Monte Carlo techniques have become popular in different areas of medical physics with advantage of powerful computing systems. In particular, they have been extensively applied to simulate processes involving random behavior and to quantify physical parameters that are difficult or even impossible to calculate by experimental measurements. Recent nuclear medical imaging innovations such as single-photon emission computed tomography (SPECT), positron emission tomography (PET), and multiple emission tomography (MET) are ideal for Monte Carlo modeling techniques because of the stochastic nature of radiation emission, transport and detection processes. Factors which have contributed to the wider use include improved models of radiation transport processes, the practicality of application with the development of acceleration schemes and the improved speed of computers. In this paper we present a derivation and methodological basis for this approach and critically review their areas of application in nuclear imaging. An overview of existing simulation programs is provided and illustrated with examples of some useful features of such sophisticated tools in connection with common computing facilities and more powerful multiple-processor parallel processing systems. Current and future trends in the field are also discussed.

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Relevance of accurate Monte Carlo modeling in nuclear medical imaging.

The purpose of this study was to investigate the importance of 2D versus 3D compensation methods in SPECT. The compensation methods included in the study addressed two important degrading factors, namely attenuating and collimator-detector response in SPET. They can be divided into two general categories. The conventional methods are based on the filtered backprojection algorithm, the Chang algorithm for attenuation compensation and the Metz filter for detector response compensation. These methods, which were computationally efficient, could only achieve approximate compensation due to the assumptions made. The quantitative compensation methods provide accurate compensation by modelling the degrading effects at the expense of large computational requirements. Both types of compensation methods were implemented in 2D and 3D reconstructions. The 2D and 3D reconstruction/compensation methods were evaluated using data from simulation of brain and heart, and patient thallium SPECT studies. Our results demonstrate the importance of compensation methods in improving the quality and quantitative accuracy of SPECT images and the relative effectiveness of the different 2D and 3D reconstruction/compensation methods. We concluded that 3D implementation of the quantitative compensation methods provides the best SPECT image in terms of quantitative accuracy, spatial resolution, and noise at a cost of high computational requirements.

https://iopscience.iop.org/article/10.1088/0031-9155/39/3/015/pdf

The importance and implementation of accurate 3D compensation methods for quantitative SPECT.

Time-of-flight PET

In this paper the authors present a method for analytically calculating the distribution of photons detected in single photon emission computed tomography (SPECT) projections. The technique is applicable to sources in homogeneous and nonhomogeneous media. The photon distribution (primary, first-, and second-order Compton scatter) is computed using a precalculated camera-dependent look-up table in conjunction with an attenuation map of the scattering object and a map of the activity distribution. The speed and accuracy of this technique is compared to that of Monte Carlo simulations. The cases considered are a point source in a homogeneous and also in a nonhomogeneous scattering medium, an extended source in a nonhomogeneous medium, and a homogeneous cylinder filled uniformly with activity. The method is quantitatively accurate and faithfully reproduces the spatial distribution of the unscattered and scattered photons. For comparable statistical precision in the peak of the calculated distribution, their approach can result in a gain in calculation time over Monte Carlo simulators. For point sources, the computation times are improved by a factor of 20-150. However, this gain depends on the source configuration, and calculation times become comparable for an 800 voxel source and are five times slower for a 55000 voxel source. The method also offers an increase in the speed of computation of higher order Compton scatter events over a similar analytical technique.

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Analytical calculation of scatter distributions in SPECT projections

Due to the availability of digitally stored human anatomy images, 3-dimensional surfaces of internal structures of the body can be stored in computer volume arrays. Such a volume based software phantom delineates internal human organs with millimeter resolution and lends itself to fully 3-dimensional Monte Carlo simulations. Our simulation models 45 internal human organs (each with an associated radioisotope concentration and attenuation coefficient), calculates gamma radiation histories through these structures, and accepts gamma events onto a collimated planar camera. Variance reduction techniques are applied to decrease the time required to compute a given number of events at the detector. Stratification and two implementations of forced detection variance reduction techniques are compared to ”brute force” calculations for their efficiency speed-ups in this heterogeneous geometry. Simulated clinical images of the liver are shown.

