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MC methods

Monte Carlo methods 

Monte Carlo (MC) methods are numerical calculation methods based on random variable sampling. The technique of random sampling to solve mathematical problems is known from 1770. Only with the advent of quantum mechanics in which matter-radiation interactions were interpreted using cross sections as probabilities, the random sampling technique (named "Monte Carlo method" because the Monte Carlo casino was the most famous centre for playing games involving random drawing) was applied to nuclear physics. In the early 1960s, the Monte Carlo method was used by H. O. Anger to simulate the physical response of his new scintillation camera. Since then, thanks to the possibility of modelling different physical processes independently, the method has been applied in medical radiation physics to a wide range of problems that could not be easily addressed using experimental or analytical approaches. As proofs, an increasing number of scientific papers concerning Monte Carlo studies in nuclear medicine, radiation therapy, diagnostic X-rays as well as radiation protection came in the scientific literature.

In Nuclear Medicine, and particularly in SPET and in PET, the use of Monte Carlo methods was advantaged by the possibility of using general purpose codes developed for high energy physics or dosimetry. High-energy (> 1 MeV) processes, secondary and low-energy radiations could be neglected as they were not involved in SPET and PET. On the other hand, the similarity of physical and geometrical characteristics of most emission tomographs suggested specific models to be developed thus favoring the creation of codes dedicated to simulations of emission tomography configurations.

Several SPET/PET dedicated Monte Carlo software packages were developed for simulating a variety of emission tomography studies. Among them, public-domain codes were made available in the last years by the newborn Internet web communication, allowing the use of the Monte Carlo method by the whole scientific community and even in the clinical environment.Several topics were addressed by Monte Carlo simulations in both SPET and PET, among which optimization of imaging system design (including detector, collimator, and shield design), development of correction methods for improved image quantitation, evaluation of correction techniques (scatter/ randoms/ attenuation correction, partial volume effect), assessment of image reconstruction algorithms, ROC studies, pharmaco-kinetic modeling. The theoretical aspects of Monte Carlo methods and the results that have been obtained using Monte Carlo simulations in SPET and PET have been widely presented in recent reviews and books. 

Monte Carlo simulation codes in SPET and PET

Two types of Monte Carlo codes can be used for simulating SPET and PET: 1) general purpose codes, which simulate particle transportation and were developed for high energy physics or for dosimetry, and 2) dedicated codes, designed specifically for SPET or PET simulations.

Modelling SPET and PET configurations using general purpose Monte Carlo codes initially developed to simulate particle transportation in a broad context (e.g. EGS and GEANT) has proven feasible and presents several advantages. As they have been designed for a large community of researchers, these codes are well documented and in the public domain. The fact that they are actually widely used (e.g., EGS, developed for radiation dosimetry, is used by more than 5000 persons) results in several valuable characteristics: support regarding the codes can be easily found through user groups, mailing lists, continuing education and Web sites; many of the code components have been extensively tested, hence can be considered as bug-free; although not guaranteed, regular releases, long-term existence and maintenance of the codes can be expected. As computer scientists are sometimes involved in the development of these codes (e.g., GEANT 4), the successive releases can also be expected to make the most of the current programming tools and hardware facilities. However, using general purpose codes for SPET and PET simulations also raise some issues. Indeed, these codes actually include many features irrelevant to SPET and PET (like electron transportation), which inflate the code sizes and complicate their use for specific applications. Learning the code is therefore often tedious, as one has to sort out useful from unnecessary options. In addition, intensive programming is usually required to model SPET and PET, hence validation remains to be extensively performed. As it may not be easy to know a priori if the code is well suited to the application of interest, the code features must be carefully examined to make sure that the code is appropriate for simulating the considered configurations.

Dedicated codes, designed especially for SPET and/or PET, could a priori be thought more suitable since they are directly concerned with SPET and PET configurations. Indeed, they are usually relatively convenient to implement and learning the use of the code is fast. On the other hand, because the SPET and PET community is not as large as communities involved in high particle physics or dosimetry, these dedicated codes are often developed by small research groups, hence maintenance and long-term existence are uncertain. Because the task force involved in the development of these codes is usually rather limited, the codes are also more prone to incomplete documentation, bugs and slower evolution than general purpose codes. As the dedicated codes are often designed with some specific applications in mind, they do not always offer the flexibility that would be necessary to adapt them to the evolution occurring in SPET and PET (modelling transmission acquisition in SPET for instance).

Whether general purpose or dedicated codes should be preferred for SPET and PET simulations obviously strongly depends on the user's needs. Scientists who are not willing to program should favour the dedicated code that best fulfils their requirements. On the other hand, scientists willing to use Monte Carlo simulations for studying original configurations (for instance new detector designs) will find more flexibility and potentialities by considering general purpose codes. Table I summarises the main codes currently available (by internet download or from authors) in each category together with their associated references and Web URL when available.

Table 1

Generic codes

Dedicated codes

EGS4 (radiation dosimetry)

MCNP (radiation dosimetry)

ITS (high energy physics)

GEANT (high energy physics)

SPET only:




PET only:










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