21/12/55

1

FUNDAMENTAL TO ADVANCED

RADIOTHERAPY TREATMENT TECHNIQUES:

Lakkana APIPANYASOPON

Department of Radiation Oncology,

Siriraj Hospital

Dose Calculation Algorithms

10th SEACOMP and 12th AOCMP: The Convergence of Imaging and Therapy

11-14 December 2012 at Khum Phu Come Hotel, Chaing Mai, Thailand

FROM MEASURED DOSE TO CALCULATED DOSE IN WATER

Because absorbed dose distributions cannot be directly measured in a patient, they must be calculated.

In the past, the method for dose calculation was derived from the hand calculation.

Example of basic beam parameters: ◦ PDDs, TARs or TMRs

◦ Lateral dose profiles

◦ Collimator and Phantom scatter factor (Sc and Sp)

◦ Transmission factor (Wedge, Block, Tray, MLC)

◦ Beam calibrated output (MU/Gy)

SCATTER CORRECTION BY CLARKSON INTEGRATION

Johns and Cunningham based the separation of primary and scattered radiation dose on a separation of the tissue air ratio.

The field is divided in an angular sector of angle and radius.

0( , ) ( , 0) ( , )TAR z r TAR z r SAR z r

SAR = the scattered radiation in a circular beam with radius r

TAR0 = the TAR at the depth z for a field of zero area

The total dose in P, DP = Dprimary + Dscatter The first treatment planning assumed the patient to be

composed of water and was generally carried out though the manual manipulation of standard isodose charts onto patient body contours.

The patient body contour were generated by direct tracing or lead-wire representation.

FROM WATER TO CALCULATED DOSE IN PATIENT

With the introduction of CT , full anatomical information of the patient became available and though a conversion.

To relate such measurements to the actual dose distribution in a patient, corrections for irregular surface and tissue inhomogeneities have to be applied.

DOSE CALCULATION: Correction-Based method

The starting point is always the dose distribution for all-

water absorber, with secondary corrections introduced

to account for tissue density and surface irregularity.

The dose distribution, corrected for patient contour and

tissue heterogeneity is given by:

Dinhom (x,y,z) = ICF (x,y,z) DH20 (x,y,z)

where Dinhom is the dose distribution within inhomogeneous tissue, ICF is the in

homogeneity correction factor, and DH2O is the ref. dose distribution in a homogeneous water absorber.

Correction-Based: Semi-empirical methods

◦ Empirical: Standard measurements

◦ Analytical: Correction factors There are many methods to correct

for tissue heterogeneities effect.

PATIENT CONTOUR & HETEROGENEITIES COREECTIONS Three methods for 1D contour correction are used:

◦ Effective source to surface distance

◦ Tissue-air (or Tissue maximum) ratio

◦ Isodose shift

1D: Linear attenuation Effective Attenuation Coefficient Ratio of Tissue-Air Ratios (RTAR) Power Law method (Batho)

3D: Equivalent Tissue Air Ratios (ETAR) Differential Scatter Air Ratios (dSAR) Delta volume (DVOL) 3D Beam Subtraction

21/12/55

2

Linear Attenuation:

DOSE CALCULATION METHODS: Heterogeneity corrections

ICF = (% per cm) × inhomogeneity thickness

In this method, patient specific densities can be used in the

evaluation of d’, but treatment beam parameters are still ignored.

In this method, the patient specific densities and the geometric

treatment beam parameters dose not include .

• Effective Attenuation

Coefficient:

Ratio of Tissue-Air Ratios (RTAR):

where d is the physical depth, d’ is the equivalent

path length, w is the field size at the level of calculated point.

Weakness: an over-correction when the density is less than that of water

and an under-correction when the density is greater than water.

DOSE CALCULATION METHODS: Heterogeneity corrections

• Power Law method (Batho):

Weakness: an under-correction when the density is less than that of water

and an over-correction when the density is greater than water.

DOSE CALCULATION METHODS: Heterogeneity corrections

• Equivalent Tissue Air Ratio (ETAR):

Weakness: This method always predicts a decrease in scatter

when the density is less than unity and an increase in scatter

when the density is greater than unity.

ETAR include 3D density information in an explicit

calculation of the scattered photon dose, but still assume

electronic equilibrium.

DOSE CALCULATION: Summary of Correction-Based method

Advantages: fast method

Weakness: usually assume electronic equilibrium and inaccurate near heterogeneities

Based on separating the dose into primary and scatter component and including with the correction factor.

The accuracy provided by

this method suffered due to

limited modeling of the scatter dose component.

Model-based methods are based on physical principles of the radiation behavior rather than on direct beam data measurements.

Combine an analytical calculation of primary photon interactions with subsequent transport and energy deposition by secondary particles described by pre-calculated kernels.

DOSE CALCULATION ALGORITHM FOR TREATMENT PLANNING

The distribution is also known as

“dose spread functions”, “scatter kernels”, “point kernels”, “dose spread arrays”, “differential pencil beams” or “influence functions”.

