Treatment head modelling using Monte CarlotechniquesMonteCarlo modelling is a computerized mathematical algorithm based on repeatedrandom sampling to obtain a numerical result that allows you to see allpossible outcomes that would occur for a choice of action. (1) Monte Carlocalculation is used in treatment head planning as it is one of the mostaccurate ways to calculate dose distribution. Individual particle transportcalculation is completed using Monte Carlo simulations, first in the geometryof the external or internal source, followed by tracking energy deposition in awater phantom or certain tissues. Patient geometries can be extremely complex,having a large range of atomic numbers and densities, therefore water phantomswill only be investigated in this project as there are certain time constraints.

Monte Carlo simulations using many different codes can investigate thedifferent effects of physical parameters on photon and electron beams fromlinear accelerators (linacs) on the dose distribution in a water phantom. PRIMOand BEAM are two common programmes used to run Monte Carlo simulations. PRIMOis the program that I will be using when running simulations during theresearch project. PRIMO consists of a graphical user interface and acomputational engine based on PENELOPE the Monte Carlo (MC) code. The purposeof PRIMO is to simulate linear accelerators and their absorbed dosedistribution in water phantoms (2). PRIMOallows simulations of Varian Clinac and Fakebeam linacs.

Varian Clinac containsa flattening filter and Fakebeam is flattening filter free. This differencebetween these are discussed later. Millions of histories are simulated andphase space can be determined. A phase space file is when particles that aretraversing a plane are stopped and their energy, direction of flight, positionetc. can be determined and saved on a file. (2) Beam modelling andcharacterization is now possible. Dose profiles and percent depth dose (PDD)curves can also be calculated using this software.

The MC method can be used inthe treatment head modelling of photon or electron beams. The calculation powerof computers is constantly increasing which therefore leads to improvementsbeing made in the MC modelling of external radiotherapy beams on an ongoingbasis. (3) The treatment head of a linacconsists of components that are designed to shape and monitor the treatment beam.Components include bending magnet, shielding material, x-ray target, primarycollimator, secondary collimator, beam monitoring device, and the jaws. Aflattening filter may be included in some linacs. The flattening filter in astandard linac is located between the primary collimator and the monitorchamber. The main role of the flattening filter is to make the photon beam dosedistribution uniform at reference depth.

When the accelerated primary electronbeam emerges from the source, it has a narrow energy and angular distribution.The beam hits the target and electrons produce bremsstrahlung photons. Thebremsstrahlung photons are then collimated by the primary collimator and photonfluence is attenuated by the flattening filter (if present) to produce flatdose distribution in water. The monitorchamber only produces small attenuation to the photon beam. Lastly, the jaws(or Multi leaf collimator, wedges, or blocks) shape the photon beam.

(2) Adiagram of a linac treatment head and component modules are seen in Figure 1. Figure 1. Illustration of the treatment head andthe component modules (not to scale) used in the MC simulations for VarianClinac machines (different linac manufacturers may place components indifferent order.) (6) Thebremsstrahlung photon emission at high electron energies is given by m0/E0, where m0 is the rest energy of electron, and E0is the total energy. This results in a strong forward peaked angulardistribution.

(2) The target in a clinical linac is usually thick enough to stopthe primary electrons completely. In these targets, the bremsstrahlung photonangular distribution will be spread out as electrons undergo multiplescattering. The photon intensity will be anisotropic but the photon spectrumwill be isotropic. Due to this being complex, it is difficult to obtain acorrect spectral and angular bremsstrahlung photon distribution from thicktargets. The most comprehensive method developed to generate bremsstrahlungphoton distributions from targets in linacs is MC simulation. (2) Othertheories such as Schiff theory are simple analytical theories and are onlyapproximations. The use of the MC method in treatment headsimulation gives the highest accuracy and detail of the external radiotherapybeam and is now crucial in treatment head design.

