Treatment head modelling using Monte Carlo

techniques

Monte

Carlo modelling is a computerized mathematical algorithm based on repeated

random sampling to obtain a numerical result that allows you to see all

possible outcomes that would occur for a choice of action. (1) Monte Carlo

calculation is used in treatment head planning as it is one of the most

accurate ways to calculate dose distribution. Individual particle transport

calculation is completed using Monte Carlo simulations, first in the geometry

of the external or internal source, followed by tracking energy deposition in a

water phantom or certain tissues. Patient geometries can be extremely complex,

having a large range of atomic numbers and densities, therefore water phantoms

will only be investigated in this project as there are certain time constraints.

Monte Carlo simulations using many different codes can investigate the

different effects of physical parameters on photon and electron beams from

linear accelerators (linacs) on the dose distribution in a water phantom. PRIMO

and BEAM are two common programmes used to run Monte Carlo simulations. PRIMO

is the program that I will be using when running simulations during the

research project. PRIMO consists of a graphical user interface and a

computational engine based on PENELOPE the Monte Carlo (MC) code. The purpose

of PRIMO is to simulate linear accelerators and their absorbed dose

distribution in water phantoms (2). PRIMO

allows simulations of Varian Clinac and Fakebeam linacs. Varian Clinac contains

a flattening filter and Fakebeam is flattening filter free. This difference

between these are discussed later. Millions of histories are simulated and

phase space can be determined. A phase space file is when particles that are

traversing a plane are stopped and their energy, direction of flight, position

etc. can be determined and saved on a file. (2) Beam modelling and

characterization is now possible. Dose profiles and percent depth dose (PDD)

curves can also be calculated using this software. The MC method can be used in

the treatment head modelling of photon or electron beams. The calculation power

of computers is constantly increasing which therefore leads to improvements

being made in the MC modelling of external radiotherapy beams on an ongoing

basis. (3)

The treatment head of a linac

consists of components that are designed to shape and monitor the treatment beam.

Components include bending magnet, shielding material, x-ray target, primary

collimator, secondary collimator, beam monitoring device, and the jaws. A

flattening filter may be included in some linacs. The flattening filter in a

standard linac is located between the primary collimator and the monitor

chamber. The main role of the flattening filter is to make the photon beam dose

distribution uniform at reference depth. When the accelerated primary electron

beam emerges from the source, it has a narrow energy and angular distribution.

The beam hits the target and electrons produce bremsstrahlung photons. The

bremsstrahlung photons are then collimated by the primary collimator and photon

fluence is attenuated by the flattening filter (if present) to produce flat

dose distribution in water. The monitor

chamber only produces small attenuation to the photon beam. Lastly, the jaws

(or Multi leaf collimator, wedges, or blocks) shape the photon beam. (2) A

diagram of a linac treatment head and component modules are seen in Figure 1.

Figure 1. Illustration of the treatment head and

the component modules (not to scale) used in the MC simulations for Varian

Clinac machines (different linac manufacturers may place components in

different order.) (6)

The

bremsstrahlung photon emission at high electron energies is given by m0/E0, where m0 is the rest energy of electron, and E0

is the total energy. This results in a strong forward peaked angular

distribution. (2) The target in a clinical linac is usually thick enough to stop

the primary electrons completely. In these targets, the bremsstrahlung photon

angular distribution will be spread out as electrons undergo multiple

scattering. The photon intensity will be anisotropic but the photon spectrum

will be isotropic. Due to this being complex, it is difficult to obtain a

correct spectral and angular bremsstrahlung photon distribution from thick

targets. The most comprehensive method developed to generate bremsstrahlung

photon distributions from targets in linacs is MC simulation. (2) Other

theories such as Schiff theory are simple analytical theories and are only

approximations. The use of the MC method in treatment head

simulation gives the highest accuracy and detail of the external radiotherapy

beam and is now crucial in treatment head design. (4) Accurate source modelling

is essential in accurate treatment planning with MC simulations. The planning

system is physically based, therefore the beam used in the dose calculation has

to be very accurate and detailed. Parameters for linacs can be defined using

various MC programmes PRIMO, BEAM etc. When the energy of an x-ray beam is

given, the angular distribution of intensity can be calculated using MC techniques

over a range of clinical field sizes. Information about the material

specification and geometry is essential in treatment head modelling.

