2. Radiation units
โข The International Commission on Radiation Units and Measurement
(ICRU) reviews and updates, from time to time, the concepts related
to quantities and their units in radiation physics, dosimetry and
radiological protection.
โข ICRU recommended SI units for following radiation associated
quantities in 1980
โข Internal radiation dosimetry: describes the method of calculating
absorbed doses in various organs from radionuclides ingested
internally either purposely (e.g. Medical procedures) or accidentally.
3. Radiation units
โข Units of radiation measurement are:
1. Activity or Radioactivity [A] is measured usually in curie-SI units:
Becquerel (Bq)
2. Roentgen (R)- for Exposure
3. Radiation absorbed dose (rad)- for absorbed dose, Kerma (โrad):
sum of initial kinetic energies of all charged particles liberated by
uncharged ionizing radiation per unit mass of material.
4. Roentgen equivalent man (rem)- for dose equivalent
4. Exposure (X)
โข Exposure is the Absolute value of the total charge of the ions of single sign
produced in air when all the secondary electrons (inclusive of positrons
and electrons) liberated by photons in air of mass ฮm are completely
stopped in air.
โข 1 C/kg is the amount of X-ray or gamma radiation that produces ionization
of 1 C of wither positive or negative charge when all secondary electrons
are stopped completely by air of mass 1 kg at standard temperature and
pressure
โข S.I. Unit : C/kg
5. Roentgen
โข Amount of x- or ฮณ-radiation that produces ionization of one
electrostatic unit of either positive or negative charge per cm3 of air
at 0o C and 760 mm Hg, standard temperature & pressure(STP).
โข It only applies for air and to x- or ฮณ-radiation upto <3 MeV.
โข 1 cm3 air = 0.001293 g at STP, charge of either sign carries 1.6ร10-19 C
or 4.8ร10-10 electrostatic units, so
1๐ = 2.58ร10-4 C/kg
6. Radiation absorbed dose(rad)
โข Energy deposited per unit mass of any material by any type of
radiation.
โข It is independent of the weight of the material.
โข c/a gray (Gy) in SI units- energy absorbed per kg of air due to an
exposure of 1 R.
โข 1 rad = 100 ergs/g absorber = 10-2 J/kg
โข 1 Gy = 100 rad = 1 J/kg absorber
โข 1 R = 86.9ร10-4 J/kg in air = 0.869 rad in air = 0.00869 Gy in air
7. Radiation absorbed dose(rad)
โข For soft tissue, 1 R = 0.96rad = 0.0096 Gy
โข Radiation absorbed dose depends upon:
a. Amount of radioactivity administered
b. Physical and biological half lives of the radioactivity
c. Fractional abundance of the radiation in question from the
radionuclides
d. The biodistribution of radioactivity in the body
e. Fraction of absorbed energy from the source in to the target
volume
variable ... approximated for a โstandardโ or โaverageโ 70 kg man
8. Roentgen equivalent man(rem)
โข Accounts for effectiveness of different types of radiations to cause
biological damage.
โข In radiobiology, it is defined as rem = rad ร RBE = rad ร Wr
โข RBE (relative biological effectiveness): is the ratio of the dose of a
standard radiation to produce a particular biological response to the
dose of the radiation in question to produce the same biological
response.
โข Normally radiations of 250 KV x-rays is taken as standard radiation ...
of its widespread use.
9. Roentgen equivalent man(rem)
โข RBE varies with:
a. LET of the radiation
b. Radiation dose
c. Dose rate
d. Biological system
โข RBE โ Radiation weighting factor(Wr) in radiation protection
โข US Nuclear Regulatory Commission(NRC) uses โQuality Factorsโ(QF) โ
Wr for regulation.
โข SI Unit of dose equivalent is sievert, 1 sievert = 100 rem
10.
11.
12. Effective dose
โข Term given by ICRP
โข prev. c/a Effective dose equivalent
โข Accounts for the different sensitivity of tissues to radiation& is Age
independent values .
โข ED (HE) is defined as the sum of weighted dose equivalents in all tissues
and organs, HE= ๐ ๐๐ ๐ป ๐
Where WT is the tissue weighting factor for an organ,
HT is the dose equivalent (rem) to the organ
HE= ๐ ๐๐ ๐ ๐๐ ร (๐๐๐) ๐,๐
Where (๐๐๐) ๐,๐ is the absorbed dose to tissue (T) from radiation of type r
& ๐๐is radiation weighting factor
13.
