1. Woong Cho tarotblue@gmail.com
11 of February, 2014
Principle of convolution/superposition algorithm for dose calculation for Treatment Planning System
Woong Cho

2. What is RTP System? Radiation Treatment Planning System
Eclipse, Pinnacle, RayStation, Xio ….
CorePlan (?)
Determining treatment parameters to deliver acceptable radiation dose to the patient
Contouring
Treatment simulation (planning)
Dose calculation
Evaluation of plans

3. Architecture of general RTP System
RTP Main Module
Patient DB
ETC module
Study information
Images(CT, MRI…)
Planning Data
Dose Data
Patient Data I/O
3D Visual rendering
Contouring
Planning GUI
Dose calculation
Planning result analysis
DVH calculator
Isodose generator
NTCP/TCP calculator
Beam Data DB
Linac geometry info
Dosimetric Data
PDD data
Profile data
Output factor
Wedge/MLC info
CT HU-density table
ETC…
Kernel table (hidden)
Commissioning module
RTP commissioning
Data I/O interface
Spectrum optimization
Source modeling optimization
Determine output factor: value/MU, cGy/MU
Wedge shape…
Dose calc Engine
Photon Dose calculation
- ETAR , CCC, AAA…
Electron Dsoe
- PBC Hogstrom algorithm
IMRT Module
Optimization engine
Beam-let extraction
Make Voxel lists per organ
Constraint I/O
Run optimization
MLC sequencing
Steepest decent method
- for spectrum
- for beam source model
- for IMRT

4. Dose calculation engines
Most important to predict dose distribution
Consisted of two parts
Dose calculation part
Interpolation based method: ETAR
Semi-analytic model method
Superposition/Convolution algorithm
FFT, CCC, AAA…
LBTE algorithm
Acuros XB
Monte Carlo based method
Beam modeling part
Based on measured dosimetric data
Directly linked to RTP commissioning module

5. Convolution/superposition method
Two step of the process at depositing doses
Photon and a media interaction making TERMA
Electrons from a interaction point are traversed through the media making excitation and ionization (kernel)
TERMA
Total energy released per media
Temporal energy deposition before electron transport
Considering attenuation and divergence effect
Kernel
Relative energy spread from unit TERMA
Energy deposition from electron transport
Function of energy and media
Dose = TERMA ⓧ kernel

6. Convolution/superposition method
Dose:
Superposition: Sun of all kerma map at each voxel.
Same as convolution of TERMA and kernel
TERMA deposition:
Pencil beam transfer energy at each voxels in tissue through its traveling way.
Assume that directly give potential energy to each volume element
Kernel spread:
Deposited dose spread to 3D space from TERMA at each voxel.

7. General Process of Dose Calculation
Consider geometric infomations
Calculate
Photon fluence
Calculate 3D TERMA
Do convolution
Photon beam source
2 source model
3 source model
Beam aperture
Collimators
MLC
Horn effects
Beam Divergence
Inverse square law
Poly-energetic kernels
C/S or CCC or AAA
Differential kernels or Accumulative kernels
Attenuation
Beam hardening/softening
Transmission through MLC /block/collimators

8. Geometric transformation1
Block
Source xb zb yb
isocenter
Beam coordinate
Geometric definition
Freedom of beam directions
Gantry angles
Collimator angles
Couch angles
Translations of couch 1
Block
Source xb zb yb
Beam coordinate
Patient coordinate system
World (global) coordinators
Based on CT coordinators
Define 3D dose
Define contours xg yg zg
CT coordinate
Beam coordinate system
Origin is beam source
Z axis is beam center
Fluence. Beam source, TERMA, kernels
Defined per beams
Transformation between Patient coordinate and Beam coordinate

9. Geometric transformation
Simple Example
Pb at iso-center ( Xb, Yb, Zb) = (0, 0, 100)
Assume Iso-center (Pg ) is (0, 5, 5)
Converting Pb to Pg?
Rotate based on Xb axis by 90’ counter clock wise
Pb = (0,-100, 0)
Translate Beam coordinate by (0, -100, 0)
Beam coordinate origin shifted to isocenter
Pb = ( 0,0,0)
Translate Beam coordinate by (0, -5, -5)
Beam coordinate is same to patient coordinate
Pb = (0, 5, 5) = Pg xb zb yb
Beam coordinate xb zb yb
Beam coordinate
Source
Sb ( 0, 0, 0) xg yg zg xb zb yb
Beam coordinate xb zb yb
Beam coordinate 5
Isocenter Pb
CT Origin
Pg (0,0,0) 5

10. Process of TERMA Calculation
Calculation of Fluence and TERMA distribution in media 1
Source
Beam source model
Binary MLC plane
Using Hit test
Considering partially block
Calculate
Fluence at each voxel
Calculate
Beam divergence
Calculate Horn effect
Calculate effective depth
for each voxels
Calculate
beam softening effect
Calculation point
Calculate Attenuation

11. Beam source Model: 3 source model
Gantry head
Collimator or MLC
Point of calculation
(xb,yb,zb)
Isocenter
SCD = 100 cm
Primary photon source
Point source: Cp
Srcprimary plane
Point source
Scattered photon source from other structures
Disk shape
Intensity function with r
Srcsf plane
Disk source
Zsf = 12.5 cm
Srcsp plane
Annulus source
Zsp = 4cm
Scattered photon source from primary collimator
Annulus shape

