Abstract
Monte Carlo (MC) simulations play an important role in radiotherapy, especially as a method to evaluate physical properties that are either impossible or difficult to measure. For example, MC simulations (MCSs) are used to aid in the design of radiotherapy devices or to understand their properties. The aim of this article is to review the MC method for device simulations in radiation therapy. After a brief history of the MC method and popular codes in medical physics, we review applications of the MC method to model treatment heads for neutral and charged particle radiation therapy as well as specific in-room devices for imaging and therapy purposes. We conclude by discussing the impact that MCSs had in this field and the role of MC in future device design.
Keywords: Monte Carlo method, device simulation, radiation treatment
1. Introduction
1.1. Early applications of the Monte Carlo method
From its first suggestion in 1947 (Ulam and von Neumann 1947), the Monte Carlo (MC) method for stochastic simulations was proposed by Metropolis and Ulam in 1949 as an alternative approach to solve problems occurring in various branches of the natural sciences (Metropolis and Ulam 1949). For its first usage, nuclear disintegrations produced by high-energy particles were investigated by using random numbers between zero and one to decide the momentum of a target particle weighted by the cross-section for a collision (Goldberger 1948). In the 1950s, several studies investigated the reflection of gamma rays for different types of matters using the MC method (Hayward and Hubbell 1954, Berger and Doggett 1956, Berger and Raso 1960). Energy loss distributions were calculated for 1 MeV electrons considering multiple scattering in aluminum and gold (Hebbard and Wilson 1955). Backscattering of gamma rays was simulated in various materials such as water, hydrogen, lead, etc, which includes the probability of reflection (often called albedo) of various materials for 0.02–2 MeV gamma rays. The first application of MC for electron transport focused on evaluating the range and straggling of high energy electrons (Wilson 1951). Electron energies from 50 to 1000 MeV were assessed and the average range against the energy was studied for aluminum, copper, and lead.
1.2. Advent of multi-purpose codes
Most early MC applications were based on user-developed codes which were not designed for use by the general research community. As computers became more powerful and more frequently available, various simulation codes were developed that served as platforms for a variety of applications for the research community. In 1962, Ranft and Geibel developed a simulation code for hadron beams, which was subsequently named FLUKA (FLUktuierende KAskade, German for fluctuating cascade) in 1970. The MC codes known as MC simulation (MCS) and MC neutron (MCN) were developed by scientists at Los Alamos National Laboratory in 1963 and 1965, respectively. They were eventually merged into the MCN-particle transport code (MCNP) in 1977. Influential work was done by (Berger 1963) who calculated the penetration and diffusion of fast charged particles. For charged particle beams the explicit tracking of every particle and its interactions is very inefficient due to the high frequency of interactions. Berger developed the idea of approximating individual interactions by combining multiple interactions (Berger 1963). He introduced the concepts of transport equations and condensed histories, considering charged particle histories as snapshots of a moving picture, and suggested methods related to parameterize path length, energy loss, and angular deflection leading to solutions for various physical problems with charged particles. These methods became fundamental in the development of MC algorithms and codes. Based on this work, the ETRAN (Electron TRANsport) code was developed in 1968 (Seltzer 1991). Electron Gamma Transfer 3 (EGS3) was introduced by Ford and Nelson in 1973, followed by EGS4 by Nelson et al in 1985 (Ford and Nelson 1978, Nelson et al 1985).
The first version of the GEometry ANd Tracking (Geant) code was written in 1974 as a bare framework to simulate particle transport in simple geometry detectors (Brun et al 1978). In 1982, Geant version 3 was released incorporating continuous developments from contributors (Brun et al 1993). In 1993, CERN and KEK started the Geant4 project, building on Geant3 (Agostinelli et al 2003) but with the vision to design a modular code in a (at that time) modern programming language, C++. The research and development phase and first production release of Geant4 was completed in 1998 (Glani et al 1998). For proton transport with energies from 50 to 250 MeV, PTRAN (Berger 1993) was introduced in 1993–1994, when MCN Photon (MCNP) could not consider proton transport and Geant did not have reliable low-energy transport modules (Palmans 2004). At that time, the first version of PENetration and Energy Loss of Positrons and Electrons (PENELOPE), which was written in Fortran 77, was also reported (Salvat et al 1996).
1.3. Early use of MC in medical physics
Even though most MC codes were originally designed for high-energy particle physics research, MC techniques started to be applied in the field of medical physics (MP) in the 1960s to early 1980s by providing alternatives to photon measurements. For radiotherapy physics, MCSs mainly aimed at investigating particle transmission and dose deposition. Berger studied the interface effect on dose distributions with 60Co gamma rays (Berger 1971). Kuspa and Tsoulfanidis calculated build-up factors for gamma-rays with slab shields (Kuspa and Tsoulfanidis 1973). Electron production in aluminum, iron, and lead was investigated for low energy gamma rays (Wecksung et al 1971, Minato 1973). The full electromagnetic cascade in water was studied by Andreo who calculated the energy spectra of electrons in water (Andreo and Brahme 1981). In 1978, ion chamber correction factors were calculated as a function of wall thicknesses for 60Co gamma rays (Bond et al 1978). This work was extended to the calculation of the chamber response curve of 60Co gamma rays with the attenuation and scattering in matter (Nath and Schulz 1981b).
The use of MCS for proton beams began in the late 1970s. Researchers in proton therapy were looking for methods to accurately predict dose without the ability of exit dose verification as in photon therapy. In 1978, Goitein et al simulated dose distributions in inhomogeneous geometries to study the influence of thick inhomogeneities within the beam path (Goitein and Sisterson 1978). This work was followed by Urie’s work to evaluate the effect of beam modifiers on the beam penumbra (Urie et al 1986).
The more widespread use of MCSs prompted the American Association of Physicists in Medicine (AAPM) to form a Task Group to develop a protocol for the determination of absorbed dose by photons and electrons (1983) and a protocol for heavy charged particles (1986). The reports included quantities, constants, and correction factors that were calculated using MC method (Task Group 21 RTC (1983), Task Group 20 R T C (1986)).
1.4. MC codes in MP
1.4.1. EGS
The electron gamma transfer (EGS) code system, consisting of EGS and PEGS (Preprocessor for EGS), was named in 1974 as a revised version of the code SHOWER (Ford and Nelson 1976). The first version of the EGS system was simply called EGS1 and PEGS1. By the end of 1975, the EGS system was rewritten as version 2 to handle more complex three-dimensional geometries. In 1978, EGS3 was introduced by Ford and Nelson as a Mortran-based simulation code. The first purpose of the EGS code was to simulate high-energy particle shielding and to design radiation detectors. The first accelerator model of a Clinac-35 treatment head was built using the EGS system by (Petti et al 1983). It was reported that EGS3 produced step-size artifacts in the simulation which led to observable errors in the calculation of ion chamber response. Larsen explained that shortening steps can solve the problem but it increased the computational time. In 1985, a new version of the EGS code (EGS4) was developed (Nelson et al 1985). Compared to EGS3, the accuracy of radiation delivery in EGS4 was improved by including revised definitions of radiation length for materials with low atomic numbers. In addition, possible electron energies were extended to as low as 10 keV. The step size artifacts were removed by reducing the step size in the simulations of ion chamber response (Bielajew et al 1985, Rogers et al 1985) followed by EGS/PRESTA (Parameter Reduced Electron-Step Transport Algorithm for electron MC transport) which automatically selects the optimum step-size to reduce calculation time (Bielajew and Rogers 1986).
In the 1990s, the use of EGS4 rapidly increased, particularly to simulate photon and electron transport for energies from a few keV to MeV in various geometries (Simpkin and Mackie 1990, Thomason et al 1991, Metcalfe et al 1993, Mobit et al 1997, Kapur et al 1998). Subsequently, the EGS codes were further improved resulting in the development and revision of the code. A new version of EGS known as EGSnrc was released in 2000 (Kawrakow and Rogers 2000, Rogers et al 2003, Hirayama et al 2005, Rogers et al 2009). The EGSnrc code became computationally more efficient owing to improvements in the electron step algorithm, boundary crossings, and evaluation of energy loss (Kawrakow 2000). In 2001, BEAMnrc and DOSXYZnrc were introduced for modeling radiotherapy beams and calculating dose distributions, respectively, and a combined version was released in 2002 (Walters et al 2005, Rogers et al 2009). In 2004, EGS5 was introduced, which included improvements in electron and photon physics models and the merged EGS and PEGS (Hirayama et al 2005). The family of EGS codes became the codes of choice in medical applications including brachytherapy, gamma knife, as well as intensity modulated radiation therapy (IMRT) and volumetric modulated arc therapy (VMAT), which require 4D simulation capabilities (Jones et al 2003, Stapleton et al 2005, Pourfallah et al 2009, Lobo and Popescu 2010, Belec and Clark 2013, Granton and Verhaegen 2013, Breitkreutz et al 2017, Ishihara et al 2017, Molazadeh et al 2017).
1.4.2. MCNP and MCNPX
In 1963, MCS, the first general-purpose MC code, was developed, followed by MCN in 1965, which could solve neutron-related problems in a 3D geometry (Cashwell et al 1972, Forster et al 1990). To solve problems involving photons, codes called MC Gamma (MCG) and MC Photon (MCP) were developed, which dealt with photons of higher energies and energies down to 1 keV, respectively (Cashwell et al 1973). In the same year, the MC coupled Neutron and Gamma (MCNG) code was developed by merging MCN and MCG to model photon-neutron interactions (Briesmeister 2000). In 1977, MCNG was merged with MCP to form MCNP, for time-dependent transport of neutrons, photons, and electrons (Briesmeister 2000). MCNP incorporated several improvements with user-defined structures and offered a generalized tally, automatic calculation of volumes, and determination of nuclear criticality (Briesmeister 2000).
In 1983, MCNP version 3 was released (Briesmeister 2000). This version further satisfied user requirements such as tally-plotting graphics, various source terms, repeated structures and lattices, and multigroup/adjoint transport. MCNP still required modifications to solve problems of perturbation for material density, angle biasing, and special tallies for detector response (Forster et al 1990). MCNP version 4 was released in 1990 with efforts to provide new capabilities including electron transport, a new bremsstrahlung photon model, a multitask processor for running in parallel on workstations, and a pulse-height tally (Forster et al 1990, Briesmeister 2000). The pulse-height tally provided energy distributions in a detector, as well as the detector response. However, the new tally did not work with variance reduction techniques such as energy cutoff, Russian roulette, or particle biasing until the next version (version 5) was developed.
