Implementation of three-dimensional image reconstruction for multi-ring positron tomographs

Iterative image reconstruction with polar coordinate discretized system matrix for optical CT radiochromic gel dosimetry

BACKGROUND

Gel dosimeters are a potential tool for measuring the complex dose distributions that characterize modern radiotherapy. A prototype tabletop solid-tank fan-beam optical CT scanner for readout of gel dosimeters was recently developed. This scanner does not have a straight raypath from source to detector, thus images cannot be reconstructed using filtered backprojection (FBP) and iterative techniques are required. Iterative image reconstruction requires a system matrix that describes the geometry of the imaging system. Stored system matrices can become immensely large, making them impractical for storage on a typical desktop computer.

PURPOSE

Here we develop a method to reduce the storage size of optical CT system matrices through use of polar coordinate discretization while accounting for the refraction in optical CT systems.

METHODS

A ray tracing simulator was developed to track the path of light rays as they traverse the different mediums of the optical CT scanner. Cartesian coordinate discretized system matrices (CCDSMs) and polar coordinate discretized system matrices (PCDSMs) were generated by discretizing the reconstruction area of the optical CT scanner into a Cartesian pixel grid and a polar coordinate pixel grid, respectively. The length of each ray through each pixel was calculated and used to populate the system matrices. To ensure equal weighting during iterative reconstruction, the radial rings of PCDSMs were asymmetrically spaced such that the area of each polar pixel was constant. Two clinical phantoms and several synthetic phantoms were produced and used to evaluate the reconstruction techniques under known conditions. Reconstructed images were analyzed in terms of spatial resolution, signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), signal nonuniformity (SNU), and Gamma map pass percentage.

RESULTS

A storage size reduction of 99.72% was found when comparing a PCDSM to a CCDSM with the same total number of pixels. Images reconstructed with a PCDSM were found to have superior SNR, CNR, SNU, and Gamma (1 mm, 1%) pass percentage compared to those reconstructed with a CCDSM. Increasing spatial resolution in the radial direction with increasing radial distance was found in both PCDSM and CCDSM reconstructions due to the outer regions refracting light more severely. Images reconstructed with a PCDSM showed a decrease in spatial resolution in the azimuthal directions as radial distance increases, due to the widening of the polar pixels. However, this can be mitigated with only a slight increase in storage size by increasing the number of projections. A loss of spatial resolution in the radial direction within 5 mm radially from center was found when reconstructing with a PCDSM, due to the large innermost pixels. However, this was remedied by increasing the number of radial rings within the PCDSM, yielding radial spatial resolution on par with images reconstructed with a CCDSM and a storage size reduction of 99.26%.

CONCLUSIONS

Discretizing the image pixel elements in polar coordinates achieved a system matrix storage size reduction of 99.26% with only minimal reduction in the image quality.

Comparison of the scanning linear estimator (SLE) and ROI methods for quantitative SPECT imaging

In quantitative emission tomography, tumor activity is typically estimated from calculations on a region of interest (ROI) identified in the reconstructed slices. In these calculations, unpredictable bias arising from the null functions of the imaging system affects ROI estimates. The magnitude of this bias depends upon the tumor size and location. In prior work it has been shown that the scanning linear estimator (SLE), which operates on the raw projection data, is an unbiased estimator of activity when the size and location of the tumor are known. In this work, we performed analytic simulation of SPECT imaging with a parallel-hole medium-energy collimator. Distance-dependent system spatial resolution and non-uniform attenuation were included in the imaging simulation. We compared the task of activity estimation by the ROI and SLE methods for a range of tumor sizes (diameter: 1-3 cm) and activities (contrast ratio: 1-10) added to uniform and non-uniform liver backgrounds. Using the correct value for the tumor shape and location is an idealized approximation to how task estimation would occur clinically. Thus we determined how perturbing this idealized prior knowledge impacted the performance of both techniques. To implement the SLE for the non-uniform background, we used a novel iterative algorithm for pre-whitening stationary noise within a compact region. Estimation task performance was compared using the ensemble mean-squared error (EMSE) as the criterion. The SLE method performed substantially better than the ROI method (i.e. EMSE(SLE) was 23-174 times lower) when the background is uniform and tumor location and size are known accurately. The variance of the SLE increased when a non-uniform liver texture was introduced but the EMSE(SLE) continued to be 5-20 times lower than the ROI method. In summary, SLE outperformed ROI under almost all conditions that we tested.

