Topic 7  Dose Limits
Radiation Protection 


Review of Basic Concepts
 Absorbed dose
 Physical quantity
 D = dε/dm
 dε is the mean energy imparted by ionizing radiation in
mass m
 erg/g or J/kg
 Dose equivalent (H)
 Considers biological effectiveness of radiation
 H = DQ or DW_{R}
Radiation Weighting Factors (Q, W_{R})
 ICRP 1979
 Alpha particles assigned value of 20
 Beta particles (negatron/positron), 1
 Gamma rays, 1
 Xrays, 1
 Other values…neutrons etc
 ICRP (later)
 Some changes in neutrons, other radiations
Calculating Internal Dose
 Arbitrarily shaped container
 Distributed activity
 Calculate energy absorbed per unit mass
 Consider:
 Energy per decay
 Total activity
 Mass of container (think: organ)
 Fraction of energy emitted absorbed in container (called “target”)
 “absorbed fraction”
 φ
 (Energy absorbed by target)/(energy emitted by source)
Absorbed fraction, φ
 Consider
 Photons (“penetrating radiation”)
 Fraction absorbed in target
 Fraction escapes
 Betas (“nonpenetrating radiation”)
 All energy absorbed in target
 (exception extremely small targets)
 Alphas (nonpenetrating)
 All energy absorbed in target
 (exception  even smaller target than for betas)
Generic Equation for Calculating Absorbed Dose Rate
 D = absorbed dose rate, rad/h or Gy/s
 A = activity, μCi or MBq
 n_{i} = # of radiations of energy E emitted per transformation
 E = energy per radiation (MeV/dis)
 Φ = absorbed fraction
 m = mass of target
 K = proportionality constant
 (radg/ μCihrMeV or Gykg/MBqsMeV
Generic Equation for Calculating Total Absorbed Dose
 D = absorbed dose rad or Gy
 Ã = cumulative activity, μCihr or MBqs
Cumulative Activity, Ã
 Ã: integrated area under timeactivity curve
 Units typically
Evaluating Multiple Contaminated Objects
 Contaminated object irradiates
 How is dose calculated?
Calculating Total Dose
 Relationships to consider
 Object irradiating itself: φ(1¬1)
 Object being irradiated by others:
 Source (S) and Target (T)
 φ(1¬2)
 φ(1¬3)
 Repeated for multiple targets and sources
 φ(2¬1), φ(2¬2), φ(3¬1), φ(3¬2),..etc
Target/Source Configurations
Calculating Total Dose
 Generic equation
 Expressed in many ways (see Cember, pp 201 )
 Parameters grouped
 Computers used to evaluate
Calculating Total Dose  ICRP 2
Calculating Total Dose  ICRP 30
 Cumulative dose equivalent
ICRP 2 vs ICRP 30
 ICRP 30
 Organ weighting factors used to derive effective dose eqiuvalent
 ICRP 2
 Individual organ doses calculated
 Organs assumed to be spheres
 No irradiation of other organs
MIRD System
 Medical Internal Radiation Dose
 Simple equation (lots of lumped parameters)
 See Cember, pps 201  …
Other Considerations
 Kinetic Models
 Biological
 GI Tract
 Lung
 Intake (backcalculating intake from measured data)
 Ã
 U_{S}
 λ_{effective}
Determination of CDE
Total Disintegrations, Total Dose
ICRP : Determination of the Committed Dose Equivalent, H_{T,50}
 Total dose equivalent averaged throughout any tissue over
the 50 y after an intake is the CDE:
 M = mass of specified organ or tissue
 i = radiation type
 D_{50,i }= total absorbed dose during a period 50 y after
intake of the radionuclide in the element dm of the specified organ
or tissue
 Q_{i } = quality factor
 N_{i} = product of other modifying factors (dose rate,
fractionation, etc.)
Comments
 Q_{i} is a function of collision stopping power; varies along
track of ionizing particle and may be different for each element mass.
However, due to other uncertainties constant values are given for each
radiation type (and energy).
 ICRP recommends N = 1.
 Now called (ICRP 60) w_{R} radiation weighting factor.
 Using constant Q_{i} values:
 Where
 Total absorbed dose during 50 y after intake averaged throughout
the specified organ or tissue for each radiation type