Originally, most studies using MCNP were focused on neutron transportation (Brugger and Herleth 1990, Liu et al 1992, Metzger et al 1993, Wallace et al 1995, Evans and Blue 1996). With the development of the extended version of MCNP 4A, known as MCNPX in 1994, extended particle and energy libraries were available with new variance reduction and data analysis techniques. In addition, photon benchmarks exhibited good agreement between MCNP and measurements (Whalen et al 1991, DeMarco et al 1995, Wallace and Allen 1998, Edwards and Mountford 1999, Boudou et al 2005, Serrano et al 2006, Ferrari and Gualdrini 2007). With the revisions and benchmarks of the code, a sharp increase in the number of studies employing the MCNP series was observed in late 1990s and early 2000s (section 1.5). Note that source code access to MCNPX is restricted. The research subjects also varied from external beam radiotherapy to internal dosimetry (Anagnostopoulos et al 2004, Barquero et al 2005, Boudou et al 2005, Serrano et al 2006, Ferrari and Gualdrini 2007).
MCNP version 5 (MCNP5), released in 2003, provided solutions for the perturbation problem, low-energy correction for electrons, and more accurate calculations for detector response (Brown et al 2002). A history deconvolution approach was employed to solve the problem that the pulse-height tally did not work with variance reduction techniques in MCNP 4A. In addition, MCNP5 included new features such as photonuclear collision physics, superimposed mesh tallies, and support for message passing interface parallel processors. MCNP5 was also validated across different hardware and software with benchmarks that employed various test suites (Brown et al 2011). The developers of the MCNP5 and MCNPX merged their codes, which subsequently became the MCNP version 6 (Goorley et al 2012). More detailed validation was carried out on MCNP6 with expanded validation suites (Goorley et al 2012). The latest version of MCNP (version 6.2) was released in 2018, with improvements of physics models for secondary emissions and decay productions, decay sources and cosmic ray sources. The version also included revised libraries for cross section data, improved or newly imported tally options, functions related to unstructured mesh, and other code enhancements to improve ease of usage of MCNP. Moreover, faster calculation became available, which was 1.5–2 times faster, compared to the previous MCNP version.
1.4.3. GEANT
The first version of the Geant code was written in 1974, which emphasized tracking particles for a single generation of a primary particle in detectors of simple geometries (Brun et al 1993). Through a series of revisions of the code, Geant version 3 was eventually written in 1982 following an idea of Brun and McPherson (Brun et al 1993). In 1993, CERN and KEK separately investigated the application of modern computing techniques on the simulation to improve Geant3 (Agostinelli et al 2003). These two different studies were merged and the Geant4 project was started in 1994. Based on Geant3 (Fortran), Geant4 (C++) was developed to meet the increasing demand for large-scale, accurate simulations of various particle types, which required more flexibility, complexity, and efficiency. Geant4 was first released in 1998, and the Geant4 Collaboration was established in early 1999 to continue developing and refining the toolkit and coordinate the tasks by many developers (Glani et al 1998).
The code was designed as an object-oriented toolkit using the C++ language with a versatile and comprehensive software package, which led to flexibility for reproducing several experimental conditions and simulating complex geometries, allowing particle transportation with various physics models, different scoring options and 4D functionality. These features were well suited for simulating modern radiotherapy such as IMRT, VMAT, and Image-guided Radiation Therapy (Carrier et al 2004, Rogers 2006). Compared to other simulation codes, its object-oriented design helped users to effectively manage complexity and the open source design allowed users to add functionality if needed. The detailed technical and historical developments of the early Geant4 software system are summarized by (Agostinelli et al 2003).
With continuing validation of the code, the number of papers employing Geant4 increased in a short period of time and exceeded those using other general MC codes, e.g. it was predominantly used after 2011 (section 1.5). Carrier et al (2004) reported a study on the validation of Geant4 for simulations in the field of MP and showed its suitability by comparing depth-dose curves with measurements by Lockwood et al MCNP by Chibani et al and EGSnrc by Wang and Li (Lockwood et al 1980, Wang and Li 2001, Chibani and Li 2002, Carrier et al 2004). Paganetti and Gottschalk tested nuclear models of Geant3 and Geant4 for 160 MeV protons stopping in Cu and CH2 (Gottschalk et al 1999, Paganetti and Gottschalk 2003) followed by experimental validation of nuclear halo simulations (Hall et al 2015). A comprehensive validation with experiments was done for proton therapy (Testa et al 2013).
With the release of Geant4 version 6.2, a better distribution of electrons at geometrical boundaries was observed with corrections in multiple scattering processes (Poon and Verhaegen 2005), but a problem related to electron transport near the geometrical boundaries according to step sizes led to distortions of the particle fluence (Poon et al 2005, Poon and Verhaegen 2005). It was important to apply a realistic multiple scattering model for better accuracy. The model decides the step characteristics of charged particles, such as the step length, scattering angle and particle direction, displacement of end point, and step limits (Ivanchenko et al 2010). In late 2004, Geant4 version 7.0 was introduced with an improvement to the multiple scattering model to reduce the step size dependency (Allison et al 2006). Furthermore, for advanced geometry simulations, new twisted solid models were provided in this version. Meanwhile, computational efficiency was still limited compared to other codes.
In a report by Allison to introduce new developments from the 8.1 to 10.1 releases, Geant4 enabled an improved estimation of the isotropic safety, which is the distance to a boundary in any direction from its current position (Allison et al 2016). This prevented the lateral displacement of particles in order to avoid unintended crossing of boundaries within a step and solved the step-related problems mentioned above. During the same period, Geant4 also revised the electromagnetic scatter models offering a range of multiple and single scattering models. This enabled faster and more accurate simulations. Another noteworthy improvement was enabling multi-threading (Allison et al 2016). Recent radiotherapy techniques such as IMRT required a large amount of calculation time and memory space. Multi-threaded applications that share part of the key data between the independent threads saved memory and boosted simulation speed. Geant4 versions starting with 10.0 provided multithreading, the message passing interface processor and a hybrid approach with an efficient memory usage during simulations. According to Allison et al simulation efficiency in a problem with Compact Muon Solenoid detector geometry was increased by more than 95% with 32 threads compared to a single thread (Allison et al 2016).
1.4.4. FLUKA
FLUKA is a multipurpose tool for particle transport and began its history as a Fortran-based code in 1962 (Ranft and Routti 1973). FLUKA is classified into three different generations—the FLUKA of the 70s, 80s, and today. Each generation originated from the previous one, but each stage had significant developments in the physics, design and goals (Ferrari et al 2005). The origin of FLUKA was a non-analogue code for designing shielding of high energy proton accelerators (Ferrari et al 2005). The first generation of FLUKA (70s), a fully analogue version of the code, was written and published between 1967 and 1969. The code was used in evaluating the performance of NaI crystals used as hadron calorimeters (Ranft 1970). The version described inelastic hadronic interactions with an event generator and only the deposited energy could be scored. However, simple ionization losses and multiple Coulomb scattering were implemented with a transport cut-off set at 50 MeV for all particles.
For the second generation of the code, a complete re-design began in 1978 with the goal of supplying more flexible geometries and modern hadron interaction models. Cuboidal and spherical geometries were added in FLUKA82 while only cylinders were available in FLUKA81. The EGS4 code was linked to FLUKA86 allowing the transport of gammas and photon induced hadrons. New features were introduced in the version of 1987 to solve limitations in high energy hadron simulations with the transport cut-off at 50 MeV. FLUKA specialized on high energy accelerator shielding in its second generation.
The third generation of FLUKA evolved into a multipurpose code to be applied in a wide range of research areas. In 1989, an independent model of multiple scattering for charged particles was implemented (Ferrari et al 1992, Ferrari et al 2005). In the same year, the model for ionization losses was re-written and light ions such as deuterons, and tritons were added. In the 1990s, neutrons with energy lower than 20 MeV could be handled in FLUKA. In 1993, developments and improvements in FLUKA were reviewed with the introduction of benchmarks and applications for hadron transport (Aarnio et al 1993). Ferrari et al Collazuol et al and Ballarini et al described hadronic interactions in FLUKA (Ferrari et al 1996, Collazuol et al 2000, Ballarini et al 2006). The number of particle types that could be simulated in FLUKA was also increased from 25 in 1990 to 63 in 1999. In 2003, the physics models of particle interactions in FLUKA such as hadron–neutron interaction and nucleus collisions was reviewed (Fasso et al 2003). Aiginger introduced capabilities of FLUKA for ion beams showing its suitability for the transport of ions with energies up to 1 GeV (Aiginger et al 2005).
In hadron therapy, FLUKA was benchmarked against models and experimental data (Sommerer et al 2006). Battistoni et al reviewed code descriptions with benchmarks in electromagnetic, muon, and charged particle transport (Battistoni et al 2007). Bohlen benchmarked nuclear models of FLUKA and Geant4 for carbon ion therapy. More recently, the capabilities of the FLUKA code for transporting various particle types were summarized (Battistoni et al 2007, Bohlen et al 2010). FLUKA has been consistently used in various research fields including dosimetry for external radiation therapy, medical applications with high energy particles, and internal dosimetry (Pignol et al 1998, Pignol and Slabbert 2001, Soderberg et al 2003, Sommerer et al 2009, Sinha et al 2016, Sunil 2016, Chiriotti et al 2018,Kozlowska et al 2019).
1.4.5. PENELOPE
The Nuclear Energy Agency Data bank distributed the first version of PENELOPE in 1996 for simulation of the coupled transport of electrons, positrons and photons with energies from hundreds of eV to 1 GeV in complex geometries and arbitrary materials (Salvat et al 1996). PENELOPE, which was written in Fortran 77, consisted of various programs and packages, i.e. MAIN program to control overall simulation from geometry to particle transportations, MATERIAL program to define material data file, and other subroutine packages such as PENGEOM.
