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 14photon 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 iterTORT p3 full

TORT p3 2 iter

TORT p3 1 iterEGSnrc

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 fullTORT p5 2 iterTORT p5 1 iterTORT p3 fullTORT p3 2 iter

TORT p3 1 iterEGSnrc

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 iterp5 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 60Voxel Number

0.10

0.30

0.50

0.70

0.90

1.10W

ater

Den

sity

(g/c

m3 )

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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 60Voxel Number (4mm thick voxels)

100

8

9

2

3

4

5

6

7

Tota

l Pho

ton

Flux

(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 60Voxel Number (4 mm thick voxels)

10-1

3

4

5

6

7

8

9

Tota

l Ele

ctro

n Fl

ux (c

m-2

s-1) EGSnrc

MCNPANISN 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 60Voxel Number (4 mm thick voxels)

3

4

5

Tota

l Ele

ctro

n Fl

ux (c

m-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 60Voxel Number (4 mm thick voxels)

3

4

5

Tota

l Ele

ctro

n Fl

ux (c

m-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 ?