Hoffman Brain Phantom Research Articles

Defining ischemic burden after traumatic brain injury using 15O PET imaging of cerebral physiology.

Whereas postmortem ischemic damage is common in head injury, antemortem demonstration of ischemia has proven to be elusive. Although 15O positron emission tomography may be useful in this area, the technique has traditionally analyzed data within regions of interest (ROIs) to improve statistical accuracy. In head injury, such techniques are limited because of the lack of a priori knowledge regarding the location of ischemia, coexistence of hyperaemia, and difficulty in defining ischemic cerebral blood flow (CBF) and cerebral oxygen metabolism (CMRO2) levels. We report a novel method for defining disease pathophysiology following head injury. Voxel-based approaches are used to define the distribution of oxygen extraction fraction (OEF) across the entire brain; the standard deviation of this distribution provides a measure of the variability of OEF. These data are also used to integrate voxels above a threshold OEF value to produce an ROI based upon coherent physiology rather than spatial contiguity (the ischemic brain volume; IBV). However, such approaches may suffer from poor statistical accuracy, particularly in regions with low blood flow. The magnitude of these errors has been assessed in modeling experiments using the Hoffman brain phantom and modified control datasets. We conclude that this technique is a valid and useful tool for quantifying ischemic burden after traumatic brain injury.

Study of the normal database that affects 3D-SSP Z-score mapping

The effects of image reconstruction conditions and devices used on 3D-SSP analysis (Z-score mapping) were investigated. Images of the 3D Hoffman brain phantom were taken with the IRIX device or E.CAM. Using two methods of image reconstruction (FBP and OSEM), several kinds of phantom normal databases (PNDB) and signal data, with or without correction for attenuation, were obtained at varying Butterworth filter cutoff frequencies. The results of 3D-SSP analyses were compared between combinations of PNDB and signal data obtained under the same conditions of image reconstruction and combinations obtained under different conditions. The results of PNDB obtained with different devices were also analyzed. For combinations of PNDB and signal data both obtained with OSEM, the Z-score of signals was high. When FBP was used to obtain both PNDB and signal data, the Z-score and signal size tended to become greater and the false-positive rate tended to decrease as the Butterworth filter cutoff frequency became lower. Whether or not correction for attenuation was incorporated did not affect the results of analysis when the same method was used to collect both PNDB and signal data. If the method for image reconstruction differed between PNDB and signal data, the false-positive rate was relatively high. Using a different device to obtain PNDB resulted in a relatively high false-positive rate. We therefore recommend that the conditions for image reconstruction from signal data should be matched to the conditions for image reconstruction from PNDB. It seems impossible to share the same NDB among different devices.

Brain lesion detectability studies with a high resolution PET operating in no-septa and partial-septa configurations

We investigated the effect of partial-septa on the noise equivalent sensitivity and lesion detectability for a high resolution PET camera. For this purpose we used the MDAPET camera to detect small lesions in brain images obtained from the scan of the Hoffman brain phantom. The three-dimensional (3-D) positron emission tomography (PET) acquisition in comparison to two-dimensional (2-D) PET acquisition improves the sensitivity of the system at the cost of higher scatter and accidental coincidence contributions. A partial-septa allowing 3D-acquisition may provide a better alternative. For this work, three small lesion phantoms with diameters of 3, 5 and 8.6 mm were embedded into the Hoffman brain phantom. The activity concentration ratio of the lesions to the surrounding brain gray matter was ranging from 1.5 to 10. For this study, the eight detectors modules of the prototype MDAPET scanner were modified axially to extend from 38.5 mm to 131 mm in order to simulate more closely the performance of a clinical size camera. Data for the hot lesion phantoms and the normal Hoffman brain phantom were taken separately. Then, the two sets of the sinograms data were selectively combined to generate the sinograms data for the desired SUVs. Visual inspection of the lesion images show that we could clearly see the 8.6 mm lesion, with or without septa, at even the lowest activity ratio that we measured. The 5 mm and 3 min lesions were observable at activity ratio of 2.2 and 5.4, respectively. We found that even though the use of septa could increase the noise equivalent count rate and lower the image noise, it does not necessary translate into improvement of the lesion detectability. For partial-septa configurations the white matter regions of brain have less count and the brain images visually looked better; however, images from no-septa data had slightly higher contrast.

