Direct reconstruction of kinetic parameter images from dynamic PET data

Abstract

Our goal in this paper is the estimation of kinetic model parameters for each voxel corresponding to a dense three-dimensional (3-D) positron emission tomography (PET) image. Typically, the activity images are first reconstructed from PET sinogram frames at each measurement time, and then the kinetic parameters are estimated by fitting a model to the reconstructed time-activity response of each voxel. However, this "indirect" approach to kinetic parameter estimation tends to reduce signal-to-noise ratio (SNR) because of the requirement that the sinogram data be divided into individual time frames. In 1985, Carson and Lange proposed, but did not implement, a method based on the expectation-maximization (EM) algorithm for direct parametric reconstruction. The approach is "direct" because it estimates the optimal kinetic parameters directly from the sinogram data, without an intermediate reconstruction step. However, direct voxel-wise parametric reconstruction remained a challenge due to the unsolved complexities of inversion and spatial regularization. In this paper, we demonstrate and evaluate a new and efficient method for direct voxel-wise reconstruction of kinetic parameter images using all frames of the PET data. The direct parametric image reconstruction is formulated in a Bayesian framework, and uses the parametric iterative coordinate descent (PICD) algorithm to solve the resulting optimization problem. The PICD algorithm is computationally efficient and is implemented with spatial regularization in the domain of the physiologically relevant parameters. Our experimental simulations of a rat head imaged in a working small animal scanner indicate that direct parametric reconstruction can substantially reduce root-mean-squared error (RMSE) in the estimation of kinetic parameters, as compared to indirect methods, without appreciably increasing computation.

Evaluation of a direct 4D reconstruction method using generalised linear least squares for estimating nonlinear micro-parametric maps

“…Parametric image reconstruction, based on a two-tissue compartment model, is a rather challenging and computationally intensive task, when all individual kinetic parameters are to be estimated [21,22,40]. Often, nonlinear optimisation procedures are employed to estimate these micro-parameters, which are rather impractical in a voxelby-voxel estimation scenario, since they lead to overall very long reconstruction times.…”

“…This problem has been previously solved, for nonlinear two-tissue compartment models, using approaches including iterative coordinate ascent [21] and optimisation transfer [22]. Recently, Matthews et al [23] proposed a generalised spatiotemporal image reconstruction algorithm, which is a direct implementation of the EM algorithm [27].…”

“…However, an initial estimate that is closer to the global optimum (i.e. FBP reconstruction) would not only provide faster convergence [18,19,21], but also would allow the algorithm to avoid being trapped in a local optimum. In addition, because the truth is not known for clinical data, the direct and post-reconstruction parametric maps were also compared, on a region of interest (ROI) basis, to a regularly used and well-established method.…”

“…a mixture of exponentials). These approaches allow the estimation of individual kinetic parameters, but due to the coupling between the reconstruction and the nonlinear parameter estimation, they tend to be computationally impractical, forcing Kamasak et al [21] to employ a multi-resolution grid technique to accelerate convergence. On the other hand, Wang and Qi [22] proposed a generalised reconstruction method, based on the optimisation transfer framework, to decouple the reconstruction problem from the nonlinear kinetic fitting, allowing well-established least squares optimisation procedures to be used.…”

A Variational Bayesian inference method for parametric imaging of PET data

“…Prior information could also be included in hybrid approaches that combine reconstruction and kinetic modelling (Kamasak et al, 2005). Moreover, it is possible to incorporate structural and anatomical information obtained from magnetic resonance imaging (Loeb et al, 2015;Tang et al, 2010).…”