Internal%20Radiation%20Dosimetry

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Internal Radiation Dosimetry
J.D. Kalen, Ph.D.
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Radiation Dose (Quantities and Units)

• Radiation Dose (D)
• The quantity of radiation energy deposited in an
  absorber/gm of absorber material
• Units rad radiation absorbed dose
• 1 rad 100 ergs deposited/gm of absorber
• SI units gray (Gy) 1 Gy 1 joule/kg absorber
• note 1 joule 107 ergs 1Gy 100 rads

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Calculation of Radiation Dose(Absorbed Fraction
Method)
3 Step Process 1) Amount of activity and time
within the source organ 2) Amount of radiation
emitted from the source organ energy and
emission frequency dependent 3) Fraction of
energy absorbed by the target organ
dependent on a) characteristics of organ
(tissue) b) positional relationship of
source to target.
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Calculation of Radiation DoseCumulative
Activity (A)

Cumulative Activity The amount of radiation
delivered to the organ and the length of
time the activity is present within the
organ. Units(mCi-hr)
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A ? A(t) dt
A(t)
Activity (mCi)
0
time activity curve
time (hr)
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Cumulative Activity (A)

• Four situations
• Instantaneous uptake with physical decay
• 90Y Microspheres (Unresectable Hepatocellular
  Carcinoma)
• Instantaneous uptake with clearance by biologic
  excretion.
• Radionuclide T1/2 gtgt Biologic T1/2
• Instantaneous uptake with clearance by biologic
  excretion and physical decay.
• 131I (Hyperthyroidism and Thyroid Cancer)
• 90Y (Zevalin) and 131I (Bexxar)
  radioimmunotherapy
• Non-instantaneous uptake with clearance by
  biologic excretion and physical decay.

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Cumulative Activity (A)
Situation 1 Instantaneous uptake no biologic
excretion (Unresectable Hepatocellular
Carcinoma) i.e. 90Y Microspheres

• MicroSphere Properties
• Glass sphere diameter 20-30 mm
• Trapped in the vasculature
• 1 mg contains ? 22,000 73,000 spheres

• 90Y Properties
• Pure ß- emitter
• Decays to 90Zr
• T1/2 (hr) 64.1
• Eß ave (MeV) 0.9348 Range (mm) 4

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Cumulative Activity (A)
Situation 1 Instantaneous uptake no biologic
excretion
A(t) A0 exp(-0.693t/Tp)
Activity (mCi)
Tp physical half-life of radionuclide A0
initial activity present in organ
time (hr)

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?
A A0 exp(-0.693t/Tp )dt
Semi-log
0
Activity (mCi)
A TpA0 1.44(A0Tp) 0.693
time (hr)
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Cumulative Activity
Trap vs Shunt to Lungs inject 4 mCi of 99mTc MAA
Shunt (F) Lungs/(Lungs Liver) x 100
10
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Cumulative Activity (A)
Situation 1 Example (90Y Unresectable
Hepatocellular Carcinoma) 90 retention in
Liver (1-F) 10 shunting to the Lung (F)
A(Liver) 1.44(Tp)(1-F)(A0)
1.44(64.16 hr)(0.9)A0(?Ci)


A(Lung) 1.44(Tp)(F)(A0) 1.44(64.16
hr)(0.1)A0 (?Ci)
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Cumulative Activity
Situation 2 Instantaneous uptake biologic
excretion
no physical decay, or Tp (1/2) gtgt biologic
excretion i.e. 131I (8.04 days) gtgt Tb ( few hrs)
Decay fraction (lt 5)
Tb1
Semi-log
f1
Tb2
f2
Activity
Tb3
f3
time

A 1.44 Tb1 f1 A0 1.44 Tb2 f2 A0 1.44 Tb3
f3 A0
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Cumulative Activity
Situation 3 Instantaneous uptake
Clearance by biologic and Physical decay
Determine effective T1/2
Effective T1/2 Te
1
Te Tp Tb
1 1

Te Tp Tb
Tp Tb

A 1.44(Te)(A0)
note Te is always shorter than Tp and Tb
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Cumulative Activity
Situation 3 Instantaneous uptake
131I (Hyperthyroidism)
131I Tp (days) 8.04 Tb (days) 13.22
Te Tp Tb
5 days
Tp Tb

