Denoising non-steady state dynamic PET data using a feed-forward neural network.

The quality of reconstructed dynamic PET images, as well as the statistical reliability of the estimated pharmacokinetic parameters is often compromised by high levels of statistical noise, particularly at the voxel level. Many denoising strategies have been proposed, both in the temporal and spatial domain, which substantially improve the signal to noise ratio of the reconstructed dynamic images. However, although most filtering approaches are fairly successful in reducing the spatio-temporal inter-voxel variability, they may also average out or completely eradicate the critically important temporal signature of a transient neurotransmitter activation response that may be present in a non-steady state dynamic PET study. In this work, we explore an approach towards temporal denoising of non-steady state dynamic PET images using an artificial neural network, which was trained to identify the temporal profile of a time-activity curve, while preserving any potential activation response. We evaluated the performance of a feed-forward perceptron neural network to improve the signal to noise ratio of dynamic [11C]raclopride activation studies and compared it with the widely used highly constrained back projection (HYPR) filter. Results on both simulated Geant4 Application for Tomographic Emission data of a realistic rat brain phantom and experimental animal data of a freely moving animal study showed that the proposed neural network can efficiently improve the noise characteristics of dynamic data in the temporal domain, while it can lead to a more reliable estimation of voxel-wise activation response in target region. In addition, improvements in signal-to-noise ratio achieved by denoising the dynamic data using the proposed neural network led to improved accuracy and precision of the estimated model parameters of the lp-ntPET model, compared to the HYPR filter. The performance of the proposed denoising approach strongly depends on the amount of noise in the dynamic PET data, with higher noise leading to substantially higher variability in the estimated parameters of the activation response. Overall, the feed-forward network led to a similar performance as the HYPR filter in terms of spatial denoising, but led to notable improvements in terms of temporal denoising, which in turn improved the estimation activation parameters.

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.

Rigid motion correction of dual opposed planar projections in single photon imaging.

Awake and/or freely moving small animal single photon emission imaging allows the continuous study of molecules exhibiting slow kinetics without the need to restrain or anaesthetise the animals. Estimating motion free projections in freely moving small animal planar imaging can be considered as a limited angle tomography problem, except that we wish to estimate the 2D planar projections rather than the 3D volume, where the angular sampling in all three axes depends on the rotational motion of the animal. In this study, we hypothesise that the motion corrected planar projections estimated by reconstructing an estimate of the 3D volume using an iterative motion compensating reconstruction algorithm and integrating it along the projection path, will closely match the true, motion-less, planar distribution regardless of the object motion. We tested this hypothesis for the case of rigid motion using Monte-Carlo simulations and experimental phantom data based on a dual opposed detector system, where object motion was modelled with 6 degrees of freedom. In addition, we investigated the quantitative accuracy of the regional activity extracted from the geometric mean of opposing motion corrected planar projections. Results showed that it is feasible to estimate qualitatively accurate motion-corrected projections for a wide range of motions around all 3 axes. Errors in the geometric mean estimates of regional activity were relatively small and within 10% of expected true values. In addition, quantitative regional errors were dependent on the observed motion, as well as on the surrounding activity of overlapping organs. We conclude that both qualitatively and quantitatively accurate motion-free projections of the tracer distribution in a rigidly moving object can be estimated from dual opposed detectors using a correction approach within an iterative reconstruction framework and we expect this approach can be extended to the case of non-rigid motion.

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.

Attenuation correction for freely moving small animal brain PET studies based on a virtual scanner geometry.

Attenuation correction in positron emission tomography brain imaging of freely moving animals is a very challenging problem since the torso of the animal is often within the field of view and introduces a non negligible attenuating factor that can degrade the quantitative accuracy of the reconstructed images. In the context of unrestrained small animal imaging, estimation of the attenuation correction factors without the need for a transmission scan is highly desirable. An attractive approach that avoids the need for a transmission scan involves the generation of the hull of the animal's head based on the reconstructed motion corrected emission images. However, this approach ignores the attenuation introduced by the animal's torso. In this work, we propose a virtual scanner geometry which moves in synchrony with the animal's head and discriminates between those events that traversed only the animal's head (and therefore can be accurately compensated for attenuation) and those that might have also traversed the animal's torso. For each recorded pose of the animal's head a new virtual scanner geometry is defined and therefore a new system matrix must be calculated leading to a time-varying system matrix. This new approach was evaluated on phantom data acquired on the microPET Focus 220 scanner using a custom-made phantom and step-wise motion. Results showed that when the animal's torso is within the FOV and not appropriately accounted for during attenuation correction it can lead to bias of up to 10% . Attenuation correction was more accurate when the virtual scanner was employed leading to improved quantitative estimates (bias < 2%), without the need to account for the attenuation introduced by the extraneous compartment. Although the proposed method requires increased computational resources, it can provide a reliable approach towards quantitatively accurate attenuation correction for freely moving animal studies.

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.

A custom-built PET phantom design for quantitative imaging of printed distributions.

This note presents a practical approach to a custom-made design of PET phantoms enabling the use of digital radioactive distributions with high quantitative accuracy and spatial resolution. The phantom design allows planar sources of any radioactivity distribution to be imaged in transaxial and axial (sagittal or coronal) planes. Although the design presented here is specially adapted to the high-resolution research tomograph (HRRT), the presented methods can be adapted to almost any PET scanner. Although the presented phantom design has many advantages, a number of practical issues had to be overcome such as positioning of the printed source, calibration, uniformity and reproducibility of printing. A well counter (WC) was used in the calibration procedure to find the nonlinear relationship between digital voxel intensities and the actual measured radioactive concentrations. Repeated printing together with WC measurements and computed radiography (CR) using phosphor imaging plates (IP) were used to evaluate the reproducibility and uniformity of such printing. Results show satisfactory printing uniformity and reproducibility; however, calibration is dependent on the printing mode and the physical state of the cartridge. As a demonstration of the utility of using printed phantoms, the image resolution and quantitative accuracy of reconstructed HRRT images are assessed. There is very good quantitative agreement in the calibration procedure between HRRT, CR and WC measurements. However, the high resolution of CR and its quantitative accuracy supported by WC measurements made it possible to show the degraded resolution of HRRT brain images caused by the partial-volume effect and the limits of iterative image reconstruction.

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.