Direct 4D List Mode Parametric Reconstruction for PET with a Novel EM Algorithm

Direct estimation of kinetic parametric images for dynamic PET

Dynamic positron emission tomography (PET) can monitor spatiotemporal distribution of radiotracer in vivo. The spatiotemporal information can be used to estimate parametric images of radiotracer kinetics that are of physiological and biochemical interests. Direct estimation of parametric images from raw projection data allows accurate noise modeling and has been shown to offer better image quality than conventional indirect methods, which reconstruct a sequence of PET images first and then perform tracer kinetic modeling pixel-by-pixel. Direct reconstruction of parametric images has gained increasing interests with the advances in computing hardware. Many direct reconstruction algorithms have been developed for different kinetic models. In this paper we review the recent progress in the development of direct reconstruction algorithms for parametric image estimation. Algorithms for linear and nonlinear kinetic models are described and their properties are discussed.

Direct 4-D PET list mode parametric reconstruction with a novel EM algorithm

The production of images of kinetic parameters is often the ultimate goal of positron emission tomography (PET) imaging. The indirect method of PET parametric imaging, also called the frame-based method (FM), is performed by fitting the time-activity curve (TAC) for each voxel with an appropriate compartment model after image reconstruction. The indirect method is simple and easily implemented, however, it usually leads to some loss of accuracy or precision, due to the use of two separate steps. This paper presents a direct 4-D method for producing 3-D images of kinetic parameters from list mode PET data. In this application, the TAC for each voxel is described by a one-tissue compartment model (1T). Extending previous EM algorithms, a new spatiotemporal complete data space was introduced to optimize the maximum likelihood function. This leads to a straightforward closed-form parametric image update equation. This method was implemented by extending the current list mode platform MOLAR to produce a parametric algorithm PMOLAR-1T. Using an ordered subset approach, qualitative and quantitative evaluations were performed using 2-D (x, t) and 4-D (x, y, z, t) simulated list mode data based on brain receptor tracers and also with a human brain study. Comparisons with the indirect method showed that the proposed direct method can lead to accurate estimation of the parametric image values with reduced variance, especially at low count levels. In the 2-D test, the direct method showed similar bias to the frame-based method but with variance reduction of 23%-60%. In the 4-D test, bias values of both methods were no more than 4% and the direct method had lower variability (coefficient of variation reduction of 0%-64% compared to the frame-based method) at the normal count level. The direct method had a larger reduction in variability (27%-81%) and lower bias (1%-5% for 4-D and 1%-19% for FM) at low count levels. The results in the human brain study are similar with PMOLAR-1T showing lower noise than FM.

Advances in 4D radiation therapy for managing respiration: part I - 4D imaging

Techniques for managing respiration during imaging and planning of radiation therapy are reviewed, concentrating on free-breathing (4D) approaches. First, we focus on detailing the historical development and basic operational principles of currently-available "first generation" 4D imaging modalities: 4D computed tomography, 4D cone beam computed tomography, 4D magnetic resonance imaging, and 4D positron emission tomography. Features and limitations of these first generation systems are described, including necessity of breathing surrogates for 4D image reconstruction, assumptions made in acquisition and reconstruction about the breathing pattern, and commonly-observed artifacts. Both established and developmental methods to deal with these limitations are detailed. Finally, strategies to construct 4D targets and images and, alternatively, to compress 4D information into static targets and images for radiation therapy planning are described.

An optimization transfer algorithm for nonlinear parametric image reconstruction from dynamic PET data

Direct reconstruction of kinetic parameters from raw projection data is a challenging task in molecular imaging using dynamic positron emission tomography (PET). This paper presents a new optimization transfer algorithm for penalized likelihood direct reconstruction of nonlinear parametric images that is easy to use and has a fast convergence rate. Each iteration of the proposed algorithm can be implemented in three simple steps: a frame-by-frame maximum likelihood expectation-maximization (EM)-like image update, a frame-by-frame image smoothing, and a pixel-by-pixel time activity curve fitting. Computer simulation shows that the direct algorithm can achieve a better bias-variance performance than the indirect reconstruction algorithm. The convergence rate of the new algorithm is substantially faster than our previous algorithm that is based on a separable paraboloidal surrogate function. The proposed algorithm has been applied to real 4-D PET data.

