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.

A method is described for preprocessing projection data prior to image reconstruction in single -photon emission computed tomography. The projection data of the desired spatial distribution of emission activity is blurred by the pointresponse function of the collimator that is used to define the range of directions of gamma -ray photons reaching the detector. The point-response function of the collimator is not stationary, but depends on the distance from the collimator to the point. Conventional methods for deblurring collimator projection data are based on approximating the actual depth -dependent pointresponse function by a spatially-invariant blurring function, so that deconvolution methods can be applied independently to the data at each angle of view. The method described in this paper is based on Fourier analysis of the multi-angular data set as a whole, using special depth-dependent characteristics of the Fourier coefficients to achieve spatially-variant inverse filtering of the data in all views simultaneously. Preliminary results are presented for simulated data with a simple collimator model.

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.

In single-photon emission computed tomography (SPECT), projection data are acquired by rotating the photon detector around a patient, either in a circular orbit or in a noncircular orbit. The projection data of the desired spatial distribution of emission activity is blurred by the point-response function of the collimator that is used to define the range of directions of gamma-ray photons reaching the detector. The point-response function of the collimator is not spatially stationary, but depends on the distance from the collimator to the point. Conventional methods for deblurring collimator projection data are based on approximating the actual distance-dependent point-response function by a spatially invariant blurring function, so that deconvolution methods can be applied independently to the data at each angle of view. A method is described here for distance-dependent preprocessing of SPECT projection data prior to image reconstruction. Based on the special distance-dependent characteristics of the Fourier coefficients of the sinogram, a spatially variant inverse filter can be developed to process the projection data in all views simultaneously. The algorithm is first derived from Fourier analysis of the projection data from the circular orbit geometry. For circular orbit projection data, experimental results from both simulated data and real phantom data indicate the potential of this method. It is shown that the spatial filtering method can be extended to the projection data from the noncircular orbit geometry. Experiments on simulated projection data from an elliptical orbit demonstrate correction of the spatially variant blurring and distortion in the reconstructed image caused by the noncircular orbit geometry.