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Topic 7 - Dose Limits

Radiation Protection

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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 DWR

Radiation Weighting Factors (Q, WR)

  • ICRP 1979
    • Alpha particles assigned value of 20
    • Beta particles (negatron/positron), 1
    • Gamma rays, 1
    • X-rays, 1
    • Other values…neutrons etc
  • ICRP (later)
    • Some changes in neutrons, other radiations

Calculating Internal Dose

  • Arbitrarily shaped container
    Diagram of hot liquid being poured from a pitcher into a cup
  • 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 (“non-penetrating radiation”)
      • All energy absorbed in target
      • (exception- extremely small targets)
    • Alphas (non-penetrating)
      • 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
  • ni    = # of radiations of energy E emitted per transformation
  • E    = energy per radiation (MeV/dis)
  • Φ    = absorbed fraction
  • m   = mass of target
  • K    = proportionality constant
    • (rad-g/ μCi-hr-MeV or Gy-kg/MBq-s-MeV

Generic Equation for Calculating Total Absorbed Dose

  • D  = absorbed dose rad or Gy
  • Ã = cumulative activity, μCi-hr or MBq-s

Cumulative Activity, Ã

  • Ã: integrated area under time-activity curve
  • Units typically
    • Bq-s
    • μCi-hr

Evaluating Multiple Contaminated Objects

  • Contaminated object irradiates
    • Itelf
    • Others
  • How is dose calculated?
Hot Cups

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
    • Physical
    • Biological
  • Computers used to evaluate

Calculating Total Dose - ICRP 2

  • Dose equivalent rate

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 (back-calculating intake from measured data)
  • Ã
  • US
  • λeffective

Determination of CDE


Total Disintegrations, Total Dose


ICRP : Determination of the Committed Dose Equivalent,  HT,50

  • Total dose equivalent averaged throughout any tissue over the 50 y after an intake is the CDE:equation
    • M = mass of specified organ or tissue
    • i = radiation type
    • D50,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 = quality factor
    • Ni = product of other modifying factors (dose rate, fractionation, etc.)


  • Qi 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) wR radiation weighting factor.
    • Using constant Qi values:
  • Where   equation
    • Total absorbed dose during 50 y after intake averaged throughout the specified organ or tissue for each radiation type
    • ICRP 30 makes estimates of HT,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 HT,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 (Us).
    • 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
    • Us 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
    • 103 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 H50 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:
  • Yi is the yield of radiations of type i per transformation of radionuclide j
  • Ei (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
  • Qi is the quality factor appropriate to the radiation
  • MT 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 SB-90 Sources
Targets Lungs ULI Content LLI Content Cortical Bone Trabecular Bone
Red Marrow 0.0 0.0 0.0 0.0 4.6E-05
Lungs 2.0E-04 0.0 0.0 0.0 0.0
Bone Surface 0.0 0.0 0.0 2.4E-05 4.1E-05
ULI Wall 0.0 4.4E-04 0.0 0.0 0.0
LLI Wall 0.0 0.0 7.2E-04 0.0 0.0


Specific effictive energy (MeV per gram per transformation) of Y-90 Sources
Targets Lungs ULI Content LLI Content Cortical Bone Trabecular Bone
Red Marrow 2.4E-12 3.5E-12 1.6E-11 1.5E-10 2.2E-04
Lungs 9.3E-04 4.3E-18 1.5E-19 7.2E-13 7.2E-13
Bone Surface 2.2E-12 8.3E-13 3.9E-12 1.2E-04 1.9E-04
ULI Wall 1.7E-17 2.1E-03 4.1E-11 6.5E-13 6.5E-13
LLI Wall 4.1E-19 9.1E-12 3.5E-03 2.0E-12 2.0E-12



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
Region Compartment T day F T day F T day F
(DN-P = 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
(DT-B = 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
(DP = 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 half-times, Ta-1 and compartmental fractions, Fa-1 are given in the tabular portion of the figure for each of the three cleasses of retained materials. The values given for DN-P, DT-B and DP (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 a-i in the four respiratory regions, N-P, T-B, 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 N-P, T-B 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 N-P can be assumed. The model does not apply to aerosols with of greater than 20 μm, complete deposition in N-P can be assumed. The model does not apply to aerosols with AMADs of less than 0.1 μm.

Particle Size Correction


Where DN-P, 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

  Ingestion Inhalation
Class     D W Y
GI Absorp 3.0E-01 1.0E-02 3.0E-01   1.0E-02
Lungs     1.7E-04   2.1E-04
3/5/92   0/17/83
Gonads 7.4E-05 8.5E-05 1.7E-05    
ST Wall 3.5E-04 306E-04 5.9E-05    
SI Wall 4.1E-04 4.8E-04 6.3E-05   4.8E-05
93/4/3   66/29/5
ULI Wall 5.2E-04 6.3E-04 8.1E-05   6.3E-05
93/3/2   66/29/5
LLI Wall 2.1E-04 2.5E-04 3.6E-05    
C.E.D.E. 1.1E-04 1.2E-04 3.8E-05   3.2E-05

  Ingestion Inhalation
Class     D W Y
GI Absorp 3.0E-01 1.0E-02 3.0E-01   1.0E-02
Lungs     3.4E-03   7.8E-03
2/3/95   0/7/93
Gonads 7.8E-04 9.3E-04 2.4E-04    
R Marrow     4.4E-04    
ST Wall 3.2E-03 3.1E-03      
SI Wall 5.2E-03 6.7E-03 8.9E-04    
ULI Wall 1.4E-02 1.8E-02 2.2E-03   4.1E-03
95/3/2   67/24/9
LLI Wall 1.4E-02 1.9E-02 2.3E-03   4.4E-03
95/3/2   67/23/10
C.E.D.E. 2.4E-03 3.0E-03 8.4E-04   1.4E-03

  Ingestion Inhalation
Class     D W Y
GI Absorp 3.0E-01 1.0E-02 3.0E-01   1.0E-02
Lungs     8.1E-03   3.1E-01
7/4/89   0/0/100
Gonads     1.6E-03    
R Marrow 1.2E-02   2.1E-02    
Bone Surf 1.8E-02   3.1E-02    
ULI Wall 2.7E-02 3.7E-02 5.5E-03    
LLI Wall 7.8E-02 1.1E-01 1.3E-02    
C.E.D.E. 8.2E-03 8.7E-03 5.9E-3   3.7E-02

  Ingestion Inhalation
Class     D W Y
GI Absorp 3.0E-01 1.0E-02 3.0E-01   1.0E-02
Lungs     2.6E-03   4.1E-03
2/2/96   0/12/88
Gonads 3.0E-04        
ST Wall 2.0E-03 1.9E-03      
SI Wall 4.1E-03 5.2E-03 7.0E-04   1.0E-03
93/4/3   68/26/6
ULI Wall 1.1E-02 1.4E-02 1.7E-03   2.3E-03
97/2/1   67/27/6
LLI Wall 7.8E-03 1.0E-02 1.2E-03   1.4E-03
96/3/1   67/28/5
C.E.D.E. 1.6E-03 1.9E-03 5.4E-04   7.7E-04

  Ingestion Inhalation
Class     D W Y
GI Absorp 3.0E-01 1.0E-02 3.0E-01   1.0E-02
Lungs         1.1E+01*
R Marrow 7.0E-01 2.4E-02* 1.2E+00*    
Bone Surf 1.6E+00* 5.2E-02* 2.7E+00*    
ULI Wall   2.3E-02      
LLI Wall   9.6E-02      
C.E.D.E. 1.3E-01* 1.2E-02* 2.3E-01*   1.3E+00*
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