Monte-Carlo in RadiotherapyWhy do we need it?How does it work?Why should we trust it?

Alan E. Nahum PhDPhysics DepartmentClatterbridge Centre for OncologyBebington, Wirral CH63 4J Y UK(alan.nahum@ccotrust.nhs.uk)

XI. ULUSAL MEDIKAL FIZIK KONGRESI, 14-18 KASIM 2007, CONCORDE HOTEL, ANTALYA

Photons

e-e+

Bremsstrahlung

Comton-scattered photon

Pair production

Photoelectric absorption

Delta ray

There are no analytical solutions to radiation transport except in very simple approximations

COMPTON

COMPTON

RAYLEIGH

PHOTO. ABS.

e-

e-

Photon

mediumvacuum

A. Choose photon energy from spectrum (if, say, bremsstrahlung source).

B. Compute distance from surface/entrance point in medium to 1st interaction

C. Choose interaction type (Pair, Compton, Photoelectric, Rayleigh/coherent)

D. If COMPTON, ‘choose’ (i.e. sample from Klein-Nishina differential cross-section using pseudo-random numbers) energy of scattered photon, angular deflection and secondary electron (kinetic) energy

If PAIR, terminate photon history; choose energy of positron and electron, then ‘choose’ directions of these particles.

If PHOTO, terminate photon history, deposit energy at position of interaction

If RAYLEIGH, ‘choose’ angular deflection, no energy loss.

E. IF COMPTON or RAYLEIGH then transport scattered photon to next interaction and repeat above etc. ELSE if either PAIR or PHOTO then start new photon history.

Distance to next interaction Probability of interaction occurring between x and x + dx is exp (-x ) dx Thus x

F(x) = exp (-x ) dx = 1 – exp (-x) o R = 1 – exp (-x ) X = -1/tot loge (1 – R)

COMPTON

COMPTON

RAYLEIGH

PHOTO. ABS.

e-

e-

Photon

mediumvacuum

A. Choose photon energy from spectrum (if, say, bremsstrahlung source).

B. Compute distance from surface/entrance point in medium to 1st interaction

C. Choose interaction type (Pair, Compton, Photoelectric, Rayleigh/coherent)

COMPTON

COMPTON

RAYLEIGH

PHOTO. ABS.

e-

e-

Photon

mediumvacuum

A. Choose photon energy from spectrum (if, say, bremsstrahlung source).

B. Compute distance from surface/entrance point in medium to 1st interaction

C. Choose interaction type (Pair, Compton, Photoelectric, Rayleigh/coherent)

D. If COMPTON, ‘choose’ (i.e. sample from Klein-Nishina differential cross-section using pseudo-random numbers) energy of scattered photon, angular deflection and secondary electron (kinetic) energy

If PAIR, terminate photon history; choose energy of positron and electron, then ‘choose’ directions of these particles.

If PHOTO, terminate photon history, deposit energy at position of interaction

If RAYLEIGH, ‘choose’ angular deflection, no energy loss.

E. IF COMPTON or RAYLEIGH then transport scattered photon to next interaction and repeat above etc. ELSE if either PAIR or PHOTO then start new photon history.

Electrons

AN ELECTRON “PENCIL”

Monte Carlo transport of electrons

In principle similar to photon transport, but…-photons travel relatively long distances before interacting -electrons interact with every atom they encounter

transporting electrons in an analogue fashion takes a very long time – many thousands of individual scattering/energy-loss events

However, for Radiotherapy (and many other applications) we do not need to simulate (electron) transport on a microscopic scale – macroscopic is sufficient

”Condensed-history” transport scheme: multiple scatter, stopping power etc. (Berger, 1963)

MACROSCOPIC e- MC:Grouping of collisions -> Multiple scattering Stopping Power dE/ds

Multiple scattering angular distributions for 1-MeV electrons in graphite

electron

Multiple scatt.

Multiple scatt.

Bremss. loss.

-rayMultiple scatt.

CUTOFF

mediumvacuum.