A modification of PENELOPE in 2000 was done as an intermediate step to the version of 2001, which included several revisions in physics models and MAIN programs (Salvat et al 2001). The physics model for electron/positron elastic scattering was revised from the previous Wentzel model. This enabled PENELOPE to more accurately define particle angular distributions, which were abnormally wide or narrow according to the particle energies. The bramsstrahlung emission was simulated by using partial-wave data rather than analytical approximate formulae. Fluorescence radiation from K- and L-shells was followed, which was not possible with the previous version. With the PENELOPE version 2003, inner-shell ionization of electron/positron was described as an independent mechanism to give realistic values of the cross sections not available in the version of 2001 (Salvat et al 2003). The code was experimentally benchmarked especially in terms of the bremsstrahlung model (Sempau et al 2003). Ye et al verified the PENELOPE code for low-energy photon simulations by comparing dose distribution to MCNP4 and EGS4 (Ye et al 2004).
In the PENELOPE version 2006, a rational inverse transform with aliasing algorithm was implemented to enable faster determination of random variables (Salvat et al 2006). In 2008, PENELOPE was given enhanced algorithms for particle transport, e.g. the ionization of inner shells were described by newly calculated cross sections (Salvat et al 2008). Photon polarization effects during the scattering was added as well as algorithm for modeling Rayleigh photon scattering, and electron/positron inelastic collisions were refined. The MAIN program was also given new options such as extended sources and calculation of energy distributions in selected geometries.
In 2011, both algorithms for defining geometry and physics phenomena were revised (Salvat et al 2011, Salvat 2014). Improved modeling of polarized photon beams than the previous version was possible. The inelastic collision model for electron/positron was improved by replacing discrete excitation spectra of the electron subshells with continuous ones. For the geometry package, the innermost part of the PENGEOM was revised to solve problems from regarding the limiting surfaces as quadrics. This caused ambiguities in determining whether the particle is located at the correct side of the surface. The problem was solved by regarding the limiting surface as fuzzy, which slightly swells or shrinks when the particle crosses it. In the PENELOPE of 2014, description of ionization was extended to N shells and ionizing events were regarded as proper inelastic collisions (Salvat 2015). The variance reduction routines were reformulated as well as the bremsstrahlung splitting was newly included (Salvat 2015). For the recent version, some of the cross section databases were recalculated or expanded (Salvat 2019). The MAIN program was also extended to include the option of radioactive sources with a single radionuclide (Salvat 2019).
From its early usage, PENELOPE has been applied to the transport and dosimetry of high-energy electron beams or photons (DesRosiers et al 2000, Sempau et al 2001,Moskvin et al 2002). The code also underwent various benchmarks related from x-rays of different energies and other charged particles such as protons (Chica et al 2009, Sterpin et al 2013). The code has been used in the simulations of electrons, as accordance with its acronym, and also photons and protons (Uusijärvi et al 2009, Moskvin et al 2010, Benmakhlouf et al 2014, Hult 2015, Mirzakhanian et al 2018, Lee et al 2018, Verbeek et al 2021).
1.4.6. User-friendly frameworks for general codes
BEAM is a general purpose code to simulate photon and electron beams from radiotherapy devices and was developed by the National Research Council of Canada as part of the Ottawa-Madison Electron Gamma Algorithm project (1990). The BEAM code was developed based on EGS4/PRESTA (Rogers et al 1995). The code was designed to produce phase space files including the beam information such as position, energy, and direction at any specified plane. In addition, the geometry models available for treatment heads consisted of individual component modules that could cover various types of accelerators. In 2001, a graphical user interface (GUI) for the BEAM code was reported to provide users with better accessibility, simplified input processes and graphical representations of geometries (Treurniet et al 2001). In 2002, the BEAMnrc based on the EGSnrc system was released. Since 2002, new versions of the BEAMnrc code are being developed such as adapting BEAMnrc for multi-platform versions to also run on Windows (Rogers et al 2009).
In Geant4 users typically have to spend significant time to learn the underlying C++ architecture and to tailor the code to their needs (Arce et al 2008). The Geant4 application for tomographic emission (GATE) provides a collection of pre-written Geant4 code to make Geant4 simulations more user-friendly. The OpenGATE collaboration originally developed GATE to allow simulations of PET and single-photon emission computed tomography (SPECT) radiographic systems without detailed knowledge of the C++ programming language (Strulab et al 2003). The code structure, physics, benchmarks and validations was summarized by Jan et al (2004). Following continuous refinement of the GATE code, GATE version 6 was released in 2011 and recently GATE version 8 was released in 2017 as open-source code.
The Geant4-based architecture for medicine-oriented simulations (GAMOS) was first introduced in 2006 to provide an easy way to use Geant4 applications in nuclear medicine with a script-based language (Arce and Rato 2006, Arce et al 2007, Arce et al 2008, Arce et al 2009, Arce and Lagares 2010, Arce et al 2011, Arce et al 2014). The latest version of GAMOS (6.1.0) was released in 2019. The applications of GAMOS have mainly been in nuclear medicine to simulate devices such as PET (Chmeissani et al 2009, De Lorenzo et al 2013, Kolstein and Chmeissani 2016).
TOPAS is a wrapper around Geant4 for MP application and was developed by (Perl et al 2012). It allows users to run complex simulations without any C++ knowledge and with the underlying Geant4 structure hidden to make the code user-friendly and easy to use. TOPAS was originally developed for proton therapy, however, since TOPAS provides a flexible interface to all functions available in Geant4, it has been applied in nearly all fields related to radiation therapy. The TOPAS system has been extensively validated particularly for proton therapy (Testa et al 2013, Grassberger et al 2015, Hall et al 2016). Since 2018, TOPAS has been included in the ‘Informatics Technology for Cancer Research’ program of the National Cancer Institute in the US. TOPAS simulations are generally controlled by text based parameter files, but since TOPAS version 3.3, TOPAS also provides a GUI (Faddegon et al 2020).
Many other codes are aiming at a wider user community. For instance, a GUI for FLUKA, which is called FLAIR, was developed by Vlachoudis (2009). PENELOPE also has branches for specific uses, such as PeneloPET for PET simulation (España et al 2009). Other codes and interfaces exist, but not all can be listed here.
1.5. Scope of this review
This manuscript is not meant to be a general Introduction into the MC method. This would be a review by itself. Instead, the manuscript solely focuses on applications of MCSs for device simulation problems. We assume that readers have the general background about this method, and hence introductory information about this method is not provided. Such introductions into the MC method can be found elsewhere.
Several review papers regarding applications of the MC method to radiotherapy have been published since the mid-1970s (Raeside 1976, Turner et al 1985, Rogers and Bielajew 1990, Andreo 1991, Bielajew 2001, Verhaegen and Seuntjens 2003, Rogers 2006). There have been several books on the employment of MCSs in radiation therapy (Jenkins et al 1988, Bielajew 2013, Haghighat 2016, Seco and Verhaegen 2013, Vassiliev 2017). First, Raeside explained the fundamentals of the technique suggested by Metropolis and Ulam in terms of the principles such as random number generation and variance reduction (Raeside 1976). He also illustrated MC applications not only in MP but also in general radiological sciences. Andreo supplemented Raeside’s overview with new developments related to MCSs including inverse MC techniques and the vectored MC method (Andreo 1991). This work introduced studies on various other research fields in MP from nuclear medicine to microdosimetry. Later, Seco and Verhaegen reviewed the MC techniques used in radiation therapy (Seco and Verhaegen 2013). They well summarized the application of MC techniques in radiation therapy and the fundamentals of MC method including history, basics and applied techniques such as variance reduction techniques. Rogers and Bielajew reviewed MC applications in MP mainly with the EGS code (Rogers 2006, Bielajew 2013). The MC studies on external photon beam modeling used in radiotherapy were reviewed by Verhaegen and Seuntjens (2003). They summarized the studies on each part of the linear accelerator (LINAC) head, such as the target, flattening filter, and multi-leaf collimators (MLSs). They also explained the history of MC application on modeling radiotherapy units for kilovolt x-rays and gamma rays. Today, the majority of MC applications in radiation therapy are concerning dose calculation. In this review, we focus on device simulation in radiation therapy. We thus mainly review studies using multi-purpose codes, whereas codes specialized only on accelerated dose calculation, for example using graphics processing units (GPUs)(Jia et al 2014), will not be included.
For this review, the representative journals MP and physics in medicine and biology (PMB) were selected and the number of MC-related papers in each was assessed by searching in PubMed, a free resource supporting the search and retrieval of biomedical and life sciences literature. The keywords ‘Monte Carlo’ with ‘Medical Physics’ or ‘Physics in Medicine and Biology’ were applied. Conference abstracts were manually removed from the search results. Figure 1 shows the numbers of MC-related papers published in MP and PMB from 1968 to 2019, with a total number of 5240 papers. For both journals, the number of publications significantly increased in the mid-1990s when MC codes became more widely available outside of particle physics laboratories as computation power increased.
Figure 1.
The number of MC-based studies published in medical physics (MP) and physics in medicine and biology (PMB) from 1965 to 2019 obtained through PubMed.
Figure 2 illustrates the number of publications on MCSs from 1985 to 2019 (4247 in total) that were registered in PubMed relating to the general MC codes Geant4, MCNP, EGS, and FLUKA. There are many other codes in the field of radiation therapy but we limit our overview to these widely used codes. The number of studies continuously increased from the 1980s. The earliest study employing a general MC code in PubMed was written by Rogers (Rogers and Bielajew 1986).
Figure 2.
Annual number of papers in PubMed according to various MC codes.
2. MC applications for device simulations in radiation therapy
2.1. MCSs for radiation therapy treatment devices
2.1.1. High-energy gamma therapy units and gamma knife
The first study on modeling a 60Co therapy unit was reported by the International Commission on Radiation Units (ICRU) with a simplified geometry (ICRU 1970). An EGS3-based model was developed for a Theratron 780 teletherapy machine equipped with a Ni-capsulated 60Co source that was used for investigating photon fluence distributions and dosimetric parameters such as depth-dose curves (figure 3)(Han et al 1987). The energy spectra of the source were evaluated according to different beam conditions. Suitability of the model was assessed by comparing simulated and measured tissue-air ratios in water at different depths. Rogers et al also modeled the same modality employed in Han’s study with the EGS code and evaluated electron contamination of a photon beam because it increased the maximum dose by up to 15% (Rogers et al 1988). They found that the electron contamination of the photon beam was decreased by the presence of a filter and small beam sizes.
Figure 3.
Energy spectrum of 60Co gamma source obtained byEGS3 simulation (left) and tissue-air ratios according to the depth in water (right)(Han et al 1987). The figures were reproduced with kind permissions of medical physics from Han et al. John Wiley & Sons. © 1987 American Association of Physicists in Medicine.