(4) Accurate source modellingis essential in accurate treatment planning with MC simulations. The planningsystem is physically based, therefore the beam used in the dose calculation hasto be very accurate and detailed. Parameters for linacs can be defined usingvarious MC programmes PRIMO, BEAM etc. When the energy of an x-ray beam isgiven, the angular distribution of intensity can be calculated using MC techniquesover a range of clinical field sizes. Information about the materialspecification and geometry is essential in treatment head modelling.

As previously mentioned, the mostpractical way to determine the characteristics of a photon beam is to use MCtechniques to simulate the transport of particles through the treatment head.Using this approach, electrons are injected through the exit window of thetreatment head one at a time and their passing through the treatment head isfollowed by computer simulation. This approach provides us with highly detailedphase space information that can be recorded for every particle that leaves thetreatment head. (6) Unfortunately, storage space for these phase space filesthat contain millions of photons can be very large and the simulation time fora single beam can take days on an average computer. (6) Instead of using phasespace information as the direct input to dose calculation we use beammodelling. This will combat the large storage and simulation running timeproblem.

Beam representation is the first step of beam modelling. This includesdevising an appropriate representation of the beam for a certain design of thetreatment head based on the known characteristics of the beam. Beamrepresentation is a mathematical description of phase space.

The next step isbeam reconstruction. This involves reconstruction of the phase space from thebeam representation. We can forego theneed to store phase space data as the phase space can be reconstructed andinput into the dose calculation code one particle at a time. Beamrepresentation and beam reconstruction together form beam modelling. (6) Beam representationFor thisbeam modelling procedure a programme such as PRIMO or BEAM is used to calculatethe raw beam. A beam model can be selected for each photon beam energy and theparameters of the beam representation can be input into the programme. A rangeof energies such as 4MV, 6MV, 15MV and 20MV are typical energies that would bechosen to model a treatment head.

The Varian Clinac 2100 and Fakebeam linacscan be simulated. These linacs would be operated in photon mode. The materialsand geometries used in MC simulations have to be a realistic construction of alinac. The phase space 1 is construction of the beam model and phase space 2 isverification of the source modelled in a water phantom when dose distributionswere calculated (2) (6).

Full phase space data is one of the most essentialelements from a MC simulation. For a beam to be fully parametrized, exactknowledge of the beam characteristics are required. The binning approach usedin both PRIMO and BEAM does not require parametrization, only small knowledgeof beam characteristics is required. E.g. field size and maximum energy. (6) Abasic illustration of the process carried out in beam characterization and beammodelling for photon beams from a linac is shown below.

Note this illustrationuses BEAM, however procedure is similar for PRIMO and other MC programmes. Figure 2. Illustrationshowing procedures in beam characterization and beam modelling for photon beamsfrom a linac.Beam reconstructionToreconstruct phase space data it is best to use a multiple source model. Thismultiple source model is a simplified way to replace the large phase spacefiles that are generated from a MC simulation. (7) The multiple source modeltreats particles coming from different parts of an linac as if they are comingfrom different sources.

Particles coming from different components of a linacvary in energy, spatial and angular distributions. In comparison, particlescoming from the same component have similar values in terms of energy and angular/spatialdistributions. Beam reconstruction entails the use of the multiple source modelfor dose calculation. The energy, position and direction i.

e. the phase spaceinformation for every particle is reconstructed from the scored sourceparameters. (7) Firstly, a source is selected according to relative sourceintensity. Next, a position on the phase space plane is determined for theparticle based on the spatial distributions of the source. (6) Then a positionon the source is sampled. When the position on the phase space plane and theposition on the source is determined this will give the incident direction ofthe particle. Finally, the particle energy can be sampled from the energy distributionfor the source. The particle position and energy can be sampled independentlyas there is a weak correlation between particle energy and position forparticles from the same source.

