Fast formation of statistically reliable FDG parametric images based on clustering and principal components

Segmentation of Dynamic Total-Body [18F]-FDG PET Images Using Unsupervised Clustering

Clustering time activity curves of PET images have been used to separate clinically relevant areas of the brain or tumours. However, PET image segmentation in multiorgan level is much less studied due to the available total-body data being limited to animal studies. Now, the new PET scanners providing the opportunity to acquire total-body PET scans also from humans are becoming more common, which opens plenty of new clinically interesting opportunities. Therefore, organ-level segmentation of PET images has important applications, yet it lacks sufficient research. In this proof of concept study, we evaluate if the previously used segmentation approaches are suitable for segmenting dynamic human total-body PET images in organ level. Our focus is on general-purpose unsupervised methods that are independent of external data and can be used for all tracers, organisms, and health conditions. Additional anatomical image modalities, such as CT or MRI, are not used, but the segmentation is done purely based on the dynamic PET images. The tested methods are commonly used building blocks of the more sophisticated methods rather than final methods as such, and our goal is to evaluate if these basic tools are suited for the arising human total-body PET image segmentation. First, we excluded methods that were computationally too demanding for the large datasets from human total-body PET scanners. These criteria filtered out most of the commonly used approaches, leaving only two clustering methods, k-means and Gaussian mixture model (GMM), for further analyses. We combined k-means with two different preprocessing approaches, namely, principal component analysis (PCA) and independent component analysis (ICA). Then, we selected a suitable number of clusters using 10 images. Finally, we tested how well the usable approaches segment the remaining PET images in organ level, highlight the best approaches together with their limitations, and discuss how further research could tackle the observed shortcomings. In this study, we utilised 40 total-body [18F] fluorodeoxyglucose PET images of rats to mimic the coming large human PET images and a few actual human total-body images to ensure that our conclusions from the rat data generalise to the human data. Our results show that ICA combined with k-means has weaker performance than the other two computationally usable approaches and that certain organs are easier to segment than others. While GMM performed sufficiently, it was by far the slowest one among the tested approaches, making k-means combined with PCA the most promising candidate for further development. However, even with the best methods, the mean Jaccard index was slightly below 0.5 for the easiest tested organ and below 0.2 for the most challenging organ. Thus, we conclude that there is a lack of accurate and computationally light general-purpose segmentation method that can analyse dynamic total-body PET images.

SLICR super-voxel algorithm for fast, robust quantification of myocardial blood flow by dynamic computed tomography myocardial perfusion imaging

We created and evaluated a processing method for dynamic computed tomography myocardial perfusion imaging (CT-MPI) of myocardial blood flow (MBF), which combines a modified simple linear iterative clustering algorithm (SLIC) with robust perfusion quantification, hence the name SLICR. SLICR adaptively segments the myocardium into nonuniform super-voxels with similar perfusion time attenuation curves (TACs). Within each super-voxel, an α-trimmed-median TAC was computed to robustly represent the super-voxel and a robust physiological model (RPM) was implemented to semi-analytically estimate MBF. SLICR processing was compared with another voxel-wise MBF preprocessing approach, which included a spatiotemporal bilateral filter (STBF) for noise reduction prior to perfusion quantification. Image data from a digital CT-MPI phantom and a porcine ischemia model were evaluated. SLICR was ∼ 50 -fold faster than voxel-wise RPM and other model-based methods while retaining sufficient resolution to show clinically relevant features, such as a transmural perfusion gradient. SLICR showed markedly improved accuracy and precision, as compared with other methods. At a simulated MBF of 100 mL/min-100 g and a tube current-time product of 100 mAs (50% of nominal), the MBF estimates were 101 ± 12 , 94 ± 56 , and 54 ± 24    mL / min - 100    g for SLICR, the voxel-wise Johnson-Wilson model, and a singular value decomposition-model independent method with STBF, respectively. SLICR estimated MBF precisely and accurately ( 103 ± 23    mL / min - 100    g ) at 25% nominal dose, while other methods resulted in larger errors. With the porcine model, the SLICR results were consistent with the induced ischemia. SLICR simultaneously accelerated and improved the quality of quantitative perfusion processing without compromising clinically relevant distributions of perfusion characteristics.