Gamma rays from a 60Co source with both narrow and broad field sizes were simulated to accomplish a more realistic evaluation of the electron components on the buildup region of a depth dose curve (Mora et al 1999). The Eldorado 6 teletherapy machine using a rectangular collimator assembly and leaf collimators was modeled using BEAM/EGS4 (figure 4). Subsequently, studies aiming at accurately modeling 60Co teletherapy units or employing a cobalt source in other treatment techniques were published (Smilowitz et al 2001, Sichani and Sohrabpour 2004, Joshi et al 2008). An investigation using EGSnrc was carried out for the source design to improve beam delivery in 60Co tomotherapy (Joshi et al 2008). The authors highlighted the potential of a rectangular source for the fan beam by comparing radiation outputs between cylindrical shapes and rectangular shapes with various sizes.
Figure 4.
Monte Carlo model of the Eldorado 6 cobalt-60 unit with BEAM/EGS4 proposed by G. M. Mora, A. Maio, and D. W. O. Rogers (Mora et al 1999). The figure was reproduced with kind permissions of medical physics from Mora et al. Mora et al 1999 John Wiley & Sons. © 1999 American Association of Physicists in Medicine.
The 60Co source is also employed in radiosurgery techniques such as the gamma knife. Various studies were conducted wherein MCSs were performed in collimation geometries of the helmets and some of them recorded the information on photon fluence distributions at the output surface of the helmets in phase-space files (Cheung et al 1998, Moskvin et al 2002, Moskvin et al 2004, Romano et al 2007, Trnka et al 2007, Battistoni et al 2013, Pappas et al 2016). A gamma knife consisting of 201 sources with a collimator hole was first modeled, and dose profiles of a single beam were validated by Cheung et al using PRESTA/EGS4 (Cheung et al 1998). In this study, the collimator produced beam diameters of 4, 8, 14, and 18 mm with cylindrical 60Co pellets. Moskvin et al reported a Leksell Gamma Knife model based on PENELOPE which was reported to be more accurate than EGS and MCNP in calculating low energy electron transport (Das et al 2001, Das et al 2002, Moskvin et al 2002, Moskvin et al 2004). For the same beam delivery system, an MCNP-based study was carried out by developing a full geometry model. The results were compared with dose distribution from Moskvin’s work (Trnka et al 2007). The dose output factor showed good agreement with a difference of 1.9%, 0.7%, and 0.9% for 4, 8, 14 mm collimator holes, respectively. FLUKA based simulations to model the Leksell Gamma Knife system were carried out by Battistoni et al with the purpose of testing FLUKA as an alternative to previously validated codes (figure 5) (Battistoni et al 2013). Figure 6 shows the results of studies on the simulation to obtain dose distributions with 8 mm collimators. The simulation results were compared to computation results using Leksell GammaPlan.
Figure 5.
FLUKA-based model of 16 mm collimators equipped in Leksell Gamma Knife Perfexion (Battistoni et al 2013). Reprinted from Battistoni et al 2013,© 2012 Associazione Italiana di Fisica Medica. Published by Elsevier Inc. All rights reserved.
Figure 6.
Dose distribution of 8 mm collimators simulated by Cheung (a), Trnka (b), and Battistoni (c)(Cheung et al 1998, Trnka et al 2007, Battistoni et al 2013). The figures were reproduced with permissions of medical physics from Cheung et al Trunka et al and Physica Medica from Battistoni et al.
2.1.2. LINAC based treatment device
The earliest simplified models of LINACs were developed from the late 1970s to 1980s (McCall et al 1978, Patau et al 1978, Petti et al 1983, Nilsson and Brahme 1981, Mohan et al 1985). The first published MC-based LINAC model of a complete photon beam was developed with an in-house code (Patau et al 1978). Patau created bremsstrahlung photons with a tungsten target of 0.1 cm thickness and a 5.7 MeV electron beam. With the tungsten target, a copper foil was added as a filter to reduce fluence along the central axis of the beam similar to the flattening filter today. McCall calculated depth-dose curves in water and the relationship between the depth of the maximum dose (dmax) and the average photon energy (McCall et al 1978).
In 1985, a study obtaining energy spectra and angular distributions of photons from LINACs was reported for different photon energies (4–24 MV) using EGS3 (Mohan et al 1985). This study included the first accurate model of flattening filters in a LINAC and reported the average photon energy from a LINAC as one-third of the nominal electron energy, which is still widely accepted (figure 7). In the late 1980s, studies on the energy spectra and angular distributions of bremsstrahlung photons in different materials were carried out (Bielajew et al 1989, Ahnesjo and Andreo 1989, Faddegon et al 1991). The bremsstrahlung production in various targets was modeled with the EGS4 code, and the angular distribution of bremsstrahlung yields was also assessed with cylindrical targets of Be, Al, or Pb using EGS4/PRESTA (Faddegon et al 1991).
Figure 7.
Photon energy spectra and tissue-maximum ratio (TMR) with 10×10 field size according to different nominal energies from 4 to 24 MV of Varian Clinac machines (Mohan et al 1985). The figures were reproduced with kind permission of medical physics from Mohan.
To increase the computational efficiency, source models which randomly and functionally produce particles in each component inside the treatment head were introduced as an alternative to using phase space files. The first source models for electron and photon beams were reported in 1993 and 1997, respectively (Ma 1998, Ma et al 1993, Liu et al 1997a, 1997b). A multiple-source model for the Varian LINAC was developed with BEAM consisting of different sub-sources defined at each component inside the treatment head (Ma 1998). This method reconstructed the phase-space data and randomly produced photons from each component. The suggested source model showed agreement within 2% compared to measurements for depth dose and lateral dose distributions. The source model enabled similar results requiring less than 10% of the particles necessary with a phase-space file. This remarkably reduced the calculation time by 25%, including dose calculation and, additionally, there was a considerable reduction in data-storage requirements. With these suggestions, various source models were introduced for efficient simulation of LINAC heads (DeMarco et al 1998, Chetty et al 2000, Deng et al 2000). In 1999, Faddegon et al redesigned a flattening filter for a 6 MV Siemens MXE accelerator to produce uniform large 6 MV beam fields using BEAM simulations (Faddegon et al 1999). This included the change of the material from steel to brass. Compared to the unflattened beam, the new model of the flattener exhibited a 23% decrease in beam output at the central axis, which was reported as a 30%–40% decrease with a conventional one.
Over the last decades, full models of LINACs have been introduced for various photon energies with different MC codes (Chaney et al 1994, Lovelock et al 1995, Van Laere and Mondelaers 1997, Kuster 1999, Libby et al 1999, Chetty et al 2000, Tzedakis et al 2004, Mesbahi et al 2005, Aljarrah et al 2006, Constantin et al 2011, Grevillot et al 2011, Bergman et al 2014). A LINAC model known as ‘McRad’ was developed based on EGS4 with a similar approach introduced by Rogers using the BEAM code (Lovelock et al 1995, Rogers et al 1995). In 1999, BEAM and DOSXYZ were introduced for LINAC modeling including commissioning processes and dose calculations for radiation treatment planning (Ma et al 1999). A study on photon output factors used variance reduction techniques and Bremsstrahlung splitting (Libby et al 1999). Gu et al and Ding et al developed MCNPX-based treatment head models to calculate patient organ doses including therapeutic doses and doses from radiography for therapy planning (Ding et al 2007, Ding et al 2008). A Geant4-based LINAC model was developed with computer aided Design files to accurately model the LINAC treatment head including the waveguide, bending magnets and secondary jaws (Constantin et al 2011). This geometry modeling approach allowed accurate definitions of LINAC components or detector systems that often include parts with complex geometries.
The MLC is the most challenging geometrical structure to simulate inside a LINAC gantry head, however, an accurate implementation is critical for accurate dose calculations. Various studies have been carried out on elaborately modeling the MLC geometries from the end of 1990s (Verhaegen and Seuntjens2003). Starting in the late 1990s, studies to model MLC geometries in MCSs were reported. Küster was the first including the MLC leaf geometry in an MC study (Kuster 1999). In the study, a Siemens Primus accelerator was modeled with the Geant3 code, and the leaf face shape was optimized to reduce penumbra and leakage radiation but a comparison with measurements was not reported. The first comparison between measurements and simulation of an MLC was published by De Vlamynck et al with the BEAM/EGS4 to model an Elekta LINAC head (De Vlamynck et al 1999). They compared depth dose and lateral profiles to the measurement according to different field sizes and obtained the largest dose difference of 5% for small fields (10 × 2cm2).
Based on these initial MCSs, many studies to accurately model the MLC and patient dose with complex beam delivery techniques have been carried out (Kapur et al 2000, Palmans et al 2000, Keall et al 2001, Kim et al 2001, Deng et al 2001, Siebers et al 2002, Van de Walle et al 2003, Tzedakis et al 2004, Depuydt et al 2011, Okamoto et al 2014, Bergman et al 2014, Serna et al 2015, de Oliveira et al 2015). The dosimetric accuracy of MLC models was evaluated for tongue-and-grooves as well as leaf ends using comparisons between simulations and measurements (figure 8)(Siebers et al 2002). In 2003, a new MLC module in the BEAM code was validated by (Van de Walle et al 2003). They also evaluated leakage and transmission through the MLC leaves and employed a more complex beam aperture to make each leaf pair produce a different field size, thereby enabling increased dose prediction accuracy. Subsequently, a geometry model of the Varian High Definition MLC (HD120) with 120 tungsten-leaf pairs of 0.5 mm thickness was developed and the model was used to investigate the effect of narrow leaf widths in treatment planning (Bergman et al 2014, Serna et al 2015). They found that the MLCs with narrower widths result in better dose conformity. Simulations of flattening filter-free treatment was carried out in early 2000s (Vassiliev et al 2006, Titt et al 2006).
Figure 8.
Geometry of a single MLC leaf (a) and validation of the MLC model in terms of inter-leaf leakage (b), dose distribution with picket fence fields (c), and tongue-and-groove effects (d)(Siebers et al 2002). The figures were reproduced with permission of physics in medicine and biologyfrom Siebers et al.