Thirty years from now: future physics contributions in nuclear medicine

Background

This paper is the first in a series of invited perspectives by pioneers of nuclear medicine imaging and physics. A medical physicist and a nuclear medicine physician each take a backward and a forward look at the contributions of physics to nuclear medicine. Here, we provide a forward look from the medical physicist’s perspective.

Discussion

The author examines a number of developments in nuclear medicine and discusses the ways in which physics has contributed to these. Future developments are postulated in the context of an increasingly personalised approach to medical diagnostics and therapies.

Conclusions

A skill set for the next generation of medical physicists in nuclear medicine is proposed in the context of the increasing complexity of ‘Molecular Imaging’ in the next three decades. The author sees a shift away from ‘traditional’ roles in instrumentation QA to more innovative approaches in understanding radiobiology and human disease.

Dynamic single photon emission computed tomography--basic principles and cardiac applications

The very nature of nuclear medicine, the visual representation of injected radiopharmaceuticals, implies imaging of dynamic processes such as the uptake and wash-out of radiotracers from body organs. For years, nuclear medicine has been touted as the modality of choice for evaluating function in health and disease. This evaluation is greatly enhanced using single photon emission computed tomography (SPECT), which permits three-dimensional (3D) visualization of tracer distributions in the body. However, to fully realize the potential of the technique requires the imaging of in vivo dynamic processes of flow and metabolism. Tissue motion and deformation must also be addressed. Absolute quantification of these dynamic processes in the body has the potential to improve diagnosis. This paper presents a review of advancements toward the realization of the potential of dynamic SPECT imaging and a brief history of the development of the instrumentation. A major portion of the paper is devoted to the review of special data processing methods that have been developed for extracting kinetics from dynamic cardiac SPECT data acquired using rotating detector heads that move as radiopharmaceuticals exchange between biological compartments. Recent developments in multi-resolution spatiotemporal methods enable one to estimate kinetic parameters of compartment models of dynamic processes using data acquired from a single camera head with slow gantry rotation. The estimation of kinetic parameters directly from projection measurements improves bias and variance over the conventional method of first reconstructing 3D dynamic images, generating time-activity curves from selected regions of interest and then estimating the kinetic parameters from the generated time-activity curves. Although the potential applications of SPECT for imaging dynamic processes have not been fully realized in the clinic, it is hoped that this review illuminates the potential of SPECT for dynamic imaging, especially in light of new developments that enable measurement of dynamic processes directly from projection measurements.

Optimization of signal in positron emission tomography scans: present and future developments

The absolute sensitivity of a state-of-the-art, commercial neuroPET tomograph with interplane septa is about 0.5%. This poor utilization of the available photons could be improved by increasing the intrinsic efficiency of the detection process and, more significantly, by increasing the solid angle coverage of the tomography. While multi-ring scanners currently have an axial length of about 10 cm, the useful solid angle is limited by the presence of interplane septa. These septa reduce the acceptance rate not only of scattered photons but also of true unscattered coincidences, although in studies performed at high photon counting rates the loss of potential signal may be less important than a reduction in scatter. Removal of the septa increases the absolute sensitivity of the scanner to about 3%, a figure which also includes an unavoidable increase in scattered photons. However, in studies performed at low photon counting rates, any increase in scattered and random (uncorrelated) coincidences resulting from septa removal may be an acceptable price to pay for the accompanying increase in signal, provided that there is a real improvement in the signal-to-noise ratio. Recently, scanners with automatically retractable septa have become commercially available, thus enabling the configuration (i.e. septa extended or retracted) to be selected according to the study to be performed.

[Technical limitations of the positron emission tomography (PET) for small laboratory animals]

Visualization and quantification of organ function by PET in small laboratory animals is becoming an outstanding tool for characterization of phenotype of transgenic and knock-out animals, for the study of animal models of human diseases, and for the development of new therapeutic drugs and diagnostic biochemical probes. To be able to make use of the PET with small laboratory animals in the same way as it is operated with humans it is necessary to account for the volumetric scale factor as well as for the requirement of maintaining the counting statistics. This work sketches the problems that these requirements represent for the technical design of the scanners and for the execution of the experiments. Finally, some characteristics of commercially available scanners (microPET/ FOCUS, HiDAC, eXplore VISTA, MOSAIC, YAP-(S)PET and rPET) are briefly discussed.

