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Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_5545_Библиотеки_им_академика_М_И_Перельмана.pdf
re
()
()
ev
DfAm Tvr
ioie i
rad
()
=⋅
()
←
()
144./∆
φ
Tv
i
n
dr
()
()←()
=
∑
DA
()
Af
oe
=.
S
i
n
=∑1
/m
16.2 Dose Calculation
Drad
()=()
fA mvredt
./
=
fA mv
./
()
=
../ ∆
∆
0
∆
0
fA mT
()
0
←
φ
()
ii
←
φ
()
ii
−
()
ie
t
t
−
λ
e
∫
0
1
λ
−−
λ
t
e
1
−
e
t
−
λ
e
←
φ
i
r1441
297
(16.14)
Here, Te is the effective half-life of the radiopharmaceutical in hours (discussed
in Chap. 3). If t=∞, that is, the radiopharmaceutical is completely eliminated, then
the exponential term e
−λet
approaches zero, and the absorbed dose in Eq. (16.14)
may be written as
(16.15)
If the radionuclide has n radiations with energies E1, E2, … En and fractional
abundances N1, N2, … Nn per disintegration, then the total dose D can be obtained
by summing Eq. (16.15) over all radiations. Thus,
DfAm
ra
=⋅
1441./ ∆
oe
φ
ii
(16.16)
This summation can also be applied to Eq. (16.12) for the dose rate Ri. The total
dose to the target from different sources of radiation can be calculated by summing
Eq. (16.16) over all sources.
In the MIRD pamphlets, the values of Δi have been compiled based on various
nuclear characteristics of the radionuclide in question. The ϕi values have been calculated on the basis of different sizes and compositions of the targets receiving the
radiation dose and the radiation characteristics of the radionuclide. In the MIRD
pamphlet no. 11, Eq. (16.16) has been substituted by
Srad
= .
(16.17)
where
∆
AT
φ
(16.19)
ii
(16.18)
144.
=
The quantity à is called the cumulated activity and has the unit of μCi⋅h. The
quantity S is called the mean absorbed dose per cumulated activity and has the unit
of rad/μCi⋅h. These two quantities are further discussed next.
298
Af
oe
=.
TT
QU
()
./
Af
oB
=.
Af
oP
=.
Sv
m
vr
=←
()
1
16.2.3 Factors Affecting Ã
The cumulated activity à in Eq. (16.18) is given as
16 Internal Radiation Dosimetry
144.
AT
This is calculated on the assumption that the radiopharmaceutical localizes in the
organs instantaneously and is cleared by both physical decay and biological
elimination.
There are situations when the uptake of the tracer is gradual and the clearance
also is slow. In these cases,
AfAT
=.
144
oe
(16.20)
where TU is the biological uptake half-time, Te is the effective excretion halftime
(Eq. 3.12 in Chap. 3), and TQ is the effective uptake half-time. TQ is calculated by
Eq. (3.12) using the physical half-life TP and the biological uptake halftime TU.
Two other situations can occur when the uptake is instantaneous, but the TP of the
radionuclide is greater than the biological half-life TB, or TB is greater than TP. When
TP>>TB, the cumulated activity is given by
AT
144.
(16.21)
If the tracer is excreted by several excretion routes such as urinary excretion and
fecal excretion the fraction of activity excreted and the effective halftime of each
mode are used to calculate the fractional cumulated activity of each mode, which
are then summed to calculate the total cumulated activity. When TB>>TP, the cumulated activity is calculated as
In this case, it is assumed that there is no or negligible biological excretion.
16.2.4 The S Values
The mean absorbed dose per cumulated activity, S, is more appropriately expressed as
where the symbols v and r represent the target and the source, respectively. The
calculation of these values is quite laborious. The MIRD Committee of the Society
of Nuclear Medicine calculates these values for radiopharmaceuticals commonly
used in nuclear medicine and publish them periodically. Table16.3 includes a partial list of S values for
←
()
99m
Tc obtained from MIRD pamphlet no. 11.