In further investigations, studies on tuning the initial electron beam in a LINAC model have been carried out. Bramoulle et al tuned x-ray beams of 6, 18, and 25 MV from the SL-Elekta LINAC model (Bramoulle 2000). Lin et al reported that the beam quality from a PRIMUS LINAC head was sensitive to the energy and radial width of the initial electron beam (Lin et al 2001). They concluded in their work that the depth dose curve was influenced only by the electron energies while the lateral dose profile was affected by both the energy and spot size of the electrons. The effect of electron beam parameters on the depth dose distribution and the scattering in off-axis positions was evaluated for nine different beam conditions and four LINACs by S.-Bagheri and Rogers (Sheikh-Bagheri and Rogers 2002). With these results, Ding reviewed the beam characteristics of a Varian LINAC (Ding 2002), and Verhaegen and Seuntjens summarized the procedure to tune an MC linear accelerator by outlining each validation step (Verhaegen and Seuntjens 2003). Bjork et al investigated the effects of the initial electron beam characteristics on photon beam quality with various beam shapes and electron energy distributions (Björk et al 2002). The energy spectra of the initial electron beams were defined using a monoenergetic, Gaussian and a wedge with various energy spreads.
MCSs were carried out to quantify the effects of initial electron beam parameters on the resulting photon beam quality (figure 9). Three main parameters were investigated including the mean electron energy, the electron energy spread, and the radial width (of the Gaussian distribution) of the electron beam (Tzedakis et al 2004). Okamoto et al validated the dose distribution between simulations and measurements for a dynamic-MLC based IMRT simulation for a full LINAC model by comparing the one-dimensional and two-dimensional dose distributions produced by the movement of the MLC (Okamoto et al 2014). Zain et al validated GAMOS for a 12 MV photon beam from SATURNE43 LINAC (Al Zain et al 2019). They explained the process to tune the initial electron beam using a GAMOS model and compared the final water dose distributions to the measurement.
Figure 9.
Comparison of the depth doses of 6 MV photon beam with 10 × 10 cm2 field size according to various initial electron mean energies, energy spreads, and radial width ofthe initial electron beam (Tzedakis et al 2004). The results were compared between EGS4/BEAM and the measurement. The figures were reproduced with permission of medical physics from Tzedakis et al.
Neutrons can contribute to out-of-field doses in treatment facilities when photon beams have energies higher than 10 MV with (γ, n) cross-sections peaking at different energies depending on the material (Johns et al 1950, Kry et al 2017). Frequently, these photons produce secondary neutrons as they interact with metal components inside the gantry, such as jaws and collimators (Kry et al 2017). Modern treatment techniques, such as IMRT, may deliver increased secondary neutron doses with their longer beam-on time and complex usage of the collimators (Howell et al 2006). MC calculations for evaluating secondary neutron doses have been carried out with detailed modeling of treatment heads (Howell et al 2005, Pena et al 2005, Kry et al 2007, Bednarz and Xu 2009, Fujibuchi et al 2011). The models include shielding components and structural components that are potential neutron sources. Pena et al modeled a Siemens PRIMUS LINAC including the treatment room and evaluated the neutron production for a 15 MV treatment beam (Pena et al 2005). Among the components inside the gantry head, the collimators and the jaws were found to be the main sources of neutrons, e.g. more than half of the neutrons were from the primary collimator. Kry et al simulated neutron energy spectra from 18 MV photons by using a MCNPX-based treatment head model for a Varian 2100 LINAC (Kry et al 2007). They calculated neutron fluences and dose equivalent according to the distance from the beam center. While a detailed MC model is required to accurately simulate secondary neutrons, often information on the geometry is limited by the manufacturer. Simplified models only include the main beam-line components, such as target, collimators, and flattening filter, without shielding components (Ma et al 2008, Joosten et al 2011). However, AAPM (Task Group No. 158) recommended the simplified model to be used only for patient scatter components of the out-of-field dose but not to estimate head leakage and collimator scatter (Kry et al 2017). Ghiasi and Mesbahi compared the photo-neutron production between simplified and full models (Ghiasi and Mesbahi 2010). The neutron fluence, dose equivalent and capture gamma equivalent differed by up to 70% for different treatment field sizes. Similar to the AAPM recommendation, the authors suggested to use full MC models of the LINAC rather than a simplified model. With attempts to understand factors contributing to out-of-field doses, several studies were carried out on evaluating reduction in neutron production from flattening filter free photon beams (Mesbahi 2009, Kry et al 2010). Significant amount of work has been done improving the computational efficiency of photon treatment head simulations through variance reduction techniques such as bremsstrahlung splitting in BEAMnrc (Fragoso et al 2009, Kawrakow et al 2004).
In 2007, AAPM (Task Group No. 105) summarized the clinical implementation of MC-based external photon beam transport and proposed a standardized simulation process from beam commissioning to patient dose calculation (Chetty et al 2007). Recently, AAPM (Task Group No. 268) reported guidelines for MC studies in MP research (Sechopoulos et al 2018).
2.1.3. Heavy charged particle therapy
Many full MC models of proton therapy treatment heads have been developed. A 62 and 72 MeV proton beams employed in eye treatments were modeled with various beam modifiers such as collimators, scattering foils, range shifters, and modulators (Cosgrove et al 1992, Biaggi et al 1999). The eye treatment proton beam was later simulated with FLUKA to obtain proton depth doses in water and investigate contributions to the delivered dose separately for primary protons, secondary electrons and hadrons as represented in figure 10 (Biaggi et al 1999). This study exemplifies how the MC method enables the analysis of physical quantities which cannot be experimentally determined. As represented in figure 11, Paganetti proposed a three-dimensional model of a beam nozzle for a 68 MeV proton beam at the Hahn Meitner Institute in Berlin using Geant3 (Paganetti 1998). Phase-space files were recorded at the level after the vacuum window according to different proton energies to store position, angle, and energy of protons. The phase space information was used to parameterize the beam characteristics. Subsequently, effect of the absorbers and collimators on the phase space distribution of protons was investigated by evaluating the phase space distributions at 2 cm in front of the collimator and after the collimator.
Figure 10.
Simulated depth dose distribution of a 72 MeV proton beam with FLUKA and fractions of primary protons, secondary electrons and hadrons to the dose distribution (Biaggi et al 1999). The figure was reproduced with permission of nuclear instruments and methods in physics research section B from Biaggi et al.
Figure 11.
Illustration of the proton beam nozzle at the HMI (a)(Paganetti 1998) and the NPTC (b)(Paganetti et al 2004) as modeled using Geant4. The components in (a) represents Kapton foil (1), range shifter (2), range modulator (3), collimator (4), ion-chamber (5)–(6), snout (7), x-ray imaging device (8)–(9), and patient chair (10). The figures were reproduced with permissions of medical physics from Paganetti et al.
The development of full models of proton treatment heads started in the early 2000s (Cirrone et al 2003, Deng et al 2004, Paganetti et al 2004, Cirrone et al 2005, Newhauser et al 2005, Polf and Newhauser 2005, Polf et al 2007, Newhauser et al 2007, Peterson et al 2009, Testa et al 2013). Paganetti et al employed Geant4 to simulate the proton beam treatment head at the Northeast Proton Therapy Center (NPTC) as illustrated in figure 11 (b)(Paganetti et al 2004). They used low-energy model for the electromagnetic hadronic model. For the neutron interaction model, the pre-compound model was applied in the simulation. They reported that the differences between nuclear interaction models were insignificant for dose calculation. Elements with complicated geometry such as the scatterers and the range modulator wheels were modeled with groups of multiple geometric objects such as polycones or tube segments. Patient-specific geometries for apertures and compensators were directly imported from the treatment planning system and the dose distributions in water were obtained by using Geant4 (figure 12). Polf et al modeled the passive treatment nozzle at the MD Anderson Proton Therapy Center of Houston (Polf et al 2007). Lee et al modeled another proton beamline at the cyclotron in the Washington Medical Center (Lee et al 2016). They used TOPAS with its default physics list. With the developed model, they optimized the design of a collimator for radiobiology research that is related to proton mini-beam radiation therapy. Proton therapy treatment heads for passive scattering can be very complex. The efficiency depends highly on the specifics of the treatment head design (manufacturer) and field size. At the same time, the simulation efficiency can be quite low due to scattering and loss of primary protons. This has prompted the development of variance reduction techniques for proton therapy (Ramos-Méndez et al 2013).
Figure 12.
Simulated depth dose distribution of the proton beam at the NPTC (Paganetti et al 2004). Both pristine beams (a) and SOBP beams (b) were simulated with various proton ranges and modulation widths by using Geant4. Open circles refer to measured data and solid lines indicate simulation results. The figures were reproduced kind permissions of medical physics from Paganetti et al.
To simulate time-dependent components such as magnetic fields to decide the position of a proton beam spot in beam scanning, Paganetti et al implemented four-dimensional (4D) components inside their treatment head model and for organ motion (Paganetti et al 2003, Paganetti 2004). Peterson reported a Geant4-based model for an active scanning beam nozzle including scanning magnets (Peterson et al 2009). The particle interactions were defined with the physics modules including low-energy electromagnetic hadronic model, default elastic scattering model and pre-compound neutron interaction model. Magnet volumes, called steering magnets in the study, were modeled as rectangular boxes covering the magnetic regions that the beams passed through. Each box was filled with a uniform magnetic field, one for each scanning direction. The application of magnetic fields was incorporated in the Geant4 code to simulate proton transport. A simulation model for scanning proton beams was also developed using TOPAS (Shin et al 2012, Hartman et al 2018). In fact, Shin et al first modeled the scanned proton beam at Massachusetts general hospital (MGH) with time-dependent parameters (Shin et al 2012). Harman et al modeled a scanned proton beam treatment head installed at the MD Anderson Cancer Center (Hartman et al 2018).
