Mathematical Cardiac Torso Phantom Research Articles

Design consideration of a multipinhole collimator with septa for ultra high-resolution silicon drift detector modules

The aim of this study was to design a multipinhole (MP) collimator with lead vertical septa coupled to a high-resolution detector module containing silicon drift detectors (SDDs) with an intrinsic resolution approaching the sub-millimeter level. Monte Carlo simulations were performed to determine pinhole parameters such as pinhole diameter, focal length, and number of pinholes. Effects of parallax error and collimator penetration were investigated for the new MP collimator design. The MP detector module was evaluated using reconstructed images of resolution and mathematical cardiac torso (MCAT) phantoms. In addition, the reduced angular sampling effect was investigated over 180°. The images were reconstructed using dedicated maximum likelihood expectation maximization (MLEM) algorithm. An MP collimator with 81-pinhole was designed with a 2-mm-diameter pinhole and a focal length of 40mm . Planar sensitivity and resolution obtained using the devised MP collimator were 3.9cps/μCi and 6mm full-width at half-maximum (FWHM) at a 10cm distance. The parallax error and penetration ratio were significantly improved using the proposed MP collimation design. The simulation results demonstrated that the proposed MP detector provided enlarged imaging field of view (FOV) and improved the angular sampling effect in resolution and MCAT phantom studies. Moreover, the novel design enables tomography images by simultaneously obtaining eight projections with eight-detector modules located along the 180° orbit surrounding a patient, which allows designing of a stationary cardiac SPECT. In conclusion, the MP collimator with lead vertical septa was designed to have comparable system resolution and sensitivity to those of the low-energy high-resolution (LEHR) collimator per detector. The system sensitivity with an eight-detector configuration would be four times higher than that with a standard dual-detector cardiac SPECT.

Diminishing the impact of the partial volume effect in cardiac SPECT perfusion imaging

The partial volume effect (PVE) significantly restricts the absolute quantification of regional myocardial uptake and thereby limits the accuracy of absolute measurement of blood flow and coronary flow reserve by SPECT. The template-projection-reconstruction method has been previously developed for PVE compensation. This method assumes the availability of coregistered high-spatial resolution anatomical information as is now becoming available with commercial dual-modality imaging systems such as SPECT/CTs. The objective of this investigation was to determine the extent to which the impact of the PVE on cardiac perfusion SPECT imaging can be diminished if coregistered high-spatial resolution anatomical information is available. For this investigation the authors introduced an additional parameter into the template-projection-reconstruction compensation equation called the voxel filling fraction (F). This parameter specifies the extent to which structure edge voxels in the emission reconstruction are filled by the structure in question as determined by the higher spatial-resolution imaging modality and the fractional presence of the structure at different states of physiological motion as in combining phases of cardiac motion. During correction the removal of spillover to the cardiac region from the surrounding structures is performed first by using reconstructed templates of neighboring structures (liver, blood pool, lungs) to calculate spillover fractions. This is followed by determining recovery coefficients for all voxels within the heart wall from the reconstruction of the template projections of the left and right ventricles (LV and RV). The emission data are subsequently divided by these recovery coefficients taking into account the filling fraction F. The mathematical cardiac torso phantom was used for investigation correction of PVE for a normal LV distribution, a defect in the inferior wall, and a defect in the anterior wall. PVE correction resulted in a dramatic visual reduction in the impact of extracardiac activity, improved the uniformity of the normally perfused heart wall, and enhanced defect visibility without undue noise amplification. No significant artifacts were seen with PVE correction in the presence of mild (one voxel) misregistration. A statistically significant improvement in the accuracy of the count levels within the normal heart wall was also noted. However, residual spillover of counts from within the myocardium creates a bias in regions of decreased wall counts (perfusion defects/abnormal wall motion) when the anatomical imaging modality does not allow definition of templates for defects present in the heart during emission imaging.