 ICRP 30 makes estimates of H_{T,50} in a number of target
organs from the activity in a given source organ
Dose Calculations, cont’d
 For each radiation type, i, the H_{T,50,i} in a target organ,
T, resulting from a radionuclide j in a source organ S, is the product
of two factors:
 The total number of transformations of nuclide j in S over a
period of 50 y after intake (U_{s}).
 The energy absorbed per gram in T, modified by Q from radiation
of type i per transformation of radionuclide j in S.
 This is known as the Specific Effective Energy
 (MeV g^{1} per transformation)
 (SEE(T ¬ S)_{i}).
Target/Source Calculations
 For each radiation of type i from radionuclide j
 And:
 Where
 U_{s} is the number of transformations of j in S over
the 50 years following intake of the radionuclide
 1.6 x 10^{13} is the number of joules in 1 MeV
 SEE (T¬S)_{i} (in MeV g^{1} per transformation)
is the specific effective energy for radiation typ I, suitably modified
by quality factor, absorbed in T from each transformation in S
 10^{3} is the conversion factor from g^{1} to
kg^{1}
For all radiations by nuclide j
For progeny
 With progeny j^{’} present
Mixtures of Radionuclides
 In cases with parent and progeny the organ dose is:
Multiple Sources
 Target T may be irradiated by radiations arising in multiple sources
(S). The total value of H_{50} is then given by:
Specific Effective Energy (SEE)
 SEE (T¬S) = S SEE (T¬S)_{i}
 For any radionuclide j, SEE (T¬S)_{j} for target T and source
S is given by:
 Y_{i} is the yield of radiations of type i per transformation
of radionuclide j
 E_{i} (in MeV) is the average or unique energy of radiation
i as appropriate
 AF(T ¬S)_{i} is the fraction of energy absorbed in T per
emission of i in S
 Alphas and electrons are completely absorbed in S
 Exceptions are mineral bone and GI
 Photon absorptions are given in ICRP 23
 Q_{i} is the quality factor appropriate to the radiation
 M_{T} is the mass of the target organs
More stuff
Table 4.1 Masses of organs and tissues of Reference
Man used in this Report 
Source organs 
Mass (g) 
Target organs 
Mass (g) 
Ovaries 
11 
Ovaries 
11 
Testes 
35 
Testes 
35 
Muscle 
28,000 
Muscle 
28,000 
Red marrow 
1,500 
Red marrow 
1,500 
Lungs 
1,000 
Lungs 
1,000 
Thyroid 
20 
Thyroid 
20 
ST content 
250 
Bone surface 
120 
SI content 
400 
ST wall 
150 
ULI content 
220 
SI wall 
640 
LLI content 
135 
ULI wall 
210 
Kidneys 
310 
LLI wall 
160 
Liver 
1,800 
Kidneys 
310 
Pancreas 
100 
Liver 
1,800 
Cortical bone 
4,000 
Pancreas 
100 
Trabecular bone 
1,000 
Skin 
2,600 
Skin 
2,600 
Spleen 
180 
Spleen 
180 
Thymus 
20 
Adrenals 
14 
Uterus 
80 
Bladder content 
200 
Adrenals 
14 
Total body 
70,000 
Bladder wall 
45 
SEE Examples (ICRP)
Specific effictive energy (MeV per gram per transformation)
of SB90 Sources 
Targets 
Lungs 
ULI Content 
LLI Content 
Cortical Bone 
Trabecular Bone 
Red Marrow 
0.0 
0.0 
0.0 
0.0 
4.6E05 
Lungs 
2.0E04 
0.0 
0.0 
0.0 
0.0 
Bone Surface 
0.0 
0.0 
0.0 
2.4E05 
4.1E05 
ULI Wall 
0.0 
4.4E04 
0.0 
0.0 
0.0 
LLI Wall 
0.0 
0.0 
7.2E04 
0.0 
0.0 
Specific effictive energy (MeV per gram per transformation)
of Y90 Sources 
Targets 
Lungs 
ULI Content 
LLI Content 
Cortical Bone 
Trabecular Bone 
Red Marrow 
2.4E12 
3.5E12 
1.6E11 
1.5E10 
2.2E04 
Lungs 
9.3E04 
4.3E18 
1.5E19 
7.2E13 
7.2E13 
Bone Surface 
2.2E12 
8.3E13 
3.9E12 
1.2E04 
1.9E04 
ULI Wall 
1.7E17 
2.1E03 
4.1E11 
6.5E13 
6.5E13 
LLI Wall 
4.1E19 
9.1E12 
3.5E03 
2.0E12 
2.0E12 
Phantoms
Kinetic Models for Organs
Fig. 4.1 Mathematical model usually used to describe the kinetics of
radionuclides in the body: exception to this model are noted in the metabolic
data for individual elements.
Respiratory Model
Limits for Intakes of Radionuclides by Workers 

