Positron Volume Imaging Research Articles

Evaluation of low energy threshold settings for PVI PET systems

The authors studied the effects of adjusting the low level energy discriminator (LLD) for positron volume imaging (PVI) mode acquisitions using a GE Advance PET system. NEMA scatter fraction and count loss measurements were performed for a 20 cm right circular cylinder at LLD between 300 keV and 450 keV. From these data, noise equivalent count rate (NECR) curves were calculated to estimate effects of LLD on scans of head sized objects. To evaluate the effects of LLD on whole-body image quality, contrast-to-noise ratio (CNR) values were obtained from images processed without attenuation or scatter correction. CNR data were acquired for 1.6 cm and 1.0 cm spherical lesions within the liver region of a Data Spectrum torso phantom scanned with arms, and activity outside the field of view. The results indicate that the NECR for a head-sized object is fairly insensitive to LLD differences between 300 keV and 425 keV for activity concentrations up to 0.4 μCi/cc. The NECR improved slightly for higher concentrations with 375 keV < LLD < 425 keV. Torso phantom images processed without scatter or attenuation correction show some CNR improvement with increasing LLD up to 425 keV for clinically relevant activity concentrations.

Effect of lower energy threshold on single and multiple scatter distributions in positron volume imaging

Simulations of the scatter distributions in the Advance tomograph have been performed using the SimSET software package. The Zubal phantom was used, centered at the heart with activity only in the heart or in all soft tissues except the lungs. Data were binned axially for: (1) -7.6 to 7.6 cm (the full axial field of view); (2) -0.884 to 0.844 cm; and (3) 2.53 to 4.22 cm. Simulations were performed with both a 45.6 cm long (full object) and a 15.2 cm long (short object) section of the phantom with 250 million decays. The total scatter to trues ratio for the full object varied from 1.20 (300 keV, all soft tissues) to 0.35 (425 keV, heart only). The ratio of single scatters from the short object simulation compared to the total scatters from the full object varied from 40% at 300 keV to 60% at 425 keV. While the multiple scatters were well estimated with a Gaussian convolution of the single scatter events (for the full object), significant errors may occur if the attenuation and activity outside the FOV is not included in the estimation of the single scatters.

Fast accurate iterative three-dimensional Bayesian reconstruction for low-statistics positron volume imaging

Direct use of list-mode data for image reconstruction improves accuracy for some imaging systems, and permits fast reconstructions for low-statistics situations. A list-mode based three-dimensional implementation of an iterative Bayesian reconstruction algorithm has been developed (FAIR-B). The approach starts with an initial 2-D filtered backprojection (FBP) of Fourier rebinned data and employs a Gibbs prior to encourage images with local continuity, using the method of iterative conditional averages to obtain a sequence of estimates. Ten iterations are sufficient to significantly affect the image, incorporating the benefits of list-mode data and the Gibbs prior. The method has been tested with simulated data for rotating planar detector based systems and can offer improved noise contrast behaviour over FBP and list-mode driven expectation maximisation-maximum likelihood (EM-ML). However, for low-contrast regions whilst improved structural accuracy is still obtained, contrast losses are observed.

Intercomparison of four reconstruction techniques for positron volume imaging with rotating planar detectors

Four reconstruction techniques for positron volume imaging have been evaluated for scanners based on rotating planar detectors using measured and simulated data. The four techniques compared are backproject then filter (BPF), the 3D reprojection (3D RP) method for 3D filtered backprojection (FBP), Fourier rebinning (FORE) in conjunction with 2D FBP (FORE+2D FBP) and 3D ordered subsets expectation maximization (3D OSEM). The comparison was based on image resolution and on the trade-off between contrast and noise. In general FORE+2D FBP offered a better contrast-noise trade-off than 3D RP, whilst 3D RP offered a better trade-off than BPF. Unlike 3D RP, FORE+2D FBP did not suffer any contrast degradation effect at the edges of the axial field of view, but was unable to take as much advantage from high-accuracy data as the other methods. 3D OSEM gave the best contrast at the expense of greater image noise. BPF, which demonstrated generally inferior contrast-noise behaviour due to use of only a subset of the data, gave more consistent spatial resolution over the field of view than the projection-data based methods, and was best at taking full advantage of high-accuracy data.

Fast accurate iterative reconstruction for low-statistics positron volume imaging

A fast accurate iterative reconstruction (FAIR) method suitable for low-statistics positron volume imaging has been developed. The method, based on the expectation maximization-maximum likelihood (EM-ML) technique, operates on list-mode data rather than histogrammed projection data and can, in just one pass through the data, generate images with the same characteristics as several ML iterations. Use of list-mode data preserves maximum sampling accuracy and implicitly ignores lines of response (LORs) in which no counts were recorded. The method is particularly suited to systems where sampling accuracy can be lost by histogramming events into coarse LOR bins, and also to sparse data situations such as fast whole-body and dynamic imaging where sampling accuracy may be compromised by storage requirements and where reconstruction time can be wasted by including LORs with no counts. The technique can be accelerated by operating on subsets of list-mode data which also allows scope for simultaneous data acquisition and iterative reconstruction. The method is compared with a standard implementation of the EM-ML technique and is shown to offer improved resolution, contrast and noise properties as a direct result of using improved spatial sampling, limited only by hardware specifications.