Energy deposited kernel: Absorbed dose from both secondary electrons and

photon around the interaction point.

Calculated by MC infinite medium to water

There are three types of kernel:

Point kernel: the deposited energy

in an infinite medium around a

primary interaction point.

Pencil kernel: the deposited energy

in a semi-infinite medium from

a point mono-directional beam.

Planar kernel:

the energy spread from

primary interactions

located in a plane of an

infinite broad beam.

DOSE CALCULATION: Model-Based method

21/12/55

3

MODEL-BASED METHOD:

Convolution (1D)

The deposition of energy in tissue from a photon beam is

fundamentally a two processes:

1) Photons interact in the medium to impart kinetic

energy to charged particles.

2) Charged particles then deposit their given energy

through ionization and excitation events along a finite

track .

MODEL-BASED METHOD:

Convolution-Superposition

The deposition of energy in homogeneous tissue can be

described through a convolution of energy released by the

primary beam with an energy deposition kernel.

For non-water equivalent tissue: scaling the kernel with the

mean energy density.

Photon fluence Kernel Dose

MODEL-BASED METHOD: Dose Calculation Algorithm for TPS

TPS ALGORITHMS

Varian Eclipse Anisotropic Analytical (AAA)

Pencil-Beam Convolution/Superposition

Nucletron Oncentra Master Plan

Collapsed Cone (CC)

Pencil-Beam Convolution/Superposition

Philips Pinnacle Collapsed Cone (CC)

CMS Xio Multigrid Superposition/Convolution (MGS)

Fast Fourier Transform Convolution (FFTC)

Type B: Models the electron transport in the medium accounting for density changes, sampled along the full three dimensions.

Type A: Models primarily and the density changes are sampled along the 1D primary rays.

Dose Calculation Algorithm for TPS:

Pencil-Beam Convolution

The energy spread or dose kernel at a point is summed

along a line in phantom to obtain a pencil-type beam or

dose distribution.

Superposition of pencil beam kernels in 2D.

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.

Dose Calculation Algorithm for TPS:

Collapsed-Cone Convolution

Uses an analytical kernel represented by a set of cones,

the energy deposited in which is collapsed onto a line.

When the angular kernel is convolved with TERMA

distribution, all energy released into the cone direction is

approximated to be rectilinearly transported, attenuated,

and deposited in voxel on that axis.

CC: Most accurate / Time consuming

Adaptive: Based on gradient from TERMA / Compromise

Fast: Useful for optimized beam / Rough estimated dose

Dose Calculation Algorithm for TPS:

Anisotropic Analytical Algorithm (AAA)

Three separate sources:

Primary photons

Extra-focal photons

Contaminating electrons

AAA is not account for chemical material/ tissue

properties, hence the computed dose can be defined as

dose to water, rescaled according to the specific density.

A MC simulation of the treatment unit head was used to

develop a fundamental parameterized model of radiation

output for a clinical linac,

21/12/55

4

Type A: the averaged

dose distribution is

slightly larger probably

due to different scatter

volume integration

techniques.

Type B: the variation in

average dose is less.

For the estimation of lung

dose, the choice of model

has no impact on the

DVH.

The PB plans are about 2% and 4% higher than the MC plan and CC

is approximately 1.5% lower.

A lower dose was also found for the CC model combined with high

energy compared to the MC simulations.

The CC model for high energy x-rays combined with low density

has tendency to spread out the energy too much.

Limitation of Model-Based methods

The development of model-based convolution methods

has significantly improved the accuracy of dose

calculations for heterogeneous materials.

However:

Patients are not infinite.

Beams are not parallel and not mono-energetic.

The development of computer hardware and variance

reduction techniques for MC methods has largely

reduced the computation time, making MC feasible in

clinical TPS.

MONTE CARLO-BASED METHOD

Results are obtained by following the histories of a large

number of particles as they emerge from the source of

radiation and undergo multiple scattering interactions both

inside and outside the patient.

Monte Carlo technique of radiation transport consists of

using knowledge of probability distributions governing the

individual interactions of electrons and photons to simulate

their transport though matter.

The linac can be divided into:

Upper part: Components

Lower part: Beam modifier

The AAA dose predictions differ from MC up to 11.6% in the

lung region and small field size for 18 MV.

The CCC has slightly larger difference relative to MC than

AXB (up to 4.5% in lung region).

The AXB dose predictions agree with MC within 2%.

AXB have better dose predictions than AAA and CCC at the

tissue interfaces where backscatter occurs.

3D gamma index analyses (Percent of dose voxels passing a 2%/2mm criterion),

The difference between AXB and CCC was generally small

except in the lung region for 18 MV and in the bone region

for 10 cm square fields.

The dose differences between AAA and AXB are significant in the

bone region for all field sizes of 6 MV and in the lung region for

most of field sizes of both energies.

This limitation of the convolution method for interface

dosimetry is due to its inability to model the coupled

photon-electron transport across the interface.

21/12/55

5

The AAA had the shortest time among these three methods.

AXB times were comparable to CCC for the small

field plans but were about 5X longer for 10 cm square field.