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Internal radiation dosimetry
Dr. Pradeep chaurasia
Radiation units
โ€ข 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.
โ€ข ICRU recommended SI units for following radiation associated
quantities in 1980
โ€ข 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.
Radiation units
โ€ข 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 (โ‰ˆrad):
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
Exposure (X)
โ€ข 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 ฮ”m are completely
stopped in air.
โ€ข 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
โ€ข S.I. Unit : C/kg
Roentgen
โ€ข 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).
โ€ข It only applies for air and to x- or ฮณ-radiation upto <3 MeV.
โ€ข 1 cm3 air = 0.001293 g at STP, charge of either sign carries 1.6ร—10-19 C
or 4.8ร—10-10 electrostatic units, so
1๐‘… = 2.58ร—10-4 C/kg
Radiation absorbed dose(rad)
โ€ข Energy deposited per unit mass of any material by any type of
radiation.
โ€ข It is independent of the weight of the material.
โ€ข c/a gray (Gy) in SI units- energy absorbed per kg of air due to an
exposure of 1 R.
โ€ข 1 rad = 100 ergs/g absorber = 10-2 J/kg
โ€ข 1 Gy = 100 rad = 1 J/kg absorber
โ€ข 1 R = 86.9ร—10-4 J/kg in air = 0.869 rad in air = 0.00869 Gy in air
Radiation absorbed dose(rad)
โ€ข For soft tissue, 1 R = 0.96rad = 0.0096 Gy
โ€ข 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 โ€œstandardโ€ or โ€œaverageโ€ 70 kg man
Roentgen equivalent man(rem)
โ€ข Accounts for effectiveness of different types of radiations to cause
biological damage.
โ€ข In radiobiology, it is defined as rem = rad ร— RBE = rad ร— Wr
โ€ข 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.
โ€ข Normally radiations of 250 KV x-rays is taken as standard radiation ...
of its widespread use.
Roentgen equivalent man(rem)
โ€ข RBE varies with:
a. LET of the radiation
b. Radiation dose
c. Dose rate
d. Biological system
โ€ข RBE โ‰ˆ Radiation weighting factor(Wr) in radiation protection
โ€ข US Nuclear Regulatory Commission(NRC) uses โ€œQuality Factorsโ€(QF) โ‰ˆ
Wr for regulation.
โ€ข SI Unit of dose equivalent is sievert, 1 sievert = 100 rem
Effective dose
โ€ข Term given by ICRP
โ€ข prev. c/a Effective dose equivalent
โ€ข Accounts for the different sensitivity of tissues to radiation& is Age
independent values .
โ€ข ED (HE) is defined as the sum of weighted dose equivalents in all tissues
and organs, HE= ๐‘‡ ๐‘Š๐‘‡ ๐ป ๐‘‡
Where WT is the tissue weighting factor for an organ,
HT is the dose equivalent (rem) to the organ
HE= ๐‘‡ ๐‘Š๐‘‡ ๐‘Ÿ ๐‘Š๐‘Ÿ ร— (๐‘Ÿ๐‘Ž๐‘‘) ๐‘‡,๐‘Ÿ
Where (๐‘Ÿ๐‘Ž๐‘‘) ๐‘‡,๐‘Ÿ is the absorbed dose to tissue (T) from radiation of type r
& ๐‘Š๐‘Ÿis radiation weighting factor
Collective effective dose (S)
โ€ข 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
Annual limit on intake (ALI)
โ€ข 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.
โ€ข 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.
โ€ข SI unit: Bq
Annual limit on intake (ALI)
โ€ข ALI values are given for ingestion if intake is through mouth and for
inhalation if intake is through inhalation.
โ€ข ALI values for some of the important radio nuclides used in research
are:
ALI values for inhalation are
โ€ข I-131 1 MBq [0.027 mCi]
โ€ข 99mTc 2000 MBq [54 mCi]
โ€ข 99Mo 50 MBq [1.35 mCi]
Derived air concentration (DAC)
โ€ข 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.
โ€ข DAC = ALI / 2.4 x 103 Bq/m3
Radiation dose rate
โ€ข aka energy absorbed per hour and is given by Ri
โ€ข For non penetrating radiations (meaning all energy is absorbed in the
absorber)
๐‘…แตข = 2.13
๐ด
๐‘š
๐‘แตข๐ธแตข
โ€ข For penetrating radiations (total or part of the radiation may be absorbed)
๐‘…แตข = 2.13
๐ด
๐‘š
๐‘แตข๐ธแตขฯ•แตข ฮฝ โ† ๐‘Ÿ
=
๐ด
๐‘š
ฮ”แตขฯ•แตข ฮฝ โ† ๐‘Ÿ
Radiation dose rate
= ๐‘“ โ‹…
๐ดโ‚’
๐‘š
ฮ”แตข๐‘’โˆ’ฮปโ‚‘๐‘กฯ•แตข ฮฝ โ† ๐‘Ÿ
๐‘“ is fraction of localized activity from the administered activity, ฮปโ‚‘ is
effective decay constant,
ฮ”แตข=2.13NiEi aka Equilibrium Dose Constant calculated in gยทrad/(ฮผCiยทh)
Radiation dosimetry
โ€ข Scientific determination of amount, rate and distribution of radiation
in the body emitted from a source of ionizing radiation.
