Robustness of post-reconstruction and direct kinetic parameter estimates under rigid head motion in dynamic brain PET imaging.

OBJECTIVE: Dynamic PET imaging is extensively used in brain imaging to estimate parametric maps. Inter-frame motion can substantially disrupt the voxel-wise time-activity curves (TACs), leading to erroneous maps during kinetic modelling. Therefore, it is important to characterize the robustness of kinetic parameters under various motion and kinetic model related factors. METHODS: Fully 4D brain simulations ([15O]H2O and [18F]FDG dynamic datasets) were performed using a variety of clinically observed motion patterns. Increasing levels of head motion were investigated as well as varying temporal frames of motion initiation. Kinetic parameter estimation was performed using both post-reconstruction kinetic analysis and direct 4D image reconstruction to assess bias from inter-frame emission blurring and emission/attenuation mismatch. RESULTS: Kinetic parameter bias heavily depends on the time point of motion initiation. Motion initiated towards the end of the scan results in the most biased parameters. For the [18F]FDG data, k4 is the more sensitive parameter to positional changes, while K1 and blood volume were proven to be relatively robust to motion. Direct 4D image reconstruction appeared more sensitive to changes in TACs due to motion, with parameter bias spatially propagating and depending on the level of motion. CONCLUSION: Kinetic parameter bias highly depends upon the time frame at which motion occurred, with late frame motion-induced TAC discontinuities resulting in the least accurate parameters. This is of importance during prolonged data acquisition as is often the case in neuro-receptor imaging studies. In the absence of a motion correction, use of TOF information within 4D image reconstruction could limit the error propagation.

Impact of time-of-flight on indirect 3D and direct 4D parametric image reconstruction in the presence of inconsistent dynamic PET data.

Kinetic parameter estimation in dynamic PET suffers from reduced accuracy and precision when parametric maps are estimated using kinetic modelling following image reconstruction of the dynamic data. Direct approaches to parameter estimation attempt to directly estimate the kinetic parameters from the measured dynamic data within a unified framework. Such image reconstruction methods have been shown to generate parametric maps of improved precision and accuracy in dynamic PET. However, due to the interleaving between the tomographic and kinetic modelling steps, any tomographic or kinetic modelling errors in certain regions or frames, tend to spatially or temporally propagate. This results in biased kinetic parameters and thus limits the benefits of such direct methods. Kinetic modelling errors originate from the inability to construct a common single kinetic model for the entire field-of-view, and such errors in erroneously modelled regions could spatially propagate. Adaptive models have been used within 4D image reconstruction to mitigate the problem, though they are complex and difficult to optimize. Tomographic errors in dynamic imaging on the other hand, can originate from involuntary patient motion between dynamic frames, as well as from emission/transmission mismatch. Motion correction schemes can be used, however, if residual errors exist or motion correction is not included in the study protocol, errors in the affected dynamic frames could potentially propagate either temporally, to other frames during the kinetic modelling step or spatially, during the tomographic step. In this work, we demonstrate a new strategy to minimize such error propagation in direct 4D image reconstruction, focusing on the tomographic step rather than the kinetic modelling step, by incorporating time-of-flight (TOF) within a direct 4D reconstruction framework. Using ever improving TOF resolutions (580 ps, 440 ps, 300 ps and 160 ps), we demonstrate that direct 4D TOF image reconstruction can substantially prevent kinetic parameter error propagation either from erroneous kinetic modelling, inter-frame motion or emission/transmission mismatch. Furthermore, we demonstrate the benefits of TOF in parameter estimation when conventional post-reconstruction (3D) methods are used and compare the potential improvements to direct 4D methods. Further improvements could possibly be achieved in the future by combining TOF direct 4D image reconstruction with adaptive kinetic models and inter-frame motion correction schemes.

Application of adaptive kinetic modelling for bias propagation reduction in direct 4D image reconstruction.

Parametric imaging in thoracic and abdominal PET can provide additional parameters more relevant to the pathophysiology of the system under study. However, dynamic data in the body are noisy due to the limiting counting statistics leading to suboptimal kinetic parameter estimates. Direct 4D image reconstruction algorithms can potentially improve kinetic parameter precision and accuracy in dynamic PET body imaging. However, construction of a common kinetic model is not always feasible and in contrast to post-reconstruction kinetic analysis, errors in poorly modelled regions may spatially propagate to regions which are well modelled. To reduce error propagation from erroneous model fits, we implement and evaluate a new approach to direct parameter estimation by incorporating a recently proposed kinetic modelling strategy within a direct 4D image reconstruction framework. The algorithm uses a secondary more general model to allow a less constrained model fit in regions where the kinetic model does not accurately describe the underlying kinetics. A portion of the residuals then is adaptively included back into the image whilst preserving the primary model characteristics in other well modelled regions using a penalty term that trades off the models. Using fully 4D simulations based on dynamic [(15)O]H2O datasets, we demonstrate reduction in propagation-related bias for all kinetic parameters. Under noisy conditions, reductions in bias due to propagation are obtained at the cost of increased noise, which in turn results in increased bias and variance of the kinetic parameters. This trade-off reflects the challenge of separating the residuals arising from poor kinetic modelling fits from the residuals arising purely from noise. Nonetheless, the overall root mean square error is reduced in most regions and parameters. Using the adaptive 4D image reconstruction improved model fits can be obtained in poorly modelled regions, leading to reduced errors potentially propagating to regions of interest which the primary biologic model accurately describes. The proposed methodology, however, depends on the secondary model and choosing an optimal model on the residual space is critical in improving model fits.