Accelerated proton beams undergo nuclear interactions in beam delivery devices and in patients and, subsequently, secondary neutrons are released. These neutrons affect the out-of-field dose and also induce treatment-related side effects, e.g. secondary cancers. MCSs of proton beam delivery systems were applied to evaluate dose equivalents for secondary neutrons from the treatment head and to determine shielding requirements for proton therapy devices (Agosteo et al 1998, Newhauser et al 2002, PolfandNewhauser 2005, Zheng et al 2007, Zacharatou Jarlskog and Paganetti 2008, Dowdell et al 2012). Similar to photon treatments, the MC models of proton delivery systems should include not only beam-line components but also the shielding or structural components (Kry et al 2017). Most of the published studies used detailed models of the proton beam treatment head. Agosteo et al modeled three different proton beam devices installed at proton therapy facilities in France, South Africa, and Switzerland (Agosteo et al 1998). They analyzed the proton dose and the dose due to secondary photons and neutrons. They concluded that the dose from the secondaries depends on material, geometry of the beam delivery components and proton energy. Later, Zheng et al calculated radiation weighting factors for protons as a function of proton energy and mean neutron energy (Zheng et al 2008). Newhauser et al simulated a treatment facility including a 235 MeV cyclotron to verify neutron shielding of a center (Newhauser et al 2002). The authors calculated neutron dose equivalent values with energy spectra according to different locations inside the facility. Neutron doses to patients were assessed for passive scattering proton therapy, which led to an out-of-field dose on the order of 0.01% of the in-field dose at 20 cm from the treatment field edge (Paganetti et al 2004). The neutron dose equivalent per proton dose was assessed for multiple gantry angles and the neutron dose equivalent spectra at various locations in the room (Polf and Newhauser 2005). Later, Dowdell et al evaluated out-of-field doses including secondary neutrons in pencil beam scanning therapy when using patient-specific apertures at the treatment head exit (Dowdell et al 2012). They compared out-of-field dose between the treatment with the aperture and the conventional treatment with no aperture. The neutron dose in the out-of-field region was higher with the apertures even though the total out-of-field dose was reduced. Considerable uncertainties still exist when it comes to simulating neutron production because of the required double differential production cross sections for tissues, beam shaping devices and shielding materials. Because of uncertainties in the cross section data, the validation of neutron measurements with simulations is quite challenging (Clasie et al 2010, Chen and Ahmad 2009). In addition, accurate neutron modeling is difficult due to the problem caused in validation for the MC model (Kry et al 2017). Accurate validation for the neutron model requires evaluation of the neutron dose only from the mixed radiation fields, which is not available (Halg and Schneider 2020). Neutron detectors are also selective for specific neutron energies depending on type of the detector (Kry et al 2017). This is more difficult for accurate modeling of secondary neutrons from protons because of the variety of different energies, compared to photo-neutrons with a relatively narrow energy range.
There are only a few studies on evaluating heavy ion therapy treatment heads using MCS models until 2005 (Pshenichnov et al 2005). Parodi et al used FLUKA and a simplified model of the beamline for ion therapy at the Heidelberg Ion Therapy Center (Parodi et al 2012). They made approximations for modeling the vacuum window, beam monitor system, and ripple filters. They compared depth dose distributions of MCS, measurement and TPS and proved that their model could be a valuable tool to support ion beam delivery and treatment planning. Subsequently, they improved the model to be more realistic by using geometry data offered by the vendor (Parodi et al 2013). The model showed good agreements with measured data in terms of the depth dose and lateral profiles in water. Later, this model was used to generate phase space data to be used by external users of the facility (Tessonnier et al 2016). The study employed HADROTHErapy physics settings with the EVAPORation physics in FLUKA. These models generally allowed simulations of physical processes relevant to heavy ion therapy, such as generation and transport of secondary fragments.
2.1.4. Brachytherapy
In brachytherapy, it is quite challenging to perform accurate dosimetric measurements due to the short distance between the source and the point of interest, the sharp dose gradient, and the relatively low energy of radiation. Hence, MCS is an even more important tool in this context. With flexible geometry functions available in MC tools, it is straightforward to build a model of a brachytherapy source containing a radioactive core material and other materials encapsulating the core. An infinite water phantom, large enough in practice, is often used as the surrounding medium to tally the dose rate distribution. One challenge of MCSs in this low-energy range is that the results are often sensitive to data and simulation configuration, such as photon cross section data, material properties, source geometry etc Therefore, it is crucial to use accurate cross section data in MCSs and to cross validate the results, e.g. by comparing with measurements or results from different MC codes. The material definition has to precisely follow the standard. For instance, the AAPM Task Group No.43 Update 1 (TG-43) specifies the reference media as pure, degassed water ‘composed of two parts hydrogen atoms and one part oxygen atoms’ with density of 0.998 g cm−3 at 22 °C (Rivard et al 2004).
The clinical standard dose rate calculation method in brachytherapy is defined by the AAPM TG-43 (Nath et al 1995) and subsequent updates (Rivard et al 2004, Rivard et al 2007). This method expresses dose rate at a point of interest as the product of a few terms with the values interpolated from data tables pre-generated for each source. In fact, most of the data tables in this TG-43 formalism were created based on the combination of MCS results and source characterization measurements (Perez-Calatayud et al 2012), highlighting the particularly important role of MCS for brachytherapy. Over the years, extensive MCS studies have been performed for a number of radioactive sources in brachytherapy, covering different source geometries and radioactive isotopes, such as 308 keV gamma rays from 169Yb (Perera et al 1994), 35 keV gamma rays from 125I (Kirov and Williamson 2001), 20- and 23 keV gamma rays from 103Pd (Bohm et al 2003), gamma rays with an average energy of 370 keV from 192Ir (Wang and Sloboda 1998), 1.17 and 1.33 MeV gamma rays from 60Co (Badry et al 2018) etc. There was also a miniature x-ray source for brachytherapy and Taylor et al modeled this source and derived its TG-43 parameters that agreed with measurement (Taylor et al 2006). A comprehensive database of TG-43 parameters of commonly used brachytherapy sources has been created by the Carleton Laboratory for Radiotherapy Physics using the EGSnrc user code BrachyDose (Taylor and Rogers 2008, Safigholi et al 2020).
In high dose-rate (HDR) brachytherapy, applicators are used to place the radioactive source in the treatment positions. The presence of an applicator may affect the dose rate distribution, hence calling for MCSs to understand its impacts. Lymperopoulou et al studied the dose rate distribution under vaginal shielded cylinder applicators (Lymperopoulou et al 2004) and found that in the unshielded side of the applicator, calculations using the standard TG-43 method overestimate dose rate. In HDR brachytherapy for accelerated partial breast irradiation, simulations were performed to evaluate dose rate distribution under different applicators, such as Mammosite (Oshaghi et al 2013) and SAVI (Richardson and Pino 2010). As an example highlighting the importance of MCS, in the SAVI applicator case, MCSs revealed that the air cavity inside the applicator leads to an overestimated dose rate by 3%–5% by the TG-43 dose rate calculation method. Other studies on applicator simulations included intracavitary mold applicator for endorectal cancer brachytherapy (Poon et al 2006), eye plaque (Thomson et al 2008), and air-filled balloon applicator (Jiang et al 2018). There are too many studies for different applicators to enumerate here. The studies selected here demonstrate the versatility and value of MCSs for research and clinical practice of brachytherapy.
Due to various clinical needs, novel radioactive seeds and devices in brachytherapy have been continuously developed. The development and characterization of these seeds were largely supported by MCSs. For example, Aima et al characterized dosimetric properties of a new directional low-dose rate brachytherapy source CivaDot (Aima et al 2018). Reed et al studied dose rate distribution of a new 1 cm long elongated 103Pd source (Reed et al 2014). Bohm generated a dose rate table for a32P intravascular source (Bohm et al 2001). Yao et al computed dose rate distributions around an 125I seed loaded biliary stent (Yao et al 2017). In these studies, results were generally verified by comparing MC predictions with measurements to confirm their validity. Another example for which MCS plays a critical role is the design of novel applicators for intensity modulated brachytherapy. MCSs were often the first step to conceptualize the design and initially verify the functions (Webster et al 2013, Skinner et al 2020).
Last, but not the least, MCSs are also essential in the characterization of ion chambers for brachytherapy. The well-type ionization chamber has been specifically designed for convenient use in brachytherapy source strength calibration. Using MCSs, Bohm et al investigated the effect of ambient pressure on chamber response and found that the standard temperature and pressure correction factor is insufficient in accounting for the change in chamber response with air pressure for low-energy (<100 keV) photon and low-energy (<0.75 MeV) beta sources (Bohm et al 2005). They subsequently used MCS to design an improve chamber to solve this problem (Bohm et al 2007).
2.1.5. Ion chamber models for treatment dosimetry
Ionization chambers have been used in treatment rooms not only for the determination of the beam output but also for the calibration of high-energy x-ray and electron beams. Originally, MCSs of ion chambers were dedicated to the calculation of air/water stopping power ratios and correction factors for chamber responses employing different wall materials. However, most studies on the stopping power ratios for air/water or other materials were excluded in this review because they did not focus on modeling the geometry of the ion chambers and the calculation of air/water stopping power ratios is too extensive to cover here.
A MC study on correction factors was performed by Nath and Schulz based on an in-house developed code from their previous work with Bond, which calculated wall correction factors for simple spherical ion chambers (Bond et al 1978, Nath and Schulz 1981a). They modeled the geometry of an ion chamber used at the National Bureau of Standards and the Bureau Internationale des Poids et Mesures for 60Co exposure calibrations. They calculated the wall correction factors and response for 60Co beams. However, their response curve showed 10% variation as the chamber radius was increased from 0.1 to 10 cm. Assuming a similar chamber geometry, Rogers et al calculated wall correction factors and chamber responses for 60Co beams by using the CAVITY code in 1985 (Rogers et al 1985). They showed differences in chamber response compared to the Nath and Schulz’s values despite similar wall correction factors. The response values varied less than 2% as a function of chamber radius. In 2003, Rogers and Kawrakow used EGSnrc to calculate correction factors using the geometry of a 3C cavity ion chamber, which was used as standard measurement for air kerma (Rogers and Kawrakow 2003). They compared chamber responses and correction factors with different versions of the EGS code suchasEGS4/PRESTA and EGS4. Chamber response was remarkably decreased with EGS4 in default mode by 45% from the EGSnrc in default mode while other modes or versions, such as EGS4/PRESTA, EGSnrc with single scatter, or with binding effects in Compton scattering, showed difference within 1.5%. The authors concluded that the reason for this result was different transport algorithms employed in the EGS4 and EGSnrc codes. Meanwhile, wall correction factors and graphite/air stopping power ratios were in good agreement within a difference of 0.04% and 0.002%, respectively.
Correction factors for a farmer type ion chamber were calculated by Pena et al for a 6 MV clinical beam (Pena et al 2006). They modeled a PTW 30001 chamber with the BEAMnrc/EGSnrc code and evaluated correction factors in the build-up region of the treatment beam. Wulff assessed the uncertainties in correction factors for beam qualities calculated by the EGSnrc code (Wulff et al 2010). They delivered a 60Co beam and 15 MV photon beam to a NE2571 ion chamber model. The influence of various simulation conditions on calculating the beam quality factor, such as source/geometry variation, and varying cross sections, were evaluated. Muir and Rogers calculated beam quality conversion factors with the EGSnrc code according to various chamber geometries of 10 plane-parallel and 18 cylindrical ion chamber models (Muir and Rogers 2014).