14. Collective effective dose (S)
โข ICRP utilizes collective dose estimation for a exposed group or
population by taking into account the number of people exposed to a
source multiplied by the average dose to the exposed group from the
source
15. Annual limit on intake (ALI)
โข ALI means the greatest value of the annual intake of the specified
radionuclide that would result in a committed dose equivalent not
exceeding the annual dose equivalent limit, prescribed by the
Competent Authority, even if intake occurred every year for 50 years.
โข USA-NRC definition: ALI is the derived limit for the amount of radioactive
material taken into the body of an adult worker by inhalation or
ingestion in a year. ALI is the smaller value of intake of a given
radionuclide in a year by the "reference man" that would result in a
committed effective dose equivalent (CEDE) of 5 rems (0.05 sievert) or
a committed dose equivalent (CDE) of 50 rems (0.5 sievert) to any
individual organ or tissue.
โข SI unit: Bq
16. Annual limit on intake (ALI)
โข ALI values are given for ingestion if intake is through mouth and for
inhalation if intake is through inhalation.
โข ALI values for some of the important radio nuclides used in research
are:
ALI values for inhalation are
โข I-131 1 MBq [0.027 mCi]
โข 99mTc 2000 MBq [54 mCi]
โข 99Mo 50 MBq [1.35 mCi]
17.
18. Derived air concentration (DAC)
โข DAC means the maximum concentration of a radionuclide in the
ambient air which, if inhaled by a person for 2000 hrs in a year, at a
breathing rate of 1.2 m3/h, will not result in annual effective dose
equivalent in excess of the limits prescribed by the competent
authority.
โข DAC = ALI / 2.4 x 103 Bq/m3
19. Radiation dose rate
โข aka energy absorbed per hour and is given by Ri
โข For non penetrating radiations (meaning all energy is absorbed in the
absorber)
๐ แตข = 2.13
๐ด
๐
๐แตข๐ธแตข
โข For penetrating radiations (total or part of the radiation may be absorbed)
๐ แตข = 2.13
๐ด
๐
๐แตข๐ธแตขฯแตข ฮฝ โ ๐
=
๐ด
๐
ฮแตขฯแตข ฮฝ โ ๐
20. Radiation dose rate
= ๐ โ
๐ดโ
๐
ฮแตข๐โฮปโ๐กฯแตข ฮฝ โ ๐
๐ is fraction of localized activity from the administered activity, ฮปโ is
effective decay constant,
ฮแตข=2.13NiEi aka Equilibrium Dose Constant calculated in gยทrad/(ฮผCiยทh)
21. Radiation dosimetry
โข Scientific determination of amount, rate and distribution of radiation
in the body emitted from a source of ionizing radiation.
โข Broadly divided into โ
1. External radiation dosimetry
2. Internal radiation dosimetry
22. Internal radiation dosimetry
โข Two types of estimate: Type I and Type II
๏Type I : Phantom based (as per MIRD committee)
Two reasons for type I estimate
a. Legal considerations- FDA IND application or use by radiation safety
committee at local institution. A very common type I result.
b. Scientific dose comparison of โฅ pharmaceuticals that target the same
structure, tissue or molecule. A rare type I result.
๏Type II: patient specific computation and direct clinical relevance.
Calculation done as treatment plans for an individual receiving
Radioimmunotherapy(RIT) or other forms of internal emitter therapy. Here
anatomical data (CT, MRI etc) is required.
23. Critical organ and its calculation
โข Critical Organ: the organ or physiological system that for a given
source of radiation would first reach its legally defined maximum
permissible radiation exposure as the dose of radiation is increased.
โข For the development of radiation protection guides, the identification
of the particular organs or tissues that are critical because of the
damage they may suffer is the essential simplifying step.
โข For general irradiation of the whole body, the critical organs and
tissues are the gonads (fertility, hereditary effects), the
haematopoietic organs, or more specifically the bone marrow
(leukaemia), and the eye (cataracts).
25. Critical organs determination
โข Done most commonly by MIRD scheme.
โข Here radiation dose exposure is determined for various organs and
the organ receiving the highest radiation exposure is the critical
organ.
โข Limitations with the critical organ concept:
does not define the overall risk as it does not allow summation of risks
according to the relative radio-sensitivities of the irradiated tissues.
26. MIRD Scheme
โข Medical Internal Radiation Dose (MIRD) Committee is a part of The
Nuclear Medicine Society (NMS) since 1965.
โข Aim :
a. to standardize internal dosimetry calculations,
b. improve published emission data for radionuclide,
c. enhance data on pharmacokinetics for radiopharmaceuticals
โข For use in diagnostic nuclear medicine, radionuclide therapy and in
internal contamination.
