Mird by saumya shrivastav

MIRD
Saumya Shrivastav
RSO, Dept. of Nuclear Medicine
AIIMS, Raipur

Internal Radiation Dosimetry
Contents :
• Basic definitions
1. Absorbed dose
2. Equivalent dose
3. Source and Target organs
• Calculation of Radiation dose (MIRD Method)
1. Basic procedure
2. Cumulated activity
3. Equilibrium absorbed dose constant
4. Absorbed fraction
5. Mean Dose per Cumulated Activity (S)

Absorbed Dose
• The quantity of radiation energy deposited in an absorber per
kg of absorber material.
• SI Unit : Gray (Gy)
1 Gy = 1 j/kg
• Other unit : rad
1 Gy = 100 rad
1 rad = 100 ergs/gm
D(Gy) =
Energy deposited (joule)
Mass of absorber (Kg)
Basic definitions :
1. Absorbed dose
2. Equivalent dose

Equivalent Dose
HT = DT,R × wR
Where,
HT = Equivalent Dose
DT ,R = Absorbed dose from radiation R in a tissue or organ T
wR = Radiation weighting factor
• SI Unit : Severt (Sv)
• Other Unit : rem
1 Sv = 100 rem
Basic definitions :
1. Absorbed dose
2. Equivalent dose

Source and Target organs
• Source organs : ??
• Target organs : ??
• The source and target organ
may be the same organ…..
Basic definitions :
1. Absorbed dose
2. Equivalent dose

Basic Procedure
The basic procedure for calculating the radiation dose to a
target organ from radioactivity in a source organ is a
three-step process, as follows :
1. The amount of activity and time spent by the radioactivity in the
source organ.
2. The total amount of radiation energy emitted by the radioactivity
in the source organ.
3. The fraction of energy emitted by the source organ that is
absorbed by the target organ.
Calculation of Radiation dose (MIRD Method)
1. Basic procedure

Cumulated Activity
Activity in an organ depends on various factors :
1. Uptake of radiopharmaceutical
2. Excretion from the organ
3. Physical decay
Where , Ã = Cumulated activity
A(t) = A0 exp^(-0.693t /Tp)
• SI unit : Becquerel • sec (Bq • sec)
1. Basic procedure

1. Basic procedure

• Residence time  :
How long the radionuclide stay in an organ
 = Ã/A injected
Where,
Ã = Cumulated Activity
 = Residence time
1. Basic procedure

Calculation : (four cases)
1. Instantaneous uptake with physical decay
2. Instantaneous uptake with clearance by biological excretion
TP  TB
3. Instantaneous uptake with clearance by biological excretion
and physical decay
4. Non-instantaneous uptake with biological and physical decay
1. Basic procedure

Special case 1 : Instantaneous uptake with physical decay
A(t) = A0 exp^(-0.693t /Tp)
Tp = Physical half life
A0 = Initial Activity Present in
source organ
Therefore ,
1. Basic procedure

Example : What is the cumulated activity in the liver for an injection
of 100 MBq of a 99mTc-labeled sulfur colloid, assuming that 60% of
the injected colloid is trapped by the liver and retained there
indefinitely?
Ã= 1.44 TP A0
1. Basic procedure

Special case 2 : Instantaneous uptake with biological decay
1. Basic procedure

Example : Suppose that 100 MBq of 99mTc-labeled microspheres
are injected into a patient,
1. If 60% excreted from the lungs with a Tb of 15 mins
2. And 40% with a Tb of 30 minutes
then , Cumulated activity
1. Basic procedure

Special case 3 : Instantaneous uptake with clearance by
biological excretion and physical decay
Effective half life Te
1. Basic procedure

Example :100 MBq of 99mTc-labeled microspheres
are injected into a patient,
1. 60% is excreted from the lungs with a TB of 2 hours
2. and 40% with a Tb 3 hours
1. Basic procedure

Special case 4 : Non-instantaneous uptake with biological
and physical decay
where ,Tu = biologic uptake half-time
Tue = effective uptake half-time
1. Basic procedure

Equilibrium absorbed dose constant
• Energy emitted per unit of cumulated activity is given by the
equilibrium absorbed dose constant Δ
Δi = 1.6 × 10−13 NiEi (Gy • kg /Bq • sec)
(1MeV/dis = 1.6 × 10−13Gy • k/Bq • sec)
Δi = 2.13NiEi (rad • g / μCi • hr)
Where,
Ei = average energy (in MeV) of the ith emission
Ni = relative frequency of that emission
1. Basic procedure

Step 1 : Example (90Y)
90Y emits β particles: 100% of its disintegrations
with E b ave = 0.9348 MeV.
 Di = 2.13 Ni Ei
 Dtotal = Si Di = Dβ
 Dtotal = Db = 2.13 (1.0) 0.9348 = 1.99
mCi-hr
g-rad
1. Basic procedure