12. Beam source model: 3 source model
Collimator or MLC
Point of calculation
(xb,yb,zb)
Isocenter
Srcsp plane
Annulus source
Gantry head
Srcprimary plane
Point source
Srcsf plane
Disk source
Fluence at an arbitrary point

13. Implementation of Beam source model
Define Binary MLC Grid from the position of MLC leaves
Considering partially block
Hit Test algorithm
Beam Source center (0, 0, 0)
Binary Block Plane 1
Prepare Binary 2DGrid
For all voxels (xb,yb,zb) {
Src1_fluence = Calc_OpenRatio(Subboxels)
for (3x3x3 Subvoxels)
do HitTest(SubVoxels) }
Src2_fluene =Calc_ScatterSource2()
Src3_fluene =Calc_ScatterSource3()
Fluence
Voxel
(xb, yb, zb)

14. Implementation of Beam source model
MLC plane
Z= 67 cm
0.1mm resolution
Source plane
Z = Z_src
5mm resolution
(Xb,Yb,Zb)
Calculation point:
101 x 101 x 101 Xs Ys 1
Hit_corner_grid: partially block
Sub voxel
Blocking ratio=
9/25 = 0.36
Src2_fluene =Calc_ScatterSource(): For all SourceGrid { Hit-test 4 corner bloks at first If not blocked Calculate Radius (Xb,Yb,Zb) Get source value from source functions Src_flue += source_value }

15. Process of TERMA Calculation
Calculation of Fluence and TERMA distribution in media 1
Source
Calculate
Fluence at each voxel
Calculate
Beam divergence
Calculate Horn effect
SPD
Distref
Calculate effective depth
for each voxels
Calculate
beam softening effect
Calculation point
Calculate Attenuation

16. Process of TERMA Calculation
Calculation of Fluence and TERMA distribution in media 1
Source
Calculate
Fluence at each voxel
Calculate
Beam divergence
Calculate Horn effect
Calculate effective depth
for each voxels
OAD
Calculate
beam softening effect
Calculation point
Calculate Attenuation

17. Process of Dose Calculation
Calculation of Fluence and TERMA distribution in media 1
Source
Calculate
Fluence at each voxel
Calculate
Beam divergence
Calculate Horn effect
Calculate effective depth
for each voxel
Calculate
beam softening effect
Calculation point
Calculate Attenuation

18. Process of Dose Calculation
Calculation of Fluence and TERMA distribution in media 1
Source
Calculate
Fluence at each voxel
Calculate
Beam divergence
Calculate Horn effect
Calculate effective depth
for each voxels
Calculate
beam softening effect
Calculation point
Calculate Attenuation

19. Process of Dose Calculation
Calculation of Fluence and TERMA distribution in media 1
Source
Calculate
Fluence at each voxel
Calculate
Beam divergence
Calculate Horn effect
Calculate effective depth
for each voxels
Beam hardening effect
Calculate
beam softening effect
Calculate Attenuation

20. Implementation of convolution
Photon source
for all r’…(N voxels in volume) { Get TERMA(r’) for all r…. Get Kernel (r-r’) from Table Accumulate TERMA(r’) x Kernel (r-r’) to the r’ voxel }
D(r)
T(r’) r' r

21. Why Collapse Cone Convolution?
Limitation of convolution/superposition method
Center of kernel has too steep gradient.
Discrete kernel data  Significant error at the center voxels in dose calculation.
Too long calculation time
FFT is a good method. But no inhomogeneity correction.
Not invariant kernel at inhomogeneous medium
Iterative calculation: N6 number of iteration at N x N x N voxels
From “Current Concepts in Dose Calculations”, Anders Ahnesjö.

22. Collapsed cone approximation
N number of Voxels
M Number of Cones N
M rays
N voxels
No of Iterations: N3
No of Iterations : M x N
Can reduce calculation time because of computing dose to MxN points instead of NxNxN points.
More accurate dose calculation in heterogeneous media by considering effective pathway through cone lines

23. Scatter particle transport directions
Near center voxels
Spherical voxels are generally smaller than cubic voxels
Far away voxels
One spherical voxels covers several cubic voxels
Only consider the voxels in axial lines
Too much energy imparted.
But small errors because of small fraction energy at far site.

24. Process of Convolution
Sphere Convolution Process
Total 288 cone rays
24 divisions of theta
12 divisions of phi angle
Extracting voxel lists traversed by each ray vector r.
Heterogeneity correction by effective pathway through vector r
Convolution kernel table with spherical coordinate system.
Consideration of kernel tilting effect
Adaption of accumulative kernel Y -Z θ φ
A Collapsed Cone X
A TERMA Voxel

25. Process of convolution
Prepare Poyenrgetic_Spherical_Kernel (r, θ, φ) Make Accumulative_Kernel (r, θ, φ) For (all 3D voxels with (Xp,Yp,Zp) ) { for (all r, θ, φ) Calc_vector() Get_transversed_voxel_Lists() Calculate eff_pathlength(voxel_Lists) for (all Listed voxels) Calculate θtilt Energy = Accumulative_Kernel(rinner) - Accumulative_Kernel(router) Get_TERMA(voxel) Dose +=TERMA x Energy }
(r, θ, φ)
(Xp, Yp, Zp)

26. Kernel tilting TERMA Voxel Dose Voxel θcone θbeam Divergent Beam

27. Considering Beam hardening
Poly-energetic kernel
Photon spectrum is changed according to depths
Solve:
Get changed spectrums at every 10 cm depth
Prepare each kernel tables from the changed spectrum
Calculate interpolate kernel values between two tables using the depth of voxels

28. Discussion & Question