Evaluation of simulation-based scatter correction for 3-D PET cardiac imaging

Quantitative imaging of the human thorax poses one of the most difficult challenges for three-dimensional (3-D) (septaless) positron emission tomography (PET), due to the strong attenuation of the annihilation radiation and the large contribution of scattered photons to the data. In [/sup 18/F] fluorodeoxyglucose (FDG) studies of the heart with the patient's arms in the field of view, the contribution of scattered events can exceed 50% of the total detected coincidences. Accurate correction for this scatter component is necessary for meaningful quantitative image analysis and tracer kinetic modeling. For this reason, the authors have implemented a single-scatter simulation technique for scatter correction in positron volume imaging. Here, they describe this algorithm and present scatter correction results from human and chest phantom studies.

The local noise property in positron volume imaging and optimal conditions for the signal-to-noise ratio of the 3D reconstructed image

The local noise property of a 3D PET reconstructed image is investigated for a uniform-activity sphere distributed in a constantly attenuating spherical object. The positional dependence of the statistical noise is approximately derived and calculated for some special cases. It is suggested that a larger diameter of the activity sphere causes noise amplification, and the noise property for the large attenuating sphere is close to that for a non-attenuating object with the same total number of measuring counts. By considering noise propagation of two spherical activity distributions, we suggest that the signal-to-noise ratio of the image depends on a set of projection directions and the sizes and intensities of the activity distributions. In a simple case, we derive an optimal value of the maximum acceptance angle for the projection directions to improve the signal-to-noise ratio of the image.

Addition of noise by scatter correction methods in PVI

Effective scatter correction techniques are required to account for errors due the high scatter fraction seen in positron volume imaging (PVI). To be effective, the correction techniques must be accurate and practical, but they also must not add excessively to the statistical noise in the image. The authors have investigated the noise added by three correction methods: a convolution/subtraction method; a method that interpolates the scatter from the events outside the object; and a dual energy window method with and without smoothing of the scatter estimate. The methods were applied to data generated by Monte Carlo simulation to determine their effect on the variance of the corrected projections. The convolution and interpolation methods did not add significantly to the variance. The dual energy window subtraction method without smoothing increased the variance by a factor of more than twelve, but this factor was improved to 1.2 by smoothing the scatter estimate.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Two new strategies to increase the signal to noise ratio in positron volume imaging

Two new hardware techniques which improve the scatter fraction of positron volume imaging (PVI) systems are presented. The first uses the fact that Compton scattered rays scattered through a large angle have a lower energy. The range of angles through which rays can be scattered and still be in the scanner field of view (FOV) depends on the radius of the line of response. By using a low-energy threshold which is proportional to the line of response's (LOR's) radius, the scatter fraction at the edges of the image is substantially reduced. The second technique is based on the observation that in NaI crystals many of the 511-keV rays are backscattered, and the scattered photon then escapes undetected. The use of a notched energy acceptance window, which includes the photo-peak and the backscatter peak, but discards the scattered events in between, is proposed. >

The problem of scatter correction in positron volume imaging

Thin, dense interslice septa have long been used to reduce the scattered radiation collected in positron emission tomography (PET). These septa prevent the acquisition of coincident gamma rays that are oblique to the scanning planes. Several volume imaging systems that acquire oblique rays have been built. The reasons why the scatter fraction is intrinsically higher in these systems are discussed, and two different scatter compensation techniques are compared. The comparison uses Monte Carlo simulations to generate average profiles and spectra for typical phantoms and scanning geometries. Comparison results indicate that deconvolution of the total event profiles with a filter adjusted to the object size and good energy discrimination provide an excellent scatter estimate as long as the object's diameter is less than the detector's radius. The profiles derived from a second, lower, energy window are always much flatter than the scattered counts in a window covering the photopeak. They do not match the scattered event profile and are less reliable, being based on a lower number of counts.

Monte Carlo Simulation of the Scatter Component in Small Animal Positron Volume-Imaging Devices

Monte Carlo techniques were used to describe the distribution and the fraction of scattered radiation in a detector system for small animal positron volume imaging. The idealized geometry consisted of a continuous, tube-shaped BGO detector (inner diameter: 10 cm (15 cm), outer diameter: 16 cm (21 cm)) without septa and a water cylinder (diameter: 6 cm) as scattering medium. Line sources and homogeneous flood sources of two gamma rays with opposing directions were simulated. An event was registered as a valid coincident event if both gamma rays were detected in the scintillation crystal and the energy deposit was above a given threshold. Scatter fractions were determined as a function of the angle of the coincidence line relative to the symmetry axis of the system. The contribution of scattered quanta to coincidences within axial slices was simulated for the two detector diameters as a function of energy threshold. The results showed that a system with a small inner diameter of the detector and a high energy threshold is feasible for positron volume imaging.

