Implementation of angular response function modeling in SPECT simulations with GATE.

Among Monte Carlo simulation codes in medical imaging, the GATE simulation platform is widely used today given its flexibility and accuracy, despite long run times, which in SPECT simulations are mostly spent in tracking photons through the collimators. In this work, a tabulated model of the collimator/detector response was implemented within the GATE framework to significantly reduce the simulation times in SPECT. This implementation uses the angular response function (ARF) model. The performance of the implemented ARF approach has been compared to standard SPECT GATE simulations in terms of the ARF tables' accuracy, overall SPECT system performance and run times. Considering the simulation of the Siemens Symbia T SPECT system using high-energy collimators, differences of less than 1% were measured between the ARF-based and the standard GATE-based simulations, while considering the same noise level in the projections, acceleration factors of up to 180 were obtained when simulating a planar 364 keV source seen with the same SPECT system. The ARF-based and the standard GATE simulation results also agreed very well when considering a four-head SPECT simulation of a realistic Jaszczak phantom filled with iodine-131, with a resulting acceleration factor of 100. In conclusion, the implementation of an ARF-based model of collimator/detector response for SPECT simulations within GATE significantly reduces the simulation run times without compromising accuracy.

Fast modelling of the collimator-detector response in Monte Carlo simulation of SPECT imaging using the angular response function.

Interactions of incident photons with the collimator and detector, including septal penetration, scatter and x-ray fluorescence, are significant sources of image degradation in applications of SPECT including dual isotope imaging and imaging using radioisotopes that emit high- or medium-energy photons. Modelling these interactions using full Monte Carlo (MC) simulations is computationally very demanding. We present a new method based on the use of angular response functions (ARFs). The ARF is a function of the incident photon's direction and energy and represents the probability that a photon will either interact with or pass through the collimator, and be detected at the intersection of the photon's direction vector and the detection plane in an energy window of interest. The ARFs were pre-computed using full MC simulations of point sources that include propagation through the collimator-detector system. We have implemented the ARF method for use in conjunction with the SimSET/PHG MC code to provide fast modelling of both interactions in the patient and in the collimator-detector system. Validation results in the three cases studied show that there was good agreement between the projections generated using the ARF method and those from previously validated full MC simulations, but with hundred to thousand fold reductions in simulation time.

A mathematical model of motion of the heart for use in generating source and attenuation maps for simulating emission imaging.

This manuscript documents the alteration of the heart model of the three-dimensional (3D) mathematical cardiac torso (MCAT) phantom to represent cardiac motion. The objective of the inclusion of motion was to develop a digital simulation of the heart such that the impact of cardiac motion on single-photon emission computed tomography (SPECT) imaging could be assessed and methods of quantitating cardiac function could be investigated. The motion of the gated 3D MCAT's (gMCAT) heart is modeled using 128 separate and evenly spaced time samples from a blood volume curve approximating an average heart cycle. Sets of adjacent time samples can be grouped together to represent a single time interval within the heart cycle. Maximum and minimum chamber volumes were selected to be similar to those of a normal healthy person while the total heart volume stayed constant during the cardiac cycle. Myocardial mass was conserved during the cardiac cycle and the bases of the ventricles were modeled as moving towards the static apex. The orientation of the 3D MCAT heart was changed during contraction to rotate back and forth around the long axis through the center of the left ventricle (LV) using the end systolic time interval as the time point at which to reverse direction. Simple respiratory motion was also introduced by changing the orientation of the long axis of the heart to represent its variation with respiration. Heart models for 24 such orientations spanning the range of motion during the respiratory cycle were averaged together for each time sample to represent the blurring of the heart during the acquisition of multiple cardiac cycles. Finally, an option to model apical thinning of the myocardium was included. As an illustration of the application of the gMCAT phantom, the gated heart model was evaluated by measuring myocardial wall thickening. A linear relationship was obtained between maximum myocardial counts and myocardial thickness, similar to published results. Similar results were obtained for full width at half maximum (FWHM) measurements. With the presence of apical thinning, an apparent increase in counts in the apical region compared to the other heart walls in the absence of attenuation compensation turns into an apparent decrease in counts with attenuation compensation. The apical decrease was more prominent in end systole (ES) than end diastole (ED) due to the change in the partial volume effect. These observations agree with clinical trends. It is concluded that the gMCAT phantom can be used to study the influence of various physical parameters on radionuclide perfusion imaging.

Fast implementations of reconstruction-based scatter compensation in fully 3D SPECT image reconstruction.

Accurate scatter compensation in SPECT can be performed by modelling the scatter response function during the reconstruction process. This method is called reconstruction-based scatter compensation (RBSC). It has been shown that RBSC has a number of advantages over other methods of compensating for scatter, but using RBSC for fully 3D compensation has resulted in prohibitively long reconstruction times. In this work we propose two new methods that can be used in conjunction with existing methods to achieve marked reductions in RBSC reconstruction times. The first method, coarse-grid scatter modelling, significantly accelerates the scatter model by exploiting the fact that scatter is dominated by low-frequency information. The second method, intermittent RBSC, further accelerates the reconstruction process by limiting the number of iterations during which scatter is modelled. The fast implementations were evaluated using a Monte Carlo simulated experiment of the 3D MCAT phantom with 99mTc tracer, and also using experimentally acquired data with 201Tl tracer. Results indicated that these fast methods can reconstruct, with fully 3D compensation, images very similar to those obtained using standard RBSC methods, and in reconstruction times that are an order of magnitude shorter. Using these methods, fully 3D iterative reconstruction with RBSC can be performed well within the realm of clinically realistic times (under 10 minutes for 64 x 64 x 24 image reconstruction).

