photon beam transport in a voxelized human phantom model: discrete ordinates vs monte carlo r. a....
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Photon Beam Transport in a Voxelized Human Phantom Model:
Discrete Ordinates vs Monte Carlo
R. A. Lillie, D. E. Peplow, M. L. Williams, B. L. Kirk, M. P. Langer†, T. L. Nichols††, and Y. Y. Azmy†††
Oak Ridge National Laboratory†Indiana University School of Medicine††University of Tennessee Medical Center†††The Pennsylvania State University
The ANS 14th Biennial Topical Meeting of the Radiation Protection and Shielding Division, Carlsbad NM, April 3-6, 2006
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Introduction Background
NIH Proposal Assess accuracy of 3-D coupled electron-photon transport
calculations performed with existing discrete-ordinates transport codes
Establish a plan to develop a new deterministic code system optimized for voxel geometries to be used in Radiation Treatment Planning
Presentation 3-D Photon only comparisons – TORT vs EGSnrc (preliminary
study for NIH proposal) Total flux and Energy Deposition Local (point by point) and Global agreement
1-D Coupled electron-photon comparisons - ANISN vs EGSnrc and MCNP (first portion of NIH proposal)
Investigated effect of mesh size and quadrature order Did not investigate effect of Legendre Order
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Important Calculation Parameters in 3-D TORT vs EGSnrc Comparisons
Voxel size (TORT mesh size) = 4 mm
Number of voxels = 124 x 62 x 75 = 576600
All voxels contained water (densities = shifted CT number / 1000)
Number of material zones = 1991 (number of different densities)
TORT space mesh and EGSnrc geometry built from reformated CT Scan data obtained from the Department of Radiation Oncology at UNC Chapel Hill
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Important Calculation Parameters in 3-D TORT vs EGSnrc Comparisons
All TORT calculations were performed using: Fully symmetric S12 quadrature (196 directions) Optimal xyz nodal flux extrapolation in space Maximum of 20 inner iterations per group Space flux convergence criterion of 10-3 (not all groups
converged)
FSD of 0.5 % in isocenter voxel targeted in EGSnrc calculations
Photon cross sections used in TORT taken from Vitamin-B6 fine group library (ENDF/B-VI based) 40 energy groups below 12 MeV P5 scattering
Photon cross sections used in EGSnrc processed from continuous cross section data supplied with EGSnrc
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Photon Beam Parameters
Photon beam approximated by employing two point sources positioned 100 cm from CT scan isocenter Collimated component
Isotropic within solid angle subtended by 10 by 10 cm square centered at CT scan isocenter
Normalized to 0.77 photons Scattered component
Isotropic over 35.35 cm radius disc also centered at CT scan isocenter
Normalized to 0.23 photons Energy distribution derived from previously
calculated phase space data supplied by Dept. of Radiation Oncology at UNC Chapel Hill
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Photon Beam Parameters
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0 2 4 6 8 10 12 14
photon energy (MeV)
collimated
scattered
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
P3 Scattering Produces More Beam Spread than P5 Scattering and EGSnrc
Energy Deposited Sagittal Profiles
EGSnrc TORT (p3 scattering) TORT (p5 scattering)
