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Michael B. Wayson
November 10, 2010
The University of Florida
Department of Nuclear and Radiological Engineering
The United States of America
IAEA IDOS Symposium
Vienna, Austria
Photon and electron specific absorbed fractions for the University of Florida
paediatric hybrid computational phantoms
Outline
IntroductionComputational dosimetry
Internal dosimetry formalism
Materials and MethodsPhoton specific absorbed fractions (SAFs)
Electron SAFs
ResultsPhoton SAFs
Electron SAFs
Conclusion
The University of Florida -
Department of Nuclear and Radiological Engineering
Introduction
Computational dosimetryUse of virtual representations of humans in conjunction with radiation transport codes
“Quick” dose estimation
Accurate and detailed
Logistically feasible
Measures of interestAbsorbed fraction (AF)
Unitless
Specific absorbed fraction (SAF)Units of kg-1
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Department of Nuclear and Radiological Engineering
sourceby emittedEnergy by target absorbedEnergy )( =← ST rrAF
T
STST m
rrAFrrSAF )()( ←=←
Introduction
MIRD Pamphlet No. 21 internal dosimetry formalism
( ) ( ) ( ) ( ) ( )∑∑ ∫ ←=←⎥⎦⎤
⎢⎣⎡=
∞
SS rSTS
rSTST rrSrArrSdttrArD ~,
0
( ) ( ) ( )∑∑ ←ΦΔ=←
=←i
STii T
STiiST rr
mrrYE
rrSφ
( )srA~
( )ST rrS ←
iE
iY
( )ST rr ←φ
iΔ
( )ST rr ←Φ= number of decays occurring in rS
= radionuclide S value (mGy/MBq s)
= energy of the ith
radiation
(MeV)
= yield of the ith
radiation
= delta value for the ith
radiation (MeV/decay)
= AF for rS
irradiating rT
= SAF for rS
irradiating rT
(g-1)
The University of Florida -
Department of Nuclear and Radiological Engineering
Photon SAFs
Monte Carlo N-Particle eXtended (MCNPX), Version 2.6
Phantom preparation – VoxelizationThree-dimensional continuous surface geometry converted to a three-dimensional matrix of voxels (rectangular prisms)
In-house MATLABTM code (Choonsik Lee, Ph.D.) to voxelize
Desired voxel dimensions equal to the skin thickness of the phantom of interest (ideally isotropic)
Skin added with in-house MATLABTM code (replaces outermost voxels with skin voxels)
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Department of Nuclear and Radiological Engineering
Photon SAFs
Figure 1. (A) Axial, (B) coronal, and (C) sagittal views of the UFH00F phantom voxelized at an isotropic resolution of 0.663 mm.
(A) (B) (C)
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Department of Nuclear and Radiological Engineering
Photon SAFs
Reading phantom geometry into MCNPXLattice file
In-house MATLABTM code to generate
Communicates to MCNPX the organ tags associated with each voxel
Creating internal sourceSource file
In-house MATLABTM code to generate
Defines source organ voxel coordinates
Defines sampling probability
For most organs, sp = 1
For active marrow and trabecular bone, sp ≠ 1AM and TB not explicitly modeled in NURBS/voxel phantom
Utilize skeletal AM and TB volume distribution for sampling probabilities
55 unique source organs for each phantom
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Department of Nuclear and Radiological Engineering
Photon SAFs
21 photon energies ranging from from 10 keV to 4 MeVNumber of histories selected according to initial photon energy (based on experience)Tallies
General OrgansEnergy deposition averaged over target cell – Thick-target bremsstrahlung model
10 keV ≤ E ≤ 100 keVUnits of MeV/g
Total energy deposition in target cell100 keV < E ≤ 4 MeVUnits of MeV
Spongiosa (for skeletal targets)Volume-averaged photon fluence
10 keV ≤ E ≤ 4 MeVGeneral organ SAFs
SAFTTB = tallyTTB / Ephoton
SAFE-dep = tallyE-dep / (Ephoton mT)
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Department of Nuclear and Radiological Engineering
Photon SAFs
Figure 2. (A) Hand, (B) right humerus, (C) pelvis, and (D) L-spine of the UFH00MF skeleton.
(A) (B) (C) (D)
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Department of Nuclear and Radiological Engineering
Photon SAFs
Skeletal target SAFs (skeletal averaged dose)
( ) ( )( ) ( )∑ ∑ ←Φ⎥
⎦
⎤⎢⎣
⎡Φ
=←j i
isi
TTST Erj
ErDw
EkrrSAF
j,
0
jTw( )is Erj ,←Φ
k
= 6.24142 x 1013
(cm2
MeV kg) / (m2
J g)
E0 = initial monoenergetic photon energy (MeV)
= mass fraction of target tissue T
in each bone site j
= fluence incident on spongiosa of each bone site j
for
photons of energy Ei
(photons / cm2
/ history)
Ei = upper energy bin boundary for fluence tally and DRF (MeV)
( ) ( )iT ErD Φ = skeletal photon DRF (Gy m2
/ photon)
The University of Florida -
Department of Nuclear and Radiological Engineering
Electron SAFs
Novel method for minimizing poor statistics anticipated for cross-organ dose from bremsstrahlung photons
Spectrum of energies with many low energy photonsNumber of photons emitted is less than the number of starting electron historiesPTRAC file
In lieu of conventional talliesTracks many parameters for event of interest (e.g. source, bank, collision …)
Type of interactionCell of interactionX-, Y-, and Z-coordinatesU-, V-, and W-cosinesWeightEnergyTimeOther parameters
Assume bremsstrahlung emission is isotropic
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Department of Nuclear and Radiological Engineering
Electron SAFs
Low error photon SAFs already calculated
Bremsstrahlung photons are still photons!
