Three-gamma annihilation imaging in positron emission tomography

It is argued that positron annihilation into three photons, although quite rare, could still be used as a new imaging modality of positron emission tomography. The information gained when the three decay photons are detected is significantly higher than in the case of 511 keV two-gamma annihilation. The performance of three-gamma imaging in terms of the required detector properties, spatial resolution and counting rates is discussed. A simple proof-of-principle experiment confirms the feasibility of the new imaging method.     

Optimizing rod window width in positron emission tomography

A technique determines the optimal window width for orbiting rod transmission studies in positron emission tomography (PET). Windowing reduces noise in orbiting rod transmission studies. Lines-of-response (LOR) which intersect the rods generate primarily true coincidence events. LOR which pass far from the rods generate random and scatter events. Since the angular position of the orbiting rods is known in real-time, LOR which produce mostly noise are gated off. When optimally determined, the rod window width maximizes the noise equivalent counts (NEC) collected in the transmission study. Transaxial rod projection profiles of trues, randoms, and scatter produce NEC versus window width plots. For the ECAT EXACT line of PET systems and a 20-cm water cylinder, optimal is five LOR wide.     

Stationary positron emission tomography and its image reconstruction

Feasibility of stationary positron emission tomography (PET) using discrete detectors has been investigated by simulation studies. To enable full utilization of detector resolution, a "bank array" of detectors is proposed and an EM algorithm is adopted for image reconstruction. The bank array consists of an odd number of detector banks arranged on a circular ring with a gap equal to one half the detector width. The EM algorithm [11] is used with some modifications for reducing the quantity of computation, improving the convergence speed, and suppressing statistical noise, so as to meet the present purpose. Simulation studies involving several phantoms show that the stationary PET with the new detector array provides image quality which is good enough for clinical applications. For fast dynamic studies with low spatial resolution, the convolution-backprojection method is efficient, but for high-resolution static imaging, resolution enhancement by an iterative method is required. Problems arising in the corrections for attenuation of photons and detector sensitivity, etc., are also discussed. A totally stationary PET avoids the mechanical problems associated with accurate movement of heavy assemblies and is particularly advantageous in gated cardiac imaging or in fast dynamic studies. Elimination of a scan along the detector plane allows a quick scan in the axial direction to achieve three-dimensional imaging with a small number of detector rings.     

Regularized image reconstruction algorithms for positron emission tomography

We develop algorithms for obtaining regularized estimates of emission means in positron emission tomography. The first algorithm iteratively minimizes a penalized maximum-likelihood (PML) objective function. It is based on standard de-coupled surrogate functions for the ML objective function and de-coupled surrogate functions for a certain class of penalty functions. As desired, the PML algorithm guarantees nonnegative estimates and monotonically decreases the PML objective function with increasing iterations. The second algorithm is based on an iteration dependent, de-coupled penalty function that introduces smoothing while preserving edges. For the purpose of making comparisons, the MLEM algorithm and a penalized weighted least-squares algorithm were implemented. In experiments using synthetic data and real phantom data, it was found that, for a fixed level of background noise, the contrast in the images produced by the proposed algorithms was the most accurate.     

Penalized weighted least-squares image reconstruction for positron emission tomography

Presents an image reconstruction method for positron-emission tomography (PET) based on a penalized, weighted least-squares (PWLS) objective. For PET measurements that are precorrected for accidental coincidences, the author argues statistically that a least-squares objective function is as appropriate, if not more so, than the popular Poisson likelihood objective. The author proposes a simple data-based method for determining the weights that accounts for attenuation and detector efficiency. A nonnegative successive over-relaxation (+SOR) algorithm converges rapidly to the global minimum of the PWLS objective. Quantitative simulation results demonstrate that the bias/variance tradeoff of the PWLS+SOR method is comparable to the maximum-likelihood expectation-maximization (ML-EM) method (but with fewer iterations), and is improved relative to the conventional filtered backprojection (FBP) method. Qualitative results suggest that the streak artifacts common to the FBP method are nearly eliminated by the PWLS+SOR method, and indicate that the proposed method for weighting the measurements is a significant factor in the improvement over FBP.     