(6) Energy spectra can be scored based on theparticle position on the phase space plane. For spatial and energy sampling onthe source and on the phase space plane the binning approach was taken.Efficient and accurate reconstruction of the energy and spatial distributionsrequires appropriate bin widths. As mentioned previously, reconstruction of thebeams are used for calculation of 3D dose distributions in water (or patient)phantoms. (6) These results can be compared to calculations made using theoriginal phase space data as seen in Figure 2.Variance reductionVariancereduction techniques including bremsstrahlung splitting and Russian rouletteare used in MC simulations to improve the efficiency of the system.

Splittingand Russian roulette are used together in PENELOPE MC code. The combined use ofthese allow for a more efficient simulation. Splitting is generating multiplephotons from each electron interaction, the weight of the photon isproportionally reduced (6). In PRIMO a value for the ‘splitting factor’ can beraised to reduce computing time and to give a more accurate result. Photonforcing also increases efficiency when combined with photon splitting. Thephoton forcing technique increases the probability of a photon interaction withdifferent components of a linac. Range rejection is another variance reductiontechnique that improves the efficiency of a treatment head.

This depends on theinitial energy of the electron. If an electron has a lower energy than the cutoff, which is determined by the user, the electron history is terminated. It isan approximation as no bremsstrahlung is possible. The low energy cut-off forelectrons led to reduced simulation time and affects dose distribution (8).

Overall, we know that implementing variance reduction techniques to the MCsimulations increases accuracy and efficiency. Flattening filterAsmentioned previously a linac can contain a component called a flattening filterto produce a flat dose distribution in water. It has a very good impact whendetermining beam profile and ensures uniform intensity distribution of X-raybeams generated from the target. It also acts as a metal absorber of low-energyX-ray beams. This ensures that the mean energy of the beam increases. Inflattening filter free linacs the flatness of the beam is lower. However, inthe case of small-field size radiation treatment there is very little differencein flatness observed when the flattening filter is removed. (3)(9) Inconclusion, it is clear Monte Carlo simulations are the most powerful method oftreatment head modelling and dose calculation in radiotherapy.

The MC methodused in radiotherapy gives the most accuracy between 2 and 3%. It has beenemphasised in this essay the capabilities of the MC method when used formodelling external radiotherapy photon beams, but it has also proven to beextremely capable of modelling external radiotherapy electron beams and patienttreatment verification. As technology evolves and computing power increases(according to Moore’s Law) the problem of simulation running time and phasespace storage may be significantly reduced. The MC method will become the mainmethod in treatment planning for radiotherapy and become increasingly importantin imaging diagnostics also. References1. Monte Carlo Simulationhttp://www.

palisade.com/risk/monte_carlo_simulation.asp2. PRIMO User Manual Brualla,Rodriguez, Sempau3. “Monte Carlo modelling of external radiotherapyphoton beams” by Frank Verhaegen and Jan Seuntjens 2003 Phys. Med. Biol. 48R1074.

Monte Carlo for Radiotherapy I: Source Modellingand Beam Commissioning for Monte Carlo Treatment Planning AAPM 2005 ContinuingEducation Course, C Ma, B Faddegon, B Curranhttps://www.aapm.org/meetings/05AM/pdf/18-4011-55406-780.pdf5. Unflattened photon beams from the standardflattening filter free accelerators for radiotherapy: Advantages, limitationsand challengeshttps://www.ncbi.

nlm.nih.gov/pmc/articles/PMC3159217/6. “Photon beam characterization and modelling forMonte Carlo treatment planning”Jun Deng,Steve B Jiang, Ajay Kapur, Jinsheng Li, Todd Pawlicki, C-M Ma2000 Phys.

Med. Biol. 45 411 7. “Electronbeam modelling and commissioning for Monte Carlo treatment planning”SteveB. Jiang, Ajay Kapur, and C.-M. Ma PublishedOct. 19998.

“Evaluation of variance reduction techniques inBEAMnrc Monte Carlo simulation to improve the computing efficiency”MagedMohammed, E.Chakira, H.Boukhal.

MroanSaeed. T.El Bardouni9. “A study on the effect of using a flattening filterin 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