The design and implementation of a motion correction scheme for neurological PET

A method is described to monitor the motion of the head during neurological positron emission tomography (PET) acquisitions and to correct the data post acquisition for the recorded motion prior to image reconstruction. The technique uses an optical tracking system, Polaris™, to accurately monitor the position of the head during the PET acquisition. The PET data are acquired in list mode where the events are written directly to disk during acquisition. The motion tracking information is aligned to the PET data using a sequence of pseudo-random numbers, which are inserted into the time tags in the list mode event stream through the gating input interface on the tomograph. The position of the head is monitored during the transmission acquisition, and it is assumed that there is minimal head motion during this measurement. Each event, prompt and delayed, in the list mode event stream is corrected for motion and transformed into the transmission space. For a given line of response, normalization, including corrections for detector efficiency, geometry and crystal interference and dead time are applied prior to motion correction and rebinning in the sinogram.A series of phantom experiments were performed to confirm the accuracy of the method: (a) a point source located in three discrete axial positions in the tomograph field of view, 0 mm, 10 mm and 20 mm from a reference point, (b) a multi-line source phantom rotated in both discrete and gradual rotations through ±5° and ±15°, including a vertical and horizontal movement in the plane. For both phantom experiments images were reconstructed for both the fixed and motion corrected data. Measurements for resolution, full width at half maximum (FWHM) and full width at tenth maximum (FWTM), were calculated from these images and a comparison made between the fixed and motion corrected datasets. From the point source measurements, the FWHM at each axial position was 7.1 mm in the horizontal direction, and increasing from 4.7 mm at the 0 mm position, to 4.8 mm, 20 mm offset, in the vertical direction. The results from the multi-line source phantom with ±5° rotations showed a maximum degradation in FWHM, when compared with the stationary phantom, of 0.6 mm, in the horizontal direction, and 0.3 mm in the vertical direction. The corresponding values for the larger rotation, ±15°, were 0.7 mm and 1.1 mm, respectively.The performance of the method was confirmed with a Hoffman brain phantom moved continuously, and a clinical acquisition using [11C]raclopride (normal volunteer). A visual comparison of both the motion and non-motion corrected images of the Hoffman brain phantom clearly demonstrated the efficacy of the method. A sample time-activity curve extracted from the clinical study showed irregularities prior to motion correction, which were removed after correction.A method has been developed to accurately monitor the motion of the head during a neurological PET acquisition, and correct for this motion prior to image reconstruction. The method has been demonstrated to be accurate and does not add significantly to either the acquisition or the subsequent data processing.

Evaluation of the effect of filter apodization for volume PET imaging using the 3-D RP algorithm

We investigated the influence of filter apodization and cutoff frequency on the image quality of volume positron emission tomography (PET) imaging using the three-dimensional reprojection (3-D RP) algorithm. An important parameter in 3-D RP and other filtered backprojection algorithms is the choice of the filter window function. In this study, the Hann, Hamming, and Butterworth low-pass window functions were investigated. For each window, a range of cutoff frequencies was considered. Projection data were acquired by scanning a uniform cylindrical phantom, a cylindrical phantom containing four small lesion phantoms having diameters of 3, 4, 5, and 6 mm and the 3-D Hoffman brain phantom. All measurements were performed using the high-resolution PET camera developed at the M.D. Anderson Cancer Center (MDAPET), University of Texas, Houston, TX. This prototype camera, which is a multiring scanner with no septa, has an intrinsic transaxial resolution of 2.8 mm. The evaluation was performed by computing the noise level in the reconstructed images of the uniform phantom and the contrast recovery of the 6-mm hot lesion in a warm background and also by visually inspecting images, especially those of the Hoffman brain phantom. For this work, we mainly studied the central slices which are less affected by the incompleteness of the 3-D data. Overall, the Butterworth window offered a better contrast-noise performance over the Hann and Hamming windows. For our high statistics data, for the Hann and Hamming apodization functions a cutoff frequency of 0.6-0.8 of the Nyquist frequency resulted in a reasonable compromise between the contrast recovery and noise level and for the Butterworth window a cutoff frequency of 0.4-0.6 of the Nyquist frequency was a reasonable choice. For the low statistics data, use of lower cutoff frequencies was more appropriate.

