Absorbed Dose
Dose is a measure of the amount of energy from an ionizing radiation deposited
in a mass of some material.
? SI unit used to measure absorbed dose is the gray (Gy).
1 J
? 1 Gy =
kg
? Gy can be used for any type of radiation.
? Gy does not describe the biological effects of the different radiations.
Dosimetric Quantities
Quantity
Definition
New Units
Old Units
Exposure
Charge per unit mass of
air
1 R = 2.58 x 10-4 C/kg
---
Roentgen
(R)
Absorbed dose to
tissue T from
radiation of type R
DT,R
Energy of radiation R
absorbed per unit mass
of tissue T
1 rad = 100 ergs/g
1 Gy = 1 joule/kg
1 Gy = 100 rads
gray
(Gy)
Radiation absorbed
dose
(rad)
Equivalent dose to
tissue T
HT
Sum of contributions of
dose to T from
different radiation
types, each multiplied
by the radiation
weighting factor (wR)
HT = ΣR wR DT,R
Sievert
(Sv)
Roentgen
equivalent man
(rem)
Effective Dose
E
Sum of equivalent
doses to organs and
tissues exposed, each
multiplied by the
appropriate tissue
weighting factor (wT)
E = ΣT wT HT
Sievert
(Sv)
rem
Radiological Protection
For practical purposes of assessing and regulating the hazards of ionizing radiation
to workers and the general population, weighting factors (previously called quality
factors, Q) are used.
A radiation weighting factor is an estimate of the effectiveness per unit dose of the
given radiation relative a to low-LET standard.
Weighting factors are dimensionless multiplicative factors used to convert physical
dose (Gy) to equivalent dose (Sv) ; i.e., to place biological effects from exposure to
different types of radiation on a common scale.
A weighting factor is not an RBE.
Weighting factors represent a conservative judgment of the envelope of
experimental RBEs of practical relevance to low-level human exposure.
Radiation Weighting factors
Radiation Type and Energy
Range
Radiation Weighting Factor, WR
X and γ rays, all energies
1
Electrons positrons and muons, all
energies
1
Neutrons:
< 10 keV
5
10 keV to 100 keV
10
> 100 keV to 2 MeV
20
> 2 MeV to 20 MeV
10
> 20 MeV
5
Protons, (other than recoil protons)
and energy > 2 MeV,
2-5
α particles, fission fragments,
heavy nuclei
20
[ICRU 60, 1991]
For radiation types and energies not listed in the Table above, the following
relationships are used to calculate a weighting factor.
[Fig. 1 in ICRP, 1991]
Q = 1.0 L < 10 keV/μm
Q = 0.32L – 2.2 10 ≤ L ≤ 100 keV/μm
Q = 300/(L)1/2 L ≥ 100 keV/μm
L = unrestricted LET in water (keV/ μm )
Radiation Typical LET values
1.2 MeV 60Co gamma 0.3 keV/μm
250 kVp x rays 2 keV/μm
10 MeV protons 4.7 keV/μm
150 MeV protons 0.5 keV/μm
14 MeV neutrons 12 keV/μm
Heavy charged particles 100-2000 keV/μm
2.5 MeV alpha particles 166 keV/μm
2 GeV Fe ions 1,000 keV/μm
Tissue weighting factors
Tissue Tissue Weighting Factor, WT
Gonads 0.20
Red bone marrow 0.12
Colon 0.12
Lung 0.12
Stomach 0.12
Bladder 0.05
Breast 0.05
Liver 0.05
Esophagus 0.05
Thyroid 0.01
Bone surfaces 0.01
Remainder 0.05
(ICRU 60, 1991; NCRP 116, 1993)
Committed Equivalent Dose: for radionuclides incorporated into the body, the
integrated dose over time. 50 years for occupational exposure, 70 years for
members of the general public.
Committed Effective Dose: effective dose integrated over 50 or 70 years.
Measurement of Exposure: photons
Ionizations in air for electromagnetic radiation only
Measures charge (coulombs) produced by ionizations in air at STP.
