A Bayesian spatial temporal mixtures approach to kinetic parametric images in dynamic positron emission tomography

Mathematical Models for FDG Kinetics in Cancer: A Review

Compartmental analysis is the mathematical framework for the modelling of tracer kinetics in dynamical Positron Emission Tomography. This paper provides a review of how compartmental models are constructed and numerically optimized. Specific focus is given on the identifiability and sensitivity issues and on the impact of complex physiological conditions on the mathematical properties of the models.

Kernel-based curve-fitting method with spatial regularization for generation of parametric images in dynamic PET

Due to high levels of noise in pixel-wise time-activity curves, the indirect method that generates kinetic parametric images from dynamic positron emission tomography (PET) images often results in poor parametric image quality. We have demonstrated that the quality of parametric images can be improved by denoising dynamic PET images, using gradient-free curve-fitting and applying a kernel-based post-filtering to parametric images. However, many gradient-free curve-fitting methods are time-consuming. Moreover, some parameter estimates (e.g. k₂ and k₃) have large variability. To provide high-quality PET parametric images with low computational cost, we propose a curve-fitting method that incorporates the kernel-based denoising method and the highly constrained backprojection technique into the Levenberg-Marquardt (LM) algorithm. We conducted a simulation study to evaluate the performance of the proposed curve-fitting method. Dynamic PET images were reconstructed using the expectation-maximization (EM) algorithm and were denoised before parameter estimation. Compared to the LM algorithm with and without the kernel-based post-filtering, the proposed method achieved superior performance, offering a decrease in both bias and coefficient of variation (CV) on all parametric images. Overall, the proposed method exhibited lower bias and slightly higher CV than the gradient-free pattern search method with the kernel-based post-filtering (PatS-K). Moreover, the computation time of the proposed method was about 18 times lower than that of the PatS-K method. Finally, we show that the proposed method can further improve the quality of parametric images when dynamic PET images are reconstructed using the kernel-based EM algorithm.

Spatial and spatio-temporal statistical analyses of retinal images: a review of methods and applications

Background

Clinical research and management of retinal diseases greatly depend on the interpretation of retinal images and often longitudinally collected images. Retinal images provide context for spatial data, namely the location of specific pathologies within the retina. Longitudinally collected images can show how clinical events at one point can affect the retina over time. In this review, we aimed to assess statistical approaches to spatial and spatio-temporal data in retinal images. We also review the spatio-temporal modelling approaches used in other medical image types.

Methods

We conducted a comprehensive literature review of both spatial or spatio-temporal approaches and non-spatial approaches to the statistical analysis of retinal images. The key methodological and clinical characteristics of published papers were extracted. We also investigated whether clinical variables and spatial correlation were accounted for in the analysis.

Results

Thirty-four papers that included retinal imaging data were identified for full-text information extraction. Only 11 (32.4%) papers used spatial or spatio-temporal statistical methods to analyse images, others (23 papers, 67.6%) used non-spatial methods. Twenty-eight (82.4%) papers reported images collected cross-sectionally, while 6 (17.6%) papers reported analyses on images collected longitudinally. In imaging areas outside of ophthalmology, 19 papers were identified with spatio-temporal analysis, and multiple statistical methods were recorded.

Conclusions

In future statistical analyses of retinal images, it will be beneficial to clearly define and report the spatial distributions studied, report the spatial correlations, combine imaging data with clinical variables into analysis if available, and clearly state the software or packages used.

