Steven Staelens

GATE: a simulation toolkit for PET and SPECT.

Monte Carlo simulation is an essential tool in emission tomography that can assist in the design of new medical imaging devices, the optimization of acquisition protocols and the development or assessment of image reconstruction algorithms and correction techniques. GATE, the Geant4 Application for Tomographic Emission, encapsulates the Geant4 libraries to achieve a modular, versatile, scripted simulation toolkit adapted to the field of nuclear medicine. In particular, GATE allows the description of time-dependent phenomena such as source or detector movement, and source decay kinetics. This feature makes it possible to simulate time curves under realistic acquisition conditions and to test dynamic reconstruction algorithms. This paper gives a detailed description of the design and development of GATE by the OpenGATE collaboration, whose continuing objective is to improve, document and validate GATE by simulating commercially available imaging systems for PET and SPECT. Large effort is also invested in the ability and the flexibility to model novel detection systems or systems still under design. A public release of GATE licensed under the GNU Lesser General Public License can be downloaded at http:/www-lphe.epfl.ch/GATE/. Two benchmarks developed for PET and SPECT to test the installation of GATE and to serve as a tutorial for the users are presented. Extensive validation of the GATE simulation platform has been started, comparing simulations and measurements on commercially available acquisition systems. References to those results are listed. The future prospects towards the gridification of GATE and its extension to other domains such as dosimetry are also discussed.

Monte Carlo simulations of a scintillation camera using GATE: validation and application modelling

Geant4 application for tomographic emission (GATE) is a recently developed simulation platform based on Geant4, specifically designed for PET and SPECT studies. In this paper we present validation results of GATE based on the comparison of simulations against experimental data, acquired with a standard SPECT camera. The most important components of the scintillation camera were modelled. The photoelectric effect. Compton and Rayleigh scatter are included in the gamma transport process. Special attention was paid to the processes involved in the collimator: scatter, penetration and lead fluorescence. A LEHR and a MEGP collimator were modelled as closely as possible to their shape and dimensions. In the validation study, we compared the simulated and measured energy spectra of different isotopes: 99mTc, 22Na, 57Co and 67Ga. The sensitivity was evaluated by using sources at varying distances from the detector surface. Scatter component analysis was performed in different energy windows at different distances from the detector and for different attenuation geometries. Spatial resolution was evaluated using a 99mTc source at various distances. Overall results showed very good agreement between the acquisitions and the simulations. The clinical usefulness of GATE depends on its ability to use voxelized datasets. Therefore, a clinical extension was written so that digital patient data can be read in by the simulator as a source distribution or as an attenuating geometry. Following this validation we modelled two additional camera designs: the Beacon transmission device for attenuation correction and the Solstice scanner prototype with a rotating collimator. For the first setup a scatter analysis was performed and for the latter design. the simulated sensitivity results were compared against theoretical predictions. Both case studies demonstrated the flexibility and accuracy of GATE and exemplified its potential benefits in protocol optimization and in system design.

Validation of the GATE Monte Carlo simulation platform for modelling a CsI(Tl) scintillation camera dedicated to small-animal imaging

Monte Carlo simulations are increasingly used in scintigraphic imaging to model imaging systems and to develop and assess tomographic reconstruction algorithms and correction methods for improved image quantitation. GATE (GEANT4 application for tomographic emission) is a new Monte Carlo simulation platform based on GEANT4 dedicated to nuclear imaging applications. This paper describes the GATE simulation of a prototype of scintillation camera dedicated to small-animal imaging and consisting of a CsI(Tl) crystal array coupled to a position-sensitive photomultiplier tube. The relevance of GATE to model the camera prototype was assessed by comparing simulated 99mTc point spread functions, energy spectra, sensitivities, scatter fractions and image of a capillary phantom with the corresponding experimental measurements. Results showed an excellent agreement between simulated and experimental data: experimental spatial resolutions were predicted with an error less than 100 microns. The difference between experimental and simulated system sensitivities for different source-to-collimator distances was within 2%. Simulated and experimental scatter fractions in a [98-182 keV] energy window differed by less than 2% for sources located in water. Simulated and experimental energy spectra agreed very well between 40 and 180 keV. These results demonstrate the ability and flexibility of GATE for simulating original detector designs. The main weakness of GATE concerns the long computation time it requires: this issue is currently under investigation by the GEANT4 and the GATE collaborations.

