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

Abstract

Due to high noise levels in the voxel kinetics, development of reliable parametric imaging algorithms remains as 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), 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) 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 11C-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 vs. 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 (COV) 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-minute 11C- raclopride patient study performed on the high resolution research tomograph (HRRT) 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 whole-body Patlak parametric imaging for enhanced quantification in clinical PET

“…This common process poses limitations due to the poor characterization of the complex noise distribution in the reconstructed images. On the contrary, direct 4D reconstruction schemes enable kinetic modeling within a comprehensive reconstruction framework, allowing accurate noise characterization directly in the projection-space (Tsoumpas et al 2008, Rahmim et al 2009 and 2012, Tang et al 2010, Wang et al 2010, 2012 and 2013). As such, 4D parametric reconstruction methods could be particularly important for gPatlak, where noise is relatively higher than sPatlak.…”

3.5D dynamic PET image reconstruction incorporating kinetics-based clusters

“…However, this approach tends to require more complex optimization algorithms than conventional methods (Carson and Lange, 1985; Kamasak et al , 2005; Wang and Qi, 2009b). Though closed-form direct 4D parametric imaging algorithms have been developed, they are primarily based on linear graphical models (Wang et al , 2008; Tang et al , 2010; Rahmim et al , 2012). By comparison, while our proposed 3.5D dynamic PET reconstruction does extract and incorporate 4D kinetics information from the overall data, it maintains a straightforward approach to 3D reconstruction of individual frames, and does not require the use of temporal basis functions, complex transforms or sophisticated optimization algorithms.…”

“…For a given plasma input C p (t), the factional plasma volume in tissue V p , and the four standard rate parameters K 1 (ml/min/g), k 2 (1/min), k 3 (1/min) and k 4 (1/min), the measured total radioactivity C(t) is given by (Bentourkia and Zaidi, 2007): $$C(t)=\frac{K_1}{{\alpha }_2-{\alpha }_1}[(k_3+k_4-{\alpha }_1)e^{-{\alpha }_{1}t}+({\alpha }_2-k_3-k_4)e^{-{\alpha }_{2}t}]*C^p(t)+V^p{C}^p(t)$$ where * denotes the convolution operation, and $$\raisebox{1ex}{${\alpha }_{1,2}=[k_2+k_3+k_4\mp \sqrt{{(k_2+k_3+k_4)}^2-4k_2{k}_4}]$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$$ For our simulations, we used 55 11 C-raclopride dynamic PET human scans, from which K 1 , k 2 , k 3 and k 4 rate constants were estimated for multiple regions across the brain for each study (V p was set to 0.03), as elaborated by Rahmim et al (2012). The estimated parameters were then employed within equation (16) to generate a set of dynamic images using a mathematical brain phantom (Rahmim et al , 2008).…”

Bias Reduction for Low-Statistics PET: Maximum Likelihood Reconstruction With a Modified Poisson Distribution

“…It is based on a well chosen combination of KL distances [9] such that when applying the natural constraints of MLEM, A = 0 and B = ∞, minimizing the KL cost function is equivalent to maximizing the Poisson likelihood. By setting A to negative values, negative values in the image and sinogram domain are allowed, resulting in bias reduction behavior [10]–[12]. The convergence of different regions is still dependent on the activity but to a lesser extent.…”