Clinical validation of fully 3-D versus 2.5-D RAMLA reconstruction on the Philips-ADAC CPET PET scanner

INTRODUCTION

Fully three-dimensional (3-D) reconstruction algorithms have the potential to better utilize PET data acquired in true 3-D acquisition modes, as compared to 2-D approaches involving data reduction through rebinning procedures followed by a 2-D or 2.5-D reconstruction. Our previous studies, involving simulated and real phantom data from PET scanners working purely in 3-D acquisition mode, showed that the fully 3-D reconstruction approaches bring appreciable improvement on physical measures and visual image quality as well. Reconstruction procedures utilized in those studies were based upon the row action maximum likelihood algorithm (RAMLA) implemented on our clinical scanners. The purpose of this study was to investigate if the fully 3-D RAMLA reconstruction software brings an appreciable improvement in clinical image quality and reader confidence.

MATERIALS AND METHODS

Ninety patient scans acquired on the Philips CPET scanner at our institution were reconstructed using 2.5-D RAMLA and 3-D RAMLA with differing reconstruction parameters. These scans were blindly presented to four experienced PET scan readers who graded various aspects of image quality.

RESULTS

Our study concluded that 3-D RAMLA on the CPET scanner reduces artifacts and image noise and improves clinical confidence in interpreting PET images.

CONCLUSION

This study led to the routine use of 3-D RAMLA reconstruction on the CPET scanner at our institution.

The role of σ-receptors in levodopa-induced dyskinesia in patients with advanced Parkinson disease: a positron emission tomography study

Object. Levodopa-induced dyskinesia (LID) in patients with Parkinson disease (PD) mimics acute dystonic reactions induced by antipsychotic agents, possibly mediated by σ-receptors; however, there are few reports in which the relationship between σ-receptors and LID in advanced PD is investigated. The binding potential of cerebellar σ-receptors before and after a pallidal surgery for dyskinesia in patients with advanced PD is assessed.

Methods. Six patients with advanced PD (male/female ratio 3:3, age 56.7 ± 9.8 years) underwent stereotactic pallidal surgery (two posteroventral pallidotomy procedures and four deep brain stimulation of the globus pallidus internus, including one bilateral case). Clinical features of patients with PD were assessed using Hoehn and Yahr (H & Y) stages, the Unified Parkinson's Disease Rating Scale (UPDRS), and the Schwab and England Activities of Daily Life Scale (S & E). The LID was evaluated by LID severity score. The binding potential of cerebellar σ-receptors was determined before and after the surgery by 11C-nemonapride positron emission tomoraphy, a specific radioligand for σ-receptors in the cerebellum. All clinical scores, especially the LID severity score, were dramatically improved after the surgery (p < 0.05). Preoperatively, contralateral cerebellar binding potential was significantly elevated (p < 0.01), and it was reduced after the surgery, but it was still higher than that of healthy volunteers (p < 0.05). The ipsilateral cerebellar binding potential remained unchanged after the surgery. The level of binding potential did not correlate with H & Y stage, UPDRS, or S & E score, but a strong positive correlation was seen between the binding potential and the preoperative LID severity score when the patients were receiving medication (r = 0.893, p < 0.05).

Conclusions. Cerebellar σ-receptors may potentially involve the genesis of LID in advanced PD.

Kinetic parameter estimation from renal measurements with a three-headed SPECT system: a simulation study

We present here a direct least-squares estimation (DLSE) method for the determination of renal kinetic parameters from sequences of very fast acquisitions performed with a three-headed single photon emission computed tomography (SPECT) system. A simple linear model for the behavior of the radiopharmaceutical, as well as a spatial model for its spatial distribution are defined. The model enables one to estimate the kinetic parameters directly from the projections, once the plasma concentration function is known. A new technique for the accurate reconstruction of time-radioactivity curves based on the direct reconstruction of the region-of-interest contents from a series of data from three-projections is presented. The technique is used to determine the plasma concentration function with a sub-second time resolution. The spatially-variant geometrical response is also included in the model to compensate for the spatial resolution of the SPECT system. Results obtained from simulations are presented. Basic spatial and time features of the simulations are derived from a patient study. Noise and segmentation errors are also simulated. The DLSE method is compared with the conventional one of deriving kinetic parameters from the time series of reconstructed images. The standard deviation of results given by DLSE is less than 2%, whereas with the conventional method it is between 5% and 6%. Within the limit of statistical fluctuations, DLSE results are unbiased whereas those of the conventional method are overestimated by 24%.