Step 2: Example (131I)
131I emits b,  particles
Di = 2.13 Ni Ei
Db1 = 2.13 (0.0213) 0.069 = 0.003
Db4 = 2.13 (0.894) 0.192 = 0.365
D14 = 2.13 (0.812) 0.364 = 0.629
D7 = 2.13 (0.0606) 0.284 = 0.036
D17 = 2.13 (0.0727) 0.637 = 0.098
mCi-hr
g-rad
Dtotal = Si Di = Dβ1 + D β2 + …+ D βn + D1+ D2+ …+ Dn
Emission Eave (MeV) Emission Rate
β1 0.069 2.13%
β4 0.192 89.4%
14 0.364 81.2%
7 0.284 6.06%
17 0.637 7.27%
= 1.133
1. Basic procedure

Absorbed Fraction
The fraction of radiation emitted by the source organ that is absorbed
by the target organ.
Absorbed Fraction f is dependent on:
1) type and energy of the emission
2) anatomical relationship of target-source pair
Total energy absorbed (g-rad) = ÃSi fi Di
Average absorbed Dose (rad) = Ã Si fi Di
mt
mt : organ mass “average female/male”
fi: fraction of energy delivered to target organ
from all source organs
Di: amount of energy emitted from source organ
1. Basic procedure

Example: (non-penetrating radiation)
Compute absorbed dose delivered to the Liver.
100mCi of 90Y emits b particles: 100% of its disintegrations
with Eb ave = 0.9348 MeV.
Di = 2.13 Ni Ei
Dtotal = Db = 2.13 (1.0) 0.9348 = 1.99
mCi-hr
g-rad
Dtotal = Si Di = Dβ= Dnp
Dtotal = Db=1.6x10-13 NiEi
Bq-Sec
kg-Gy
=1.49x10-13
1. Basic procedure

1. Basic procedure
GBqmCinoteGy
kg
GBq
GyD
m
FGBqA
GyD
BqGBqnote
m
FBqAx
GyD
Bq
kgGy
x
m
hr
hrFA
D
m
TFA
D
m
A
D
Liver
Liver
Liver
np
Liver
P
np
Liver
7.3100:92
809.1
)9.0)(7.3(50
)(
)1]()[(50
)(
101:
)1]([109.4
)(
)]
sec
(1049.1[
)]
min
sec
60)(
min
60)(1.64)(1)()(44.1[(
)])(1)()(44.1[(
0
90
8
13
0
0
~










D


D




f is complicated for energies > 10 keV (penetrating; g-rays)
f < 10 keV (non-penetrating radiation; b, x-rays)
)1(50
))((
)(0
F
mGyD
GBqA Liver



Mean Dose per Cumulated Activity (S)
1. Basic procedure
Average absorbed Dose (rad) = A Si fi Di
mt
Non-penetrating radiation: fi=1
Source and target organs: same
Source/
Targettarget
Penetrating radiation: fi=0
Source and target organs: Different
target

For penetrating radiation: -rays….
1. Basic procedure
S = Si Fi Di
F = f
mt
specific absorbed fraction
S = 1 Si fi Di
mt
rad
mCi-hr

D = Ã x S
Ã : Cumulative Activity (mCi-hr)
(calculate)
S: Mean dose per cumulated Activity (rad/ mCi-hr)
(look-up table)
D: Average dose (rad)
1. Basic procedure

1. Basic procedure
Adrenals Kidneys Lungs Thyroid
Adrenals 3.1E-02 3.2E-05 6.7E-06 5.2E-07
Kidneys 3.2E-05 1.5E-03 2.5E-06 1.4E-07
Lungs 6.7E-06 2.5E-06 4.5E-04 2.9E-06
Thyroid 5.2E-07 2.4E-07 2.9E-06 2.2E-02
Source Organs S(rad/ mCi-hr) for I131
TargetOrgans
I-131 WB Scan

Average Dose to an Organ (D)
Example:
A patient is to be treated with 131I for Hyperthyroidism. It is determined by
prior studies with a tracer dose of 131I that the thyroidal uptake is 60%, and the
effective half-life of iodine in the thyroid gland is 5 days.
Hyper-Thyroid Uptake
1
10
100
0 500 1000 1500 2000 2500 3000
Time (hr)
PercentUptake
Assume instantaneous
uptake (Tu << Tp = 8 days).

Te = Tp Tb
Tp + Tb
A = 1.44(Te)(A0)
~
Te = 5 days = 120 hrs
A = 1.44(120 hr)(0.6)(1,000 mCi)
~
= 103,680 mCi-hr/mCi administered

S(Thy Thy) = 2.2 x 10-2 rad/(mCi-hr)
D = A x S
~
_
D = 103,680 mCi-hr/mCi admin. x 2.2 x 10-2 rad/(mCi-hr)
= 2,280 rad/mCi administered
Note:
Inspection of the S table for 131I reveals that in
comparison to the Thyroid as the source organ,
all other organs produce a much smaller S value.
S-factor assumes
20 gm

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