27. MIRD Scheme
โข MIRD Reference Man: The MIRD Committee has developed a
hypothetical "reference man", actually a bisexual construct that
permits estimation of the factors required to calculate dose to one
organ attributable to a source in another organ.
โข Target Organ (T): The target organ is the organ in which the dose is to
be determined.
โข Source Organ (S): The source organ is the point of origin of the
ionising radiation. The source organ includes all other surrounding
organs which contribute to dose to the target organ. Additionally the
source organ may also be the target organ. In this case, energy so
deposited is termed as self dose.
30. Mean Energy Per Transition (ฮแตข)
โข The mean energy per transition (โณ) released in the source organ is equal to the
mean particle energy (E) multiplied by the average number of particles per
transition (n), together with a conversion factor K. This gives the first equation:
ฮ = ๐พ โ ๐ธ โ ๐
โข If we now consider a radiopharmaceutical that emits several kinds of radiation
(e.g. beta and gamma), each is characterized by its own mean energy per particle
(Ei) and number of particles (ni), then:
ฮแตข = ๐พ โ ๐ธแตข โ ๐แตข
31. Cumulated Activity (รh)
โข Represented by the area under the time activity curve and has the dimensions of
activity x time (ฮผCiโ hr). The cumulated activity รh is the total number of
transitions that occur in a target organ from time = 0 to time = T.
ฤ = ๐
๐
๐จ ๐ โ ๐ ๐
โข Where, The function A(t) is: ๐ด ๐ก = ๐ดโ โ ๐โฮปโ๐ก
โข For total dose estimation, Time T= infinity, hence ๐ดh = 0
โ
๐ดh(t)dt
โข Affected by
1. rate of uptake
2. Physical half life
3. Biological half life
32. Cumulated Activity (รh)
โข In MIRD pamphlet no.11, รh has been substituted by
D(rad) = ร ยท S
Where,
ร=1.44 ยท f ยทAoยทTe
S= ๐=1
๐
ฮแตข
ฮฆแตข
๐
where S is mean absorbed dose per cumulated activity
33. Cumulated Activity (รh)
โข Effective half life (Te)
Te=
๐ ๐ร๐ ๐ต
๐ ๐+๐ ๐ต
1
๐๐
=
1
๐๐
+
1
๐๐ต
Where TP& TB are physical and biological half life
34. Models of Cumulated Activity
1. Uptake by organ is instantaneous with no biologic excretion
ร=1.44ยทfยทAoTP
2. Uptake by organ is instantaneous with elimination by biologic excretion
only
ร=1.44ยทfยทAoTB
3. Uptake by organ is instantaneous with removal by both physical decay
and biologic excretion
ร=1.44 ยท f ยทAoยทTe
4. Uptake by organ is not instantaneous
ร=1.44 ยท f ยทAoยทTe (
๐ ๐
๐ ๐
)
35. Residence Time (ฯh)
โข Useful to describe an organ into which the activity Ao is administered at time t = 0. The area under
Ah(t) equals the area of the rectangle as shown
โข Hence, Cumulated activity, รh = base x Height= Ao x ฯh, then
ฯh =
รh
Ao
โข When uptake phase can be neglected and maximal source activity is Ah ,
ฯh =
1.443 ๐โ ๐๐๐ ๐ดโ
๐ด ๐
โข In case of bolus administration where all the activity (Ao) is located in organ at T = 0 (e.g. blood,
ฯh=1.443(Th)eff (Ah=Ao)
โข Hence cumulated activity may be represented as ร =1.44โ f โ AoโจฏTe
where, Ao = Initial administered activity in unit of ฮผCi,
f = ( % or fraction of activity localised in an organ) X (Total activity administered)
36. Absorbed fraction(ฯแตข)
โข ฯแตข(vโr) is called the absorbed fraction
โข The ratio of the energy absorbed by the target volume v from the ith
radiation to the energy emitted by the ith radiation from the source
volume r.
โข Depends on:
a. Type and energy of the radiation
b. The shape and size of the source volume
c. The shape, composition & distance of the target volume as well as
the type of material separating them
37. Absorbed fraction(ฯแตข)
โข For ฮฒ, ฮฑ, conversion electrons and x- & ฮณ-rays of energies โค 11 KeV;
If source and target are same, ฯแตข = 1
If source and target are different than, ฯแตข =0
โข For x- & ฮณ-rays of energies of energies โฅ 11 KeV;
photons: for all source target combinations 0< ฯแตข <1
โข ฯแตข values are calculated by statistical monte carlo methods on the
basis of interaction of radiation with matter.
โข Available in MIRD pamphlets by Society of Nuclear medicine.