โ€ข Broadly divided into โ€œ
1. External radiation dosimetry
2. Internal radiation dosimetry
Internal radiation dosimetry
โ€ข Two types of estimate: Type I and Type II
๏ƒ˜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 โ‰ฅ pharmaceuticals that target the same
structure, tissue or molecule. A rare type I result.
๏ƒ˜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.
Critical organ and its calculation
โ€ข 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.
โ€ข 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.
โ€ข 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).
Radiopharmaceutical Critical organ
68Ga-DOTA PET or Octreoscan Spleen
111In-Prostascint Liver
131/123I- metastatic survey Thyroid
99mTc-Labelled RBC for bleed Spleen>Heart
99mTc-HIDA Colon
HMPAO brain perfusion Dall bladder, Lacrimal gland
99mTc-MAG3,DTPA Bladder
99mTc-DMSA Kidney
Xenon ventilation Trachea
99mTc-DTPA ventilation Bladder
Lung perfusion Lungs
DTPA cisternogram Spinal cord
mIBG therapy,
90Y & 177Lu-SSA
Kidney(Lu- octreotate 23)
90Y-Zevalin Kidney
131I-Bexxar Thyroid
Radiopharmaceutical Critical organ
99mTc-MDP Bladder
99mTc-Sulphur colloid Liver
67Ga citrate Colon
mIBG scan Adrenal medulla
99mTc-Meckels scan Stomach > thyroid
SestaMIBI Upper colon
OIH Thyroid
99mTc-MUGA Spleen > heart
Thallium Kidney
Testicular/ scrotal scintigraphy Stomach
99mTc-pertechnetate Stomach > thyroid
32P-phosphate Red bone marrow
89Strontium chloride Bone surface
153Sm-EDTMP Bone surface
177Lu-PSMA Kidneys
18F-FDG Bladder
Critical organs determination
โ€ข Done most commonly by MIRD scheme.
โ€ข Here radiation dose exposure is determined for various organs and
the organ receiving the highest radiation exposure is the critical
organ.
โ€ข 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.
MIRD Scheme
โ€ข Medical Internal Radiation Dose (MIRD) Committee is a part of The
Nuclear Medicine Society (NMS) since 1965.
โ€ข Aim :
a. to standardize internal dosimetry calculations,
b. improve published emission data for radionuclide,
c. enhance data on pharmacokinetics for radiopharmaceuticals
โ€ข For use in diagnostic nuclear medicine, radionuclide therapy and in
internal contamination.
MIRD Scheme
โ€ข 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.
โ€ข Target Organ (T): The target organ is the organ in which the dose is to
be determined.
โ€ข 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.
MIRD Reference
man
Basic concepts
Mean Energy Per Transition (ฮ”แตข)
โ€ข The mean energy per transition (โ–ณ) 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” = ๐พ โ‹… ๐ธ โ‹… ๐‘›
โ€ข 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:
ฮ”แตข = ๐พ โ‹… ๐ธแตข โ‹… ๐‘›แตข
Cumulated Activity (รƒh)
โ€ข Represented by the area under the time activity curve and has the dimensions of
activity x time (ฮผCiโ‹…hr). The cumulated activity รƒh is the total number of
transitions that occur in a target organ from time = 0 to time = T.
ฤ€ = ๐ŸŽ
๐’•
๐‘จ ๐’• โ‹… ๐’…๐’•
โ€ข Where, The function A(t) is: ๐ด ๐‘ก = ๐ดโ‚’ โˆ™ ๐‘’โˆ’ฮปโ‚‘๐‘ก
โ€ข For total dose estimation, Time T= infinity, hence ๐ดh = 0
โˆž
๐ดh(t)dt
โ€ข Affected by
1. rate of uptake
2. Physical half life
3. Biological half life
Cumulated Activity (รƒh)
โ€ข In MIRD pamphlet no.11, รƒh has been substituted by
D(rad) = รƒ ยท S
Where,
รƒ=1.44 ยท f ยทAoยทTe
S= ๐‘–=1
๐‘›
ฮ”แตข
ฮฆแตข
๐‘š
where S is mean absorbed dose per cumulated activity
Cumulated Activity (รƒh)
โ€ข Effective half life (Te)
Te=
๐‘‡ ๐‘ƒร—๐‘‡ ๐ต
๐‘‡ ๐‘ƒ+๐‘‡ ๐ต
1
๐‘‡๐‘’
=
1
๐‘‡๐‘ƒ
+
1
๐‘‡๐ต
Where TP& TB are physical and biological half life
Models of Cumulated Activity
1. Uptake by organ is instantaneous with no biologic excretion
รƒ=1.44ยทfยทAoTP
2. Uptake by organ is instantaneous with elimination by biologic excretion
only
รƒ=1.44ยทfยทAoTB
3. Uptake by organ is instantaneous with removal by both physical decay
and biologic excretion
รƒ=1.44 ยท f ยทAoยทTe
4. Uptake by organ is not instantaneous
รƒ=1.44 ยท f ยทAoยทTe (
๐‘‡ ๐‘„
๐‘‡ ๐‘ˆ
)
Residence Time (ฯ„h)
โ€ข 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
โ€ข Hence, Cumulated activity, รƒh = base x Height= Ao x ฯ„h, then
ฯ„h =
รƒh
Ao
โ€ข When uptake phase can be neglected and maximal source activity is Ah ,
ฯ„h =
1.443 ๐‘‡โ„Ž ๐‘’๐‘“๐‘“ ๐ดโ„Ž
๐ด ๐‘œ
โ€ข In case of bolus administration where all the activity (Ao) is located in organ at T = 0 (e.g. blood,
ฯ„h=1.443(Th)eff (Ah=Ao)
โ€ข Hence cumulated activity may be represented as รƒ =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)
Absorbed fraction(ฯ†แตข)
โ€ข ฯ†แตข(vโ†r) is called the absorbed fraction
โ€ข 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.