An evaluation of the effect of filtering in 3-D OSEM reconstruction by using data from a high-resolution PET scanner

We evaluated the effect of filtering in the three-dimensional (3-D) ordered subset expectation maximization (OSEM) algorithm for reconstruction of projection data obtained with a high-resolution 3-D positron emission tomography (PET) scanner. For this study, we used the inter-update Metz filtered OSEM (IMF-OSEM) algorithm, which was developed by the PARAPET project. IMF-OSEM is an implementation of the OSEM algorithm with some additional capabilities such as inter-update filtering. The projection data were acquired using the high-resolution PET camera developed at the University of Texas M. D. Anderson Cancer Center (MDAPET). This prototype camera, which is a multiring scanner without any septa, has a transaxial resolution of 2.8 mm, which allows better evaluation of the algorithm. We scanned three phantoms: a cylindrical uniform phantom, a cylindrical phantom containing four small lesion phantoms, and the Hoffman brain phantom. The effect of inter-filtering in OSEM reconstruction was evaluated by computing the noise level of the reconstructed images of the uniform phantom, studying the contrast recovery for the hot lesions in a warm background, and visually inspecting images especially those of the Hoffman brain phantom. In addition, the effect of post-filtering on the reconstructed images was evaluated. For the high statistics data, a good compromise between contrast recovery and noise level was achieved using 20-50 iterations for the plain OSEM algorithm. By visually inspecting the images of the Hoffman brain phantom and hot lesions, we observed that the plain OSEM algorithm, especially when followed by post-filtering, and the inter-update filtering with Metz power of 1 could reasonably reproduce the phantom's structure. We also found that inter-update filtering has the potential to produce a noise level and contrast recovery comparable with that using the plain OSEM algorithm at a lower iteration number; however, it also has a greater tendency to develop noise artifacts.

A new high-resolution PET scanner dedicated to brain research

A high-resolution positron emission tomography (PET) scanner dedicated to brain studies has been developed and its physical performance was evaluated. The block detector consists of a new compact position-sensitive photomultiplier tube (PS-PMT, Hamamatsu R7600-C12) and an 8/spl times/4 bismuth germanate (BGO) array. The size of each crystal is 2.8 mm/spl times/6.55 mm/spl times/30 mm. The system has a total of 11 520 crystals arranged in 24 detector rings 508 mm in diameter (480 per ring). The field of view (FOV) is 330 mm in diameter/spl times/163 mm, which is sufficient to measure the entire human brain. The diameter of the scanner's opening is equal to the transaxial FOV (330 mm). The system can be operated in three-dimensional (3-D) data acquisition mode, when the slice septa are retracted. The mechanical motions of the gantry and bed are specially designed to measure the patient in various postures; lying, sitting, and even standing postures. The spatial resolution of 2.9 mm in both the transaxial and axial directions is obtained at the center of the FOV. The total system sensitivity is 6.4 kc/s/kBq/ml in two-dimensional (2-D) mode, with a 20-cm-diameter cylindrical phantom. The imaging capabilities of the scanner were studied with the Hoffman brain phantom and with a normal volunteer.

Correction for head movements in positron emission tomography using an optical motion-tracking system

Methods capable of correcting for head motion in all six degrees of freedom have been proposed for positron emission tomography (PET) brain imaging but not yet demonstrated in human studies. These methods rely on the accurate measurement of head motion in relation to the reconstruction coordinate frame. We present methodology for the direct calibration of an optical motion-tracking system to the reconstruction coordinate frame using paired coordinate measurements obtained simultaneously from a PET scanner and tracking system. We also describe the implementation of motion correction, based on the multiple acquisition frame method originally described by Picard and Thompson (1997), using data provided by the motion tracking system. Effective compensation for multiple six-degree-of-freedom movements is demonstrated in dynamic PET scans of the Hoffman brain phantom and a normal volunteer. We conclude that reduced distortion and improved quantitative accuracy can be achieved with this method in PET brain studies degraded by head movements.