A 1.44(Te)(A0)
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Cumulative Activity
Situation 3 Uptake is NOT Instantaneous
significant amount of physical decay
occurs during uptake
process.
A(t) A0(1-e-0.693t/T(u,e))
Activity

A 1.44 Ao Te Tue
Tu
Tue effective uptake Tu uptake half-life Te
effective excretion
time
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Equilibrium Absorbed Dose Constant (D)
Step 2 Determine amount of radiation emitted
by source organ
g-rad
Di 2.13 Ni Ei
mCi-hr
Ei ave. energy (MeV) of the ith emission
Ni emitted per disintegration
Dtotal Si Di D1 D2 Dn
Dtotal is obtained from tables
the energy emitted per nuclear disintegration
1 MeV/dis 2.13 g-rad/(mCi-hr)
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Equilibrium Absorbed Dose Constant (D)
Step 2 Example (90Y) 90Y emits b particles
100 of its disintegrations
with E b ave 0.9348 MeV.
Di 2.13 Ni Ei
Dtotal Si Di Dß
g-rad
Dtotal Db 2.13 (1.0) 0.9348 1.99
mCi-hr
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Equilibrium Absorbed Dose Constant (D)
Emission Eave (MeV) Emission Rate
ß1 0.069 2.13
ß4 0.192 89.4
?14 0.364 81.2
?7 0.284 6.06
?17 0.637 7.27
Step 2 Example (131I) 131I emits b, ? particles
Di 2.13 Ni Ei
Dtotal Si Di Dß1 D ß2 D ßn D?1 D?2
D?n
Db1 2.13 (0.0213) 0.069 0.003 Db4 2.13
(0.894) 0.192 0.365 Dg14 2.13 (0.812) 0.364
0.629 Dg7 2.13 (0.0606) 0.284 0.036 Dg17
2.13 (0.0727) 0.637 0.098
g-rad
1.133
mCi-hr
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Equilibrium Absorbed Dose Constant (D)
Step 2 Example
g-rad
Dtotal
mCi-hr

A is the cumulated activity (mCi-hr)
D is the total energy emitted per mCi-hr

A x D total energy emitted (g-rad) or
(ergs) 1 g-rad 1 erg
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Absorbed Fraction (f)
Step 3 Determine 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) A Si fi Di
Average absorbed Dose (rad) A Si fi Di

mt
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Average Absorbed Dose (D)
Average absorbed Dose (rad) A 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
f is complicated for energies gt 10 keV
(penetrating g-rays) f lt 10 keV (non-penetrating
radiation b, x-rays)
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Average Absorbed Dose (D)
Energies lt 10 keV (non-penetrating radiation)
f 0 for (penetrating radiation) f 1 for
(non-penetrating radiation) source and
target organs are the same radiation is
locally absorbed within the source organ

Average absorbed Dose (rad) A Si fi Di
mt
f 1

ltDgt (rad) A Si Dnp
mt
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Average Absorbed Dose (D)
Example (non-penetrating radiation) Compute
absorbed dose delivered to the Liver.
90Y emits b particles 100 of its
disintegrations with Eb ave 0.9348 MeV.
Di 2.13 Ni Ei
Dtotal Si Di Dß Dnp
g-rad
Dtotal Db 2.13 (1.0) 0.9348 1.99
mCi-hr
Dtotal Db1.6x10-13 NiEi
kg-Gy
Bq-Sec
1.49x10-13
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Average Absorbed Dose (D)
Example (non-penetrating radiation)
90Y Compute absorbed dose delivered to the
Liver.
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Average Absorbed Dose (D)
Example (non-penetrating radiation) 90Y Compute
Activity to be delivered based on Dose to the
Organ.
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Average Absorbed Dose (D)
Example (non-penetrating radiation) 131I
Emission Eave (MeV) Emission Rate
ß1 0.069 2.13
ß4 0.192 89.4
?14 0.364 81.2
?7 0.284 6.06
?17 0.637 7.27
Di 2.13 Ni Ei
Dtotal Si Di Dß1 D ß2 D ßn D?1 D?2
D?n
Db1 2.13 (0.0213) 0.069 0.003 Db4 2.13
(0.894) 0.192 0.365 Dg14 2.13 (0.812) 0.364
0.629 Dg7 2.13 (0.0606) 0.284 0.036 Dg17
2.13 (0.0727) 0.637 0.098
1.133
Dt
g-rad
mCi-hr
Dnp
0.368
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Mean Dose per Cumulated Activity (S)
for penetrating radiation ?-rays
Average absorbed Dose (rad) A Si fi Di

mt
Non-penetrating radiation fi1 Source and target
organs same
Penetrating radiation fi0 Source and target
organs Different
Source/ Target
target
target
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Mean Dose per Cumulated Activity (S)
for penetrating radiation ?-rays
S 1 Si fi Di
rad
mCi-hr
mt
F f
specific absorbed fraction
mt
S Si Fi Di
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Average Dose to an Organ (D)
_