A multigrid expectation maximization reconstruction algorithm for positron emission tomography

The problem of reconstruction in positron emission tomography (PET) is basically estimating the number of photon pairs emitted from the source. Using the concept of the maximum-likelihood (ML) algorithm, the problem of reconstruction is reduced to determining an estimate of the emitter density that maximizes the probability of observing the actual detector count data over all possible emitter density distributions. A solution using this type of expectation maximization (EM) algorithm with a fixed grid size is severely handicapped by the slow convergence rate, the large computation time, and the nonuniform correction efficiency of each iteration, which makes the algorithm very sensitive to the image pattern. An efficient knowledge-based multigrid reconstruction algorithm based on the ML approach is presented to overcome these problems.     

Implementing and accelerating the em algorithm for positron emission tomography

Since the publication of Shepp and Vadi's [ 14] maximum likelihood reconstruction algorithm for emission tomography (ET), many medical research centers engaged in ET have made an effort to change their reconstruction algorithms to this new approach. Some have succeeded, while others claim they could not adopt this new approach primarily because of limited computing power. In this paper, we discuss techniques for reducing the computational requirements of the reconstruction algorithm. Specifically, the paper discusses the data structures one might use and ways of taking advantage of the geometry of the physical system. The paper also treats some of the numerical aspects of the EM (expectation maximization) algorithm, and ways of speeding up the numerical algorithm using some of the traditional techniques of numerical analysis.     

Dynamic positron emission tomography data-driven analysis using sparse Bayesian learning

A method is presented for the analysis of dynamic positron emission tomography (PET) data using sparse Bayesian learning. Parameters are estimated in a compartmental framework using an over-complete exponential basis set and sparse Bayesian learning. The technique is applicable to analyses requiring either a plasma or reference tissue input function and produces estimates of the system's macro-parameters and model order. In addition, the Bayesian approach returns the posterior distribution which allows for some characterisation of the error component. The method is applied to the estimation of parametric images of neuroreceptor radioligand studies.      

Effects of detector wobble motion on image noise in positron emission tomography

The effects of detector wobble motion on image variance is described analytically and verified by simulation studies. Simulation results in the form of variance images are presented for various phantoms, sampled under both uniform and wobble-motion conditions. It is shown that under most measurement conditions in a typical PET study, the image precision is degraded due to the nonuniform projection variance introduced by the wobble motion. Using the wobble parameters of the UBC-TRIUMF development of PETT VI, the rms noise is found to be increased by 9 percent due to wobbling.     

Detector response restoration in image reconstruction of high resolution positron emission tomography

A mathematical method was studied to model the detector response of high spatial-resolution positron emission tomography systems consisting of close-packed small crystals, and to restore the resolution deteriorated due to crystal penetration and/or nonuniform sampling across the field-of-view (FOV). The simulated detector system had 600 bismuth germanate crystals of 3.14 mm width and 30 mm length packed on a single ring of 60 cm diameter. The space between crystals was filled up with lead (i.e., septa). Each crystal was in coincidence with 200 opposite crystals so that the FOV had a radius of 30 cm. The detector response was modeled based on the attenuating properties of the crystals and the septa, as well as the geometry of the detector system. The modeled detector-response function was used to restore the projections from the sinogram of the ring-detector system. The restored projections had a uniform sampling of 1.57 mm across the FOV. The crystal penetration and/or the nonuniform sampling were compensated in the projections. A penalized maximum-likelihood algorithm was employed to accomplish the restoration. The restored projections were then filtered and backprojected to reconstruct the image. A chest phantom with a few small circular "cold" objects ( approximately 4 mm diameter) located at the center and near the periphery of FOV was computer generated and used to test the restoration. The reconstructed images from the restored projections demonstrated resolution improvement off the FOV center, while preserving the resolution near the center.     