blue: 0.1-1%, green: 1-10%, yellow: 10-50%, orange: 50-90%, and red: 90-100% of max
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Discrete Ordintates vs Monte Carlo Flux Transverse Profiles
1.E-04
1.E-03
1.E-02
10 20 30 40 50 60 70 80 90 100 110
TORT p5 full
TORT p5 2 iter
TORT p5 1 iter
TORT p3 full
TORT p3 2 iter
TORT p3 1 iter
EGSnrc
Voxel Number
Mid-plane Coronal Slice halfway between CT Isocenter and Beam Exit
TORT Calculations P5 (full) agrees very well
with EGSnrc P5 (2 iter) agrees fairly well P5 (1 iter) underestimates
flux outside beam edge P3 (full) overestimates flux
outside beam edge P3 (2 iter) better agreement P3 (1 iter) slightly better
agreement
P3 (1 and 2 iter) better agreement purely fortuitous
P5 (2 iter) agreement could result in less computational time – further study required
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Discrete Ordintates vs Monte Carlo Energy Deposited Transverse Profiles
Voxel Number
Mid-plane Coronal Slice halfwaybetween CT Isocenter and Beam Exit
1.E-07
1.E-06
1.E-05
1.E-04
10 20 30 40 50 60 70 80 90 100 110
TORT p5 full
TORT p5 2 iter
TORT p5 1 iter
TORT p3 full
TORT p3 2 iter
TORT p3 1 iter
EGSnrc
TORT Calculations (similar agreement) P5 (full) agrees very well
with EGSnrc P5 (2 iter) agrees fairly well P5 (1 iter) underestimates
energy deposited outside beam edge
P3 (full) overestimates energy deposited outside beam edge
P3 (2 iter) better agreement P3 (1 iter) slightly better
agreement
Again P3 (1 and 2 iter) better agreement purely fortuitous
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Fractional Frequency Distribution of Voxel Flux Differences in MC Standard Deviations
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
-25 -20 -15 -10 -5 0 5 10
p5 full
p5 2 iter
p5 1 iter
p3 full
p3 2 iter
p3 1 iter
MC Standard Deviations
TORT Calculations P5 (full) tightly clustered at
0 MC SD’s P5 (2 iter) clustered at -5 MC
SD’s P5 (1 iter) much larger
spread at -15 MC SD’s P3 (full) slightly less
clustered at 0 MC SD’s P3 (2 iter) slightly less
clustered at -5 MC SD’s P3 (1 iter) similar to P5 (1
iter) distribution
Small number of iters results in less scattering – therefore less particles of all energies outside beam resulting smaller total tracklengths
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Fractional Frequency Distribution of Voxel Energy Deposited Differences in MC Standard Deviations
MC Standard Deviations
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
-15 -10 -5 0 5 10 15 20 25
p5 full
p5 2 iter
p5 1 iter
p3 full
p3 2 iter
p3 1 iter
TORT Calculations P5 (full) tightly clustered at 0
MC SD’s P5 (2 iter) also tightly
clustered at -5 MC SD’s P5 (1 iter) clustered less at ~
-2 MC SD’s P3 (full) larger spread at ~ -
5 MC SD’s P3 (2 iter) similar to P3 (full) P3 (1 iter) slightly less
clustered than P3(2 iter) and P3(1 iter)
Again less scattering – however high energy particles contribute more to energy deposition thus effect of less scattering is reduced
P5 (2 iter) may be adequate ?
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Comparison of CPU Times: TORT vs EGSnrc
CPU Times Required for Discrete Ordinates and MC Calculations
Code Calculation CPU Time (minutes)
Photon Flux 88 EGSnrc Energy Deposited 5000
P3 1 iteration 23 P3 2 iteration 35 TORTa P3 fully converged 185
P5 1 iteration 62 P5 2 iteration 97 TORTa P5 fully converged 570
aIncludes GRTUNCL3D CPU times of 5 and 12 minutes for P3 and P5 calculations, respectively.