38. Absorbed Fraction (ฯ)
โข Specific absorption fraction: Absorbed fraction per unit mass of the
target organ, ฯ = ฯแตข /Mk
40. Dose equation (D)
โข The radiation energy emitted by the source activity cumulated (รh )
over the time interval of interest is given by D= รhฮ
โข Where ฮ is the total mean energy emitted per nuclear disintegration.
โข Also as it is not necessary that all emitted radiation will be absorbed
by the target organ and will depend on absorption fraction (ฯแตข), dose
is D=รhฮiฯi
41. Dose equation for single source( ๐ทk)
โข The mean absorbed dose [Dose per unit mass of the target organ] ( ๐ทk) to
target organ k with mass (Mk) from a single source organ h is given by:
๐ทk=
(รโ
ฮแตข๐แตข)
๐ ๐
โข Since, there can be multiple different emission types such as beta or gamma,
๐ทk=
(รโ ๐ ฮแตข๐แตข)
๐ ๐
โข the previous equation may be separated into two parts
1) Cumulated activity รh
2) Those factors dependent on radionuclide properties relative to a size and
position of various organ in a model phantom. This latter quantity is
labelled the โS factorโ(S) and is defined mathematically as:
42. Dose equation for single source( ๐ทk)
S ๐๐ โ ๐โ =
( ๐ ฮแตข๐แตข)
๐ ๐
โข S-factors have been tabulated for a variety of radionuclides and for different
source/target configurations in both standard man and children.
โข Hence the equation can be simplified as ๐ท = รโจฏS
โข Since dose exposure will depend on the residence time of the RP, this formula
can be suitably modified as
๐ท = รโจฏS =AoฯS
43. Multiple source organs
โข The total dose equation summed over all sources is given by:
๐ท(rk) = โ ๐ท(rkโ
rh)
โข The residence time in source organ h when uptake phase can be
neglected and maximal source activity is
ฯh =
1.443 ๐โ ๐๐๐ ๐ดโ
๐ด ๐
45. Limitations of the MIRD Methods
1) Tabulated doses do not apply to all patients
2) In the MIRD schema it is assumed that the shape, size and position
of the organs are as represented by the standard, 70kg,
hermaphrodite human phantom.
3) Diseased organs can result in both increased and decreased uptake
of activity and changes in the residence time compared with
standard values so these factors should also be considered when
assessing the dose to patients.
4) The MIRD schema calculates each dose to the target organs as an
average, without permitting the determination of a maximum or
minimum dose.
50. Physical phantoms
Main uses:
๏external radiation dosimetry: physical phantom is designed so that small TLDs (or ion
chambers or solid-state detectors) can be inserted in different locations of the phantom
to measure doses from external irradiation.
โข RANDOยฎ phantom and ATOMยฎ phantom which contain tissue equivalent slices that have
anatomical maps and cavities for organ dose measurements
๏Internal radiation dosimetry
๏Imaging quality assurance: cover only partial body and some are anatomically very
simple.
โข NEMA image quality phantom
๏Radio-bioassay calibration phantoms: for calibrating radio-bioassay detectors or nuclear
medicine imaging equipment are designed to contain either removable organs that are
doped with long-lived radioactive materials or hollow body regions that are filled with
short-lived radioactive liquids. These designs allow the phantoms to mimic internally
contaminated individuals.
โข Lawrence Livermore National Laboratory (LLNL)
โข BOttle MAnikin ABsorption (BOMAB) phantom family
54. Computational phantom
3 major generations
a. Stylized phantoms that are based on quadratic
equations (1960s to 2000s)
b. Voxel phantoms that are based on tomographic images
(1980s to present)
c. BREP phantoms that are based on advanced primitives
and are deformable
55. Computational phantom
Important examples of these include:
i. Korean Male and HDRK-man and women phantoms
ii. 3D and 4D cardiac torso phantom with gated patient organ motion
information for imaging applications
iii. Fisher-Snyder Phantom (MIRD-5) : The first anthropomorphic
phantom representing a hermaphrodite adult for internal
dosimetry. Organ masses, body weight and body height correspond
to 50th-percentile data recommended in ICRP 23. Later, age-
specific phantoms were developed by others.
iv. Snyder et al Adult phantom
61. MIRD cumulated activity
โข The activity in the source region is represented by the sum of each
biological process j that contributes to deposit and/or clearance of
radioactive material in source region
๐ด ๐ก = ๐โฮป๐ก
๐
๐ด๐ ๐โฮป ๐ ๐ก
โข The cumulated activity follows from integrating A(t) over time interval t1-t2
ร =
๐
๐ด๐
ฮป + ฮป๐
(๐โ ๐+๐ ๐ ๐ก1 โ ๐โ ๐+๐ ๐ ๐ก2)
62. MIRD half-life
โข Physical half-life/ Physical decay constant
๐ =
ln 2
๐
โข Biological half-life of biological component j
๐๐๐ =
ln 2
๐๐
โข Effective half โtime for biological component j
๐๐โ ๐ =
ln 2
(๐+๐ ๐)
1
๐๐โ ๐
=
1
๐
+
1
๐๐
= ๐ + ๐๐ = ๐ ๐โ ๐
This equation accounts for all factors and indicates that the total dose is summation of
both penetrating and non-penetrating combinations.