The effects of magnetic fields to the sensitive volume were evaluated by assessing the ion chamber response by Malkov and Rogers as magnetic resonance-guided radiation therapy started to be used clinically (Malkov and Rogers 2017). They used the EGSnrc code and simulated the geometries of PTW ion chambers with different sensitive volumes ranging from 0.01 to 0.06 cm3. In the simulation, magnetic fields from 0 to 2 T were defined and the chamber response showed larger variations with smaller sensitive volumes. Wulff et al carried out TOPAS/Geant4 simulations for ionization chamber calculations (Wulff et al 2018). Subsequently, Baumann et al calculated the beam quality correction factors in clinical photon and proton beams (Baumann et al 2019). They compared the absorbed dose to the cavity according to different MC codes and ionization chamber geometries that were plane-parallel and cylindrical volumes. Later, the beam quality correction factors were investigated for various geometries of the actual ionization chambers including both plane-parallel chambers and farmer type chambers (Baumann et al 2020). In the latter study, only Geant4/TOPAS was employed in the calculation and the factors were compared to previous studies and other codes.
Capote et al simulated the IBA-Wellhofer NAC micro ionization chamber with EGSnrc to use the chamber as the reference dosimeter for narrow and irregular IMRT beamlets (Capote et al 2004). The chamber had a sensitive volume of 0.007 cm3, which potentially shows a better spatial resolution than the conventional ion chambers with a sensitive volume of 0.6 cm3. They extended their study to IMRT verification and estimated the error in measuring the planning target volume absolute dose at a point with the micro ion chamber (Sanchez-Doblado et al 2005). Chen et al suggested a new design of proton computed tomography equipped with a multiple-layer ionization chamber (Chen et al 2020). They simulated the prototype of the ion chamber by using the TOPAS code and proposed that the ion chamber array can detect the residual energy of the proton beam as it captures the complete Bragg peak. They obtained the energy spectrum of a proton beam measured by the chamber array as well as proton stopping power ratios.
2.2. MCSs for imaging devices used in radiotherapy
2.2.1. Computed tomography
The MC models for the radiographic devices have been used to accurately assess patient imaging doses during daily patient positioning (Caon et al 1999, Caon et al 2000, DeMarco et al 2005, Ding et al 2007, Deak et al 2008, Ding et al 2008, Gu et al 2009, Alaei et al 2010, Ding et al 2010, Zhang et al 2011, Zhang et al 2013, Liu et al 2014). For the quantitative assessment of the patient dose due to the CT imaging in radiation therapy, simulations using EGSnrc/BEAMnrc were carried out. For this study, a model of an on-board imaging device was developed that consisted of a kV cone-beam CT (CBCT) on a Varian Trilogy LINAC (Ding et al 2007). The model included an x-ray tube, collimators, a bow-tie filter, and the detector as shown in figure 13 (left). The characteristics of x-ray beams from the on-board imaging device were investigated in terms of the energy spectrum, dose distributions in water, fluence distributions, and photon scattering at the detector. This work was applied to calculate imaging doses for daily patient positioning for adaptive radiotherapy (Ding et al 2008). Jarry et al investigated characteristics of scattered radiation from CBCT (Jarry et al 2006). They used BEAMnrc to model a kV x-ray tube consisted of target, window, filters and collimators. For the imaging panel, DOSXYZnrc was used. They evaluated the effect of scattered radiations on the images in terms of imaging contrast for different organs. To evaluate doses received by a pregnant patient and the fetus, an MCNPX-based model of a GE LightSpeed multi-detector CT (MDCT) was developed and the model further applied to evaluate the imaging dose as a part of treatment (Gu et al 2009, Ding et al 2010). The dose to critical organs notably increased when CT imaging was considered as in figure 13 (right). Zhang modeled a 3D Accuitomo 170 CBCT with BEAMnrc/EGSnrc (Zhang et al 2013). Similar to the previous works, the CBCT model was used to evaluate imaging dose in patient setup by using the ICRP reference phantoms. Liu et al investigated the optimal geometry of scintillators used in megavoltage CBCT with a hybrid modeling technique of MCSs, in which both simulation and empirical parameters for image quality were simultaneously obtained (Liu et al 2014). They modeled the megavoltage CBCT including the segmented scintillator array in EGSnrc to optimize the geometry for the scintillator by matching simulated modulation transfer functions to empirical values. The geometry, where the parameter obtained from MCSs best matched the empirical value, was selected as optimal.
Figure 13.
Schematics of the on-board imaging system for MC simulation (left)(Ding et al 2007) and dose-volume histogram according to the presence of MDCT doses with 45 scans (right)(Ding et al 2010). The figures were reproduced with permission of medical physics from Ding et al.
In the field of proton therapy, proton CT (pCT) is being suggested to directly obtain proton stopping powers, reducing one of the largest sources of uncertainty in determining the dose distributions: the conversion of CT-HU to proton stopping power or material composition (Schulte et al 2005). Cuttone et al reported MCSs with the Geant4 code for a proton tracking system to obtain the most likely paths (MLPs) of single protons in the object as shown in figure 14 (Cuttone et al 2005). The system consisted of multiple layers of silicon detectors with a thickness of 1 mm and a CsI calorimeter at the end to predict the proton paths and to measure the energy loss of the proton, respectively. Li et al investigated proton trajectories for reconstruction of pCT images (Li et al 2006). They compared three methods of predicting the proton path: the straight-line path, MLP, and cubic spline path approximations. As represented in figure 14 (right), this proton-tracking information was used to reconstruct a tomographic image using an algebraic reconstruction technique, an iteration-based system that applies the projection of the relative electron density along a single proton path.
Figure 14.
Schematics, simulation of proton CT with Geant4 (left)(Cuttone et al 2005) and reconstructed images (right) of proton CT with different proton path predictions (Li et al 2006). Green planes in the upper left subfigure are 2 micro strips detector. The figures were reproduced with permissions of IEEE from Cuttone et al and medical physics from Li et al.
An improvement of the spatial resolution of a pCT image with a single tracking technique was proposed by using Geant4 to overcome the limitations shown in previous studies (Schulte et al 2005, Cirrone et al 2005, Cirrone et al 2007). The proton positions at certain depths were verified by comparing simulations with measurements and revealed a difference of less than 0.1 mm. Penfold developed a model of a pCT scanner with a cesium iodide detector and proton tracking planes (Penfold 2010). In this study, different reconstruction methods were applied to the pCT image, i.e. filtered back projection and iterative projection. The energy resolution of a cesium iodide crystal coupled with a photodiode was also evaluated. The result showed protons with an energy above 100 MeV to obtain optimal performance of the pCT scanner with cesium iodide crystals. Next, the pCT scanner model was used in the optimization of the proton tracking system (Penfold et al 2011). As the proton tracking system consisted of a two-dimensional array of silicon strip detectors, the pCT image was of highest quality when the silicon pixels overlapped each other. The effect of detector spacing on the tomographic results was also investigated for the accuracy of the MLP prediction. Arbor et al simulated a pCT scanner with the GATE v6 code and found an advantage in range estimation for a proton beam in a patient body as compared to estimates based on x-ray CT (Arbor et al 2015). Recently, Dedes et al summarized the role ofMCSs and MC platforms for pCT scanners including geometry, physics, scoring information in pCT developments for functionalities required for pCT scanners (Dedes et al 2020). They proposed that Geant4 and FLUKA are the main particle transport frameworks being used for pCT imaging.
2.2.2. Nuclear imaging
SPECT is frequently used to quantify radionuclides in tumor volumes. Radionuclides produce gamma rays and can be used to evaluate patient doses during internal emitter radiotherapy. Most studies applying MCSs to SPECT dosimetry are for internal radionuclides such as 1311,111In, 177Lu, and etc Simulations of imaging nuclear detectors (SIMIND) were mainly used to obtain radiographic images (Ljungberg and Strand 1989, Dewaraja et al 2000, Ljungberg et al 2002, Dewaraja et al 2005, Ljungberg and Sjogreen-Gleisner 2011). With SIMIND, a new type of collimator with increased septal thickness for a SPECT gamma camera was suggested and the accuracy of tumor quantification for 131I was evaluated (Dewaraja et al 2000). The SPECT quantification was simulated with a NaI gamma camera model and a radioactive or cold water-filled phantom including hollow spherical tumors filled with 131I. The radionuclide distribution was explained in terms of geometric, scatter, and penetration components. Ljungberg et al used SIMIND to model a gamma camera and evaluate its characteristics such as the energy spectrum and scatter contribution (Ljungberg and Strand 1989). Lazaro simulated a full 3D MC reconstruction in SPECT and evaluated the feasibility with a GATE model (Lazaro et al 2005). They compared the reconstructed images with different reconstruction approaches, i.e. the MC reconstruction, filtered back-projection (FBP-C) and the maximum likelihood expectation maximization (MLEM-C) with corrections for scatter, depth-dependent spatial resolution and attenuation. The images with the MC reconstruction showed better similarities to the ideal image than those with the other reconstructions in terms of the quantitation, spatial resolution, and signal-to-noise ratio.
Imaging of positron emitters can be used for range verification in particle therapy (Zhu and El Fakhri 2013). While PET cameras specific for range verification have not been explicitly modeled, MCSs are widely used in the design of PET cameras. Various MCSs for PET devices were employed to model the detector geometries, evaluate the device performance, and optimize the detector parameters such as shape, dimension, and materials (Derenzo 1981, Derenzo and Riles 1982, Guerra et al 1983, Keller and Lupton 1983, Del Guerra et al 1984, Thompson et al 1992, Del Del Guerra et al 1997, Zaidi and Morel 1999, Kraan et al 2014, Buvat and Lazaro 2006). Chmeissani et al modeled a PET scanner with a pixelated solid-state detector and evaluated the detection efficiency in comparison to a crystal detector (Chmeissani et al 2009) and Lorenzo also simulated a pixelated detector to evaluate its advantage in mammographs (De Lorenzo et al 2013).
