1. Dose Calculation Algorithms
Kwangwoo 2017 Yonsei IMRT Workshop

2. Outline
The past
The present
The future

3. The past

4. Hand Calculation Scatter Correction 𝑫 𝒑 = 𝑫 𝒑𝒓𝒊𝒎𝒂𝒓𝒚 + 𝑫 𝒔𝒄𝒂𝒕𝒕𝒆𝒓
PDD, TAR or TMR
Lateral dose profile
Collimator and Phantom scatter factor (Sc and Sp)
Transmission factor (Wedge, Block, Tray, MLC)
Beam calibrated output (MU/cGy)
Clarkson’s Method
𝑇𝐴𝑅(𝑧,𝑟)=
𝑇𝐴𝑅 0 𝑧, 𝑟=0 +𝑆𝐴𝑅(𝑧,𝑟)

5. Correction-Based method
𝐷 𝑖𝑛ℎ𝑜𝑚 (𝑥,𝑦,𝑧)=𝐼𝐶𝐹 𝑥,𝑦,𝑧 × 𝐷 𝐻 2 𝑂 (𝑥,𝑦,𝑧)
Using linear attenuation, ignoring patient specific densities and treatment beam parameters
𝐼𝐶𝐹 𝑥,𝑦,𝑧 = (% per 𝑐𝑚) × inhomogeneity thickness
Using effective attenuation, including patient specific densities, excluding treatment beam parameters
𝐼𝐶𝐹 𝑥,𝑦,𝑧 = 𝑒 𝜇 ′ (𝑑− 𝑑 ′ )

6. Correction-Based method
𝐷 𝑖𝑛ℎ𝑜𝑚 (𝑥,𝑦,𝑧)=𝐼𝐶𝐹 𝑥,𝑦,𝑧 × 𝐷 𝐻 2 𝑂 (𝑥,𝑦,𝑧)
Ratio of Tissue-Air Ratios (RTAR)
𝐼𝐶𝐹 𝑥,𝑦,𝑧 = 𝑇𝐴𝑅( 𝑑 ′ ,𝑊) 𝑇𝐴𝑅(𝑑,𝑊)
Over-correction when 𝝆<𝟏
Under-correction when 𝝆>𝟏
Power law method (Batho)
𝐼𝐶𝐹 𝑥,𝑦,𝑧 = 𝑇𝐴𝑅( 𝑑 ′ ,𝑊) 𝜌 1 − 𝜌 2 𝑇𝐴𝑅(𝑑,𝑊) 1− 𝜌 2
Under-correction when 𝝆 𝟏 <𝟏
Over-correction when 𝝆 𝟏 >𝟏

7. The Present

8. Model-Based Method Terms: Kernel, Convolution & TERMA
“Kernel” is a function which define integral transform mathematically, Inversely, define propagator as in differential operator.
𝒇 and 𝒈 are convolute !
kernel
ℎ 𝑥 = 𝑓 𝑥 𝑔 𝑥−𝑦 𝑑𝑦
= 𝑓 𝑥 ⨂𝑔 𝑥
Integral
Transformation
𝑻 𝑬 𝑬, 𝒓 = 𝝁 𝑬, 𝒓 𝝆 𝒓 𝑬 𝜱 𝑬 𝑬, 𝒓
Energy fluence
Mass attenuation
“TERMA” is a total energy
released per unit mass

9. 𝑻( 𝒓 ′) 𝑲( 𝒓 − 𝒓 ′) 𝑫( 𝒓 )= 𝑻 𝒓 ′ 𝑲 𝒓 − 𝒓 ′ 𝒅𝑽′ 𝑫 𝒓 =𝑻 𝒓 ′ 𝑲 𝒓 − 𝒓 ′
Energy Fluence
Photon
TERMA
𝑻( 𝒓 ′)
Propagate
(scatter) dose
𝑲( 𝒓 − 𝒓 ′)
𝒓 ′ 𝒓
𝑫 𝒓 =𝑻 𝒓 ′ 𝑲 𝒓 − 𝒓 ′
𝑫( 𝒓 )= 𝑻 𝒓 ′ 𝑲 𝒓 − 𝒓 ′ 𝒅𝑽′
=𝑻 𝒓 ′ ⨂𝑲 𝒓 − 𝒓 ′

10. Model-Based Method Collapsed Cone Convolution (CCC)
Fluence
Pinnacle
TERMA
Dose
Depth
RayStation
Collapse
Cone
Kernel
TomoPlan

11. Model-Based Method Collapsed Cone Convolution (CCC)
𝑫( 𝒓 )= 𝑻 𝒓 ′ 𝑲 𝑪𝑪 𝒓 − 𝒓 ′ 𝝆( 𝒓 ′ )𝒅𝑽′
Energy transported and attenuated
Heterogeneity correction by effective pathway through the position vector 𝒓 ′
Including kernel tilting effect
Time consuming calculation
Less accurate at large distances from cone vertex
Errors are small due to point-spread functions
Electron transport included

12. Model-Based Method Pencil Beam Convolution (PBC)
Fluence
Dose
Depth
TERMA
Monaco
Pencil
Kernel

13. Model-Based Method Pencil Beam Convolution (PBC)
Med. Phys. 13, 1
2D pencil beam kernel
The dose distribution can be generated by integrating the pencil beam over the patient’s surface and by modifying the shape of the pencil beam with depth and tissue density
Electron transport not modeled

14. Model-Based Method Anisotropic Analytical Algorithm (AAA) Acuros XB (AXB)
AAA is a pencil beam convolution/superposition algorithm
For the fluence model used multi-source model (Eclipse, TomoPlan)
Kernel can be determined using linear Boltzmann transport equation (LBTE)

15. Comparison…
Phys. Med. Biol. 52, 1363

16. Comparison… Beam Quality (TPR20,10)
% difference w.r.t. MC
6MV MV
AAA-ECL
-0.30%
1.06%
PBC-ECL
-0.74%
1.60%
CC-TMS
1.33%
PB-TMS
-0.44%
1.46%
CCC-PIN
-1.19%
0.93%
FFTC-Xio
0.00%
MGS-Xio
-0.15%

17. Heterogeneity - Bone

18. Heterogeneity - Lung

19. Comparison…
Phys. Med. Biol. 51, 5785
PBC
CCC MC

20. PB vs MC
Med. Dosim. 26, 157
Pencil Beam MC

21. PBC, CCC, and MC
PBC
CCC
Calculation Speed MC
Calculation Accuracy

22. The future Convolution/Superposition + MC MC with hardware development
Considering BED
Developing algorithm for particle therapy
Lanchun Lu, Internaltional Journal of Cancer Therapy and Oncology