Weight energy spectrum of bremsstrahlung photons by previously calculated photon SAFs
The University of Florida -
Department of Nuclear and Radiological Engineering
Reliable cross-organ photon-attributed dose from primary electron sources
Reliable cross-organ photon-attributed dose from primary electron sources
Electron SAFs
( ) ( )T
STSWSTSW m
rrAFrrSAF
←=←
( )( )
( )electronelectron
o
i
photoni
photoniST
Eelectronelectron
Ephotonphotonphoton
ST
electronsemitted
photonsdeposited
STSW
NE
EErrAF
dEEn
dEEnErrAF
EE
rrAF electron
photon
⋅
⋅←=
⋅←==←
∑
∫
∫
;
)(
)(;
max
max
0
0
( )( )
electronelectrono
i
photoni
photoniST
STSW NE
EErrSAFrrSAF
⋅
⋅←=←∑ ;
The University of Florida -
Department of Nuclear and Radiological Engineering
Electron SAFs
Deviations from photon transport methodsTTB and fluence tallies not used, only E-depositionTwo separate simulations for each source organ
Simulation 1Primary electrons onlySame number of histories as used in photon transportE-deposition tallies for primary electron energy deposition
Simulation 2Coupled photon/electron transportNPS set to 105
No tallies used
Obtaining SAFs from tally dataSAFe-only = tallyE-dep / (Eelectron mT)SAFtotal = SAFe-only + SAFSW
The University of Florida -
Department of Nuclear and Radiological Engineering
Results –
Photon SAFs
Raw photon SAFs computed for the UFH00M and UFH00F phantoms
Reciprocity theorem
Adjoint Monte Carlo performed for UF00M phantom
Average MCNP uncertainty ~1% to 5% across all energies (most <<1%)
Variance reduction conditions and actionsSAFfinal = 0 at low initial photon energies
SAFfinal is log-linearly back-extrapolated to E = 10 keV
All target organsєadjoint < єforward at E = 4 MeV
SAFforward is replaced by SAFadjoint
Otherwise, SAFforward is retained
SAFfinal still displays poor behaviorSmoothing done subjectively by hand based on known shapes of the SAF curves
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Department of Nuclear and Radiological Engineering
)()( TSST rrSAFrrSAF ←=←
Figure 3. Variance reduction techniques for the case where (A) adjoint MC is performed and SAF = 0 at low photon energies and where (B) SAF presents poor statistics after variance reduction and manual
smoothing is performed. E
indicates back-extrapolation, and S
indicates subjective smoothing.
(A) (B)
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Department of Nuclear and Radiological Engineering
Figure 4. Photon SAFs for a uniform liver source in the UFH00M phantom before
variance reduction.
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Department of Nuclear and Radiological Engineering
Figure 5. Photon SAFs for a uniform liver source in the UFH00M phantom after variance reduction.
The University of Florida -
Department of Nuclear and Radiological Engineering
Results –
Electron SAFs
Raw electron SAFs computed for the UFH00M liver source using full photon and electron transport
Separate “electron only” and “spectrum generation” simulations performed for the same source organ and phantom
Full transport uncertainties at E = 4 MeVє < 1% – 17 target organs
1% < є < 5% – 7 target organs
5% < є < 10% – 3 target organs
10% < є – 10 target organs
The University of Florida -
Department of Nuclear and Radiological Engineering
Figure 6. Full photon/electron transport versus bremsstrahlung spectrum weighting for a uniform electron source in the UFH00M phantom.
The University of Florida -
Department of Nuclear and Radiological Engineering
Figure 7. Electron SAFs for a uniform liver source in the UFH00M phantom using full photon/electron transport (no bremsstrahlung spectrum weighting).
The University of Florida -
Department of Nuclear and Radiological Engineering
Figure 8. Electron SAFs for a uniform liver source in the UFH00M phantom using full using bremsstrahlung spectrum weighting.
The University of Florida -
Department of Nuclear and Radiological Engineering
Conclusion
Detailed hybrid computational phantoms
Improved skeletal dosimetry
Complete sets of photon and electron SAFs for the UF newborn male and female, 1-year-old male and female, 5-year-old male and female, 10-year-old male and female, and 15-year-old male and female hybrid computational phantoms
Results for the UF adult male and female produced at the National Cancer Institute
ApplicationsRadiopharmaceutical therapy
Administered activity optimization
Low-dose risk assessment
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The University of Florida -
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The University of Florida -
Department of Nuclear and Radiological Engineering
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—. Basic Anatomical and Physiological Data for Use in Radiological Protection: Reference Values.
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(submitted, 2010).
Lee, C. "Voxelizer, version 6: A Matlab Code." Gainesville, FL: University of Florida, 2008.
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52 (2007): 3309-3333.
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Internal Electron Sources." Physics in Medicine and Biology
55, no. 7 (2010): 1785-1814.
Pafundi, D, et al. "An Image-Based Skeletal Tissue Model for the ICRP Reference Newborn." Physics in Medicine and Biology
54, no. 14 (2009): 4497-4531.
The University of Florida -
Department of Nuclear and Radiological Engineering
Shah, A P, W E Bolch, D A Rajon, P W Patton, and D W Jokisch. "A
Paired-Image Radiation Transport Model for Skeletal Dosimetry." Journal of Nuclear Medicine
46, no. 2 (2005): 344-353.
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Department of Nuclear and Radiological Engineering
QUESTIONS?QUESTIONS?
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Department of Nuclear and Radiological Engineering