AT
144.
r
∑
n
i
=
∆
1
φ
ii
(16.22)
(16.23)
16.2 Dose Calculation
Tc
99m
for
b
Total
Red
299
body
1.4E-06 7.3E-07 1.3E-06
marrow Spleen Testes Thyroid
, mean absorbed dose per unit cumulated activity (rad/μCi·h)
a
Table 16.3 S
Stomach
Bladder
Source organs
content Kidneys Liver Lungs Ovaries
content
Target organs
Adrenals 1.5E-07 2.7E-06 1.1E-05 4.5E-06 2.7E-06 3.3E-07 2.3E-06 6.3E-06 3.2E-08 1.3E-07 2.3E-06
Bladder wall 1.6E-04 2.7E-07 2.8E-07 1.6E-07 3.6E-08 7.2E-06 9.9E-07 1.2E-07 4.8E-06 2.1E-09 2.3E-06
Bone (total) 9.2E-07 9.0E-07 1.4E-06 1.1E-06 1.5E-06 1.5E-06 4.0E-06 1.1E-06 9.2E-07 1.0E-06 2.5E-06
Stomach 2.7E-07 1.3E-04 3.6E-06 1.9E-06 1.8E-06 8.1E-07 9.5E-07 1.0E-05 3.2E-08 4.5E-08 2.2E-06
Kidneys 2.6E-07 3.5E-06 1.9E-04 3.9E-06 8.4E-07 9.2E-07 2.2E-06 9.1E-06 4.0E-08 3.4E-08 2.2E-06
Liver 1.7E-07 2.0E-06 3.9E-06 4.6E-05 2.5E-06 5.4E-07 9.2E-07 9.8E-07 3.1E-08 9.3E-08 2.2E-06
Lungs 2.4E-08 1.7E-06 8.5E-07 2.5E-06 5.2E-05 6.0E-08 1.2E-06 2.3E-06 6.6E-09 9.4E-07 2.0E-06
Marrow (red) 2.2E-06 1.6E-06 3.8E-06 1.6E-06 1.9E-06 5.5E-06 3.1E-05 1.7E-06 7.3E-07 1.1E-06 2.9E-06
Ovaries 7.3E-06 5.0E-07 1.1E-06 4.5E-07 9.4E-08 4.2E-03 3.2E-06 4.0E-07 0.0 4.9E-09 2.4E-06
Skin 5.5E-07 4.4E-07 5.3E-07 4.9E-07 5.3E-07 4.1E-07 5.9E-07 4.7E-07
Spleen 6.6E-07 1.0E-05 8.6E-06 9.2E-07 2.3E-06 4.9E-07 9.2E-07 3.3E-04 1.7E-08 1.1E-07 2.2E-06
Testes 4.7E-06 5.1E-08 8.8E-08 6.2E-08 7.9E-09 0.0 4.5E-07 4.8E-08 1.4E-03 5.0E-10 1.7E-06
Thyroid 2.1E-09 8.7E-08 4.8E-08 1.5E-07 9.2E-07 4.9E-09 6.8E-07 8.7E-08 5.0E-10 2.3E-03 1.5E-06
Total body 1.9E-06 1.9E-06 2.2E-06 2.2E-06 2.0E-06 2.6E-06 2.2E-06 2.2E-06 1.9E-06 1.8E-06 2.0E-06
Divide by 3.7 to convert to SI unit (Gy/MBq·h)
Adapted with permission of the Society of Nuclear Medicine from Snyder etal. (1975)
a
b
300
()
()
Problem 16.1
16 Internal Radiation Dosimetry
Calculate the absorbed dose to the lungs from the administration of 4mCi
(148 MBq)
99m
Tc-MAA particles, assuming that 99% of the particles are
trapped in the lungs. The value of S for the lungs is 5.2×10−5 rad/μCi·h.
Assume that the
99m
Tc activity is uniformly distributed in the lungs and 45%
of the activity is cleared from the lungs with a biological half-life of 3h and
55% with a biological half-life of 7h.
Answer
99m
The half-life of
Tc=6h. The effective half-life of two biological clear-
ances are
36
×
36
+
76
×
76
+
=
=hh.