The impact of stereotactic pallidal surgery on the dopamine D2 receptor in Parkinson disease: a positron emission tomography study

OBJECT

The aim of this study was to estimate the impact of stereotactic pallidal surgery on the binding potential of dopamine D2 receptors in patients with advanced Parkinson disease (PD).

METHODS

Six patients with advanced PD (three men and three women; mean age 56.7 +/- 9.8 years, Hoehn and Yahr stage 3.3 +/- 1.1/3.9 +/- 1.2 [on/off scores], mean +/- standard deviation) underwent stereotactic pallidal surgery. One underwent right posteroventral pallidotomy (PVP), one received left PVP, three were treated with deep brain stimulation (DBS) of the left globus pallidus internus (GPi), and one with bilateral DBS of the GPi. The binding potential of the dopamine D2 receptors of these patients was determined before and after surgery by using positron emission tomography scanning with 11C-nemonapride and it was compared with the value in eight healthy volunteers. The authors also examined whether changes in the D2 receptor binding potential were correlated with the clinical outcome. The clinical symptoms, especially those in the off state, were significantly improved after surgery. Preoperatively, the D2 receptor binding potential in the putamen was elevated by 27% (p < 0.01) and that in the thalamus was 29% lower than that in controls (p < 0.01). The D2 receptor binding potential in the putamen and thalamus returned to control levels after surgery. The preoperative level of the D2 receptor binding potential in the anterior cingulate cortex was comparable to that of controls, but it declined significantly after surgery, whereas the D2 receptor binding potential in other regions of both hemispheres showed no significant changes after surgery. Although the D2 receptor binding potential did not correlate with the Hoehn and Yahr stage, the Schwab and England score, or the Unified PD Rating Scale (UPDRS) score, a positive correlation was seen between the percent improvement rate of the total UPDRS score in the off state and the percentage change of the D2 receptor binding potential in the putamen (r = 0.773, p = 0.0417 according to the Pearson linear correlation).

CONCLUSIONS

The altered dopamine D2 receptor binding potential in the putamen might play a crucial role in clinical improvement after PVP or DBS of the GPi in advanced PD.

Evaluation of resting brain conditions measured by two different methods (i.v. and oral administration) with18F-FDG-PET

Our aim was to evaluate regional differences between brain activity in two resting control conditions measured by 3D PET after administration of FDG through either the intravenous (i.v.) or the oral route. Ten healthy male volunteers engaged in the study as the i.v. group (mean age, 26 +/- 9.3 years, +/- S.D.) who received FDG intravenously and another 10 volunteers as the oral group (mean age, 27.9 +/- 11.3 years, +/- S.D.) who received FDG per os. A set of 3D-PET scans (emission and transmission scans) were performed in both groups. To explore possible functional differences between the brains of the two groups, the SPM-96 software was used for statistical analysis. The results revealed that glucose metabolism was significantly higher in the superior frontal gyrus, superior parietal lobule, lingual gyrus and left cerebellar hemisphere in the i.v. group than in the oral group. Metabolically active areas were found in the superior, middle and inferior temporal gyrus, parahippocampal gyrus, amygdaloid nucleus, pons and cerebellum in the oral group when compared with the i.v. group. These differences were presumably induced by differences between FDG kinetics and/or time-weighted behavioral effects in the two studies. This study suggests the need for extreme caution when selecting a pooled control population for designated activation studies.

Physics and instrumentation for imaging in-vivo drug distribution

Several imaging methods are currently available to measure drugs noninvasively. Of these, two techniques are today central to such measurements: nuclear imaging and magnetic resonance imaging/spectroscopy (MRI and MRS). While other methods, such as optical techniques, are rapidly gaining in interest, they have not yet attained the degree of development that makes them effective in measuring drugs in living systems, except in a small number of examples. The following introduction provides some basic elements of the potential and the limitations of both nuclear imaging and MRI/MRS techniques, methods that will be used in the studies described in the articles in this issue. However, and for those desiring to gain a better understanding of both methods, the reader is advised to consult much more extensive reviews and books describing such methods. A suggested list of books and articles on Nuclear Imaging and MRI/MRS is given.