โ€ข 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
Absorbed fraction(ฯ†แตข)
โ€ข For ฮฒ, ฮฑ, conversion electrons and x- & ฮณ-rays of energies โ‰ค 11 KeV;
If source and target are same, ฯ†แตข = 1
If source and target are different than, ฯ†แตข =0
โ€ข For x- & ฮณ-rays of energies of energies โ‰ฅ 11 KeV;
photons: for all source target combinations 0< ฯ†แตข <1
โ€ข ฯ†แตข values are calculated by statistical monte carlo methods on the
basis of interaction of radiation with matter.
โ€ข Available in MIRD pamphlets by Society of Nuclear medicine.
Absorbed Fraction (ฯ†)
โ€ข Specific absorption fraction: Absorbed fraction per unit mass of the
target organ, ฯ† = ฯ†แตข /Mk
Dosimetry Equation
Dose equation (D)
โ€ข The radiation energy emitted by the source activity cumulated (รƒh )
over the time interval of interest is given by D= รƒhฮ”
โ€ข Where ฮ” is the total mean energy emitted per nuclear disintegration.
โ€ข Also as it is not necessary that all emitted radiation will be absorbed
by the target organ and will depend on absorption fraction (ฯ†แตข), dose
is D=รƒhฮ”iฯ†i
Dose equation for single source( ๐ทk)
โ€ข The mean absorbed dose [Dose per unit mass of the target organ] ( ๐ทk) to
target organ k with mass (Mk) from a single source organ h is given by:
๐ทk=
(รƒโ„Ž
ฮ”แตข๐œ‘แตข)
๐‘€ ๐‘˜
โ€ข Since, there can be multiple different emission types such as beta or gamma,
๐ทk=
(รƒโ„Ž ๐‘– ฮ”แตข๐œ‘แตข)
๐‘€ ๐‘˜
โ€ข the previous equation may be separated into two parts
1) Cumulated activity รƒh
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 โ€œS factorโ€(S) and is defined mathematically as:
Dose equation for single source( ๐ทk)
S ๐‘Ÿ๐‘˜ โ† ๐‘Ÿโ„Ž =
( ๐‘– ฮ”แตข๐œ‘แตข)
๐‘€ ๐‘˜
โ€ข S-factors have been tabulated for a variety of radionuclides and for different
source/target configurations in both standard man and children.
โ€ข Hence the equation can be simplified as ๐ท = รƒโจฏS
โ€ข Since dose exposure will depend on the residence time of the RP, this formula
can be suitably modified as
๐ท = รƒโจฏS =Aoฯ„S
Multiple source organs
โ€ข The total dose equation summed over all sources is given by:
๐ท(rk) = โ„Ž ๐ท(rkโ†
rh)
โ€ข The residence time in source organ h when uptake phase can be
neglected and maximal source activity is
ฯ„h =
1.443 ๐‘‡โ„Ž ๐‘’๐‘“๐‘“ ๐ดโ„Ž
๐ด ๐‘œ
Overall dosimetry equation
๐ท=
ฤ€T
๐‘š ๐‘‡
ฮ” ๐‘›๐‘ฮฆ ๐‘›๐‘ +
ฤ€ ๐‘ 
๐‘š ๐‘‡
โˆ†๐œ™(๐‘‡โ†๐‘†)
Tโ†S means โ€œsource to targetโ€
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.
Anthropomorphic phantoms
Phantoms for dosimetry
โ€ข VIP-Man phantom
โ€ข Walking phantoms
โ€ข ADAM phantom
โ€ข RPI Pregnant Female phantoms
โ€ข RADAR phantoms
Walking
phantom
ADAM & EVA phantom
RPI Pregnant female phantom
RADAR phantom
Physical phantoms
Main uses:
๏ƒ˜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.
โ€ข RANDOยฎ phantom and ATOMยฎ phantom which contain tissue equivalent slices that have
anatomical maps and cavities for organ dose measurements
๏ƒ˜Internal radiation dosimetry
๏ƒ˜Imaging quality assurance: cover only partial body and some are anatomically very
simple.
โ€ข NEMA image quality phantom
๏ƒ˜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.