18F-FDG-PET/CT在弥漫大B细胞淋巴瘤中的分期诊断价值

目的旨在对比18F-FDG-PET/CT与CT在弥漫大B细胞淋巴瘤(DLBCL)中的分期诊断价值,分析DLBCL病灶的18F-FDG-PET/CT显像及分布特点。方法32例以淋巴结病理确诊的DLBCL患者,同时以18F-FDG-PET/CT及CT评价分期,18F-FDG-PET/CT及CT测量肿瘤病灶的部位、大小及SUVmax,计算与纵隔大血管主动脉弓血池SUVmax比值(T/MB)。结果18F-FDG-PET/CT及CT检测DLBCL病灶的一致率为70.6%,其敏感性分别为100%、75.8%,特异性分别为96%、4%,阳性预测值分别为99.7%、91.5%,阴性预测值分别为100%、1.2%,假阳性率分别为4%、96%,假阴性率分别为0、24.2%,准确率为99.7%、70.9%。结论18F-FDG-PET/CT对DLBCL检测的敏感性、特异性均明显好于CT,对多种结外病灶尤其是骨骼侵润的诊断较CT具有优越性,能够协助临床准确分期。DLBCL病灶的18F-FDG-PET/CT显像分布特点及T/MB值可供临床医生参考。     

Fast point spread function computation from aperture functions in high-resolution positron emission tomography

The problem of extracting point spread functions from detector aperture functions in high-resolution PET is addressed. In the limit of very small size detectors relative to the ring dimensions, assumptions are made that lead to a fast and simple computation model yielding point spread functions with negligible errors due to the reconstruction algorithm. The methods allows one to assess accurately the intrinsic performance of a PET tomograph, and it appears to be adequate to relate the imaging capabilities in every point of the camera reconstruction field to the geometric and physical characteristics of the detection system. The method was developed as an investigation tool to help design the next generation of very-high-resolution PET tomographs.     

Performance evaluation of an iterative image reconstruction algorithm for positron emission tomography

An image reconstruction method motivated by positron emission tomography (PET) is discussed. The measurements tend to be noisy and so the reconstruction method should incorporate the statistical nature of the noise. The authors set up a discrete model to represent the physical situation and arrive at a nonlinear maximum a posteriori probability (MAP) formulation of the problem. An iterative approach which requires the solution of simple quadratic equations is proposed. The authors also present a methodology which allows them to experimentally optimize an image reconstruction method for a specific medical task and to evaluate the relative efficacy of two reconstruction methods for a particular task in a manner which meets the high standards set by the methodology of statistical hypothesis testing. The new MAP algorithm is compared to a method which maximizes likelihood and with two variants of the filtered backprojection method.     

Performance study of single-slice positron emission tomography scanners by monte carlo techniques

A Monte Carlo simulation of the gamma ray transport within a single-slice positron emission tomograph has been generated to study the effects of system parameters on performance. Included in the simulation are the radioactive source distribution, collimators, and detectors with intercrystal septa. Data are first presented to show the coincidence and singles sensitivities as a function of ring radius. Then, for a fixed radius of 26 cm, the variation of sensitivities are shown as a function of the following variables: slice thickness, patient port size, intercrystal septum dimensions, lower energy discriminator level, and coincidence fan angle. Simulation-generated sensitivity data are compared with experimental values for several tomographs andgood agreement is obtained. Discrepancies between two definitions used in experimentally determining scatter fractions are discussed. The Monte Carlo simulation shows that small radii rings have an effective count rate (quality factor) that is more than 90 percent of that for larger rings at low and moderate activity levels (=/< 0.25 muCi cm(-3)), contrary to what is predicted from analytical calculations. It is concluded that small radius rings are better suited for low dose-rate static studies, while larger radius rings are preferred for high dose-rate dynamic studies.     