Class 
D 
W 
Y 
Region 
Compartment 
T day 
F 
T day 
F 
T day 
F 
NP
(D_{NP} = 0.30) 
a 
0.01 
0.5 
0.01 
0.1 
0.01 
0.01 
b 
0.01 
0.5 
0.40 
0.9 
0.40 
0.99 
TB
(D_{TB} = 0.08) 
c 
0.01 
0.95 
0.01 
0.5 
0.01 
0.01 
d 
0.2 
0.05 
0.2 
0.5 
0.2 
0.99 
P
(D_{P} = 0.25) 
e 
0.5 
0.8 
50 
0.15 
500 
0.05 
f 
n.a. 
n.a. 
1.0 
0.4 
1.0 
0.4 
g 
n.a. 
n.a. 
50 
0.4 
500 
0.4 
h 
0.5 
0.2 
50 
0.05 
500 
0.15 
L 
i 
0.5 
1.0 
50 
1.0 
1000 
0.9 
j 
n.a. 
n.a. 
n.a. 
n.a. 
infinity 
0.1 
Fig. 5.2. Mathematical model used to describe clearance from the respiratory
system. The values for the removal halftimes, T_{a1} and compartmental
fractions, F_{a1} are given in the tabular portion of the figure
for each of the three cleasses of retained materials. The values given
for D_{NP}, D_{TB} and D_{P} (left column) are
the regional depositions for an aerosol with an AMAD of 1 μm. The
schematic drawing identifies the various clearance pathways from compartments
ai in the four respiratory regions, NP, TB, P and L.
n.a. = not applicable.
Fig. 5.1. Deposition of dust in the respiratory system. The percentage
of activity or mass of an aerosol which is deposited in the NP, TB and
P regions is given in relation to the Activity Median Aerodynamic Diameter
(AMAD) of the aerosol distribution. The model is intended for use with
aerosol distributions with AMADs between 0.2 an 10 μm and with geometric
standard deviations of less than 4.5. Provisional estimates of deposition
further extending the size range are given by the dashed lines. For an
unusual distribution with an AMAD of greater than 20 μm, complete
deposition in NP can be assumed. The model does not apply to aerosols
with of greater than 20 μm, complete deposition in NP can be assumed.
The model does not apply to aerosols with AMADs of less than 0.1 μm.
Particle Size Correction
Where D_{NP}, etc are the deposition probabilities
in the respiratory region for a given AMAD
Stomach Model
Section of GI tract 
Mass of walls* (g) 
Mass of contents* (g) 
Mean residence time (day) 
day^{1} 
Stomach (ST) 
150 
250 
1/24 
24 
Small Intestine (SI) 
640 
400 
4/24 
6 
Upper Large Intestine (ULI) 
210 
220 
13/24 
1.8 
Lower Large Intestine (LLI) 
160 
135 
24/24 
1 
* From ICRP Publication 23 (1975)
Fig. 6.1. Mathematical model used to describe the kinetics of radionuclides
in the gastrointestinal tract 
Quick Methods
87M_{Sr} 