A hybrid 3-D reconstruction/registration algorithm for correction of head motion in emission tomography

Even with head restraint, small head movements can occur during data acquisition in emission tomography that are sufficiently large to result in detectable artifacts in the final reconstruction. Direct measurement of motion can be cumbersome and difficult to implement, whereas previous attempts to use the measured projection data for correction have been limited to simple translation orthogonal to the projection. A fully three-dimensional (3-D) algorithm is proposed that estimates the patient orientation based on the projection of motion-corrupted data, with incorporation of motion information within subsequent ordered-subset expectation-maximization subiterations. Preliminary studies have been performed using a digital version of the Hoffman brain phantom. Movement was simulated by constructing a mixed set of projections in discrete positions of the phantom. The algorithm determined the phantom orientation that best matched each constructed projection with its corresponding measured projection. In the case of a simulated single movement in 24 of 64 projections, all misaligned projections were correctly identified. Incorporating data at the determined object orientation resulted in a reduction of mean square difference (MSD) between motion-corrected and motion-free reconstructions, compared to the MSD between uncorrected and motion-free reconstructions, by a factor of 1.9.

A Bayesian PET reconstruction method using segmented anatomical membrane as priors

In this paper a fully Bayesian PET, reconstruction method is presented for combining a segmented anatomical membrane a priori. The prior distributions are based on the fact that the radiopharmaceutical activity is similar throughout each region and the anatomical information is obtained from other imaging modalities such as CT or MRI. The prior parameters in prior distribution are considered, drawn from hyperpriors for fully Bayesian reconstruction. Dynamic Markov chain Monte chain Monte Carlo methods are used on the Hoffman brain phantom to gain estimates of the posterior mean. The reconstruction result is compared to those obtained by ML, MAP. Our results showed that the segmented anatomical membrane a priori exhibit improved the noise and resolution properties.

Objective assessment of image registration results using statistical confidence intervals

Precision of medical image registration is very important in clinical diagnosis and treatment, which is usually assessed by visual inspection or by referring to other methods that require special expertise and extensive experience. In this study, the authors proposed a novel automatic approach based on statistical theory to estimate confidence intervals of the registration parameters and allow the precision of registration results to be objectively assessed. Under the assumption of local linearity, statistical confidence intervals of model fitting (regression) can be used to evaluate registration precision. Monte Carlo simulations using the Hoffman brain phantom with various amounts of displacement, noise and spatial filtering were conducted to evaluate the formula for estimating the confidence intervals in 2D image registrations. Monte Carlo simulation results are consistent with the calculated confidence intervals, and the agreement is applicable to different amounts of translation, angular rotation and spatial smoothing. The estimated parameter values fall within the predicted 90%, 95% and 99% confidence intervals with less than /spl plusmn/1% of errors. The present results indicate that the use of statistical confidence intervals can provide an objective assessment of individual image registration results.

Linear ridge regression with spatial constraint for generation of parametric images in dynamic positron emission tomography studies

Due to its simplicity, computational efficiency, and reliability, weighted linear regression (WLR) is widely used for generation of parametric imaging in positron emission tomography (PET) studies, but parametric images estimated by WLR usually have high image noise level. To improve the stability and signal-to-noise ratio of the estimated parametric images, the authors have added ridge regression, a statistical technique that reduces estimation variability at the expense of a small bias. To minimize the bias, spatially smoothed images obtained with WLR are used as a constraint for ridge regression. This new algorithm consists of two steps. First, parametric images are generated by WLR and are spatially smoothed. Ridge regression is then applied using the smoothed parametric images obtained in the first step as the constraint. Since both ridge regression and ridge regression are used in statistical applications, we evaluated specifically in this study the relative advantages of the two when incorporated for generating parametric images from dynamic O-15 water PET studies. Computer simulations of a dynamic PET study with the spatial configuration of Hoffman's brain phantom and a real human PET study were used as the data for the evaluation. Results reveal ridge regressions improve image quality of parametric images for studies with high or middle noise level. As compared to WLR, use of generalized ridge regression offers little advantage over that of simple ridge regression.