Direct 4D parametric imaging for linearized models of reversibly binding PET tracers using generalized AB-EM reconstruction

Due to high noise levels in the voxel kinetics, development of reliable parametric imaging algorithms remains one of most active areas in dynamic brain PET imaging, which in the vast majority of cases involves receptor/transporter studies with reversibly binding tracers. As such, the focus of this work has been to develop a novel direct 4D parametric image reconstruction scheme for such tracers. Based on a relative equilibrium (RE) graphical analysis formulation (Zhou et al 2009b Neuroimage 44 661-70), we developed a closed-form 4D EM algorithm to directly reconstruct distribution volume (DV) parametric images within a plasma input model, as well as DV ratio (DVR) images within a reference tissue model scheme (wherein an initial reconstruction was used to estimate the reference tissue time-activity curves). A particular challenge with the direct 4D EM formulation is that the intercept parameters in graphical (linearized) analysis of reversible tracers (e.g. Logan or RE analysis) are commonly negative (unlike for irreversible tracers, e.g. using Patlak analysis). Subsequently, we focused our attention on the AB-EM algorithm, derived by Byrne (1998, Inverse Problems 14 1455-67) to allow inclusion of prior information about the lower (A) and upper (B) bounds for image values. We then generalized this algorithm to the 4D EM framework, thus allowing negative intercept parameters. Furthermore, our 4D AB-EM algorithm incorporated and emphasized the use of spatially varying lower bounds to achieve enhanced performance. As validation, the means of parameters estimated from 55 human (11)C-raclopride dynamic PET studies were used for extensive simulations using a mathematical brain phantom. Images were reconstructed using conventional indirect as well as proposed direct parametric imaging methods. Noise versus bias quantitative measurements were performed in various regions of the brain. Direct 4D EM reconstruction resulted in notable qualitative and quantitative accuracy improvements (over 35% noise reduction, with matched bias, in both plasma and reference-tissue input models). Similar improvements were also observed in the coefficient of variation of the estimated DV and DVR values even for relatively low uptake cortical regions, suggesting the enhanced ability for robust parameter estimation. The method was also tested on a 90 min (11)C-raclopride patient study performed on the high-resolution research tomograph wherein the proposed method was shown across a variety of regions to outperform the conventional method in the sense that for a given DVR value, improved noise levels were observed.

Generalized algorithms for direct reconstruction of parametric images from dynamic PET data

Indirect and direct methods have been developed for reconstructing parametric images from dynamic positron emission tomography (PET) data. Indirect methods are simple and easy to implement because reconstruction and kinetic modeling are performed in two separate steps. Direct methods estimate parametric images directly from dynamic PET sinograms and, in theory, can be statistically more efficient, but the algorithms are often difficult to implement and are very specific to the kinetic model being used. This paper presents a class of generalized algorithms for direct reconstruction of parametric images that are relatively easy to implement and can be adapted to different kinetic models. The proposed algorithms use optimization transfer principle to convert the maximization of a penalized likelihood into a pixel-wise weighted least squares (WLS) kinetic fitting problem at each iteration. Thus, it can employ existing WLS algorithms developed for kinetic models. The proposed algorithms resemble the empirical iterative implementation of the indirect approach, but converge to a solution of the direct formulation. Computer simulations showed that the proposed direct reconstruction algorithms are flexible and achieve a better bias-variance tradeoff than indirect reconstruction methods.

DIRECT RECONSTRUCTION OF DYNAMIC PET PARAMETRIC IMAGES USING SPARSE SPECTRAL REPRESENTATION

To generate parametric images for dynamic PET, direct reconstruction from projection data is statistically more efficient than conventional indirect methods that perform image reconstruction and kinetic modeling in two separate steps. Existing direct reconstruction methods often use nonlinear compartmental models, which require the knowledge of model order. This paper presents a direct reconstruction approach using a linear spectral representation and does not require model order assumption. A Laplacian prior is used to ensure sparsity in the spectral representation. The resultant maximum a posteriori (MAP) formulation is solved by an expectation maximization shrinkage algorithm. A bias correction step is developed to improve the MAP estimate. Computer simulations show that the proposed method achieves better bias-variance tradeoff than a conventional indirect method for estimating parametric images from dynamic PET data.