D A x S

A Cumulative Activity (mCi-hr) (calculate)
S Mean dose per cumulated Activity (rad/
mCi-hr) (look-up table)
D Average dose (rad)
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Mean Dose per Cumulated Activity (S)
Source Organs
S(rad/ mCi-hr) for I131
Target Organs
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123I Whole Body Scan
Source
Target
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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.
Assume instantaneous uptake (Tu ltlt Tp 8 days).
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Average Dose to an Organ (D)
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
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Average Dose to an Organ (D)
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.
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Thyroid Mass
Collimator Pinhole Matrix 128 x 128 Calibrate
Pixel 0.06 cm2/pixel ROI 405 pixels Mass (
pixels)(Pixel Cal)1.26(0.86) Mass 48 g
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Internal Dosimetry
Isotope 131I Thyroid Uptake 60 A0
1,000 ?Ci T1/2 eff 5 days Thyroid Mass
48 g

• MIRD
• D A x S
• A 1.44 x Ag (?Ci) x T1/2(hr)
• S (1/mnorm) ??i ?I (g-rad /?Ci-hr)
• Mnorm 20 g

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Internal Dosimetry
Isotope 131I Thyroid Uptake 60 A0
1,000 ?Ci T1/2 eff 5 days Thyroid Mass
48 g

• MIRD
• D A x S
• A 1.44 x Ag (?Ci) x T1/2(hr)
• A 103,680 (?Ci-hr)
• S (1/mnorm) ??i ?I (g-rad/?Ci-hr)
• S 0.022 g-rad/?Ci-hr
• D 2,280.9 rad (Mnorm 20 g)
• D A x S x (20/48)
• D 950 rad/?Ci administered
• note 1 rad 1 rem in tissue
• D 950 rem/?Ci administered

• Dose (rem) Dose (rad) x RBE
• RBE relative biologic effectiveness effect of
  different radiation on biologic material.
• RBE (?, ?, x-ray) 1 RBE (?) 20

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Internal Dosimetry

• MIRD
• D A x S
• A 1.44 x Ag (?Ci) x T1/2(hr)
• S (1/mnorm) ??i ?I (g-rad/?Ci-hr)
• S 0.022 g-rad/?Ci-hr
• D A x S x (20/Measured Thyroid Mass)

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Internal Dosimetry

• MIRD
• D A x S
• S 0.022 g-rad/?Ci-hr
• D (A0)(1.44)( Uptake)(Teff)(S)(20g/Measured
  Thyroid Mass)

Uptake Probe
Image Pinhole
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Internal Dosimetry
Dose Diffuse Goiter 10,000 rad Uni-nodular
Goiter 25,000 rad Multi-nodular Goiter 15,000
rad Ablate 30,000 rad
A0(?Ci) (D rads)(Measured Thyroid Mass/20g)
(1.44)( Uptake)(Teff hrs)(0.022
g-rad/?Ci-hr)
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Average Dose to an Organ (D)
Example Calculate the radiation dose to the
Liver for an injection of 3 mCi
of 99mTc sulfur colloid. Assume
60 of the activity is trapped by the liver, 30
by the spleen, and 10 by the red
bone marrow, with instantaneous
uptake and no biologic excretion.