Application of the row action maximum likelihood algorithm with spherical basis functions to clinical PET imaging

Three-dimensional (3D) reconstructions from fully 3D positron emission tomography (PET) data can yield high-quality images but at a high computational cost. The 3D row action maximum likelihood algorithm (3D RAMLA) with spherically-symmetric basis functions (blobs) has recently been modified to reconstruct multi-slice 2D PET data after Fourier rebinning (FORE) but still using 3D basis functions (2.5D RAMLA. In this study 2.5D RAMLA and 3D RAMLA were applied to several patient and phantom PET datasets to assess their clinical performance. RAMLA performance was compared to that for the reconstruction techniques in routine clinical use on the authors' PET scanners. Torso phantom and whole-body patient scans acquired on the C-PET scanner were reconstructed after FORE with filtered back-projection (FORE+FBP), the ordered subsets expectation maximization algorithm (FORE+OSEM), and FORE+2.5D RAMLA for various reconstruction parameters. The 3D Hoffman brain phantom scanned on the HEAD Penn-PET scanner was reconstructed with the 3D reprojection algorithm (3DRP) and 3D RAMLA, as well, as FORE+FBP, FORE+OSEM, and FORE+2.5D RAMLA. The authors' results demonstrate improvement of 3D and 2.5D RAMLA with blob basis functions, compared to the reconstruction methods currently in clinical use, in terms of contrast recovery and noise, especially in regions of limited statistics.

MRI-SPET and SPET-SPET brain co-registration: evaluation of the performance of eight different algorithms.

The aim of this study was to assess the accuracy and computing time needed for MRI-SPET and SPET-SPET brain co-registration using eight different algorithms (Hermes software from Nuclear Diagnostics Ltd run on a SUN Ultra Sparc 2) to determine the clinically most suitable algorithm. MRI-SPET co-registration was evaluated using phantom studies. To approximate clinical dual-headed SPET studies, a Hoffman brain phantom was filled with 99Tcm. For MRI imaging (1.5 Tesla), the phantom was filled with water and doped with Gd-DTPA for contrast enhancement. For both modalities, phantom images were acquired and reconstructed using a routine clinical protocol. MRI and SPET images were matched by Downhill Simplex minimization of the sum of absolute Count Differences (CD), the sum of the Square Root of absolute count differences (SR), the Difference in Shape between the binary masks (SD), the number of Sign Changes in the subtracted image (SC), the Variance of intensities between corresponding pixels (VAR), the sum of absolute count differences between the 2D- and 3D-Gradient images (2DG-3DG) and, finally, the standard deviation of the Uniformity Index (UI), that is the intensity ratio between spatially corresponding voxels. Six degrees of freedom were allowed (three translation and three rotation parameters, three scaling parameters were constrained). The accuracy of the matching process with these different similarity measures was evaluated via the residual mismatch between external markers. We found that CD, SR, VAR nad UI give the most accurate registration compared with the other similarity measures. For the evaluation of SPET-SPET co-registration, five 99Tcm-ECD brain perfusion SPET scans were performed with a dual-headed gamma camera. These studies were then manually misaligned, and subsequently re-aligned using the methods outlined above. For this application, CD, SR and VAR were also found to give the most accurate registration. For all of these algorithms, the computing time required was clinically acceptable (i.e. less than 10 min).

Evaluation of brain activity in FDG PET studies.