โ€ข Lawrence Livermore National Laboratory (LLNL)
โ€ข BOttle MAnikin ABsorption (BOMAB) phantom family
RANDO phantom
ATOM dosimetry verification phantom
NEMA image quality phantom
LLNL phantom
BOMAB phantom
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
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
4-D MCAT phantom
4-D XCAT phantom
Fischer-Snyder MIRD 5 phantom
Snyder et al phantom
MIRD cumulated activity
โ€ข 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
๐ด ๐‘ก = ๐‘’โˆ’ฮป๐‘ก
๐‘—
๐ด๐‘— ๐‘’โˆ’ฮป ๐‘— ๐‘ก
โ€ข The cumulated activity follows from integrating A(t) over time interval t1-t2
รƒ =
๐‘—
๐ด๐‘—
ฮป + ฮป๐‘—
(๐‘’โˆ’ ๐œ†+๐œ† ๐‘— ๐‘ก1 โˆ’ ๐‘’โˆ’ ๐œ†+๐œ† ๐‘— ๐‘ก2)
MIRD half-life
โ€ข Physical half-life/ Physical decay constant
๐‘‡ =
ln 2
๐œ†
โ€ข Biological half-life of biological component j
๐‘‡๐‘๐‘— =
ln 2
๐œ†๐‘—
โ€ข Effective half โ€“time for biological component j
๐‘‡๐‘’โ‹…๐‘— =
ln 2
(๐œ†+๐œ† ๐‘—)
1
๐‘‡๐‘’โ‹…๐‘—
=
1
๐‘‡
+
1
๐‘‡๐‘—
= ๐œ† + ๐œ†๐‘— = ๐œ† ๐‘’โ‹…๐‘—
This equation accounts for all factors and indicates that the total dose is summation of
both penetrating and non-penetrating combinations.
Dosimetry calculation
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
ฮ”npฮฆnp +
As
mT
ฮ”ฮฆ(Lโ†L) +
As
mT
ฮ”ฮฆ(Lโ†S) +
As
mT
ฮ”ฮฆ(Lโ†M)
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
Dosimetry calculation
โ€ข Ao in the liver = 3000 ฮผCi (or 3 mCi) x 0.85 = 2550 ฮผCi (86.7 MBq)
โ€ข Te = 6 hr
โ€ข ฯ„h =
1.443 ๐‘‡โ„Ž ๐‘’๐‘“๐‘“ ๐ดโ„Ž
๐ด ๐‘œ
โ€ข ฮ”iร˜i = 0.0806
โ€ข D = 1.44 x (2550/1700) x 6 x 0.0806 = 1.04 rad
MIRD Methodology
Flowchart
Identify Source
organs(s1,s2โ€ฆsm) &
Target organs(t1,t2โ€ฆtn)
Determine รƒ ๐‘  ๐‘š
from
activity-time curves
Look up ๐‘†๐‘ก ๐‘›โ†๐‘  ๐‘š
using
appropriate table or
interpolate from graph
Determine dose
delivered to tn from sm
๐ท๐‘ก ๐‘›โ†๐‘  ๐‘š
= ฤ€ ๐‘  ๐‘š
โ‹… ๐‘†๐‘ก ๐‘›โ†๐‘  ๐‘š
Sum contributions of
dose from all sources
to tn
๐ท๐‘ก ๐‘›
=
๐‘  ๐‘š
๐ท๐‘ก ๐‘›โ†๐‘  ๐‘š
Repeat for all source organs
Repeat for each pair of
source and target organ
Repeat for each target organ
Symbols and Conventions
MIRD ICRP
Mean absorbed dose (Dk) in target organ(K) โ‰ˆ Committed equivalent dose(HT) in target organ(T) โ€“
Committed effective dose
Source region (h) & target region (k) โ‰ˆ Source organ(S) and Target organ(T)
Absorbed fraction ฮฆ ๐‘Ÿ ๐‘˜โ†๐‘Ÿโ„Ž
โ‰ˆ Absorbed fraction ๐ด๐น(๐‘‡โ†๐‘†)
Mean absorbed dose per unit cumulated activity โ‰ˆ
๐‘†(๐‘Ÿ ๐‘˜โ†๐‘Ÿโ„Ž)
Specific effective energy ๐‘†๐ธ๐ธ(๐‘‡โ†๐‘†)
Cumulated activity in source region โ‰ˆ Committed number of transformations in source
organ
Mean absorbed dose in target region โ‰ˆ
๐ท ๐‘˜ =
โ„Ž
รƒโ„Ž ๐‘†(๐‘Ÿ ๐‘˜โ†๐‘Ÿโ„Ž)
๐‘† ๐‘Ÿ ๐‘˜โ†๐‘Ÿโ„Ž
=
๐‘–
โˆ†๐‘–ฮฆ๐‘–(๐‘Ÿ๐‘˜ โ† ๐‘Ÿโ„Ž) =
๐‘–
ฮ”๐‘– ๐œ™๐‘–(๐‘Ÿ๐‘˜ โ† ๐‘Ÿโ„Ž)
๐‘š ๐‘˜
Committed equivalent dose in target region
๐ป ๐‘‡ =
๐‘–
๐‘ˆ๐‘† ๐‘–
๐‘†๐ธ๐ธ(๐‘‡โ†๐‘  ๐‘–)
Paediatric dosages
โ€ข 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
๏ƒ˜In Paediatric dosage card, dose is calculated by
Baseline activity x Multiplication factor
Assumed for a 3 kg child
โ€ข Multiplication factor is a complex value derived from:
a. Body weight
b. Adult dosage
c. Type of radiopharmaceutical
Paediatric dosages
๏ƒ˜In PNMDRW guidelines, Dosage is based on:
a. Body weight
b. Body surface area
c. Radiopharmaceutical type
d. LEHR collimator
๏ƒ˜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)

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Internal radiation dosimetry

  • 2. Radiation units โ€ข 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. โ€ข ICRU recommended SI units for following radiation associated quantities in 1980 โ€ข 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 โ€ข 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 (โ‰ˆrad): 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) โ€ข 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 ฮ”m are completely stopped in air. โ€ข 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 โ€ข S.I. Unit : C/kg