(dE/ds)●s

A schematic illustration of the segments of a ‘condensed-history’ electron track.

Visualisation20 MeV electrons in water...

+ Bremsstrahlung photons...

20 MeV electrons in tungsten...

+ Bremsstrahlung photons...

An electron “pencil” (courtesy of Pedro Andreo)

Depth-dose “anatomy” 30 MeV e- (Seltzer et al)

It is important to realise that the condensed-history method is artificial, and there is no one single correct way to construct such a scheme.

Different research groups have devised different schemes

e.g. the EGS code (Nelson et al 1985) employs a so-called Class-II scheme (see Berger 1963; Andreo 1985) where secondary-particle generation is explicitly simulated at energies above user-chosen cutoffs, whereas the ETRAN code (subsequently absorbed into the ITS- and MCNP-code systems) devised by Martin Berger and Steve Seltzer (see Seltzer 1988) employs a Class-I scheme in which all energy losses, no matter how large or small, are ‘condensed’ into track segments, and secondary-particle generation is handled in a statistical fashion.

Furthermore, there are several different schemes for determining the artificial segment- or steplengths, and the appropriate choice depends on the problem being tackled.

For example, the simulation of the response of gas-filled ionisation chambers has presented many challenges to the C-H method (Rogers et al 1985; Bielajew and Rogers 1987; Nahum 1988b; Rogers 1992, 1993; Kawrakow and Bielajew 1998) and was only satisfactorily resolved with the development of EGSnrc (Kawrakow 2000a,b).

Electron beam depth-dose curves

CPU time required

1 Gy => 1 billion electrons

1 Gy => 1000 billion photons

1% uncertainty for 0.3 cm cubes requires

a few million electrons (minutes on a PC)

1% uncertainty for 0.3 cm cubes requires up to a few billion photons (hours on a PC)

EGSnrc (the new version of the Electron Gamma Shower (EGS) code system, following on from EGS4 (Nelson et al. 1985) the most widely used code in medical physics, cited thousands of times in the medical physics literature; EGSnrc is the only code demonstrated to be able to simulate (gas-filled) ion chamber response in an entirely valid manner)http://www.irs.inms.nrc.ca/inms/irs/EGSnrc/EGSnrc.html

BEAMnrc (technically not an independent code but a version of the EGS system designed for modelling radiotherapy treatment machines, primarily a research tool, as it is not optimised for speed)http://www.irs.inms.nrc.ca/inms/irs/BEAM/beamhome.html

MCNPX (includes neutron transport; extensive use in nuclear power industry and now in medical physics)http://mcnpx.lanl.gov/

GEANT4 (huge, many-particle MC toolkit; beginning to be used in medical physics)http://geant4.web.cern.ch/geant4/

PENELOPE (sophisticated electron transport; a research code)http://www.nea.fr/html/dbprog/penelope-2003.pdf

PEREGRINE (developed for radiotherapy planning; available commercially through the NOMOS corporation)http://www.llnl.gov/peregrine/

MCDOSE/MCSIM (developed for fast treatment planning, based on EGS4/BEAM but optimized for speed due to, e.g. electron-track repeating; has user-friendly, measurement-based clinical beam commissioning system)http://www.fccc.edu/clinical/radiation_oncology/monte_carlo_course.html

Voxel-MC (VMC++) (developed specifically for fast treatment planning; exploits electron-track repeating; is the MC dose engine for electron-beam treatments in the Oncentra/Masterplan TPS)

DPM (developed specifically for fast radiotherapy treatment planning; electron transport scheme involves large condensed-history steps crossing medium boundaries)http://www.upc.es/inte/downloads/dpm.htm

Summary - MC contributions to Radiotherapy

• Improved understanding of basic physics

• Accurate computations of quantities required in absolute

dosimetry: SPRs

• Dosimeter-response simulations

• Detailed modelling of linac beams

• Treatment planning - current accuracy quantified;

commercially available for e-

• Quasi-essential for (photon) IMRT especially in lung,

head and neck