As previously mentioned, the most

practical way to determine the characteristics of a photon beam is to use MC

techniques to simulate the transport of particles through the treatment head.

Using this approach, electrons are injected through the exit window of the

treatment head one at a time and their passing through the treatment head is

followed by computer simulation. This approach provides us with highly detailed

phase space information that can be recorded for every particle that leaves the

treatment head. (6) Unfortunately, storage space for these phase space files

that contain millions of photons can be very large and the simulation time for

a single beam can take days on an average computer. (6) Instead of using phase

space information as the direct input to dose calculation we use beam

modelling. This will combat the large storage and simulation running time

problem. Beam representation is the first step of beam modelling. This includes

devising an appropriate representation of the beam for a certain design of the

treatment head based on the known characteristics of the beam. Beam

representation is a mathematical description of phase space. The next step is

beam reconstruction. This involves reconstruction of the phase space from the

beam representation. We can forego the

need to store phase space data as the phase space can be reconstructed and

input into the dose calculation code one particle at a time. Beam

representation and beam reconstruction together form beam modelling. (6)

Beam representation

For this

beam modelling procedure a programme such as PRIMO or BEAM is used to calculate

the raw beam. A beam model can be selected for each photon beam energy and the

parameters of the beam representation can be input into the programme. A range

of energies such as 4MV, 6MV, 15MV and 20MV are typical energies that would be

chosen to model a treatment head. The Varian Clinac 2100 and Fakebeam linacs

can be simulated. These linacs would be operated in photon mode. The materials

and geometries used in MC simulations have to be a realistic construction of a

linac. The phase space 1 is construction of the beam model and phase space 2 is

verification of the source modelled in a water phantom when dose distributions

were calculated (2) (6). Full phase space data is one of the most essential

elements from a MC simulation. For a beam to be fully parametrized, exact

knowledge of the beam characteristics are required. The binning approach used

in both PRIMO and BEAM does not require parametrization, only small knowledge

of beam characteristics is required. E.g. field size and maximum energy. (6) A

basic illustration of the process carried out in beam characterization and beam

modelling for photon beams from a linac is shown below. Note this illustration

uses BEAM, however procedure is similar for PRIMO and other MC programmes.

Figure 2. Illustration

showing procedures in beam characterization and beam modelling for photon beams

from a linac.

Beam reconstruction

To

reconstruct phase space data it is best to use a multiple source model. This

multiple source model is a simplified way to replace the large phase space

files that are generated from a MC simulation. (7) The multiple source model

treats particles coming from different parts of an linac as if they are coming

from different sources. Particles coming from different components of a linac

vary in energy, spatial and angular distributions. In comparison, particles

coming from the same component have similar values in terms of energy and angular/spatial

distributions. Beam reconstruction entails the use of the multiple source model

for dose calculation. The energy, position and direction i.e. the phase space

information for every particle is reconstructed from the scored source

parameters. (7) Firstly, a source is selected according to relative source

intensity. Next, a position on the phase space plane is determined for the

particle based on the spatial distributions of the source. (6) Then a position

on the source is sampled. When the position on the phase space plane and the

position on the source is determined this will give the incident direction of

the particle. Finally, the particle energy can be sampled from the energy distribution

for the source. The particle position and energy can be sampled independently

as there is a weak correlation between particle energy and position for

particles from the same source. (6) Energy spectra can be scored based on the

particle position on the phase space plane.

For spatial and energy sampling on

the source and on the phase space plane the binning approach was taken.

Efficient and accurate reconstruction of the energy and spatial distributions

requires appropriate bin widths. As mentioned previously, reconstruction of the

beams are used for calculation of 3D dose distributions in water (or patient)

phantoms. (6) These results can be compared to calculations made using the

original phase space data as seen in Figure 2.