  • 5. Roentgen โ€ข 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). โ€ข It only applies for air and to x- or ฮณ-radiation upto <3 MeV. โ€ข 1 cm3 air = 0.001293 g at STP, charge of either sign carries 1.6ร—10-19 C or 4.8ร—10-10 electrostatic units, so 1๐‘… = 2.58ร—10-4 C/kg
  • 6. Radiation absorbed dose(rad) โ€ข Energy deposited per unit mass of any material by any type of radiation. โ€ข It is independent of the weight of the material. โ€ข c/a gray (Gy) in SI units- energy absorbed per kg of air due to an exposure of 1 R. โ€ข 1 rad = 100 ergs/g absorber = 10-2 J/kg โ€ข 1 Gy = 100 rad = 1 J/kg absorber โ€ข 1 R = 86.9ร—10-4 J/kg in air = 0.869 rad in air = 0.00869 Gy in air
  • 7. Radiation absorbed dose(rad) โ€ข For soft tissue, 1 R = 0.96rad = 0.0096 Gy โ€ข 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 โ€œstandardโ€ or โ€œaverageโ€ 70 kg man
  • 8. Roentgen equivalent man(rem) โ€ข Accounts for effectiveness of different types of radiations to cause biological damage. โ€ข In radiobiology, it is defined as rem = rad ร— RBE = rad ร— Wr โ€ข 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. โ€ข Normally radiations of 250 KV x-rays is taken as standard radiation ... of its widespread use.
  • 9. Roentgen equivalent man(rem) โ€ข RBE varies with: a. LET of the radiation b. Radiation dose c. Dose rate d. Biological system โ€ข RBE โ‰ˆ Radiation weighting factor(Wr) in radiation protection โ€ข US Nuclear Regulatory Commission(NRC) uses โ€œQuality Factorsโ€(QF) โ‰ˆ Wr for regulation. โ€ข SI Unit of dose equivalent is sievert, 1 sievert = 100 rem
  • 10.
  • 11.
  • 12. Effective dose โ€ข Term given by ICRP โ€ข prev. c/a Effective dose equivalent โ€ข Accounts for the different sensitivity of tissues to radiation& is Age independent values . โ€ข ED (HE) is defined as the sum of weighted dose equivalents in all tissues and organs, HE= ๐‘‡ ๐‘Š๐‘‡ ๐ป ๐‘‡ Where WT is the tissue weighting factor for an organ, HT is the dose equivalent (rem) to the organ HE= ๐‘‡ ๐‘Š๐‘‡ ๐‘Ÿ ๐‘Š๐‘Ÿ ร— (๐‘Ÿ๐‘Ž๐‘‘) ๐‘‡,๐‘Ÿ Where (๐‘Ÿ๐‘Ž๐‘‘) ๐‘‡,๐‘Ÿ is the absorbed dose to tissue (T) from radiation of type r & ๐‘Š๐‘Ÿis radiation weighting factor
  • 13.
  • 14. Collective effective dose (S) โ€ข 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) โ€ข 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. โ€ข 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. โ€ข SI unit: Bq
  • 16. Annual limit on intake (ALI) โ€ข ALI values are given for ingestion if intake is through mouth and for inhalation if intake is through inhalation. โ€ข ALI values for some of the important radio nuclides used in research are: ALI values for inhalation are โ€ข I-131 1 MBq [0.027 mCi] โ€ข 99mTc 2000 MBq [54 mCi] โ€ข 99Mo 50 MBq [1.35 mCi]
  • 17.
  • 18. Derived air concentration (DAC) โ€ข 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. โ€ข DAC = ALI / 2.4 x 103 Bq/m3
  • 19. Radiation dose rate โ€ข aka energy absorbed per hour and is given by Ri โ€ข For non penetrating radiations (meaning all energy is absorbed in the absorber) ๐‘…แตข = 2.13 ๐ด ๐‘š ๐‘แตข๐ธแตข โ€ข For penetrating radiations (total or part of the radiation may be absorbed) ๐‘…แตข = 2.13 ๐ด ๐‘š ๐‘แตข๐ธแตขฯ•แตข ฮฝ โ† ๐‘Ÿ = ๐ด ๐‘š ฮ”แตขฯ•แตข ฮฝ โ† ๐‘Ÿ
  • 20. Radiation dose rate = ๐‘“ โ‹… ๐ดโ‚’ ๐‘š ฮ”แตข๐‘’โˆ’ฮปโ‚‘๐‘กฯ•แตข ฮฝ โ† ๐‘Ÿ ๐‘“ is fraction of localized activity from the administered activity, ฮปโ‚‘ is effective decay constant, ฮ”แตข=2.13NiEi aka Equilibrium Dose Constant calculated in gยทrad/(ฮผCiยทh)
  • 21. Radiation dosimetry โ€ข Scientific determination of amount, rate and distribution of radiation in the body emitted from a source of ionizing radiation. โ€ข Broadly divided into โ€œ 1. External radiation dosimetry 2. Internal radiation dosimetry
  • 22. Internal radiation dosimetry โ€ข Two types of estimate: Type I and Type II ๏ƒ˜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 โ‰ฅ pharmaceuticals that target the same structure, tissue or molecule. A rare type I result. ๏ƒ˜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 โ€ข 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. โ€ข 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. โ€ข 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).