Attenuation correction for three-dimensional PET using uncollimated flood-source transmission measurements

An attenuation-correction method for three-dimensional PET imaging, which obtains attenuation-correction factors from transmission measurements using an uncollimated flood source, is described. This correction is demonstrated for two different phantoms using transmission data acquired with QPET, a rotating imaging system with two planar detectors developed for imaging small volumes. The scatter amplitude in the transmission projections was a maximum of 30%; to obtain accurate attenuation-correction factors the scatter distribution was first calculated and subtracted. The attenuation-corrected emission images for both phantoms indicate that their original uniform amplitudes have been restored. The attenuation correction adds only a small amount of noise to the emission images, as evaluated from the standard deviation over a central region. For the first phantom, with maximum attenuation of 48%, the noise added was 2.6%. The second phantom was attenuated by a maximum of 37%, and 1.9% noise was added. Because the transmission data are smoothed, some artifacts are visible at the edges of the phantom where the correction factors change abruptly within the emission image.

3D reconstruction for a multi-ring PET scanner by single-slice rebinning and axial deconvolution

A three-dimensional (3D) image reconstruction method, which was originally developed for a positron emission tomography (PET) system consisting of two rotating scintillation cameras, has now been implemented for a multi-ring PET scanner with retractable septa. The method is called 'single-slice rebinning with axial deconvolution' (SSAD), and can be described as follows. The projection data are sorted into transaxial 2D sinograms. Correction for the axial blurring is made by deconvolution in the sinograms. To obtain the axial spread functions, which depend on the activity distribution, 2D reconstruction is first made using a limited axial acceptance angle. The final 3D image is obtained by 2D reconstruction of transaxial planes. The method is simple but not approximate, has a modest memory requirement, and can be combined with different 2D techniques. Evaluations by Monte Carlo simulations and phantom studies have been made.

Three-dimensional image reconstruction for PET by multi-slice rebinning and axial image filtering

A fast method is described for reconstructing volume images from three-dimensional (3D) coincidence data in positron emission tomography (PET). The reconstruction method makes use of all coincidence data acquired by high-sensitivity PET systems that do not have inter-slice absorbers (septa) to restrict the axial acceptance angle. The reconstruction method requires only a small amount of storage and computation, making it well suited for dynamic and whole-body studies. The method consists of three steps: (i) rebinning of coincidence data into a stack of 2D sinograms; (ii) slice-by-slice reconstruction of the sinogram associated with each slice to produce a preliminary 3D image having strong blurring in the axial (z) direction, but with different blurring at different z positions; and (iii) spatially variant filtering of the 3D image in the axial direction (i.e. 1D filtering in z for each x-y column) to produce the final image. The first step involves a new form of the rebinning operation in which multiple sinograms are incremented for each oblique coincidence line (multi-slice rebinning). The axial filtering step is formulated and implemented using the singular value decomposition (SVD). The method has been applied successfully to simulated data and to measured data for different kinds of phantom (multiple point sources, multiple discs, a cylinder with cold spheres, and a 3D brain phantom).

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.

PET instrumentation: what are the limits?

This report has emphasized the attributes of positron emission tomography (PET) through a discussion of the historical development with attention to limitations or factors that are of importance in using and further developing this technology. As is the case for all nuclear detector developments, the factors that require consideration are spatial resolution, uniformity of resolution, sensitivity, distortions (attenuation), background noise (scatter and randoms), image volume, data acquisition capabilities (count-rate saturation), and limitations based on allowable radiation doses to the subject. Forty years ago, the fact that dual gamma-cameras could not handle the count-rates from the short half-life radionuclides that had clinical applications at that time (ie, 15O, 11C, 13N) precluded their acceptance in nuclear medicine. With the advent of 18F applications particularly with FDG in oncology, this limitations was no longer a barrier. Twenty years ago and until recently, the promise of time-of-flight PET has been stifled by the fact that the appropriately fast scintillator BaF2 had too low an efficiency (low density) to be useful in improving the signal to noise of a time-of-flight tomograph over contemporary systems. With the development of dense scintillators with high light output and high speed such as LSO30 the time-of-flight potentials are now once again worth pursuing. Twenty years ago systems that theoretically would have improved sensitivity by minimal or no septa with spherical geometric arrangements of detectors were ignored because it appeared that scatter backgrounds would lead to a signal to noise less than 1. But in the last 5 years, cylindrical systems without speta have shown that noise effective sensitivity improvements of a factor of 4 can be realized. With time-of-flight additional improvements in sensitivity will be realized. Horizons for detector development include discovery of new scintillators, new methods of registering scintillation light, deployment of larger field of view systems and methods of compensating for scatter, randoms, attenuation, and irregular sampling associated with new geometries which can encircle most of the body. The expected limit for PET is 2 mm isotropic resolution for the head and appendages including joints and breasts. Clinical realization of this resolution for the thorax and abdomen requires compensation for motion and even in this area strategies are underdevelopment which rely on the improvement in sensitivity being realized by 3D systems.