64. Dosimetry calculation
Q.1) Calculated the absorbed dose to the liver of an adult patient who receives
3mCi (111MBq) Tc99m-sulfur colloid for a liver scan, assuming 85% liver uptake
with no excretion. Weight of liver = 1700 g (for a standard man)
DT =
AT
mT
ฮnpฮฆnp +
As
mT
ฮฮฆ(LโL) +
As
mT
ฮฮฆ(LโS) +
As
mT
ฮฮฆ(LโM)
99mTc sulphur colloid localizes in the liver, spleen, and marrow. To calculate liver
dose, we must be concerned with dose from the liver to the liver, from the
spleen to the liver, and from the marrow to the liver
65. Dosimetry calculation
โข Ao in the liver = 3000 ฮผCi (or 3 mCi) x 0.85 = 2550 ฮผCi (86.7 MBq)
โข Te = 6 hr
โข ฯh =
1.443 ๐โ ๐๐๐ ๐ดโ
๐ด ๐
โข ฮiรi = 0.0806
โข D = 1.44 x (2550/1700) x 6 x 0.0806 = 1.04 rad
67. Identify Source
organs(s1,s2โฆsm) &
Target organs(t1,t2โฆtn)
Determine ร ๐ ๐
from
activity-time curves
Look up ๐๐ก ๐โ๐ ๐
using
appropriate table or
interpolate from graph
Determine dose
delivered to tn from sm
๐ท๐ก ๐โ๐ ๐
= ฤ ๐ ๐
โ ๐๐ก ๐โ๐ ๐
Sum contributions of
dose from all sources
to tn
๐ท๐ก ๐
=
๐ ๐
๐ท๐ก ๐โ๐ ๐
Repeat for all source organs
Repeat for each pair of
source and target organ
Repeat for each target organ
68. Symbols and Conventions
MIRD ICRP
Mean absorbed dose (Dk) in target organ(K) โ Committed equivalent dose(HT) in target organ(T) โ
Committed effective dose
Source region (h) & target region (k) โ Source organ(S) and Target organ(T)
Absorbed fraction ฮฆ ๐ ๐โ๐โ
โ Absorbed fraction ๐ด๐น(๐โ๐)
Mean absorbed dose per unit cumulated activity โ
๐(๐ ๐โ๐โ)
Specific effective energy ๐๐ธ๐ธ(๐โ๐)
Cumulated activity in source region โ Committed number of transformations in source
organ
Mean absorbed dose in target region โ
๐ท ๐ =
โ
รโ ๐(๐ ๐โ๐โ)
๐ ๐ ๐โ๐โ
=
๐
โ๐ฮฆ๐(๐๐ โ ๐โ) =
๐
ฮ๐ ๐๐(๐๐ โ ๐โ)
๐ ๐
Committed equivalent dose in target region
๐ป ๐ =
๐
๐๐ ๐
๐๐ธ๐ธ(๐โ๐ ๐)
69.
70. Paediatric dosages
โข Methods given by:
1. Lassmann et al. (2009) โ adapted in EANM pediatric dosage card
2. Paediatric Nuclear Medicine Dose Reduction Workgroup, US (2010)
3. Gelfand et al (2011) โ North American guidelines
๏In Paediatric dosage card, dose is calculated by
Baseline activity x Multiplication factor
Assumed for a 3 kg child
โข Multiplication factor is a complex value derived from:
a. Body weight
b. Adult dosage
c. Type of radiopharmaceutical
71.
72. Paediatric dosages
๏In PNMDRW guidelines, Dosage is based on:
a. Body weight
b. Body surface area
c. Radiopharmaceutical type
d. LEHR collimator
๏Gelfand et al. reported:
a. recommended dosage in MBq/kg based on PNMDRW guidelines.
b. Minimum and maximum recommended dosage
However needs to be adjusted for >70 kg pts. & different scanner (PET &
SPECT)
Editor's Notes
MIRD is an Medical Internal Radiation Dose
ICRP is International Commission on Radiological Protection