  • 24. Radiopharmaceutical Critical organ 68Ga-DOTA PET or Octreoscan Spleen 111In-Prostascint Liver 131/123I- metastatic survey Thyroid 99mTc-Labelled RBC for bleed Spleen>Heart 99mTc-HIDA Colon HMPAO brain perfusion Dall bladder, Lacrimal gland 99mTc-MAG3,DTPA Bladder 99mTc-DMSA Kidney Xenon ventilation Trachea 99mTc-DTPA ventilation Bladder Lung perfusion Lungs DTPA cisternogram Spinal cord mIBG therapy, 90Y & 177Lu-SSA Kidney(Lu- octreotate 23) 90Y-Zevalin Kidney 131I-Bexxar Thyroid Radiopharmaceutical Critical organ 99mTc-MDP Bladder 99mTc-Sulphur colloid Liver 67Ga citrate Colon mIBG scan Adrenal medulla 99mTc-Meckels scan Stomach > thyroid SestaMIBI Upper colon OIH Thyroid 99mTc-MUGA Spleen > heart Thallium Kidney Testicular/ scrotal scintigraphy Stomach 99mTc-pertechnetate Stomach > thyroid 32P-phosphate Red bone marrow 89Strontium chloride Bone surface 153Sm-EDTMP Bone surface 177Lu-PSMA Kidneys 18F-FDG Bladder
  • 25. Critical organs determination โ€ข Done most commonly by MIRD scheme. โ€ข Here radiation dose exposure is determined for various organs and the organ receiving the highest radiation exposure is the critical organ. โ€ข 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 โ€ข Medical Internal Radiation Dose (MIRD) Committee is a part of The Nuclear Medicine Society (NMS) since 1965. โ€ข Aim : a. to standardize internal dosimetry calculations, b. improve published emission data for radionuclide, c. enhance data on pharmacokinetics for radiopharmaceuticals โ€ข For use in diagnostic nuclear medicine, radionuclide therapy and in internal contamination.
  • 27. MIRD Scheme โ€ข 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. โ€ข Target Organ (T): The target organ is the organ in which the dose is to be determined. โ€ข 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 (ฮ”แตข) โ€ข The mean energy per transition (โ–ณ) 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” = ๐พ โ‹… ๐ธ โ‹… ๐‘› โ€ข 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: ฮ”แตข = ๐พ โ‹… ๐ธแตข โ‹… ๐‘›แตข
  • 31. Cumulated Activity (รƒh) โ€ข Represented by the area under the time activity curve and has the dimensions of activity x time (ฮผCiโ‹…hr). The cumulated activity รƒh is the total number of transitions that occur in a target organ from time = 0 to time = T. ฤ€ = ๐ŸŽ ๐’• ๐‘จ ๐’• โ‹… ๐’…๐’• โ€ข Where, The function A(t) is: ๐ด ๐‘ก = ๐ดโ‚’ โˆ™ ๐‘’โˆ’ฮปโ‚‘๐‘ก โ€ข For total dose estimation, Time T= infinity, hence ๐ดh = 0 โˆž ๐ดh(t)dt โ€ข Affected by 1. rate of uptake 2. Physical half life 3. Biological half life
  • 32. Cumulated Activity (รƒh) โ€ข In MIRD pamphlet no.11, รƒh has been substituted by D(rad) = รƒ ยท S Where, รƒ=1.44 ยท f ยทAoยทTe S= ๐‘–=1 ๐‘› ฮ”แตข ฮฆแตข ๐‘š where S is mean absorbed dose per cumulated activity
  • 33. Cumulated Activity (รƒh) โ€ข Effective half life (Te) Te= ๐‘‡ ๐‘ƒร—๐‘‡ ๐ต ๐‘‡ ๐‘ƒ+๐‘‡ ๐ต 1 ๐‘‡๐‘’ = 1 ๐‘‡๐‘ƒ + 1 ๐‘‡๐ต Where TP& TB are physical and biological half life
  • 34. Models of Cumulated Activity 1. Uptake by organ is instantaneous with no biologic excretion รƒ=1.44ยทfยทAoTP 2. Uptake by organ is instantaneous with elimination by biologic excretion only รƒ=1.44ยทfยทAoTB 3. Uptake by organ is instantaneous with removal by both physical decay and biologic excretion รƒ=1.44 ยท f ยทAoยทTe 4. Uptake by organ is not instantaneous รƒ=1.44 ยท f ยทAoยทTe ( ๐‘‡ ๐‘„ ๐‘‡ ๐‘ˆ )
  • 35. Residence Time (ฯ„h) โ€ข 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 โ€ข Hence, Cumulated activity, รƒh = base x Height= Ao x ฯ„h, then ฯ„h = รƒh Ao โ€ข When uptake phase can be neglected and maximal source activity is Ah , ฯ„h = 1.443 ๐‘‡โ„Ž ๐‘’๐‘“๐‘“ ๐ดโ„Ž ๐ด ๐‘œ โ€ข In case of bolus administration where all the activity (Ao) is located in organ at T = 0 (e.g. blood, ฯ„h=1.443(Th)eff (Ah=Ao) โ€ข Hence cumulated activity may be represented as รƒ =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(ฯ†แตข) โ€ข ฯ†แตข(vโ†r) is called the absorbed fraction โ€ข 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. โ€ข 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(ฯ†แตข) โ€ข For ฮฒ, ฮฑ, conversion electrons and x- & ฮณ-rays of energies โ‰ค 11 KeV; If source and target are same, ฯ†แตข = 1 If source and target are different than, ฯ†แตข =0 โ€ข For x- & ฮณ-rays of energies of energies โ‰ฅ 11 KeV; photons: for all source target combinations 0< ฯ†แตข <1 โ€ข ฯ†แตข values are calculated by statistical monte carlo methods on the basis of interaction of radiation with matter. โ€ข Available in MIRD pamphlets by Society of Nuclear medicine.