Kinetic parameter estimation from SPECT cone-beam projection measurements

Kinetic parameters are commonly estimated from dynamically acquired nuclear medicine data by first reconstructing a dynamic sequence of images and subsequently fitting the parameters to time-activity curves generated from regions of interest overlaid upon the image sequence. Biased estimates can result from images reconstructed using inconsistent projections of a time-varying distribution of radiopharmaceutical acquired by a rotating SPECT system. If the SPECT data are acquired using cone-beam collimators wherein the gantry rotates so that the focal point of the collimators always remains in a plane, additional biases can arise from images reconstructed using insufficient, as well as truncated, projection samples. To overcome these problems we have investigated the estimation of kinetic parameters directly from SPECT cone-beam projection data by modelling the data acquisition process. To accomplish this it was necessary to parametrize the spatial and temporal distribution of the radiopharmaceutical within the SPECT field of view. In a simulated chest image volume, kinetic parameters were estimated for simple one-compartment models for four myocardial regions of interest. Myocardial uptake and washout parameters estimated by conventional analysis of noiseless simulated cone-beam data had biases ranging between 3-26% and 0-28%, respectively. Parameters estimated directly from the noiseless projection data were unbiased as expected, since the model used for fitting was faithful to the simulation. Statistical uncertainties of parameter estimates for 10,000,000 events ranged between 0.2-9% for the uptake parameters and between 0.3-6% for the washout parameters.

Performance evaluation of a large axial field-of-view PET scanner: SET-2400W

The SET-2400W is a newly designed whole-body PET scanner with a large axial field of view (20 cm). Its physical performance was investigated and evaluated. The scanner consists of four rings of 112 BGO detector units (22.8 mm in-plane x 50 mm axial x 30 mm depth). Each detector unit has a 6 (in-plane) x 8 (axial) matrix of BGO crystals coupled to two dual photomultiplier tubes. They are arranged in 32 rings giving 63 two-dimensional image planes. Sensitivity for a 20-cm cylindrical phantom was 6.1 kcps/kBq/ml (224 kcps/microCi/ml) in the 2D clinical mode, and to 48.6 kcps/kBq/ml (1.8 Mcps/microCi/ml) in the 3D mode after scatter correction. In-plane spatial resolution was 3.9 mm FWHM at the center of the field-of-view, and 4.4 mm FWHM tangentially, and 5.4 mm FWHM radially at 100 mm from the center. Average axial resolution was 4.5 mm FWHM at the center and 5.8 mm FWHM at a radial position 100 mm from the center. Average scatter fraction was 8% for the 2D mode and 40% for the 3D mode. The maximum count rate was 230 kcps in the 2D mode and 350 kcps in the 3D mode. Clinical images demonstrate the utility of an enlarged axial field-of-view scanner in brain study and whole-body PET imaging.

A methodology for specifying PET VOI's using multimodality techniques

Volume-of-interest (VOI) extraction for radionuclide and anatomical measurements requires correct identification and delineation of the anatomical feature being studied. We have developed a toolset for specifying three-dimensional (3-D) VOI's on a multislice positron emission tomography (PET) dataset. The software is particularly suited for specifying cerebral cortex VOI's which represent a particular gyrus or deep brain structure. A registered 3-D magnetic resonance image (MRI) dataset is used to provide high-resolution anatomical information, both as oblique two-dimensional (2-D) sections and as volume renderings of a segmented cortical surface. VOI's are specified indirectly in two dimensions by drawing a stack of 2-D regions on the MRI data. The regions are tiled together to form closed triangular mesh surface models, which are subsequently transformed into the observation space of the PET scanner. Quantification by this method allows calculation of radionuclide activity in the VOI's, as well as their statistical uncertainties and correlations. The methodology for this type of analysis and validation results are presented.

Strategies to improve 3D whole-body PET image reconstruction

An algorithm is described for three-dimensional whole-body (3DWB) image reconstruction in positron emission tomography. For whole-body applications, improvements to the popular fixed-axial-acceptance-angle technique are achieved by combining axially adjacent projection data available with a long-axis data set. Time-consuming reprojection of unmeasured oblique lines of response is reduced or eliminated by axial overlap of bed positions, while pixel variance and reconstructed axial resolution are made more uniform by the overlap. Improvements in noise and resolution uniformity are accompanied by gains in reconstruction efficiency, and may be optimized against increased acquisition-time due to overlapping acquisition segments and reduced axial coverage. An 11-detector-ring overlap improves axial uniformity in coronal images of a long, uniform cylinder from 23% to 8% with uniform axial resolution. Associated with a 37% improvement in reconstruction time is a 34% reduction in axial coverage for four bed positions. A smaller degree of overlap is found to provide the best trade-off between image uniformity, total scan duration, and reconstruction time because of a proportionally greater reduction in reprojected lines of response. Using a sample optimization scheme, we find a three-ring overlap is best for a 60 cm axial field of view and a five-ring overlap for an 80 cm axial field of view.

