Applications to Patient-Specifi c Voxel Computational Phantoms in EGS Monte Carlo Codes for Radiation Treatment Involving Photons and Electrons
Butcher and Messel1,2 and Varfolomeev and Svetlolobov3 were the rst two groups that conducted a Monte Carlo simulation of high-energy cascades on electronic digital computers. Their collaboration resulted in an extensive set of tables describing the shower distribution functions, which were used by the later codes. Zerby and Moran4,5 developed a Monte Carlo computer code for high-energy electromagnetic cascade simulation, which was used by Alsmiller and others6-8 for a number of studies. Although the code was not readily available to the public, nor was it maintained, some useful ideas and
experiences were re ected in the Electron Gamma Shower (EGS) code system. Nagel’s code SHOWER9,10 represented a practical tool for the experimental physicists during the middle 1960s-and one version of his code eventually became the EGS3 Code System. The applications of SHOWER, however, were limited because of its unwieldiness and its limitations on scope. For example, its built-in geometry only allowed the use of a single cylinder of Pb and radiation transport could only be initiated for monoenergetic electrons with energies up to 1 GeV. Except for annihilation, positrons and electrons were treated alike and were followed down to 1 MeV (kinetic energy), and photons were followed down to 0.25 MeV (but this still represented cutoff energies that were, at the time, as low as or lower than those used by Messel and Crawford and Zerby and Moran). Continuing efforts were made to modify SHOWER so as to make it versatile, upward compatible, and userfriendly. As a result of the joint effort of Ford and Nelson,11 the Electron Gamma Shower version 3 (EGS3) computer code system was formally introduced. Researchers designed EGS3 to simulate electromagnetic cascades in various geometries and at energies up to a few thousand GeV and down to cutoff kinetic energies of 0.1 MeV (photons) and 1 MeV (electrons and positrons). With the PEGS (Preprocessor for EGS) auxiliary code, radiation transport could be simulated for 100 elements, any compound, or any mixture of those elements. EGS3 also included some processes that provided more ef cient sampling schemes. Researchers carried out a wide range of benchmark comparisons and applications after the release of EGS3, especially in the eld of high-energy particle physics and in the design of the electromagnetic shower counters. After the release of EGS3, more applications were found in the simulation of low-energy photon and electron transport for a variety of problems in addition to those normally associated with electromagnetic cascade showers. The requirement for the extension of the lower energy limits-i.e., down to 1 and 10 keV for photons and electrons, respectively, was growing fast. As a result of a joint effort by Nelson, Hirayama, Rogers, and other colleagues, the exibility of EGS was further improved together with an important benchmarking effort in the low-energy particle transport.12 The EGS4 code system was nally introduced in 1985.13 In the following years, the EGS4 system was widely used in medical physics and dosimetry research, especially for low-energy radiation transport problems, though it was still heavily used in high-energy particle physics. Researchers made further improvements to the EGS4 code system, including an angular distribution for the emission of photoelectrons and an electron transport algorithm called PRESTA.14 The latter simpli ed many of the cumbersome problems related to user-de ned restrictions on electron step-sizes and the limitations on electron multiple-scattering. Hirayama and Namito reported a general treatment of photoelectric-related phenomena for compounds or mixtures in EGS4.15 They introduced the energy-dependent branching ratio of each sub shell (L1-, L2-, and L3-) in this improvement by tting to a quadratic function in log-log from data provided for limited materials (Ag, Pb, and U). This addition is further improved using a generalized treatment,16 in which K-, L1-, L2-, L3-, and other sub shell photoelectric cross sections taken from the PHOTX data base (see below) are tted to cubic functions in log-log form and the tted coef cients and other associated data are initialized in a BLOCK DATA subprogram of EGS. It thus becomes possible to calculate the branching ratios for each element of compounds and mixtures inside EGS, negating the need to use approximate piece-wise linear- tted data from PEGS. Verhaegen et al. reported an accurate simulation for kilovoltage x-ray units employing these developments.17 The EGS4 electron transport was based on the Moliere multiple-scattering theory. Moliere considered his theory to be valid for a number of electron interactions ½ > 20 whereas the default EGS4 uses ½ = 1. In PRESTA, ½ was increased to e, which is the mathematical limit of the Moliere theory. It still needed improvements
to deal properly with electron backscatter,18 and also minimum electron step-sizes when different energy cut offs were used in a simulation, or if a different number of media were used in the same simulation. More recently, researchers incorporated the sampling of bremsstrahlung photon angles into EGS4.19 Duane et al.20 implemented the up-to-date stopping powers recommended by ICRU.21 Ma and Nahum implemented a new algorithm for the EGS4 low-energy electron transport to account for the change in the discrete interaction cross-section with electron energy.22 A large number of applications were reported based on the EGS4 system in radiation detector simulations,18,23,24 radiotherapy treatment machine simulations,25-28 radiotherapy treatment planning dose calculations, and plan veri cations.29-34 The results showed that the EGS4 system was suf ciently accurate for radiation therapy treatment planning dose calculations. The most recent development of the EGS code system was the signi cant improvement in electron multiple scattering simulation by Kawrakow,35 which has led to the release of the NRCC version of the EGS code system, EGSnrc, in 2000.36 EGSnrc also incorporated improvements in the implementation of photon and electron transport, better low energy photon physics, more ef cient sampling algorithms, and various bug xes compared to EGS4. In parallel, researchers made a signi cant effort to develop the next version of EGS; this EGS5 was announced in 2005.37 EGS5 incorporated many improvements in photon and electron transport improvements. In particular, the PEGS and EGS codes were combined in EGS5 so that cross-sectional data could be generated for every simulation. EGS5 also adopted an advanced electron transport algorithm, which uses a dual random hinge approach.38 The primary advantages of this technique lie in that the random multiple scattering hinge preserves near secondorder spatial moments of the transport equation over long step lengths,39 and that the hinge mechanics can be formulated so as to permit transport across boundaries between regions of differing media. The PRESTA boundary crossing logic was abandoned. Despite many new developments for the EGS system that often associate with somewhat longer computer simulation time, little has been reported on the necessity of these later EGS versions for external beam radiotherapy treatment planning and radiation protection dose calculations. Therefore, the materials presented in this chapter are mainly based on the radiation transport algorithms, geometrical packages and clinical applications of the EGS4 system and their user codes, which are still widely used for radiotherapy and radiation protection applications.