  • 38. Absorbed Fraction (ฯ†) โ€ข Specific absorption fraction: Absorbed fraction per unit mass of the target organ, ฯ† = ฯ†แตข /Mk
  • 40. Dose equation (D) โ€ข The radiation energy emitted by the source activity cumulated (รƒh ) over the time interval of interest is given by D= รƒhฮ” โ€ข Where ฮ” is the total mean energy emitted per nuclear disintegration. โ€ข Also as it is not necessary that all emitted radiation will be absorbed by the target organ and will depend on absorption fraction (ฯ†แตข), dose is D=รƒhฮ”iฯ†i
  • 41. Dose equation for single source( ๐ทk) โ€ข The mean absorbed dose [Dose per unit mass of the target organ] ( ๐ทk) to target organ k with mass (Mk) from a single source organ h is given by: ๐ทk= (รƒโ„Ž ฮ”แตข๐œ‘แตข) ๐‘€ ๐‘˜ โ€ข Since, there can be multiple different emission types such as beta or gamma, ๐ทk= (รƒโ„Ž ๐‘– ฮ”แตข๐œ‘แตข) ๐‘€ ๐‘˜ โ€ข the previous equation may be separated into two parts 1) Cumulated activity รƒh 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 โ€œS factorโ€(S) and is defined mathematically as:
  • 42. Dose equation for single source( ๐ทk) S ๐‘Ÿ๐‘˜ โ† ๐‘Ÿโ„Ž = ( ๐‘– ฮ”แตข๐œ‘แตข) ๐‘€ ๐‘˜ โ€ข S-factors have been tabulated for a variety of radionuclides and for different source/target configurations in both standard man and children. โ€ข Hence the equation can be simplified as ๐ท = รƒโจฏS โ€ข Since dose exposure will depend on the residence time of the RP, this formula can be suitably modified as ๐ท = รƒโจฏS =Aoฯ„S
  • 43. Multiple source organs โ€ข The total dose equation summed over all sources is given by: ๐ท(rk) = โ„Ž ๐ท(rkโ† rh) โ€ข The residence time in source organ h when uptake phase can be neglected and maximal source activity is ฯ„h = 1.443 ๐‘‡โ„Ž ๐‘’๐‘“๐‘“ ๐ดโ„Ž ๐ด ๐‘œ
  • 44. Overall dosimetry equation ๐ท= ฤ€T ๐‘š ๐‘‡ ฮ” ๐‘›๐‘ฮฆ ๐‘›๐‘ + ฤ€ ๐‘  ๐‘š ๐‘‡ โˆ†๐œ™(๐‘‡โ†๐‘†) Tโ†S means โ€œsource to targetโ€
  • 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.
  • 47. Phantoms for dosimetry โ€ข VIP-Man phantom โ€ข Walking phantoms โ€ข ADAM phantom โ€ข RPI Pregnant Female phantoms โ€ข RADAR phantoms Walking phantom
  • 48. ADAM & EVA phantom
  • 49. RPI Pregnant female phantom RADAR phantom
  • 50. Physical phantoms Main uses: ๏ƒ˜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. โ€ข RANDOยฎ phantom and ATOMยฎ phantom which contain tissue equivalent slices that have anatomical maps and cavities for organ dose measurements ๏ƒ˜Internal radiation dosimetry ๏ƒ˜Imaging quality assurance: cover only partial body and some are anatomically very simple. โ€ข NEMA image quality phantom ๏ƒ˜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. โ€ข Lawrence Livermore National Laboratory (LLNL) โ€ข BOttle MAnikin ABsorption (BOMAB) phantom family
  • 51. RANDO phantom ATOM dosimetry verification phantom
  • 52. NEMA image quality phantom LLNL phantom
  • 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
  • 56.