A tool (Gemini) was developed for quantifying regions of interest (ROIs) in registered MR and PET data. Its use was validated through phantom and simulated studies. Hot spheres were imaged in a phantom (3:1 and 5:1 target-to-nontarget ratios). The computerized 3D Hoffman brain phantom was used to simulate PET studies. Spherical local activity features of two diameters (4 and 10 mm) and five intensities (5, 15, 25, 50, and 100% increase over gray matter) were added to the data in the thalamus and Brodmann area 37. The data were reprojected into sinograms and blurred with a 7 mm kernel. Poisson noise was added, and the sinograms were then reconstructed and analyzed using both SPM96 and Gemini spherical ROIs. Based on phantom and simulated data, the 95th percentile of intensity within a Gemini ROI afforded a reasonable joint optimization of variance (reliability) and accuracy (validity). SPM96 and Gemini results were similar for the larger (10 mm) feature, but in this application, Gemini was more sensitive than SPM96 for the small feature (4 mm). Gemini, a tool for display and measurement of spherical ROIs in registered PET and MR data, is precise and accurate for testing hypotheses of differences in localized brain activity, comparing favorably with SPM96.

Quality of brain perfusion single-photon emission tomography images: multicentre evaluation using an anatomically accurate three-dimensional phantom.

The aim of the study was to evaluate the quality of routine brain perfusion single-photon emission tomography (SPET) images in Finnish nuclear medicine laboratories. Twelve laboratories participated in the study. A three-dimensional high resolution brain phantom (Data Spectrum's 3D Hoffman Brain Phantom) was filled with a well-mixed solution of technetium-99m (110 MBq), water and detergent. Acquisition, reconstruction and printing were performed according to the clinical routine in each centre. Three nuclear medicine specialists blindly evaluated all image sets. The results were ranked from 1 to 5 (poor quality-high quality). Also a SPET performance phantom (Nuclear Associates' PET/SPECT Performance Phantom PS 101) was filled with the same radioactivity concentration as the brain phantom. The parameters for the acquisition, the reconstruction and the printing were exactly the same as with the brain phantom. The number of detected "hot" (from 0 to 8) and "cold" lesions (from 0 to 7) was visually evaluated from hard copies. Resolution and contrast were quantified from digital images. Average score for brain phantom images was 2.7 +/- 0.8 (range 1.5-4.5). The average diameter of the "hot" cylinders detected was 16 mm (range 9.2-20.0 mm) and that of the "cold" cylinders detected, 11 mm (5.9-14.3 mm) according to visual evaluation. Quantification of digital images showed that the hard copy was one reason for low-quality images. The quality of the hard copies was good only in four laboratories and was amazingly low in the others when comparing it with the actual structure of the brain phantom. The described quantification method is suitable for optimizing resolution and contrast detectability of hard copies. This study revealed the urgent need for external quality assurance of clinical brain perfusion SPET images.

Iterative and analytical reconstruction algorithms for varying-focal-length cone-beam projections

In single photon emission computed tomography (SPECT), a varying-focal-length cone-beam collimator can be used to reduce the truncation problem and to maintain sensitivity when imaging the organ of interest. The collimator is constructed so that the collimator holes focus to a circular symmetric, spatially varying, focal point function. The focal length increases radially from the shortest focal length at the centre to the longest focal length at the periphery of the collimator. This paper describes a 3D backprojection-filtering (BF) algorithm for this varying-focal-length cone-beam geometry. The proposed algorithm is compared to an iterative ML-EM (maximum likelihood-expectation maximization) algorithm. The 3D Hoffman brain phantom and Defrise phantom are used in computer simulations. Since the maximum tilt angle of the projection rays is small for most realistic imaging geometries, the proposed algorithm provides a good approximation. When a circular orbit is used, the BF algorithm gives an exact reconstruction of the central slice.

Optimization of PET activation studies based on the SNR measured in the 3-D Hoffman brain phantom.