A 1.44(Tp)(A0)

ALIVER 1.44 (6 hr)(0.6)(3,000 mCi) 15,600
mCi-hr

Aspleen 1.44 (6 hr)(0.3)(3,000 mCi) 7,780
mCi-hr

Arbm 1.44 (6 hr)(0.1)(3,000 mCi) 2,590 mCi-hr
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Average Dose to an Organ (D)
S Values S(Liver Liver) 4.6 x 10-5
rad/mCi-hr S(Liver Spleen)
9.8 x 10-7 rad/mCi-hr S(Liver
RBM) 9.2 x 10-7 rad/mCi-hr

D A x S
D(Liver Liver) (15,600 mCi-hr) x (4.6 x
10-5 rad/mCi-hr)
D(Liver Spleen) (7,780 mCi-hr) x (9.8 x
10-7 rad/mCi-hr)
D(Liver RBM) (2,590 mCi-hr) x (9.2 x 10-7
rad/mCi-hr)
D(total) 0.718 0.0076 0.0024
0.728 rad
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Comparisons
Tc99m Inject 5,000 uCi T1/2 6.03 hr A 1.44 A0
Tp 43,416 uCi-hr
I131 Inject 100 uCi T1/2 8 days A 1.44 A0 Tp
27,648 uCi-hr
I123 Inject 300 uCi T1/2 13.2 hr A 1.44 A0
Tp 5,702 uCi-hr
Activity (uCi)
Time (hr)
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Comparisons
Tc99m
I131
Source Organs
Source Organs
Target Organs
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Comparisons
Radionuclide Tc99m l131 l123
Injection (mCi) 5 0.1 0.3
Physical Half-life (hr) 6.03 192 13.2
E? (keV) 140 364 159
Cumulative Activity (?Ci-hr) 43,416 27,648 5,702
S-Factor (rad/?Ci-hr) 2.3 x 10-3 2.2 x 10-2 3.86 x 10-3
Dose (rad) A x S 100 608 22
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Cumulative Activity Comparison

A 1.44 Ao Te Tue 1.44 Ao Te TuTp 1.44
Ao TeTp
Tu(T uT p)
Tu
(T uT p)
Tue Tu Tp
Tu Tp
Activity
Tue effective uptake Tu uptake half-life Te
effective excretion
time
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Cumulative Activity
Example A radioactive (10 mCi) gas Tp(1/2) (20
sec) is injected in an intravenous
solution. The lung uptake is
Tu (30 sec) and is excreted (by exhalation) with
a biologic Tb(1/2) (10 sec).
Effective Uptake Tue Tu Tp 30(20) 12
sec.
Tu Tp
30 20
Effective Excretion Te Te Tp 10(20)
6.7 sec.
10 20
Te Tp
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Cumulative Activity
Situation 3 Example Te 6.7 sec Tue 12
sec Tu 30 sec

A 1.44 Ao Te Tue
1.44 (10 mCi) 6.7 sec (12 sec)
Tu
30 sec
38.6 mCi-sec 10.7 mCi-hr
26.8 mCi-hr (Instantaneous Uptake)
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Cumulative Activity Comparison

A 1.44 Ao TeTp
(T uT p)
26.8 mCi-hr
D(rad) 2.5 x D(non-instantaneous uptake)
Activity
10.7 mCi-hr
time
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Medical Internal Radiation Dose

• MIRD Limitations
• Activity is uniformly distributed within a
  standard size organ
• Absorbed Fraction f is based on standard models
  of human anatomy.
• Calculation of Cumulated activity.
• First based on animal studies
• Different between disease states uptake and decay

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Medical Internal Radiation Dose

• MIRD
• New techniques are developed
• Actual distribution of activity is becoming
  available
• Easy to implement

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MIRD-Summary
Organ-specific
Length of time and the amount of the
radiopharmaceutical is within the organ. Obtained
using Nuclear Medicine Techniques.
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Radioimmunotherapy
J.D. Kalen, Ph.D.
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Non-Hodgkin's Lymphoma

• Systemic Radiation Treatment
• Monoclonal Antibodies (MAb)
• Located on the surface of malignant and normal B
  lymphocytes is the antigen CD20.
• Develop an antibody that binds with high affinity
  and specificity to the CD20 antigen.
• Bind a radionuclide (beta emitter) to the MAb.