  • 60. Snyder et al phantom
  • 61. MIRD cumulated activity โ€ข 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 ๐ด ๐‘ก = ๐‘’โˆ’ฮป๐‘ก ๐‘— ๐ด๐‘— ๐‘’โˆ’ฮป ๐‘— ๐‘ก โ€ข The cumulated activity follows from integrating A(t) over time interval t1-t2 รƒ = ๐‘— ๐ด๐‘— ฮป + ฮป๐‘— (๐‘’โˆ’ ๐œ†+๐œ† ๐‘— ๐‘ก1 โˆ’ ๐‘’โˆ’ ๐œ†+๐œ† ๐‘— ๐‘ก2)
  • 62. MIRD half-life โ€ข Physical half-life/ Physical decay constant ๐‘‡ = ln 2 ๐œ† โ€ข Biological half-life of biological component j ๐‘‡๐‘๐‘— = ln 2 ๐œ†๐‘— โ€ข Effective half โ€“time for biological component j ๐‘‡๐‘’โ‹…๐‘— = ln 2 (๐œ†+๐œ† ๐‘—) 1 ๐‘‡๐‘’โ‹…๐‘— = 1 ๐‘‡ + 1 ๐‘‡๐‘— = ๐œ† + ๐œ†๐‘— = ๐œ† ๐‘’โ‹…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 ฮ”npฮฆnp + As mT ฮ”ฮฆ(Lโ†L) + As mT ฮ”ฮฆ(Lโ†S) + As mT ฮ”ฮฆ(Lโ†M) 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 โ€ข Ao in the liver = 3000 ฮผCi (or 3 mCi) x 0.85 = 2550 ฮผCi (86.7 MBq) โ€ข Te = 6 hr โ€ข ฯ„h = 1.443 ๐‘‡โ„Ž ๐‘’๐‘“๐‘“ ๐ดโ„Ž ๐ด ๐‘œ โ€ข ฮ”iร˜i = 0.0806 โ€ข D = 1.44 x (2550/1700) x 6 x 0.0806 = 1.04 rad
  • 67. Identify Source organs(s1,s2โ€ฆsm) & Target organs(t1,t2โ€ฆtn) Determine รƒ ๐‘  ๐‘š from activity-time curves Look up ๐‘†๐‘ก ๐‘›โ†๐‘  ๐‘š using appropriate table or interpolate from graph Determine dose delivered to tn from sm ๐ท๐‘ก ๐‘›โ†๐‘  ๐‘š = ฤ€ ๐‘  ๐‘š โ‹… ๐‘†๐‘ก ๐‘›โ†๐‘  ๐‘š Sum contributions of dose from all sources to tn ๐ท๐‘ก ๐‘› = ๐‘  ๐‘š ๐ท๐‘ก ๐‘›โ†๐‘  ๐‘š 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‰ˆ Committed equivalent dose(HT) in target organ(T) โ€“ Committed effective dose Source region (h) & target region (k) โ‰ˆ Source organ(S) and Target organ(T) Absorbed fraction ฮฆ ๐‘Ÿ ๐‘˜โ†๐‘Ÿโ„Ž โ‰ˆ Absorbed fraction ๐ด๐น(๐‘‡โ†๐‘†) Mean absorbed dose per unit cumulated activity โ‰ˆ ๐‘†(๐‘Ÿ ๐‘˜โ†๐‘Ÿโ„Ž) Specific effective energy ๐‘†๐ธ๐ธ(๐‘‡โ†๐‘†) Cumulated activity in source region โ‰ˆ Committed number of transformations in source organ Mean absorbed dose in target region โ‰ˆ ๐ท ๐‘˜ = โ„Ž รƒโ„Ž ๐‘†(๐‘Ÿ ๐‘˜โ†๐‘Ÿโ„Ž) ๐‘† ๐‘Ÿ ๐‘˜โ†๐‘Ÿโ„Ž = ๐‘– โˆ†๐‘–ฮฆ๐‘–(๐‘Ÿ๐‘˜ โ† ๐‘Ÿโ„Ž) = ๐‘– ฮ”๐‘– ๐œ™๐‘–(๐‘Ÿ๐‘˜ โ† ๐‘Ÿโ„Ž) ๐‘š ๐‘˜ Committed equivalent dose in target region ๐ป ๐‘‡ = ๐‘– ๐‘ˆ๐‘† ๐‘– ๐‘†๐ธ๐ธ(๐‘‡โ†๐‘  ๐‘–)
  • 69.
  • 70. Paediatric dosages โ€ข 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 ๏ƒ˜In Paediatric dosage card, dose is calculated by Baseline activity x Multiplication factor Assumed for a 3 kg child โ€ข Multiplication factor is a complex value derived from: a. Body weight b. Adult dosage c. Type of radiopharmaceutical
  • 71.
  • 72. Paediatric dosages ๏ƒ˜In PNMDRW guidelines, Dosage is based on: a. Body weight b. Body surface area c. Radiopharmaceutical type d. LEHR collimator ๏ƒ˜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

  1. MIRD is an Medical Internal Radiation Dose
  2. ICRP is International Commission on Radiological Protection