The unit of exposure in air is the Roentgen: 1 R = 2.58 x 10-4 C/kg
Absorbed dose in air
Response is energy independent (~300 keV-2 MeV)
Compton scattering dominant in air and low-Z wall
The Bragg-Gray Principle
Goal: determine absorbed dose in tissue exposed to radiation.
B-G principle relates dose in gas to dose in material.
Tissue dose:
Dosimeter material is tissue equivalent (same elemental composition).
Conditions
? Electronic equilibrium: wall thickness > maximum range of secondary
charged particles.
? Wall thickness not great enough to attenuate the radiation.
? Wall and gas have similar electron scattering properties.
Measurement of Absorbed Dose: photons
The tissue-equivalent ionization chamber
Graphite/CO2 carbon is approximately tissue equivalent
NgW
Dw = Dg =
m
Dw = dose to the wall
Dg = dose to the gas
Ng = number of ionizations in the gas
W = energy needed to produce an ion pair in the gas
m = mass of the gas
Absorbed Dose from a charged particle beam
Dose Calculations
Alpha and Low energy Beta emitters distributed in tissue.
A radionuclide, ingested or inhaled, and distributed in various parts of the body is
called an internal emitter.
Many radionuclides follow specific metabolic pathways, acting as a chemical
element, and localize in specific tissues.
E.g., iodine concentrates in the thyroid
radium and strontium are bone seekers
tritium will distribute throughout the whole body in body water
cesium tends to distribute throughout the whole body.
If an internally deposited radionuclide emits particles that have a short range, then
their energies will be absorbed in the tissue that contains them.
Let:
A = the activity concentration in Bq g-1, of the radionuclide in the tissue
E = the average alpha or beta particle energy, in MeV per disintegration
The rate of energy absorption per gram tissue is A E (MeV g-1 s-1).
The absorbed dose rate is:
Point Source of Gamma Rays
?
D= Dose rate
?
Ψ= energy fluence rate (MeV/cm2 sec)
C = activity (Bq)
E = energy per decay (MeV)
μen/ρ = mass energy-absorption coefficient of air (cm2g-1)
(~ same for photons between ~60keV and 2MeV)
Beam of Photons
Dose = energy absorbed/mass
(μen/ρ) = mass energy absorption coefficient (cm2/g)
N = photon fluence (photons/cm2)
E = energy per photon
ρ= density
x = thickness
A = area
Absorbed dose from neutrons
? Elastic scatter (higher energies)
? Capture (thermal neutrons)
Thermal neutrons
ΦNσE
D =
ρ
Φ = thermal neutron fluence (n/cm2)
N = atom density (cm-3)
σ = capture cross section (for each element)
E = energy from capture reaction
ρ = tissue density
The major thermal neutron capture reactions in tissue
14N(n,p) 14C σ = 1.7 barns Q = 0.626 MeV
Ep = 0.58 MeV, range in water ~ 8 μm
EC = 0.04 MeV
Energy is deposited locally
1H(n,γ)2H σ = 0.33 barns 2.22 MeV gamma
(μ/ρ) = 0.05 cm2/g
(μen/ρ) = 0.025 cm2/g
contribution to dose depends on the size of the “target”
Principle elements in soft tissue of unit density
Element Atoms cm-3 Capture cross section, σ
H 5.98 x 1022 0.33 barns
O 2.45 x 1022 0.00019 barns
C 9.03 x 1021 0.0035 barns
N 1.29 x 1021 1.70 barns
Absorbed dose from fast neutrons
Scattering: assume average energy lost is ? Emax
First collision dose
? Representative of the absorbed dose when the mean free path is large
compared to the target.
? Expressed as dose delivered per individual neutron
? Units are those of dose per neutron/cm2 (Gy cm2 )
NσS Qave
D =
ρ
N = atom density (cm-3)
σS = scattering cross section (for each element)
Qave = average energy transferred in collision (? Emax)
ρ = tissue density
Must calculate dose for each element.
E.g., Calculate the first collision dose for a 5 MeV neutron with tissue hydrogen.
5 MeV neutron σS = 1.61 barns
N = 5.98 x 1022 cm-3
Mean energy per scattering collision, Qave = 2.5 MeV
D = 3.88 x 10-11 Gy cm2