High energy hadron beams used in radiation treatment also produce prompt gammas in the patient. Similar to using positron emitters, prompt gamma emission can be used to evaluate the range of the hadron beams. Several studies on prompt gamma measurements were carried out based on MCS (Min et al 2008, Min et al 2012, Zarifi 2015, Hueso-González et al 2018, Choi et al 2020). Min et al suggested an array-type detector for measuring prompt gammas and investigated the feasibility of detecting the proton range. The detection system that included scintillator detector, collimator, and housing was modeled in MCNPX (Min et al 2008) and used to investigate the relationship between prompt gamma distribution and proton range. In an extended study, the prompt gamma detection system for in-vivo proton range verification was simulated (Min et al 2012). Zarifi reported on a prompt gamma measurement and provided an overview of related physics and methodology to measure prompt gammas with Geant4-based simulations (Zarifi 2015). The emission characteristics of the prompt gamma was investigated and prompt gamma detection with an ideal condition, according to the paper, was simulated. Panaino et al recently reported 3D reconstruction algorithm for the prompt gamma images with Geant4-based simulation of the detection systeam and 180 MeV proton beams that were delivered to water phantom (Panaino et al 2019). They located the proton range in 3D coordinates within the difference of a few milimeters compared to the simulated dose distribution.
One caveat for the simulations of nuclear interactions with MC is that in general electromagnetic interactions have smaller uncertainties compared to nuclear interactions, which does impact detector studies (Bauer et al 2013). For example, to better reproduce the positron emitter production with proton beams using MC, various production channels were studied (Espana Palomares et al 2011). Similarly for prompt gamma, there are substantial uncertainties in cross section data (Verburg et al 2012, Dedes et al 2014).
As treatment systems are integrated with radiographic systems for accurate tumor tracking, MC studies on modeling the combined devices were carried out. One application is emission guided radiation therapy (EGRT) that combined the LINAC and PET (Mazin et al 2010, Fan and Zhu 2010). Fan et al modeled a EGRT system and calculated dose to patients with lung and prostate cancers (Fan et al 2012).
2.2.3. Electronic portal imaging devices
Electronic portal imaging devices (EPIDs) have been widely used in radiotherapy for patient position verification before or during treatment delivery, megavoltage cone-beam computed tomography, treatment plan quality assurance, etc (Antonuk 2002). Most current EPIDs have a structure of a metal layer, a phosphor screen, an amorphous silicon (a-Si) flat panel detector array, and a backscattering layer (along the incident beam direction). The incident beam deposits its energy in the phosphor screen and generates optical photons through the scintillation processes. The photons are then recorded at the flat panel detector to form an image. This device structure and the interactions with radiation can be modeled in MCSs to understand the data acquisition process. The geometric model often consists of multiple parallel planes of uniform materials, which can be easily achieved in modern MC packages. During the transport simulation, energy deposited at the screen layer is recorded as the signal from the EPID, assuming the signal detected by the flat panel is proportional to the deposited energy.
MCSs have played an important role in the design and characterization of EPIDs. In 1997, Radcliffe et al used EGS4 to study the impact of the thickness of phosphor and metal on imaging performance at MV x-ray irradiation (Radcliffe et al 1993), which served as a guide to the design of EPIDs. Detector energy response has been computed as a function of incident particle energy for monoenergetic photons and electrons. The photon energy response is high at low energy range due to photo-electric cross section. The response to electrons rapidly increases with energy at ~3 MeV, and for energy less than 3 MeV, the response is negligibly low, as electrons cannot penetrate the materials upstream to the screen (Siebers and Popescu 2017). Regarding the spatial distribution of signals, photon scatters within the device blurs the incident radiation fluence. Understanding this effect is necessary for the use of standard deconvolution techniques to recover the incident energy fluence, which is needed in many applications, such as EPID based dosimetry. For this purpose, Kirkby et al computed the point spread function using EGSnrc for both 6 and 15 MV photon beams (Kirkby and Sloboda 2005). The result generally agreed with experimental measurements, with small discrepancies that were likely caused by uncertainties in the MC model and limitations in the experimental method. Blake et al studied the impact of optical transport in EPID using Geant4 to investigate the blur of the signal due to the optical transport process of the optical photon signal generated by the screen (Blake et al 2013). While the simulations demonstrated a noticeable blurring effect when scoring optical absorption events relative to energy deposition in the screen, ignoring the optical blurring was found to be sufficient to predict EPID dose-response in most scenarios. Additionally, MCSs have also been employed to compute other quantities of interest to characterize EPIDs’ performance, such as modulation transfer function, noise-power spectrum, and detective quantum efficiency (Kausch et al 1999, Liaparinos et al 2006, Star-Lack et al 2014, Shi et al 2018).
The metal plate and phosphor screen in the current EPID design results in a low x-ray absorption and thus a low quantum efficiency. The metal part also leads to an over-response to low energy x-rays due to the increased photo-electric cross section, which is undesirable for dose verification applications. In recent years, a new detector design using plastic scintillating fibers has been proposed for a high quantum efficiency with low-Z materials. As we can expect, MCSs were used to investigate imaging and dosimetric characteristics of the detector (Teymurazyan and Pang 2012). The simulation results were verified by comparison with measurements in a prototype system (Blake et al 2018).
On the clinical application side, Siebers et al used an EGS4-based MC code to simulate the data formation process on an EPID in response to treatment beams, so that an accurate quantitative comparison between measured and computed images may be made (Siebers et al 2004). They developed an efficient virtual detector dose-scoring methodology. Calibrated MC-computed images reproduce measured field-size dependencies of the EPID response to within <1%. Parent et al developed an EPID calibration method that used an analytical fit of a MC simulated flood field EPID image to correct for the flood field image pixel intensity shape (Parent et al 2007). They also compared simulated EPID images with measurements for IMRT fields, and agreement within 3%–2 mm for 98% of the pixels was observed (Parent et al 2006). In the electron beam therapy context, Jarry et al proposed using the bremsstrahlung photons in an electron beam to obtain EPID images to verify patient positioning and dose delivery (Jarry and Verhaegen 2005). Feasibility was demonstrated by the agreement between simulation results and measurements in phantom cases. Additionally, MCSs have also been performed to investigate the impact of scattering from the support arm used to attach the EPID to a LINAC. Using the EGS/BEAM code, Rowshanfarzad et al calculated the backscatter kernel from the support arm (Rowshanfarzad et al 2010). Incorporating the kernels in EPID-based dose calculation models improved the dosimetry accuracy. In another study, the scattered detector-mounting hardware was modeled via an effective approach as a uniform backscattering material of water, which was found to be sufficient to reproduce the measured backscatter (Siebers et al 2004).
3. Discussions and conclusion
In this article, we have reviewed applications of the MC method for device simulations in radiation therapy. The review covered a few major applications such as the simulations of treatment heads of neutral and charged particle therapy, brachytherapy devices, ion chambers, as well as several imaging devices for in-room image guidance purposes. Over the years, with the availability of various general purposed MC codes, such as EGS, MCNP, Geant4, and FLUKA, and their flexible interfaces to support different applications, efforts on MCSs on radiotherapy devices have grown rapidly. Recent improvements in computational hardware further facilitated these studies by enabling simulations with detailed geometry descriptions and physics interaction modeling while maintaining acceptable computation time. The extensive applications of the MC method have demonstrated its essential role for the development, characterization, and optimization of various devices in radiotherapy. Being able to predict device performance and reveal factors affecting the performance without performing actual measurements, which is sometimes difficult or even impossible, makes the MC method a practical, versatile, cost-effective, and irreplaceable tool for radiotherapy device development.
As radiotherapy techniques and clinical needs are evolving, new features in MCS tools are needed. This need has triggered a continuous development of MC tools over time. For earlier studies on photon therapy devices, MC models of treatment devices were mainly used to evaluate beam characteristics under different geometry and beam conditions. These studies focused on predicting the energy spectrum or dose distribution in a water phantom to be compared to measurements considered as reference.
Since then, MCSs have advanced significantly. For example, for heavy charged particle therapy, MC codes are used to simulate complicated geometries, e.g. modules in the treatment head such as scatterers and the range modulation wheels as well as patient-specific components. To further advance the field, modeling of time-dependent components in MCSs was necessary. In the early 2000s first time-dependent simulations included magnetic fields in active proton therapy scanning beams. As more complicated devices are being developed for modern therapy techniques, computer-aided designs have been employed to enable easier modeling of complex geometries in the MCSs (Ma et al 2010, Ma et al 2015, Wu et al 2015, Wang et al 2020).
The accuracy of MCSs depends highly on physical cross section data and physics models. While the cross section data and physics models are continuously being improved as more accurate experiments are performed, there is still a need to further enhance data accuracy or fill in missing data in the energy ranges of interest to radiation therapy. This is especially challenging for MCSs considering low-energy particles, such as in brachytherapy, which are highly sensitive to the physical cross section data. Additionally, the simulation accuracy also depends on the setup of the simulation, such as the model geometry. In some cases that exact information is not avaialble. Other challenges associated with MCSs are relatively large computation time, which rapidly increases for cases with more complex geometries. There have been many techniques addressing computational efficiency, e.g. via variance reduction. MC packages often has a set of parameters that can be adjusted to improve computational efficiency, e.g. setting a higher electron transport cutoff energy level. One has to be cautious about changing these settings because they may affect simulation results. Hardware acceleration, e.g. using GPUs, has so far been mainly applied for selective applications such as patient dose calculation, but has not made it into general-purposed codes.
MCSs for radiotherapy devices have been reported as early as in the 1970s. Numerous studies have been performed since then. To date, it is almost standard practice to employ MCSs to characterize a new device’s performance during its development stage or for the continuous optimization of the devices, which greatly reduces the costs of building prototypes. Due to the rapid technological advancement of modern radiotherapy, increasing accuracy and flexibility of MC applications, and easy access to large computing power, we expect MCS will continue to play a critical role for the development of novel devices.
Acknowledgments
The authors thank the Massachusetts General Hospital research group for providing helpful discussions. This work was partially supported by a National Research Foundation of Korea (NRF) grant funded by the Ministry of Science, ICT & Future Planning of the Korean government (MSIP)(2020R1A2C2011576), the Nuclear Safety Research Program through the Korea Foundation Of Nuclear Safety (KoFONS) using the financial resource granted by the Nuclear Safety and Security Commission (NSSC) of the Republic of Korea. (2101073), the US National Cancer Institute (U24CA215123, R37CA214639, R01 CA227289), and the Cancer Prevention Research Institute of Texas (RP160661).
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