Tomographic Reconstruction of Dynamic Cardiac Image Sequences

In this paper, we propose an approach for the reconstruction of dynamic images from a gated cardiac data acquisition. The goal is to obtain an image sequence that can show simultaneously both cardiac motion and time-varying image activities. To account for the cardiac motion, the cardiac cycle is divided into a number of gate intervals, and a time-varying image function is reconstructed for each gate. In addition, to cope with the under-determined nature of the problem, the time evolution at each pixel is modeled by a B-spline function. The dynamic images for the different gates are then jointly determined using maximum a posteriori estimation, in which a motion-compensated smoothing prior is introduced to exploit the similarity among the different gates. The proposed algorithm is evaluated using a dynamic version of the 4-D gated mathematical cardiac torso phantom simulating a gated single photon emission computed tomography perfusion acquisition with Technitium-99m labeled Teboroxime. We thoroughly evaluated the performance of the proposed algorithm using several quantitative measures, including signal-to-noise ratio analysis, bias-variance plot, and time activity curves. Our results demonstrate that the proposed joint reconstruction approach can improve significantly the accuracy of the reconstruction.

Fully 4D motion-compensated reconstruction of cardiac SPECT images**This work was supported in part by the National Institutes of Health under grant no HL65425.

In this paper, we investigate the benefits of a spatiotemporal approach for reconstruction of image sequences. In the proposed approach, we introduce a temporal prior in the form of motion compensation to account for the statistical correlations among the frames in a sequence, and reconstruct all the frames collectively as a single function of space and time. The reconstruction algorithm is derived based on the maximum a posteriori estimate, for which the one-step late expectation–maximization algorithm is used. We demonstrated the method in our experiments using simulated single photon emission computed tomography (SPECT) cardiac perfusion images. The four-dimensional (4D) gated mathematical cardiac-torso phantom was used for simulation of gated SPECT perfusion imaging with Tc-99m-sestamibi. In addition to bias–variance analysis and time activity curves, we also used a channelized Hotelling observer to evaluate the detectability of perfusion defects in the reconstructed images. Our experimental results demonstrated that the incorporation of temporal regularization into image reconstruction could significantly improve the accuracy of cardiac images without causing any significant cross-frame blurring that may arise from the cardiac motion. This could lead to not only improved detection of perfusion defects, but also improved reconstruction of the heart wall which is important for functional assessment of the myocardium.

Nonparametric and nonrigid registration method applied to myocardial-gated SPECT

We have developed a nonparametric and nonrigid registration method. It requires a segmentation contour of the organ of interest in both the image to register and the image template. We use the fact that the contour template can be deduced from the contour in the image to register by a series of locally normal elementary deformations. We extend these contour deformations to the whole image domain using level sets (sets of embedded parallel contours, the organ contour being the contour of reference). This series of elementary deformations provides a way to perform an iterative (totally unrestricted, unlike parametric methods) registration by indicating the successive motions from a point in the image to register to its final position in the registered image. The use of the organ contour has two consequences: 1) Our method is consistent with the image features and 2) our method is based on image geometry (as opposed to intensity) and, therefore, it is less sensitive to noise and more robust in homogeneous regions than nonparametric methods based on optical flow. We have applied our registration method to perform a motion compensation of gated single photon emission computed tomography (SPECT) sequences, i.e., to nonrigidly register N - 1 frames with respect to the Nth one. The N registered frames were then added together to improve the signal-to-noise characteristics while minimizing motion-induced blurring. Results on three-dimensional (3-D) mathematical cardiac-torso phantom (MCAT) simulated sequences are presented.