Tracer kinetic modeling of 11C-acetate applied in the liver with positron emission tomography

It is well known that 40%-50% of hepatocellular carcinoma (HCC) do not show increased 18F-fluorodeoxyglucose (FDG) uptake. Recent research studies have demonstrated that 11C-acetate may be a complementary tracer to FDG in positron emission tomography (PET) imaging of HCC in the liver. Quantitative dynamic modeling is, therefore, conducted to evaluate the kinetic characteristics of this tracer in HCC and nontumor liver tissue. A three-compartment model consisting of four parameters with dual inputs is proposed and compared with that of five parameters. Twelve regions of dynamic datasets of the liver extracted from six patients are used to test the models. Estimation of the adequacy of these models is based on Akaike Information Criteria (AIC) and Schwarz Criteria (SC) by statistical study. The forward clearance K = K1 * k3/(k2 + k3) is estimated and defined as a new parameter called the local hepatic metabolic rate-constant of acetate (LHMRAct) using both the weighted nonlinear least squares (NLS) and the linear Patlak methods. Preliminary results show that the LHMRAct of the HCC is significantly higher than that of the nontumor liver tissue. These model parameters provide quantitative evidence and understanding on the kinetic basis of C-acetate for its potential role in the imaging of HCC using PET.     

A 100-ps time-resolution CMOS time-to-digital converter for positron emission tomography imaging applications

An integrated CMOS subnanosecond time-to-digital converter (TDC) has been developed and evaluated for positron emission tomography (PET) front-end applications. The TDC architecture combines an accurate digital counter and an analog time interpolation circuit to make the time interval measurement. The dynamic range of the TDC is programmable and can be easily extended without any timing resolution degradation. The converter was designed to operate over a reference clock frequency range of 62.5 MHz up to 100 MHz and can have a bin size as small as 312.5 ps LSB with 100-ns conversion times. Measurements indicate the TDC achieves a DNL of under /spl plusmn/0.20 LSB and INL less than /spl plusmn/0.30 LSB with an rms timing resolution of 0.312 LSB (97.5 ps), very close to the theoretical limit of 0.289 LSB (90 ps). The design is believed to be the first fully integrated CMOS subnanosecond TDC used in PET medical imaging and the first realization of a CMOS TDC that achieves an rms timing resolution below 100 ps within a 100-ns conversion time.     

Algebraic reconstruction techniques can be made computationally efficient [positron emission tomography application

Algebraic reconstruction techniques (ART) are iterative procedures for recovering objects from their projections. It is claimed that by a careful adjustment of the order in which the collected data are accessed during the reconstruction procedure and of the so-called relaxation parameters that are to be chosen in an algebraic reconstruction technique, ART can produce high-quality reconstructions with excellent computational efficiency. This is demonstrated by an example based on a particular (but realistic) medical imaging task, showing that ART can match the performance of the standard expectation-maximization approach for maximizing likelihood (from the point of view of that particular medical task), but at an order of magnitude less computational cost.     

On the relation between the ISRA and the EM algorithm for positron emission tomography

The image space reconstruction algorithm (ISRA) was proposed as a modification of the expectation maximization (EM) algorithm based on physical considerations for application in volume emission computered tomography. As a consequence of this modification, ISRA searches for least squares solutions instead of maximizing Poisson likelihoods as the EM algorithm. It is shown that both algorithms may be obtained from a common mathematical framework. This fact is used to extend ISRA for penalized likelihood estimates.     

Mapping visual field with positron emission tomography bymathematical modeling of the retinotopic organization in the calcarinecortex

We developed an objective and quantitative method of mapping the human visual field with positron emission tomography (PET) and magnetic resonance imaging (MRI). The regional cerebral blood flow (rCBF) images were acquired with H₂¹⁵O-PET under visual fixation as well as under visual stimulation with flickering diodes arranged along the ring at 0°, 3°, 7°, 14°, 21°, or 29° from the fixation point. After coregistration of PET and MR images, we extracted the surface of the calcarine cortex from the MR images and unfolded it to a two-dimensional (2-D) elliptic plane, on which the activated PET images were superimposed. Then we transformed the unfolded calcarine cortex into the visual field coordinates using the complex logarithmic function proposed by Schwartz. A large individual variation was observed in the retinotopical organization as well as in the morphology of the calcarine cortex. The formula was valid only within 15° from the center of the visual field. The constant parameter in the formula was estimated to be 1.5. The cortical linear magnification factor was 12.1, 2.8, and 1.6 at 0, 5, and 10°, respectively. The areas of the central 10° and 40° in the visual field correspond to 50% and 81% of the calcarine surface, respectively