Efficient DCE-MRI Parameter and Uncertainty Estimation Using a Neural Network

Quantitative DCE-MRI provides voxel-wise estimates of tracer-kinetic parameters that are valuable in the assessment of health and disease. These maps suffer from many known sources of variability. This variability is expensive to compute using current methods, and is typically not reported. Here, we demonstrate a novel approach for simultaneous estimation of tracer-kinetic parameters and their uncertainty due to intrinsic characteristics of the tracer-kinetic model, with very low computation time. We train and use a neural network to estimate the approximate joint posterior distribution of tracer-kinetic parameters. Uncertainties are estimated for each voxel and are specific to the patient, exam, and lesion. We demonstrate the methods' ability to produce accurate tracer-kinetic maps. We compare predicted parameter ranges with uncertainties introduced by noise and by differences in post-processing in a digital reference object. The predicted parameter ranges correlate well with tracer-kinetic parameter ranges observed across different noise realizations and regression algorithms. We also demonstrate the value of this approach to differentiate significant from insignificant changes in brain tumor pharmacokinetics over time. This is achieved by enforcing consistency in resolving model singularities in the applied tracer-kinetic model.

Direct 4D PET reconstruction with discrete tissue types

Dynamic positron emission tomography (dPET) is known for its ability to extract spatiotemporal information of a radio tracer in living tissue. In this paper, a novel direct reconstruction framework is presented, which include concurrent clustering as a potential aid in addressing high levels of noise typical of voxel-wise kinetic modeling. Core assumption is that the imaged volume is formed by a finite number of different functional regions, and that voxel-wise time courses are determined by the functional cluster they belong to. Probabilistic Graphical Modeling (PGM) theory is used to describe the problem, and to derive the inference strategy. The proposed iterative estimation scheme provides concurrent estimate of kinetic parameter maps, activity images, and segmented clusters. Simulation studies and exploratory application to real data are performed to validate the proposal.

Comparison of five cluster validity indices performance in brain [18 F]FET-PET image segmentation using k-means

PURPOSE

Dynamic [¹⁸ F]fluoro-ethyl-L-tyrosine positron emission tomography ([¹⁸ F]FET-PET) is used to identify tumor lesions for radiotherapy treatment planning, to differentiate glioma recurrence from radiation necrosis and to classify gliomas grading. To segment different regions in the brain k-means cluster analysis can be used. The main disadvantage of k-means is that the number of clusters must be pre-defined. In this study, we therefore compared different cluster validity indices for automated and reproducible determination of the optimal number of clusters based on the dynamic PET data.

METHODS

The k-means algorithm was applied to dynamic [¹⁸ F]FET-PET images of 8 patients. Akaike information criterion (AIC), WB, I, modified Dunn's and Silhouette indices were compared on their ability to determine the optimal number of clusters based on requirements for an adequate cluster validity index. To check the reproducibility of k-means, the coefficients of variation CVs of the objective function values OFVs (sum of squared Euclidean distances within each cluster) were calculated using 100 random centroid initialization replications RCI₁₀₀ for 2 to 50 clusters. k-means was performed independently on three neighboring slices containing tumor for each patient to investigate the stability of the optimal number of clusters within them. To check the independence of the validity indices on the number of voxels, cluster analysis was applied after duplication of a slice selected from each patient. CVs of index values were calculated at the optimal number of clusters using RCI₁₀₀ to investigate the reproducibility of the validity indices. To check if the indices have a single extremum, visual inspection was performed on the replication with minimum OFV from RCI₁₀₀ .

RESULTS

The maximum CV of OFVs was 2.7 × 10^-2 from all patients. The optimal number of clusters given by modified Dunn's and Silhouette indices was 2 or 3 leading to a very poor segmentation. WB and I indices suggested in median 5, [range 4-6] and 4, [range 3-6] clusters, respectively. For WB, I, modified Dunn's and Silhouette validity indices the suggested optimal number of clusters was not affected by the number of the voxels. The maximum coefficient of variation of WB, I, modified Dunn's, and Silhouette validity indices were 3 × 10^-2 , 1, 2 × 10^-1 and 3 × 10^-3 , respectively. WB-index showed a single global maximum, whereas the other indices showed also local extrema.

CONCLUSION

From the investigated cluster validity indices, the WB-index is best suited for automated determination of the optimal number of clusters for [¹⁸ F]FET-PET brain images for the investigated image reconstruction algorithm and the used scanner: it yields meaningful results allowing better differentiation of tissues with higher number of clusters, it is simple, reproducible and has an unique global minimum.