2
32
=
T
ee1
=
T
2
Using Eq. (16.17)
A =× ×× ×+ ×
144 4000 099045 2055 32
.....
=⋅ ⋅
15 200 0 562
,.
µ
Ci hGBq h
(
))
Using Eq. (16.17)
DAS=
.
=××
15200 52 10
=
.
079
rad
=
790 79
mrad mGy
−
5
.
.
16.3 Radiation Dose inSI Units
The radiation dose in System Internationale (SI) units due to the administration of a
radiopharmaceutical can be calculated by assuming a source volume r containing A
MBq of the radiopharmaceutical that emits several radiations. If the ith radiation has
energy Ei and a fractional abundance Ni per disintegration, then the energy absorbed
per hour by a target of mass m and volume v from the ith radiation emitted by the
source volume r (dose rate) is given by
ii
()=()()
ii
()=()←()
∆
iii
NE= 0 576.
16.3 Radiation Dose inSI Units
RAmNE
Gy hMBq gMeV disintegration
// //
x10
xx
xx ⋅
x
==
0 576./AmNE
6
disintegrat
−
16 10
()
110
()
3600
()
6
./
ergMeV
−
4
gGyerg
h
s/
()
i
iions MBq
/s
⋅
()
/
ii
301
When the target and the source are not the same, the absorbed fraction ϕi (v←r)
must be taken into account. Thus,
RAmNEvr
Gy h/. /
0 576
φ
ii
(16.24)
The quantity 0.576 NiEi is a constant and can be denoted by Δi as in Eq. (16.10).
Thus,
(16.25)
With this value of Δi, Eqs. (16.11) to (16.18) are equally applicable to radiation
doses in SI units. It should be understood that the equations in SI units contain a
constant Δi=0.576NiEi and activities expressed in MBq and has the unit of Gy. g/
MBq·h, whereas the equations in rad units contain the equilibrium dose constant
Δi=2.13NiEi and activities expressed in microcuries. Also note that A should be
equal to f. Ao, if a fraction f of the initial activity Ao is accumulated in the organ or
tissue of interest.
Table 16.4 lists radiation absorbed doses from various radiopharmaceuticals to
different organs in adults. All values have been obtained from their package inserts.
16.3.1 Effective Dose Equivalent andEffective Dose
Historically, the whole-body dose or total body dose was used to evaluate the relative radiation risks of different procedures involving radiations. This quantity is
calculated according to the MIRD method by using the S factor for the whole body
as the source organ as well as the target organ. This value does not take into consideration the effect of tissue sensitivity to radiation.
In 1977 the ICRP introduced the concept of effective dose equivalent (EDE) to
take into account the different sensitivity of tissues to radiation (ICRP 26). The tissue weighting factor (WT) for an organ was dened as the ratio of the whole-body
dose, which would cause a certain probability of cancer induction to the absorbed
dose in that organ which would cause the same probability of cancer induction in
that organ. For example, a dose of 3rem to the whole body causes some probability
302
16 Internal Radiation Dosimetry
Table 16.4