Effect of block-iterative acceleration on Ga-67 tumor detection in thoracic SPECT

A combination of human localization receiver operating characteristic (LROC) and channelized Hotelling observer (CHO) ROC psychophysical studies were used to investigate how accelerated ordered-subset expectation maximization (OSEM) and rescaled block-iterative (RBI) EM reconstruction affect tumor detection in simulated Ga-67 SPECT images, The tumors were 1-cm-diameter spheres within the chest region of the three-dimensional mathematical cardiac-torso phantom. Previous work with iterative detector resolution compensation showed that eight iterations of the OSEM algorithm with a subset size of eight (16 subsets) offered optimal observer performance. For the LROC study in this paper, the OSEM and RBI algorithms were implemented using subset sizes P and iterations K that satisfied the relation P=K for P=1, 2, 4, and 8. The CHO was applied to reconstruction strategies that deviated from this relation. Results show that using P/spl les/2 penalized observer performance compared to strategies with larger subset sizes. Other researchers have reported on the more stable convergence and noise properties of the RBI algorithm [(Byrne, 1996) and (Lalush and Tsui, 2000)]. In a similar vein, we found that an RBI strategy with a subset size of P produced the same performance as an OSEM strategy with subset size 2P. As neither algorithm displayed a decisive advantage in speed over the other, we conclude that the RBI algorithm is the better choice for accelerating the Ga-67 reconstructions.

Calculation of lung-heart ratios for single-photon emission computed tomography

We investigate the effectiveness of simple iterative reconstruction techniques in calculating lung-heart activity ratios (LHRs). The LHR has been shown to be an effective indicator of the severity of coronary artery disease in cardiac SPECT. A study was conducted with a mathematical cardiac torso phantom that modelled uptake of /sup 201/Tl in the heart and lung regions. The projection data included only the effects of nonuniform photon attenuation. The data were first reconstructed with zeroth-order Chang and a variant of the Bellini method, both of which utilize information from the nonuniform attenuation map. This nonuniform (NU) Bellini method compensates exactly for attenuation in the heart region, but is incorrect for other regions in the medium. These reconstructions were then used as the initial estimates in the iterative Chang, variable step-size (VSS) Chang, and Morozumi methods, for one and five iterations. The average heart count (AHC) and average lung count (ALC) were calculated using region-of-interest (ROI) templates derived from the true activity map. The population mean LHR was tabulated as the ratio of the ALC to AHC. Using the same reconstruction procedure, we also calculated the sample mean LHR and standard deviation from 21 noisy 3D reconstructions. The results showed that the NU Bellini and zeroth-order Chang methods provided good estimates of the AHC, while both estimated the ALC poorly. The NU Bellini method yielded a negative ALC, while the zeroth-order Chang method estimated the ALC at twice its true value. Application of one iteration of Chang can correct for the negative bias in the ALC for the NU Bellini estimate, and can correct for the positive bias in the ALC for the zeroth-order Chang estimate, while retaining a low bias in the AHCs for the two methods. Thus more precise LHRs are produced. Furthermore, the sample standard deviation of the LHR estimate was shown to be small in both of these cases.

An analytical approach for compensation of non-uniform attenuation in cardiac SPECT imaging

Photon attenuation can reduce the diagnostic accuracy of cardiac SPECT imaging. Bellini et al. have previously derived a mathematically exact method to compensate for attenuation in a uniform attenuator. Since the human thorax contains structures with differing attenuation properties, non-uniform attenuation compensation is required in cardiac SPECT. Given an estimate of the patient attenuation map, we show that the Bellini attenuation compensation method can be used in cardiac SPECT to provide a quantitatively accurate reconstruction of a central region in the image which includes the heart and surrounding soft tissue. Simulations using a mathematical cardiac-torso phantom were conducted to evaluate the Bellini method and to compare its performance to the ML-EM iterative algorithm, and to 180 degrees and 360 degrees filtered backprojection (FBP) with no attenuation compensation. 'Bulls-eye' polar maps and circumferential profiles showed that both the Bellini method and the ML-EM algorithm provided quantitatively accurate reconstructions of the myocardium, with a substantial reduction in attenuation-induced artifacts that were observed in the FBP images. The computational load required to implement the Bellini method is approximately equivalent to that required for one iteration of the ML-EM algorithm, thus it is suitable for routine clinical use.