Ingestion 
Inhalation 
Class 


D 
W 
Y 
GI Absorp 
3.0E01 
1.0E02 
3.0E01 

1.0E02 
Lungs 


1.7E04 

2.1E04 
3/5/92 

0/17/83 
Gonads 
7.4E05 
8.5E05 
1.7E05 


82/11/7 


ST Wall 
3.5E04 
306E04 
5.9E05 


88/4/8 


SI Wall 
4.1E04 
4.8E04 
6.3E05 

4.8E05 
93/4/3 

66/29/5 
ULI Wall 
5.2E04 
6.3E04 
8.1E05 

6.3E05 
93/3/2 

66/29/5 
LLI Wall 
2.1E04 
2.5E04 
3.6E05 


91/6/3 


C.E.D.E. 
1.1E04 
1.2E04 
3.8E05 

3.2E05 
91_{Sr} 

Ingestion 
Inhalation 
Class 


D 
W 
Y 
GI Absorp 
3.0E01 
1.0E02 
3.0E01 

1.0E02 
Lungs 


3.4E03 

7.8E03 
2/3/95 

0/7/93 
Gonads 
7.8E04 
9.3E04 
2.4E04 


71/12/17 


R Marrow 


4.4E04 


45/16/39 


ST Wall 
3.2E03 
3.1E03 



SI Wall 
5.2E03 
6.7E03 
8.9E04 


90/5/5 


ULI Wall 
1.4E02 
1.8E02 
2.2E03 

4.1E03 
95/3/2 

67/24/9 
LLI Wall 
1.4E02 
1.9E02 
2.3E03 

4.4E03 
95/3/2 

67/23/10 
C.E.D.E. 
2.4E03 
3.0E03 
8.4E04 

1.4E03 
89_{Sr} 

Ingestion 
Inhalation 
Class 


D 
W 
Y 
GI Absorp 
3.0E01 
1.0E02 
3.0E01 

1.0E02 
Lungs 


8.1E03 

3.1E01 
7/4/89 

0/0/100 
Gonads 


1.6E03 


38/15/47 


R Marrow 
1.2E02 

2.1E02 


38/15/47 


Bone Surf 
1.8E02 

3.1E02 


38/15/47 


ULI Wall 
2.7E02 
3.7E02 
5.5E03 


81/6/13 


LLI Wall 
7.8E02 
1.1E01 
1.3E02 


90/4/6 


C.E.D.E. 
8.2E03 
8.7E03 
5.9E3 

3.7E02 
92_{Sr} 

Ingestion 
Inhalation 
Class 


D 
W 
Y 
GI Absorp 
3.0E01 
1.0E02 
3.0E01 

1.0E02 
Lungs 


2.6E03 

4.1E03 
2/2/96 

0/12/88 
Gonads 
3.0E04 




ST Wall 
2.0E03 
1.9E03 



SI Wall 
4.1E03 
5.2E03 
7.0E04 

1.0E03 
93/4/3 

68/26/6 
ULI Wall 
1.1E02 
1.4E02 
1.7E03 

2.3E03 
97/2/1 

67/27/6 
LLI Wall 
7.8E03 
1.0E02 
1.2E03 

1.4E03 
96/3/1 

67/28/5 
C.E.D.E. 
1.6E03 
1.9E03 
5.4E04 

7.7E04 
90_{Sr} 

Ingestion 
Inhalation 
Class 


D 
W 
Y 
GI Absorp 
3.0E01 
1.0E02 
3.0E01 

1.0E02 
Lungs 




1.1E+01* 


0/0/100 
R Marrow 
7.0E01 
2.4E02* 
1.2E+00* 


37/15/48 


Bone Surf 
1.6E+00* 
5.2E02* 
2.7E+00* 


37/15/48 


ULI Wall 

2.3E02 



LLI Wall 

9.6E02 



C.E.D.E. 
1.3E01* 
1.2E02* 
2.3E01* 

1.3E+00* 