Voxel based Monte Carlo calculations of nuclear medicine images and applied variance reduction techniques

The development for public distribution of a general-purpose code, SIMSET, for the modeling of positron-emission and single-photon-emission tomographs (PET and SPECT) is discussed. An important part of the SIMSET project is the development of methods for efficient photon simulation which can handle heterogeneous distributions of activity and attenuation. For both positron and single-photon tomographs, the solid angle of acceptance of the detector array is small, due to collimation and to the size of the detector array itself. This results in significant computational inefficiencies with conventional Monte Carlo simulation, because only a few percent of the photons generated and tracked will actually be detected. A similar kind of problem arises in radiation shielding calculations, where the flux through the shield, although significant, may correspond to only a tiny fraction of the initial emitted photons. To improve the efficiency problem of simulations, some techniques from the radiation shielding literature have been adapted to increase the yield of detected photons. >

Improving the efficiency of emission tomography simulations using variance reduction techniques

To better understand the performance of the SP3000 time-of-flight PET (positron emission tomography), machine, the authors performed Monte Carlo calculations of photon interactions in a BaF/sub 2/ detector module and calculations of crystal optics for BaF/sub 2/ UV scintillation light. Evaluated were photon detection sensitivities, the amount of photon spillover, crystal crosstalk, interring miscodes, and true-to-random coincidence ratios as a function of the lower-level energy discriminator setting and crystal/photomultiplier tube energy resolution. UV light collection efficiencies for the timing tube and decode tube were calculated assuming different crystal geometries, reflective materials, and reflectances. For a typical SP3000 detector module the detection efficiency for single 511-keV photons varied between 20 and 60% depending on the angle of incidence. >

Monte Carlo simulation of BaF/sub 2/ detectors used in time-of-flight positron emission tomography

A data acquisition system for a time-of-flight positron emission tomograph (PET) has been designed and implemented. The primary constraint on the system was providing collection rates of 100000 events per second per image plane for a total of seven planes with minimal hardware and software resources. The system is based on Data General MV series minicomputers. The interface hardware includes a Data General 5400GP BMC general-purpose interface board and an external event bus interface (EBI) for each image plane. A software package, written in C and running under AOS/VS, was developed to control the acquisition process. The hardware and software are described. >

High speed PET data acquisition with a standard mini computer

A large software simulation system for emission tomography (SimSET) is being developed using structured analysis and design (SAD), a software engineering technique. Most of the researchers in the project were not familiar with formal software engineering. Thus several team organizations and SAD approaches were tried before a productive one was found: the computer scientists work on the software definition; the other scientists anticipate problems that will be encountered developing the simulations and work on solutions to them. Utilizing this modified SAD approach it has been possible to integrate the diverse expertise necessary to produce a large scientific software package. >

On using formal software engineering techniques in an academic environment

A data acquisition system for a time-of-flight positron emission tomograph (PET) has been designed and implemented. The primary constraint upon the system was providing collection rates of 100,000 events per second per image plane for a total of seven planes with minimal hardware and software resources. Our system is based on Data General MV series mini computers [l]. The specific interface hardware includes a Data General 5400GP BMC general purpose interface board and our external event bus interface (EBI) for each image plane. A software package, written in C and running under AOSIVS, was developed to control the acquisition process. The results to date show that we will be able to meet our performance criteria.

C.P. Anson

Papers

Improving the efficiency of emission tomography simulations using variance reduction techniques

Monte Carlo simulation of BaF/sub 2/ detectors used in time-of-flight positron emission tomography

High speed PET data acquisition with a standard mini computer

On using formal software engineering techniques in an academic environment

Data Acquisition & Simulation Systems HIGH SPEED PET DATA ACQUISITION WITH A STANDARD MINI COMPUTER