Radiation absorbed doses in adults from different radiopharmaceuticals in nuclear
medicine
Dose
Radiopharmaceutical Organ
99m
Tc-pertechnetate Thyroid 0.130 35.1
rad/mCi mGy/GBq
Upper large intestine 0.120 32.4
Lower large intestine 0.110 30.0
Stomach 0.051 13.8
Ovaries 0.030 8.1
Testes 0.009 2.4
99m
Tc-sulfur colloid Liver 0.335 91.2
Spleen 0.213 57.4
Marrow 0.028 7.4
Ovaries 0.056 15.2
99m
Tc diethylenetriaminpentacetic acid
(DTPA)
Bladder (2-h void) 0.115 31.1
Kidneys 0.090 24.3
Gonads 0.011 3.0
99m
Tc-tetrofosmin (Myoview) at rest Gallbladder 0.180 48.7
Upper large intestine 0.113 30.5
Lower large intestine 0.082 22.2
Heart (wall) 0.015 4.1
Kidneys 0.046 12.4
Ovaries 0.035 9.5
Bladder (wall) 0.071 19.2
99m
Tc-macroaggregated albumin (MAA) Lungs 0.22 59.5
Kidneys 0.011 3.0
Liver 0.018 4.9
Ovaries 0.008 2.2
Testes 0.006 1.6
99m
Tc-stannous pyrophosphate (blood pool
imaging)
Bladder 0.034 9.2
Red marrow 0.019 5.1
Ovaries 0.023 6.2
Testes 0.013 3.5
Blood 0.051 13.8
99m
Tc-methylenediphosphonate (MDP) Bone 0.035 9.5
Bladder wall (2-h void) 0.130 35.1
Kidneys 0.040 10.8
Marrow 0.026 7.0
Ovaries 0.012 3.2
Testes 0.008 2.1
(continued)
16.3 Radiation Dose inSI Units
303
Table 16.4
(continued)
Dose
Radiopharmaceutical Organ
99m
Tc-mebrofenin (Choletec) Liver 0.047 12.7
rad/mCi mGy/GBq
Lower large intestine 0.474 128.1
Upper large intestine 0.364 98.4
Gallbladder 0.137 37.0
Bladder 0.029 7.8
Red marrow 0.034 9.1
Ovaries 0.101 27.3
99m
Tc-mercaptoacetyglycylglycylglycine
(MAG3)
Bladder wall 0.480 129.7
Gallbladder 0.016 4.3
Kidneys 0.014 3.8
Lower large intestine 0.033 8.9
Ovaries 0.026 7.0
99m
Tc-hexamethylpropylene amine oxime
(Ceretec)
Brain 0.026 7.0
Thyroid 0.100 27.0
Kidneys 0.130 35.1
Ovaries 0.023 6.2
Gallbladder 0.190 51.4
Lacrymal gland 0.258 69.7
99m
Tc-dimercaptosuccinic acid (DMSA) Bladder wall 0.070 18.9
Kidneys 0.630 170.3
Liver 0.031 8.6
Bone marrow 0.022 5.9
Ovaries 0.013 3.6
Testes 0.007 1.8
99m
Tc-ethyl cysteinate dimer (Neurolite) Brain 0.020 5.4
Gallbladder wall 0.092 24.9
Upper large intestine 0.063 17.0
Kidneys 0.027 7.3
Liver 0.020 5.4
Ovaries 0.030 8.1
Bladder wall 0.270 72.9
99m
Tc-sestamibi (Cardiolite) at rest Gallbladder 0.067 18.1
Upper large intestine 0.180 48.6
Lower large intestine 0.13 35.1
Heart wall 0.017 4.6
Kidneys 0.067 18.1
Ovaries 0.050 13.5
Bladder wall 0.067 18.1
131
I-sodium iodide (25% uptake) Thyroid 1300.00 3.50×10
Ovaries 0.14 37.8
Liver 0.48 129.7
5
(continued)
304
16 Internal Radiation Dosimetry
Table 16.4
(continued)
Dose
Radiopharmaceutical Organ
123
I-ioupane (DaTscan) Brain 0.066 17.8
rad/mCi mGy/GBq
Striata 0.85 230.0
Liver 0.10 27.9
Lungs 0.15 41.2
Bladder wall 0.20 53.1
Lower large intestinal
0.16 42.0
wall
123
I-sodium iodide (25% uptake) Thyroid 12.75 3445.9
Bladder 0.30 81.1
Ovaries 0.05 13.5
I-metaiodobenzylguanidine (MIBG) Adrenals 0.059 16.0
Brain 0.018 4.8
Gallbladder 0.080 22.0