Carbon-11-labeled estrogens as potential imaging agents for breast tumors

We have prepared two estrogens labeled with carbon-11, 17 alpha-[11C] methylestradiol and 11 beta-ethyl-17 alpha-[11C]methylestradiol, at a specific activity of 300-1000 Ci/mmol (11.1-37 TBq/mmol), and we have determined their in vivo biodistribution in immature female rats. Both compounds accumulated selectively in two target tissues, the uterus and ovaries, reaching levels of 3.5-4.9%ID/g at 20 min and 4.6-6.6%ID/g at 40 min; uterus-to-blood ratios reached 12-23. Uterine uptake showed a saturation dependence with the amount of injected mass, and was displaced by unlabeled estradiol, indicating that this uptake was receptor mediated. These results suggest that these compounds may be useful in estrogen receptor-based imaging of breast tumors.

Model-based scatter correction for fully 3D PET

A method is presented that directly calculates the mean number of scattered coincidences in data acquired with fully 3D positron emission tomography (PET). This method uses a transmission scan, an emission scan, the physics of Compton scatter, and a mathematical model of the scanner in a forward calculation of the number of events for which one photon has undergone a single Compton interaction. The distribution of events for which multiple Compton interactions have occurred is modelled as a linear transformation of the single-scatter distribution. Computational efficiency is achieved by sampling at rates no higher than those required by the scatter distribution and by implementing the algorithm using look-up tables. Evaluation studies in phantoms with large scatter fractions show that the method yields images with quantitative accuracy equivalent to that of slice-collimated PET in clinically useful times.

Weighted backprojection approach to cone beam 3D projection reconstruction for truncated spherical detection geometry

A new analytical three-dimensional cone beam reconstruction algorithm is presented for truncated spherical detection geometry. The basic idea of the proposed algorithm is the formation of spatially invariant 3D blurred back-projected volumetric image by the use of the weighted backprojection of cone beam projection data and subsequent 3D filtering using an acceptance angle dependent rho filter. The backprojection weighting function is calculated on the basis of each given geometrical condition, i.e. detection geometry or degree of truncation, position of cone beam apex, and backprojection point. The proposed algorithm is derived analytically and is computationally efficient. Performance of the algorithm is evaluated by the reconstruction of 3D volumetric images using simulated data from arbitrarily truncated spherical detector geometries.

Improved detection of focal cerebral blood flow changes using three-dimensional positron emission tomography

Removal of the interplane septa and configuration of a typical multislice PET scanner to accept all possible coincidence lines of response leads to a fivefold increase in sensitivity. This can be of value in regional CBF studies using bolus 15O-labeled water injections, allowing the injected dose to be reduced by a factor of 4, while maintaining the same number of noise equivalent counts. Thus, for a given cumulative dose limit, four times as many studies can be performed in a single subject. Data from the three-dimensional Hoffman brain phantom, closely matched to count rates seen in human studies, show that for an identical cumulative dose, the noise in subtraction (stimulus minus baseline) images can be reduced by a factor of 2 using three-dimensional data acquisition, with appropriate fractionation of the dose. This improvement is dependent on axial position due to the sensitivity characteristics of three-dimensional scans; however, there is a significant gain in the signal-to-noise ratio (S/N) in all image planes. Studies performed in a human subject demonstrate how the factor of 2 gain in S/N leads to improved detectability of activation sites in PET subtraction images.

Rapid three-dimensional surface reconstruction of magnetic resonance images of large arteries and veins: a preliminary evaluation of clinical utility

We have implemented a computerized system for relatively rapid (< 1 h) three-dimensional (3D) surface rendering of flow-sensitive (gradient refocused) magnetic resonance images. The method has been applied in 8 patients with six different clinical problems and was found to enhance understanding of normal and abnormal aortic, caval, and portosystemic venous anatomy. 3D images are useful for communicating complex anatomic information and may help with difficult diagnoses. Advantages and limitations of the present system are discussed.

