
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 matterradiation 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 Xrays 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. Highenergy
(> 1 MeV) processes, secondary and lowenergy 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,
publicdomain 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, pharmacokinetic 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 bugfree; although not guaranteed,
regular releases, longterm 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 longterm 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:
SimMIND
SimSPECT
MCMATV 
PET
only:
PETSIM
EIDOLON
Reilhac
PETEGS 
SPET
and PET:
SimMIND
SimSPECT
MCMATV 