Heart 0.067 18.0
Kidneys 0.039 11.0
Liver 0.270 73.0
Red marrow 0.026 7.1
Testes 0.260 7.1
131
I-metaiodobenzylguanidine (MIBG) Bladder (wall) 2.96 800.0
Liver 2.92 789.2
Spleen 2.18 589.2
Heart (wall) 1.41 381.1
Adrenal medulla 0.78 210.8
Kidneys 0.33 89.2
Ovaries 0.27 73.0
111
In-white blood cell (WBC) Spleen 26.0 7027.0
Liver 38.0 10,270.0
Red marrow 26.0 7027.0
Skeleton 7.28 1967.6
Ovaries 3.80 1027.0
111
In-pentetreotide (OctreoScan) Kidneys 1.81 488.4
Liver 0.41 110.0
Spleen 2.46 664.9
Bladder wall 1.007 272.2
Ovaries 0.16 44.1
111
In-capromab pendetide (ProstaScint) Liver 3.70 1000.0
Spleen 3.26 881.1
Kidneys 2.48 670.3
Marrow 0.86 232.4
Testes 1.12 339.0
Prostate 1.64 443.2
(continued)
16.3 Radiation Dose inSI Units
305
Table 16.4
(continued)
Dose
Radiopharmaceutical Organ
18
F-uciclovine (Axumin) Heart wall 0.19 52
rad/mCi mGy/GBq
Liver 0.12 33
Lungs 0.13 34
Pancreas 0.38 102
Marrow 0.09 25
Bladder wall 0.09 25
Uterus 0.17 45
18
F-sodium uoride Bone surface 0.15 40.0
Bladder wall 0.81 220.0
Red marrow 0.15 40.0
18
F-orbetapir (Amyvid) Upper large intestine
0.27 74.0
wall
Small intestine 0.24 66.0
Osteogenic cells 0.104 28.0
Brain 0.037 10.0
Gallbladder wall 0.53 143.0
Liver 0.24 64.0
Bladder wall 0.10 27.0
18
F-orbetaben (Neuroceq) Brain 0.05 13.0
Kidneys 0.09 24.0
Liver 0.14 39.0.0
Lower large
0.13 35.0
intestine-wall
Small intestine 0.11 31.0
Upper large
0.14 38.0
intestine-wall
Urinary bladder wall 0.26 70.0
177
Lu-Lutathera Kidneys 2.42 654.0
Liver 1.11 299.0
Spleen 3.12 846.0
Bladder wall 1.62 437.0
Osteogenic cell 0.56 151.0
Heart wall 0.12 32.0
Lungs 0.11 31.0
18
F-utemetamol (Vizamyl) Gallbladder wall 1.06 287.0
Brain 0.041 11.0
Upper large intestinal
0.433 117.0
wall
Bladder wall 0.537 145.0
Liver 0.211 57.0
Small intestinal wall 0.377 102.0
(continued)
306
16 Internal Radiation Dosimetry
Table 16.4
(continued)
Dose
Radiopharmaceutical Organ
18
F-uorodeoxyglucose (FDG) Brain 0.07 18.9
rad/mCi mGy/GBq
Heart 0.22 59.5
Bladder 0.32 86.6
Spleen 0.14 37.9
Ovaries 0.053 14.3
Uterus 0.062 16.8
82
Rb-rubidium chloride Kidneys 0.032 8.6
Heart (wall) 0.007 1.9
201
Tl-thallous chloride Heart 0.50 135.1
Kidneys 1.20 324.3
Liver 0.55 148.6
Thyroid 0.65 175.7
Testes 0.50 135.1
68
Ga-DOTATATE Adrenals 0.31 86.0
Kidneys 0.34 93.0
Liver 0.19 50.0
Spleen 0.40 109.0
Bladder wall 0.36 98.0
67
Ga-gallium citrate Liver 0.46 124.3
Marrow 0.58 156.7
Kidneys 0.41 110.8
Spleen 0.53 143.2
Upper large intestine 0.56 151.4
Lower large intestine 0.90 243.2
Gonads 0.26 70.0
153
Sm-lexidronam (Quadramet) Bone surfaces 25.000 6756.8
Red marrow 5.700 1540.0
Bladder wall 3.600 973.0
Kidneys 0.065 17.6
Ovaries 0.032 8.6
Liver 0.019 5.1
89
Sr-strontium chloride (Metastron) Bone surfaces 63.0 17,000.0
Red bone marrow 40.7 11,000.0
Lower bowel 17.4 4700.0
Bladder wall 4.8 1300.0
Ovaries 2.9 800.0
Kidneys 2.9 800.0
(continued)