Analytic image reconstruction in PVI using the 3D Radon transform

Algorithms have been derived for 3-D image reconstruction in positron volume imaging (PVI) using the inversion of the 3-D Radon transform (RT) for a truncated cylindrical detector geometry. The RT is formed by histogramming events according to the planes in which they lie, with a weight determined by an angular acceptance function. A fast backprojection method for the RT is described in which the computation time is found to be up to 20 times faster with the new algorithm compared to the traditional X-ray transform (XT) backprojection method. Monte Carlo simulations show that statistical noise levels in images reconstructed from complete projections with the new RT algorithm are comparable to those obtained using the Fourier transform inversion of the XT. >

Full data utilization in PVI using the 3D radon transform

An algorithm is described for three-dimensional (3D) image reconstruction in positron volume imaging (PVI) using the inversion of the 3D radon transform (RT) for a truncated cylindrical detector geometry. A discrete version of the 3D RT is formed in a 3D histogram from the event-line coordinates of the detected events. The histogram entries represent the plane integrals of the activity in the field of view. Conventional inversion of the X-ray transform (XT) excludes oblique events in non-iterative reconstruction methods. By employing a spatially varying angular acceptance of events into the histogrammed plane integrals of the 3D RT, it is possible to include most of the detected oblique events in the reconstruction of the image using the standard 3D RT inversion formula. The oblique events are added to the histogram with a partial weight compared to those in complete (XT) projections. This single-pass reconstruction image has better statistical noise properties than images formed by RT inversion from complete XT projections, but only for some detector geometries is it significantly better.

Object shape dependent scatter simulations for PET

The correctness of an analytical simulation for single-scattered gamma rays in positron volume imaging was verified by comparing it to Monte Carlo simulation of single scattering. The Monte Carlo simulation was verified using measured tomograph data. The single-scatter analytical simulation was extended to estimate multiple scattering. The multiple-scatter analytical simulation showed good agreement with the Monte Carlo simulation of total object scatter. It is shown using the analytical simulation that the position of a source along the line of response and the shape of the scattering object make a substantial difference in the scatter distribution in the projections. Such projections can be generated in a much shorter time using the analytical simulation than using the Monte Carlo simulation. A scatter correction method which uses the analytical simulation and exploits the inherent smoothness of the scatter distribution to account for three-dimensional effects in scatter distribution and object shape is also proposed. >

Use of transputers in a 3-D positron emission tomograph

The use of a VME-bus-based transputer network as a parallel processing engine for positron volume imaging (PVI) is discussed. The authors find that the speedups of parallel networks depend on two major factors, the ratio of computation to communication for a task and the size of the task, and give a simple model to explore the limits on speedups. Through actual implementation it is shown that real-time PVI data acquisition can be achieved with about 20 transputer nodes, and it is estimated that three-dimensional (3-D) image reconstruction can be achieved within 10 min using 200 nodes. Larger images and a larger number of histograms can readily be accommodated using the same parallel algorithms, as the model presented places no limits on the size of the images. The versatility and scalability of transputers makes them very suitable for use in PVI tomographs in that the same transputers can be used for speeding up data acquisition, image reconstruction, and display.

Toward the design of a positron volume imaging camera

Three different computing algorithms for performing positron emission image reconstruction have been compared using Monte Carlo phantom simulations. The work was motivated by the recent announcement of the commercial availability of a positron volume imaging camera, the Siemens-CTI 953 B/31, which has improved axial (slice) resolution and retractable interslice septa. The simulations demonstrate the importance of developing a complete three-dimensional reconstruction algorithm to deal with the increased gamma detection solid angle and the increased scatter fraction that result when the interslice septa are removed from a ring tomograph. The 3-D algorithm has a lower noise level than either the conventional 2-D algorithm (appropriate to tomographs with interslice septa) or the modified 2-D algorithm (proposed to implement positron volume imaging on the new scanner). The new 3-D algorithm is free of a serious artifact that affects the modified 2-D algorithm, caused by spillover of activity from one slice to another. >

A tomograph VMEbus parallel processing data acquisition system

The authors describe a VME-based data acquisition system suitable for the development of positron volume imaging tomographs which use 3-D data for improved image resolution over slice-oriented tomographs. The data acquisition must be flexible enough to accommodate several 3-D reconstruction algorithms; hence, software-based system is most suitable. Furthermore, because of the increased dimensions and resolution of volume imaging tomographs, the raw data event rate is greater than that of slice-oriented machines. These dual requirements are met by the proposed data acquisition system. Flexibility is achieved through an array of processors connected over a VMEbus, operating asynchronously and in parallel. High raw data throughput is achieved using a dedicated high-speed data transfer device available for the VMEbus. The device can attain a raw data rate of 2.5 million coincidence events per second for raw events which are 64-bits wide. >

Design of a volume-imaging positron emission tomograph

Progress is reported in several areas of design of a positron volume imaging tomograph. As a means of increasing the volume imaged and the detector packing fraction, a lens system of detector light coupling is considered. A prototype layered scintillator detector demonstrates improved spatial resolution due to a unique Compton rejection capability. The conceptual design of a novel mechanism for measuring scattered radiation during emission scans has been tested by Monte Carlo simulation. The problem of how to use effectively the resulting sampled scattered radiation projections is discussed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>