This work investigates the noise properties of O-15 water PET images in an attempt to increase the sensitivity of activation studies. A method for computing the amount of noise within a region of interest (ROI) from the uncertainty in the raw data was implemented for three-dimensional (3-D) positron emission tomography (PET). The method was used to study the signal-to-noise ratio (SNR) of regions-of-interest (ROI's) inside a 3-D Hoffman brain phantom. Saturation occurs at an activity concentration of 2.2 mCi/l which corresponds to a 75-mCi O-15 water injection into a normal person of average weight. This establishes the upper limit for injections for human brain studies using 3-D PET on the Siemens ECAT 921 EXACT scanner. Data from human brain activation studies on four normal volunteers using two-dimensional (2-D) PET were analyzed. The biological variation was found to be 5% in 1-ml ROI's. The variance for a complete activation study was calculated, for a variety of protocols, by combining the Poisson noise propagated from the raw data in the phantom experiments with the biological variation. A protocol that is predicted to maximize the SNR in dual-condition activation experiments while remaining below the radiation safety limit is: ten scans with 45 mCi per injection. The data should not be corrected for random or scatter events since they do not help in the identification of activation sites while they do add noise to the image. Due to the lower noise level of 3-D PET, the threshold for detecting a true change in activity concentration is 10%-20% lower than 2-D PET. Because of this, a 3-D activation experiment using the Siemens 921 scanner requires fewer subjects for equal statistical power.

Projection space image reconstruction using strip functions to calculate pixels more "natural" for modeling the geometric response of the SPECT collimator.

The spatially varying geometric response of the collimator-detector system in single photon emission computed tomography (SPECT) causes loss in resolution, shape distortions, reconstructed density nonuniformity, and quantitative inaccuracies. A projection space image reconstruction algorithm is used to correct these reconstruction artifacts. The projectors F use strip functions to calculate pixels more "natural" for modeling the two-dimensional (2-D) geometric response of the SPECT collimator transaxially to the axis of rotation. These projectors are defined by summing the intersection of an array of multiple strips rotated at equal angles to approximate the ideal system geometric response of the collimator. Two projection models were evaluated for modeling the system geometric response function. For one projector each strip is of equal weight, for the other projector a Gaussian weighting is used. Parallel beam and fan beam projections of a physical three-dimensional (3-D) Hoffman brain phantom and a Jaszczak cold rod phantom were used to evaluate the geometric response correction. Reconstructions were obtained by using the singular value decomposition (SVD) method and the iterative conjugate gradient algorithm to solve for q in the imaging equation FGq = p, where p is the projection measurement. The projector F included the new models for the geometric response, whereas, the backprojector G did not always model the geometric response in order to increase the computational speed. The final reconstruction was obtained by sampling the backprojection Gq at a discrete array of points. Reconstructions produced by the two proposed projectors showed improved resolution when compared against a unit-strip "natural" pixel model, the conventional image pixelized model with ray tracing to calculate the geometric response, and the filtered backprojection algorithm. When the reconstruction is displayed on fine grid points, the continuity and resolution of the image is preserved without the ring artifacts seen in the unit-strip "natural" pixel model. With present computing power, the geometric response correction using the proposed projection space reconstruction approach is not yet feasible for routine clinical use.

Noise characteristics of 3-D and 2-D PET images.

We analyzed the noise characteristics of two-dimensional (2-D) and three-dimensional (3-D) images obtained from the GE Advance positron emission tomography (PET) scanner. Three phantoms were used: a uniform 20-cm phantom, a 3-D Hoffman brain phantom, and a chest phantom with heart and lung inserts. Using gated acquisition, we acquired 20 statistically equivalent scans of each phantom in 2-D and 3-D modes at several activity levels. From these data, we calculated pixel normalized standard deviations (NSD's), scaled to phantom mean, across the replicate scans, which allowed us to characterize the radial and axial distributions of pixel noise. We also performed sequential measurements of the phantoms in 2-D and 3-D modes to measure noise (from interpixel standard deviations) as a function of activity. To compensate for the difference in axial slice width between 2-D and 3-D images (due to the septa and reconstruction effects), we developed a smoothing kernel to apply to the 2-D data. After matching the resolution, the ratio of image-derived NSD values (NSD2D/NSD3D)2 averaged throughout the uniform phantom was in good agreement with the noise equivalent count (NEC) ratio (NEC3D/NEC2D). By comparing different phantoms, we showed that the attenuation and emission distributions influence the spatial noise distribution. The estimates of pixel noise for 2-D and 3-D images produced here can be applied in the weighting of PET kinetic data and may be useful in the design of optimal dose and scanning requirements for PET studies. The accuracy of these phantom-based noise formulas should be validated for any given imaging situation, particularly in 3-D, if there is significant activity outside the scanner field of view.