3D acquisition and reconstruction in positron emission tomography

3D positron emission tomography (PET) refers to an acquisition geometry and reconstruction procedure that allows all coincidence events within the solid angle of the tomograph to be recorded and subsequently reconstructed. The reconstruction algorithm must consider the angle of each coincidence event relative to the central axis of the scanner. The aim of the technique is to maximise the sensitivity of the system by utilising all events that it is possible to record from the object. Conventional cylindrical 2D PET systems typically detect approximately 0.4%-0.5% of decaying nuclei within the field of view; with a 3D system this can increase to over 3%. Reconstruction in 3D using filtered-backprojection techniques has been developed and provides results that show little degradation of physical characteristics compared with 2D systems, apart from an increased scatter event rate. 3D techniques may be used to (i) improve data quality using currently acceptable doses of radioactivity and scanning times; (ii) extend the scanning period for short-lived tracers, especially 11C-labeled ligands; or, conversely (iii) decrease injected doses of radiotracer or reduce scanning times to achieve similar results as those using current methods in 2D.

Fully three-dimensional reconstruction from data collected on concentric cubes in Fourier space: implementation and a sample application to MRI

An algorithm is proposed for rapid and accurate reconstruction from data collected in Fourier space at points arranged on a grid of concentric cubes. The Fourier transform of the object to be reconstructed is decomposed into the sum of three functions by subdividing its domain into three non-overlapping mutually orthogonal double pyramids. Each of the three functions is zero-valued outside one of the double pyramids and has values inside that double pyramid which are the same as those of Fourier transform of the object to be reconstructed at the same points. Inverse Fourier transforms of these individual functions can be calculated using the chirp z-transform. The outputs of these inverse transforms for the three functions are estimates of their values at points of the same rectangular grid. The function to be reconstructed is estimated for this grid by adding together the three inverse transforms. The whole process has computational complexity of the same order as required for the 3D fast Fourier transform and so (for medically relevant sizes of the data set) it is faster than backprojection into the same size rectangular grid. The design of the algorithm ensures that no interpolations are needed, in contrast to methods involving backprojection with their unavoidable interpolations. As an application, a 3D data collection method for MRI has been designed which directly samples the Fourier transform of the object to be reconstructed on concentric cubes as needed for the algorithm.

Evaluation of a 3D reconstruction algorithm for multi-slice PET scanners

A fully 3D reconstruction algorithm based on filtered backprojection was evaluated for the reconstruction of data obtained with multi-slice positron emission tomography (PET) scanners which have had the septa removed. This algorithm uses forward-projection through the reconstructed images of a 2D subset of the data to complete the 3D dataset thus satisfying the condition of shift invariance. This is followed by 3D filtered backprojection. Axial sampling was doubled by combining adjacent polar angles, thus improving reconstructed axial resolution. The algorithm was tested using real and simulated datasets and gave high quality reconstructions without artifacts over a wide range of imaging conditions. Events are placed accurately throughout the imaging volume as determined by measurements with a MRI/PET registration phantom. The forward-projection step leads to degradation in image resolution due to insufficient axial and transaxial sampling. This effect is amplified if multiple iterations of the algorithm are used, with little decrease in image noise. Changing the filter employed in the initial 2D reconstruction can be used to alter the noise and resolution characteristics of the 3D images. This algorithm has proved very robust at reconstructing 3D PET data and is relatively fast. Those small problems which exist can be attributed to detector sampling problems, especially in the axial direction, which is a consequence of the geometry of these scanners, which are designed primarily for 2D data acquisition.

Fully three-dimensional reconstruction for a PET camera with retractable septa

A fully 3-D reconstruction algorithm has been developed to reconstruct data from a 16 ring PET camera (a Siemens/CTI 953B) with automatically retractable septa. The tomograph is able to acquire coincidences between any pair of detector rings and septa retraction increases the total system count rate by a factor of 7.8 (including scatter) and 4.7 (scatter subtracted) for a uniform, 20 cm diameter cylinder. The reconstruction algorithm is based on 3-D filtered backprojection, expressed in a form suitable for the multi-angle sinogram data. Sinograms which are not measured due to the truncated cylindrical geometry of the tomograph, but which are required for a spatially invariant response function, are obtained by forward projection. After filtering, the complete set of sinograms is backprojected into a 3-D volume of 128x128x31 voxels using a voxel-driven procedure. The algorithm has been validated with simulation, and tested with both phantom and clinical data from the 953B.