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Recent 1-D Coupled Photon-Electron Calculations
Isotropic photon source in 1 cm interval at entrance to phantom
ANISN photon cross sections 40 group P5 Vitamin-B6 (same as used in TORT) 40 group P15 (same group structure as Vitamin-B6) generated by
CEPXS Both sets of photon cross sections produced similar results
ANISN electron cross sections 40 group (linear energy grid) P15 from CEPXS-BFP (Russian
modified version of CEPXS) Original CEPXS – smooth component of scattering adjusted using
diamond difference approximation on CSD term to relate group boundary fluxes and group fluxes (as expected ANISN would not run with these cross sections)
Modified CEPXS (CEPXS-BFP) – smooth component adjusting using double 2-step approximation to relate fluxes
Photon and electron cross sections used in EGSnrc and MCNP processed from continuous cross section data supplied with both codes
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Position of Voxels used in 1-D Model indicated on CT Images
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
1-D Model Density as a Function of Depth
10 20 30 40 50 60
Voxel Number
0.10
0.30
0.50
0.70
0.90
1.10W
ater
Den
sity
(g
/cm
3)
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Comparison of 1-D Calculated Total Photon Flux vs Depth in Phantom
10 20 30 40 50 60
Voxel Number (4mm thick voxels)
100
8
9
2
3
4
5
6
7
To
tal
Ph
oto
n F
lux
(cm
-2 s-1
)
EGSnrcMCNPANISN S16-4mm
Large differences in first 7 voxels is artificial and due to low density (void)
MCNP and EGSnrc total photon fluxes are almost identical
ANISN total photon flux approximately 4 percent lower in all non void voxels ANISN calculated same
total photon fluxes using both Vitamin-B6 and CEPXS cross sections
Reason for 4 % difference not known (under investigation)
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Comparison of 1-D Calculated Total Electron Flux vs Depth in Phantom
10 20 30 40 50 60
Voxel Number (4 mm thick voxels)
10-1
3
4
5
6
7
8
9
To
tal
Ele
ctro
n F
lux
(cm
-2 s-1
) EGSnrcMCNPANISN S16-4mm
Again large differences in first 7 voxels is artificial and due to low density
EGSnrc total electron flux is approximately 5 % lower than MCNP total electron flux in non void voxels Reason for difference is
unknown
ANISN total electron flux lies between MCNP and EGSnrc values - closer to MCNP except around voxels 37 and 56
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Mesh Size has Little Effect on ANISN Calculated Total Electron Flux
30 40 50 60
Voxel Number (4 mm thick voxels)
3
4
5
To
tal
Ele
ctro
n F
lux
(cm
-2 s-1
)
EGSNRCMCNPANISN S!6-4mmANISN S16-2mmANISN S16-1mm
Reduce mesh from 4 mm to 2 mm to 1 mm since Density in voxels 35 – 40
approximately 4 times higher than surrounding voxels
Density in voxels 56 - 60 approximately 10 times higher than surrounding voxels
Decreasing mesh size Improves agreement with
MCNP around voxel 56 Produces little change
around voxel 37 Similar changes occur
using S32 and S64 quadratures
Overall effect minimal
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Higher Order Quadratures Improve ANISN Total Electron Flux
30 40 50 60
Voxel Number (4 mm thick voxels)
3
4
5
To
tal
Ele
ctro
n F
lux
(cm
-2 s-1
)
EGSnrcMCNPANISN S!6-4mmANISN S32-4mmANISN S64-4mm
ANISN total electron flux agrees very well with MCNP total electron flux with S32 and S64 quadratures Very little difference between
S32 and S64 quadratures S20 (next higher order
quadrature above S16) also improved agreement with MCNP
Although not shown, agreement with MCNP also improves between voxels 15 and 27
Note: All the ANISN results were obtained using double Pl quadratures – similar results were obtained using fully symmetric quadratures
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Closing Remarks
Photon Only Calculations 3-D deterministic transport codes (TORT)
can yield accurate dose distributions in anatomical voxel based models when compared to MC codes
with less computational cost (than MC codes), and possibly much less cost if few collisions are required
Coupled Electron-Photon Calculations 1-D deterministic transport codes (ANISN) using currently
available cross sections can yield reasonable agreement with MC codes with significantly less computational cost
Further Effort Investigate photon discrepancy between ANISN and MC codes
(possibly due to poor choice of model) Investigate electron flux MC discrepancies (MCNP vs EGSnrc) –
MC calculated energy deposited agreed very well Similar couple electron-photon calculation with TORT (1-D, 2-D,
and 3-D)
Boltzmann-Fokker-Planck equation needed ?