A Monte Carlo investigation of artifacts caused by liver uptake in single-photon emission computed tomography perfusion imaging with technetium 99m-labeled agents.

BACKGROUND: Significant hepatobiliary accumulation of technetium 99m-labeled cardiac perfusion agents has been shown to cause alterations in the apparent localization of the agents in the cardiac walls. A Monte Carlo study was conducted to investigate the hypothesis that the cardiac count changes are due to the inconsistencies in the projection data input to reconstruction, and that correction of the causes of these inconsistencies before reconstruction, or including knowledge of the physics underlying them in the reconstruction algorithm, would virtually eliminate these artifacts. METHODS AND RESULTS: The SIMIND Monte Carlo package was used to simulate 64 x 64 pixel projection images at 128 angles of the three-dimensional mathematical cardiac-torso (MCAT) phantom. Simulations were made of (1) a point source in the liver, (2) cardiac activity only, and (3) hepatic activity only. The planar projections and reconstructed point spread functions (PSFs) of the point source in the liver were investigated to study the nature of the inconsistencies introduced into the projections by imaging, and how these affect the distribution of counts in the reconstructed slices. Bull's eye polar maps of the counts at the center of the left ventricular wall of filtered back-projection (FBP) and maximum-likelihood expectation-maximization (MLEM) reconstructions of projections with solely cardiac activity, and with cardiac activity plus hepatic activity scaled to have twice the cardiac concentration, were compared to determine the magnitude and location of apparent changes in cardiac activity when hepatic activity is present. Separate simulations were made to allow the investigation of stationary spatial resolution, distance-dependent spatial resolution, attenuation, and scatter. The point source projections showed significant inconsistencies as a function of projection angle with the largest effect being caused by attenuation. When consistent projections were simulated, no significant impact of hepatic activity on cardiac counts was noted with FBP, or 100 iterations of MLEM. With inconsistent projections, reconstruction of 180 degrees resulted in greater apparent cardiac count losses than did 360 degrees reconstruction for both FBP and MLEM. The incorporation of attenuation correction in MLEM reconstruction reduced the changes in cardiac counts to that seen in simulations in which attenuation was not included, but resulted in increased apparent localization of activity in the posterior wall of the left ventricle when scatter was present in the simulated images. CONCLUSIONS: The apparent alterations in cardiac counts when significant hepatic localization is present is due to the inconsistency of the projections inherent in imaging. Prior correction of these, or accounting for them in the reconstruction algorithm, will virtually eliminate them as causes of artifactual changes in localization. Attenuation correction and scatter correction are both required to overcome the major sources of apparent count changes in the heart associated with hepatic uptake.

Noise properties of the EM algorithm: II. Monte Carlo simulations.

In an earlier paper we derived a theoretical formulation for estimating the statistical properties of images reconstructed using the iterative ML-EM algorithm. To gain insight into this complex problem, two levels of approximation were considered in the theory. These techniques revealed the dependence of the variance and covariance of the reconstructed image noise on the source distribution, imaging system transfer function, and iteration number. In this paper a Monte Carlo approach was taken to study the noise properties of the ML-EM algorithm and to test the predictions of the theory. The study also served to evaluate the approximations used in the theory. Simulated data from phantoms were used in the Monte Carlo experiments. The ML-EM statistical properties were calculated from sample averages of a large number of images with different noise realizations. The agreement between the more exact form of the theoretical formulation and the Monte Carlo formulation was better than 10% in most cases examined, and for many situations the agreement was within the expected error of the Monte Carlo experiments. Results from the studies provide valuable information about the noise characteristics of ML-EM reconstructed images. Furthermore, the studies demonstrate the power of the theoretical and Monte Carlo approaches for investigating noise properties of statistical reconstruction algorithms.

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

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.

Optimum detector spatial resolution for discriminating between tumour uptake distributions in scintigraphy.

The optimum detector spatial resolution has been determined for a scintigraphic decision task in which the observer must discriminate between two different distributions of radioactivity in tumours. The two kinds of tumour used are: (i) a solid sphere of increased uptake relative to background, and (ii) a thin spherical shell with high uptake in the shell and no radioactivity within the shell. Both tumours are embedded at the same depth within a cylinder of tissue-equivalent material containing a uniform distribution of radioactivity. On the basis of statistical decision theory, the optimum detector spatial resolution for discriminating between the two tumour activity distributions is predicted. The result of an observer performance experiment substantially agreed with the theoretical prediction, though some discrepancy was found, apparently due to a decrease in observer efficiency at poorer spatial resolution. The experimental result suggests that the optimum FWHM of detector spatial response for the discrimination task considered is about 65% of the tumour radius.