern
1
2
3
4
4
4
5
6
7
8
9
Set Dose
Constraint
(µSv)
1000
1000
500
3000
5000
10000
1000
1000
1000
1000
Approx
Model
Rigorous
Model
Discrepancy
62
13
149
22
0
0
112
320
180
242
63
5
144
21
0
0
105
315
177
248
-1
8
5
1
0
0
7
5
3
-6
F L I N D E R S M E D I C A L C E N T R E , MEDICAL IMAGING DIVISION
Calculated doses using approximate and rigorous models
Actual Dose Received (µSv)
Exposure
Pattern
1
2
3
4
4
4
5
6
7
8
Set Dose
Constraint
(µSv)
1000
1000
500
3000
5000
10000
1000
1000
1000
1000
Approx
Model*
Rigorous
Model
Discrepancy
1034
864
444
2955
4530
4530
936
943
987
1030
1000
1000
500
3000
5000
10000
1000
1000
1000
1000
34
-136
-56
-45
0
0
-64
-57
-13
30
F L I N D E R S M E D I C A L C E N T R E , MEDICAL IMAGING DIVISION
Data Input
F L I N D E R S M E D I C A L C E N T R E , MEDICAL IMAGING DIVISION
Calculated Restriction Times
F L I N D E R S M E D I C A L C E N T R E , MEDICAL IMAGING DIVISION
Patient Information Sheet
F L I N D E R S M E D I C A L C E N T R E , MEDICAL IMAGING DIVISION
Measured Clearance Data
F L I N D E R S M E D I C A L C E N T R E , MEDICAL IMAGING DIVISION
Incorporated Clearance Data
(can be modified by user)
F L I N D E R S M E D I C A L C E N T R E , MEDICAL IMAGING DIVISION
Issues to be Resolved
Choice of appropriate data for the decay in
exposure rate with time.
Exposure rate versus time curves for each
patient can be obtained, but (beware!)
propagated errors in calculated restriction
times and doses can be very large.
Some consensus is needed on realistic exposure
patterns for various patient activities.
Some consensus is needed on the dose limits to
be applied to various groups of persons.
Effective dose conversion factors.
Mean or maximum doses?
F L I N D E R S M E D I C A L C E N T R E , MEDICAL IMAGING DIVISION
Published Clearance Data for Thyrotoxic Patients
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
O’Doh 1.0 m
O’Doh 0.5 m
ICRP
Hilditch
O’Doh 0.1 m
0
50
100
150
200
250
300
Time lapse in hours
Hilditch
O'Doh0.1
Odoh1.0
Odoh0.5
ICRP
350
F L I N D E R S M E D I C A L C E N T R E , MEDICAL IMAGING DIVISION
Errors in Using Fitted Clearance Data
for Individual Patients
Modelled using Monte Carlo methods
Calculated restriction times for sleeping with spouse or partner. 2000 MBq ablation dose
Exposure
Exposure rate
rate measured
measured at
at 0,
0, 12,
12, 24,
24, 48
48 and
and 96
96 hours
hours post
post administration
administration
Measurement Restriction
Precision (%) Time (h)
CV (%)
Minimum
Maximum
1
131
11
112
171
10
197
69
60
469
Exposure
Exposure rate
rate measured
measured at
at 0,
0, 12,
12, 24,
24, 96
96 and
and 360
360 hours
hours post
post administration
administration
Measurement Restriction
Precision (%) Time (h)
CV (%)
Minimum
Maximum
1
134
1
132
138
10
132
10
109
166
F L I N D E R S M E D I C A L C E N T R E , MEDICAL IMAGING DIVISION
Effect of Exposure Pattern and Dose
Limit on Calculated Restriction Times
Calculated restriction times for sleeping with spouse or partner. 2000 MBq ablation dose
Exposure Pattern
Dose Limit
(microsieverts)
Effective Exposure Required
Time (hours)
Restriction
(days)
Normally Used
8 h @ 0.1 m
6h@1m
1000
199.1
13.9
5000
199.1
5.7
5000
11.5
2.7
Normally Used
8 h @ 0.1 m
6h@1m
? More Realistic?
1 h @ 0.1 m
5 h @ 0.3 m
2 h @ 0.5 m
6 h at 1 m
F L I N D E R S M E D I C A L C E N T R E , MEDICAL IMAGING DIVISION
Further Information
Full paper and spreadsheets available
from authors
E-mail
[email protected]
F L I N D E R S M E D I C A L C E N T R E , MEDICAL IMAGING DIVISION
Effective Dose Conversion Factors
About 0.7 Sv per Gy air kerma
Hp(10) a rough surrogate for effective dose
F L I N D E R S M E D I C A L C E N T R E , MEDICAL IMAGING DIVISION
Mean or Maximum Dose – Or Both?
Regulations generally specify a maximum
dose.
However, there will always be a finite error
in calculated doses. Maximum dose may be
considerably larger than the mean dose.
Use mean dose in conjunction with 95th
percentile value as regulatory criteria?