A three-dimensional theoretical model incorporating spatial detection uncertainty in continuous detector PET.

In this paper, we will describe a theoretical model of the spatial uncertainty for a line of response, due to the imperfect localization of events on the detector heads of a positron emission tomography (PET) camera. The forward acquisition problem is modelled by a Gaussian distribution of the position of interaction on a detector head, centred at the measured position. The a posteriori probability that an event originates from a certain point in the field of view (FOV) is calculated by integrating all the possible lines of response (LORs) through this point, weighted with the Gaussian detection likelihood at the LORs end points. We have calculated these a posteriori probabilities both for perpendicular and oblique coincidences. For the oblique coincidence case it was necessary to incorporate the effect of the crystal thickness in the calculations. We found in the perpendicular incidence case as well as in the oblique incidence case that the probability density function cannot be analytically expressed in a closed form, and it was thus calculated by means of numerical integration. A Gaussian was fit to the transversal profiles of this function for a given distance to the detectors. From these fits, we can conclude that the profiles can be accurately approximated by a Gaussian, both for perpendicular and oblique coincidences. The FWHM reaches a maximum at the detector heads, and decreases towards the centre of the FOV, as was expected. Afterwards we extended this two-dimensional model to three dimensions, thus incorporating the spatial uncertainty in both transversal directions. This theoretical model was then evaluated and a very good agreement was found with theoretical calculations and with geometric Monte Carlo simulations. Possible improvements for the above-described incorporation of crystal thickness are discussed. Therefore a detailed Monte Carlo study has been performed in order to investigate the interaction probability of photons of different energies along their path in several detector materials dedicated to PET. Finally two approaches for the incorporation of this theoretical model in reconstruction algorithms are outlined.

The geometric transfer function for a slat collimator mounted on a strip detector

A theoretical formulation of the effective point spread function of a slat collimator on a strip detector has been derived. The used technique to obtain the geometric transfer function, which is the Fourier transform of the effective point source image, is based on the geometric characteristics of a single gap and it accurately describes the performance of the collimation system for system analysis. Valuable conclusions resulting from this geometric transfer function could be made on the sensitivity, on the spatial resolution, and on the line spread function of the imaging system. We found that the sensitivity was dependent on the angle of incidence and on the distance to the detector. The spatial resolution was constant in a plane at a fixed distance to the detector and closed analytical expressions were derived for transaxial line spread profiles. These results were confirmed by the appropriate Monte Carlo simulations. The presented formulation of the geometric transfer function will be useful with usage in iterative reconstruction algorithms to incorporate distance dependent effects.

Sensitivity of SPECT with rotating slat collimators

SPECT acquisition with rotating slat collimators does not have a constant sensitivity over the field of view, like in parallel hole collimated SPECT. Therefore knowledge of the sensitivity variation is required to be able to correct for this effect during reconstruction. The variation of the sensitivity in the field of view for SPECT imaging with planar collimation is determined by different factors. A primary factor are the collimator properties, but there is also an influence of the type of detector and its dimensions. The geometric sensitivity is derived from the collimator dimensions using some assumptions. It is shown that this is a valid prediction for the sensitivity when the point is far enough from the collimator. Close to the collimator the assumptions for calculating the sensitivity are not fulfilled any more, and a modified calculation method is used. It is shown that after using this modified method a constant error between the calculated and experimental (Monte Carlo simulation)values for the different distances is obtained. After calculating the sensitivity in one plane it is easy to obtain the tomographic sensitivity. This is done by rotating the maps for spin and camera rotation. The method allows to obtain an expression for the resolution of these systems. It is shown that for the same collimator dimensions the same resolution-distance relationship is obtained as for parallel hole collimators. The accuracy is shown by comparison with the resolution values from Monte Carlo simulation. Close to the detector a correction factor is needed.