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Non-Hodgkin's Lymphoma

• Radionuclide Selection
• Physical and Chemical properties
• Production methods
• High specific activity
• Biological behavior
• Disassociation of radionuclide from MAb

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Radiopharmaceutical Selection

• Match the Tb of the radiopharmaceutical with Tp
  of the radionuclide maximizes the benefit of
  Radioimmunotherapy
• Long Tb require long lived radionuclides
• Short Tb require short lived radionuclides

Tb
Activity
Tp
Time (hr)
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Non-Hodgkin's Lymphoma

• Radionuclide Selection
• 131I-Tositumomab Bexxar (GlaxoSmithKline)
• Direct coupling to the MAb-iodination
• 90Y-Ibritumomab Tiuxetan Zevalin (Biogen Idec,
  Inc.)
• Indirect coupling to the MAb chelator (Tiuxetan)
• Antibody Ibritumomab

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Beta-Particle Emitters
192 h
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131I-Tositumomab (Bexxar)

• Whole-Body Dosimetry Assumptions
• Hematologic toxicity limits the amount of
  radioactivity that may be administered.
• Red marrow absorbed dose
• Difficult to measure
• Requires repeated blood sampling over time
• Can be determined from scans, but difficult to
  accurately measure.

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Dosimetry
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131I Tositumomab (Bexxar)

• Whole-Body Dosimetry
• S ? Gender Mass ? Activity-Hours Look-up table
  
• Total Body Residence Time Determined by Imaging
• Platelet counts- Determined in Phase I studies
• 65 cGy (100,000 to lt 150,000 platelets/mm3)
• 75 cGy ( 150,000 platelets/mm3)

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WB Cumulative Activity (Act-Hr)
Cumulative Activity The amount of radiation and
the length of time the activity is present
within the whole body. Units(mCi-hr)
Assume 1. Uniform homogenous distribution 2.
Patient can be modeled as an ellipsoid 3.
Determine S values for various masses
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Total Body Residence Time (TBRT)

• TBRT is directly correlated with the effective
  T1/2 (clearance rate) of 131I-Tositumomab within
  the WHOLE-BODY.

75 cGy
Treatment Dose (mCi)
Treatment Dose (mCi)
75 cGy
time (hr)
time (hr)
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Residence Time
Day 0 Dose Patient 5 mCi 131I-Tositumomab Perfo
rm WB scan Obtain Ant and Post WB
counts Geometric Mean and subtract background!
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Calculate Injected Activity
Day 0
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Residence Time
Day 3 Perform WB scan Obtain Ant and Post WB
counts Remember to subtract background!
71.1
Calculate Injected Activity
Day 3
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Residence Time
Day 6 Perform WB scan Obtain Ant and Post WB
counts Remember to subtract background!
20.7
Calculate Injected Activity
Day 6
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131I Bexxar- Tositumomab
Day 0
Day 3
Day 6
Diagnostic Dose
Therapeutic Dose
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Residence Time (Hr)
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Total Body Residence Time (Hr)
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131I-Tositumomab (Bexxar)

• Dosimetry

Based on Platelets
Look-up table Gender/weight
Based on WB scans
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Non-Hodgkin Lymphoma

• 131I-Tositumomab Bexxar
• Multiple Dx scans To determine Whole-Body
  Residence Time
• ß-,? emitter
• Must block thyroid uptake
• Need to reduce radiation to the public
• 90Y-Ibritumomab Tiuxetan Zevalin
• One Dx scan 111In-Ibritumomab Tiuxetan scan to
  determine distribution
• Pure ß- emitter
• 90Y uptake into bone difficult to block
• Low or no radiation to the public

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Radionuclide Comparison
Radionuclide Tp (1/2) (days) A (Bq-hr) (per 37 kBq admin) D (np) (g Gy Bq-1 Hr-1) D (Gy) (per gm)
131I 8 10,229,760 0.109 1.12x106
90Y 2.7 3,452,544 0.539 1.86x106
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D (rad) A x S
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The curability of tumours of differing size by
targeted radiotherapy using 131I or 90Y T. E.
Wheldon, J. A. O'Donoghue, A. Barrette and A. S.
Michalowski Radiotherapy and Oncology Volume
21, Issue 2 , June 1991, Pages 91-99
Abstract The analysis implies that an
advantage might result from the use of a panel of
several radionuclides (including short-range
emitters) or from combining targeted radiotherapy
using long-range-emitters with external beam
irradiation or some other modality to which
microscopic tumours are preferentially
vulnerable.
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Bexxar or Zevalin?
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It DEPENDS!
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Radioimmunotherapy

• MAb Issues
• Radiolysis
• Nuclide cleaves off of the MAb
• Radionuclide distribution different than MAb

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Future Nano-Platforms