Acceleration of image-based resolution modelling reconstruction using an expectation maximization nested algorithm.

Recent studies have demonstrated the benefits of a resolution model within iterative reconstruction algorithms in an attempt to account for effects that degrade the spatial resolution of the reconstructed images. However, these algorithms suffer from slower convergence rates, compared to algorithms where no resolution model is used, due to the additional need to solve an image deconvolution problem. In this paper, a recently proposed algorithm, which decouples the tomographic and image deconvolution problems within an image-based expectation maximization (EM) framework, was evaluated. This separation is convenient, because more computational effort can be placed on the image deconvolution problem and therefore accelerate convergence. Since the computational cost of solving the image deconvolution problem is relatively small, multiple image-based EM iterations do not significantly increase the overall reconstruction time. The proposed algorithm was evaluated using 2D simulations, as well as measured 3D data acquired on the high-resolution research tomograph. Results showed that bias reduction can be accelerated by interleaving multiple iterations of the image-based EM algorithm solving the resolution model problem, with a single EM iteration solving the tomographic problem. Significant improvements were observed particularly for voxels that were located on the boundaries between regions of high contrast within the object being imaged and for small regions of interest, where resolution recovery is usually more challenging. Minor differences were observed using the proposed nested algorithm, compared to the single iteration normally performed, when an optimal number of iterations are performed for each algorithm. However, using the proposed nested approach convergence is significantly accelerated enabling reconstruction using far fewer tomographic iterations (up to 70% fewer iterations for small regions). Nevertheless, the optimal number of nested image-based EM iterations is hard to be defined and it should be selected according to the given application.

The performance of monotonic and new non-monotonic gradient ascent reconstruction algorithms for high-resolution neuroreceptor PET imaging.

Iterative expectation maximization (EM) techniques have been extensively used to solve maximum likelihood (ML) problems in positron emission tomography (PET) image reconstruction. Although EM methods offer a robust approach to solving ML problems, they usually suffer from slow convergence rates. The ordered subsets EM (OSEM) algorithm provides significant improvements in the convergence rate, but it can cycle between estimates converging towards the ML solution of each subset. In contrast, gradient-based methods, such as the recently proposed non-monotonic maximum likelihood (NMML) and the more established preconditioned conjugate gradient (PCG), offer a globally convergent, yet equally fast, alternative to OSEM. Reported results showed that NMML provides faster convergence compared to OSEM; however, it has never been compared to other fast gradient-based methods, like PCG. Therefore, in this work we evaluate the performance of two gradient-based methods (NMML and PCG) and investigate their potential as an alternative to the fast and widely used OSEM. All algorithms were evaluated using 2D simulations, as well as a single [(11)C]DASB clinical brain dataset. Results on simulated 2D data show that both PCG and NMML achieve orders of magnitude faster convergence to the ML solution compared to MLEM and exhibit comparable performance to OSEM. Equally fast performance is observed between OSEM and PCG for clinical 3D data, but NMML seems to perform poorly. However, with the addition of a preconditioner term to the gradient direction, the convergence behaviour of NMML can be substantially improved. Although PCG is a fast convergent algorithm, the use of a (bent) line search increases the complexity of the implementation, as well as the computational time involved per iteration. Contrary to previous reports, NMML offers no clear advantage over OSEM or PCG, for noisy PET data. Therefore, we conclude that there is little evidence to replace OSEM as the algorithm of choice for many applications, especially given that in practice convergence is often not desired for algorithms seeking ML estimates.

Single scan parameterization of space-variant point spread functions in image space via a printed array: the impact for two PET/CT scanners.

Incorporation of a resolution model during statistical image reconstruction often produces images of improved resolution and signal-to-noise ratio. A novel and practical methodology to rapidly and accurately determine the overall emission and detection blurring component of the system matrix using a printed point source array within a custom-made Perspex phantom is presented. The array was scanned at different positions and orientations within the field of view (FOV) to examine the feasibility of extrapolating the measured point source blurring to other locations in the FOV and the robustness of measurements from a single point source array scan. We measured the spatially-variant image-based blurring on two PET/CT scanners, the B-Hi-Rez and the TruePoint TrueV. These measured spatially-variant kernels and the spatially-invariant kernel at the FOV centre were then incorporated within an ordinary Poisson ordered subset expectation maximization (OP-OSEM) algorithm and compared to the manufacturer's implementation using projection space resolution modelling (RM). Comparisons were based on a point source array, the NEMA IEC image quality phantom, the Cologne resolution phantom and two clinical studies (carbon-11 labelled anti-sense oligonucleotide [(11)C]-ASO and fluorine-18 labelled fluoro-l-thymidine [(18)F]-FLT). Robust and accurate measurements of spatially-variant image blurring were successfully obtained from a single scan. Spatially-variant resolution modelling resulted in notable resolution improvements away from the centre of the FOV. Comparison between spatially-variant image-space methods and the projection-space approach (the first such report, using a range of studies) demonstrated very similar performance with our image-based implementation producing slightly better contrast recovery (CR) for the same level of image roughness (IR). These results demonstrate that image-based resolution modelling within reconstruction is a valid alternative to projection-based modelling, and that, when using the proposed practical methodology, the necessary resolution measurements can be obtained from a single scan. This approach avoids the relatively time-consuming and involved procedures previously proposed in the literature.