Variance reduction

Variance

reduction techniques including bremsstrahlung splitting and Russian roulette

are used in MC simulations to improve the efficiency of the system. Splitting

and Russian roulette are used together in PENELOPE MC code. The combined use of

these allow for a more efficient simulation. Splitting is generating multiple

photons from each electron interaction, the weight of the photon is

proportionally reduced (6). In PRIMO a value for the ‘splitting factor’ can be

raised to reduce computing time and to give a more accurate result. Photon

forcing also increases efficiency when combined with photon splitting. The

photon forcing technique increases the probability of a photon interaction with

different components of a linac. Range rejection is another variance reduction

technique that improves the efficiency of a treatment head. This depends on the

initial energy of the electron. If an electron has a lower energy than the cut

off, which is determined by the user, the electron history is terminated. It is

an approximation as no bremsstrahlung is possible. The low energy cut-off for

electrons led to reduced simulation time and affects dose distribution (8).

Overall, we know that implementing variance reduction techniques to the MC

simulations increases accuracy and efficiency.

Flattening filter

As

mentioned previously a linac can contain a component called a flattening filter

to produce a flat dose distribution in water. It has a very good impact when

determining beam profile and ensures uniform intensity distribution of X-ray

beams generated from the target. It also acts as a metal absorber of low-energy

X-ray beams. This ensures that the mean energy of the beam increases. In

flattening filter free linacs the flatness of the beam is lower. However, in

the case of small-field size radiation treatment there is very little difference

in flatness observed when the flattening filter is removed. (3)(9)

In

conclusion, it is clear Monte Carlo simulations are the most powerful method of

treatment head modelling and dose calculation in radiotherapy. The MC method

used in radiotherapy gives the most accuracy between 2 and 3%. It has been

emphasised in this essay the capabilities of the MC method when used for

modelling external radiotherapy photon beams, but it has also proven to be

extremely capable of modelling external radiotherapy electron beams and patient

treatment verification. As technology evolves and computing power increases

(according to Moore’s Law) the problem of simulation running time and phase

space storage may be significantly reduced. The MC method will become the main

method in treatment planning for radiotherapy and become increasingly important

in imaging diagnostics also.

References

1.

Monte Carlo Simulation

http://www.palisade.com/risk/monte_carlo_simulation.asp

2.

PRIMO User Manual

Brualla,

Rodriguez, Sempau

3.

“Monte Carlo modelling of external radiotherapy

photon beams” by Frank Verhaegen and Jan Seuntjens 2003 Phys. Med. Biol. 48

R107

4.

Monte Carlo for Radiotherapy I: Source Modelling

and Beam Commissioning for Monte Carlo Treatment Planning AAPM 2005 Continuing

Education Course, C Ma, B Faddegon, B Curran

https://www.aapm.org/meetings/05AM/pdf/18-4011-55406-780.pdf

5.

Unflattened photon beams from the standard

flattening filter free accelerators for radiotherapy: Advantages, limitations

and challenges

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3159217/

6.

“Photon beam characterization and modelling for

Monte Carlo treatment planning”

Jun Deng,

Steve B Jiang, Ajay Kapur, Jinsheng Li, Todd Pawlicki, C-M Ma

2000 Phys.

Med. Biol. 45 411

7.

“Electron

beam modelling and commissioning for Monte Carlo treatment planning”

Steve

B. Jiang, Ajay Kapur,

and C.-M. Ma

Published

Oct. 1999

8.

“Evaluation of variance reduction techniques in

BEAMnrc Monte Carlo simulation to improve the computing efficiency”

Maged

Mohammed, E.Chakira, H.Boukhal. MroanSaeed. T.El Bardouni

9.

“A study on the effect of using a flattening filter

in a medical linear accelerator on the dose distribution”

Kim, YJ.,

Dong, KR., Chung, WK. et al. Journal of the Korean Physical Society (2014) 64:

917. https://doi.org/10.3938/jkps.64.917