Transmission imaging with a moving point source: influence of crystal thickness and collimator type

Nonuniform patient attenuation maps can be acquired using an axially moving point source of a high energy isotope that emits a fanbeam of photons. We modeled the Beacon attenuation correction tool attached to multiheaded SPECT cameras which uses this approach. We investigated the scatter order of the photons from the attenuation imaging source reaching the detector, and the scatter contributions from the different detector components were evaluated for different energy windows. Additionally the scatter of the Beacon source photons in the transmission window and the degrading downscatter on an emission photopeak window in simultaneous emission and transmission scanning were investigated. We performed multiple types of simulations including different crystal thicknesses and different collimators for protocol optimization purposes. The main conclusion of this work is that a thick crystal detector coupled to a LEHR collimator is the best solution for acquiring attenuation maps in low energy applications. For medium energy studies attenuation maps have to be rescaled to account for the low sensitivity near the center of the patient. Fully Monte Carlo simulating the projector for medium energy studies on low energy collimators in order to replace the MEGP collimators by their LEHR analogons is another possibility that is currently being investigated. This last approach is however penalized by a high computational burden but can result in an improved image quality after reconstruction.

Correction for partial volume effects in brain perfusion ECT imaging

The accurate quantification of brain perfusion for emission computed tomography data (PET-SPECT) is limited by partial volume effects (PVE). This study presents a new approach to estimate accurately the true tissue tracer activity within the grey matter tissue compartment. The methodology is based on the availability of additional anatomical side information and on the assumption that activity concentration within the white matter tissue compartment is constant. Starting from an initial estimate for the white matter grey matter activity, the true tracer activity within the grey matter tissue compartment is estimated by an alternating ML-EM-algorithm. During the updating step the constant activity concentration within the white matter compartment is modelled in the forward projection in order to reconstruct the true activity distribution within the grey matter tissue compartment, hence reducing partial volume averaging. Consequently the estimate for the constant activity in the white matter tissue compartment is updated based on the new estimated activity distribution in the grey matter tissue compartment. We have tested this methodology by means of computer simulations. A T1-weighted MR brainscan of a patient was segmented into white matter, grey matter and cerebrospinal fluid, using the segmentation package of the SPM-software (Statistical Parametric Mapping). The segmented grey and white matter were used to simulate a SPECT acquisition, modelling the noise and the distance dependant detector response. Scatter and attenuation were ignored. Following the above described strategy, simulations have shown it is possible to reconstruct the true activity distribution for the grey matter tissue compartment (activity/tissue volume), assuming constant activity in the white matter tissue compartment.

Theoretical LOR model incorporating spatial uncertainty in continuous detector PET

In this paper, we will describe a theoretical model of the spatial uncertainty for a line of response, due to the imperfect localization of events on the detector heads of the Positron Emission Tomography (PET) camera. We assume a Gaussian distribution of the position of interaction on a detector head, centered at the measured position. The probability that an event originates from a certain point in the FOV is calculated by integrating all the possible LORs through this point, weighted with the Gaussian probability of detection at the LORs end points. We have calculated these probabilities both for perpendicular and oblique coincidences. For the oblique coincidence case it was necessary to incorporate the effect of the crystal thickness in the calculations. We found that the probability function can not be analytically expressed in a closed form, and it was thus calculated by means of numerical integration. A Gaussian was fitted to the probability profiles for a given distance to the detectors. From these fits, we can conclude that the profiles can be accurately approximated by a Gaussian, both for perpendicular as for oblique coincidences. The FWHM reaches a maximum at the detector heads, and decreases towards the center of the FOV, as was expected.