SLIC robust (SLICR) processing for fast, robust CT myocardial blood flow quantification

There are several computational methods for estimating myocardial blood flow (MBF) using CT myocardial perfusion imaging (CT-MPI). Previous work has shown that model-based deconvolution methods are more accurate and precise than model-independent methods such as singular value decomposition and max-upslope. However, iterative optimization is computationally expensive and models are sensitive to image noise, thus limiting the utility of low x-ray dose acquisitions. We propose a new processing method, SLICR, which segments the myocardium into super-voxels using a modified simple linear iterative clustering (SLIC) algorithm and quantifies MBF via a robust physiologic model (RPM). We compared SLICR against voxel-wise SVD and voxel-wise model-based deconvolution methods (RPM, single-compartment and Johnson-Wilson). We used image data from a digital CT-MPI phantom to evaluate robustness of processing methods to noise at reduced x-ray dose. We validate SLICR in a porcine model with and without partial occlusion of the LAD coronary artery with known pressure-wire fractional flow reserve. SLICR was ~50 times faster than voxel-wise RPM and other model-based methods while retaining sufficient resolution to show all clinically interesting features (e.g., a flow deficit in the endocardial wall). SLICR showed much better precision and accuracy than the other methods. For example, at simulated MBF=100 mL/min/100g and 100 mAs exposure (50% of nominal dose) in the digital simulator, MBF estimates were 101 ± 12 mL/min/100g, 160 ± 54 mL/min/100g, and 122 ± 99 mL/min/100g for SLICR, SVD, and Johnson-Wilson, respectively. SLICR even gave excellent results (103 ± 23 ml/min/100g) at 50 mAs, corresponding to 25% nominal dose.

Fully parametric imaging with reversible tracer 18F-FLT within a reasonable time

PET enables quantitative imaging of the rate constants K ₁, k ₂, k ₃, and k ₄, with a reversible two tissue compartment model (2TCM). A new method is proposed for computing all of these rates within a reasonable time, less than 1 min. A set of differential equations for the reversible 2TCM was converted into a single formula consisting of differential and convolution terms. The validity was tested on clinical data with ¹⁸F-FLT PET for patients with glioma (n = 39). Parametric images were generated with the formula that was developed. Parametric values were extracted from regions of interest (ROIs) for glioma from the images generated, and they were compared with those obtained with the non-linear fitting method. We performed simulation studies for testing accuracy by generating simulated images, assuming clinically expected ranges of the parametric values. The computation time was about 20 s, and the quality of the images generated was acceptable. The values obtained for K ₁ for grade IV tumor were 0.24 ± 0.23 and 0.26 ± 0.25 ml^-1 min^-1 g^-1 for the image-based and ROI-based methods, respectively. The values were 0.21 ± 0.12 and 0.21 ± 0.12 min^-1 for k ₂, 0.13 ± 0.07 and 0.13 ± 0.07 min^-1 for k ₃, and 0.052 ± 0.020 and 0.054 ± 0.021 min^-1 for k ₄. The differences between the methods were not significant. Regression analysis showed correlations of r = 0.94, 0.86, 0.71, and 0.52 for these parameters. Simulation demonstrated that the accuracy was within acceptable ranges, namely, the correlations were r = 0.99, r = 0.97, r = 0.99, and r = 0.91 for K ₁, k ₂, k ₃, and k ₄, respectively, between estimated and assumed values. This results suggest that parametric images can be obtained fully within reasonable time, accuracy, and quality.

Clustering-initiated factor analysis application for tissue classification in dynamic brain positron emission tomography

The goal is to quantify the fraction of tissues that exhibit specific tracer binding in dynamic brain positron emission tomography (PET). It is achieved using a new method of dynamic image processing: clustering-initiated factor analysis (CIFA). Standard processing of such data relies on region of interest analysis and approximate models of the tracer kinetics and of tissue properties, which can degrade accuracy and reproducibility of the analysis. Clustering-initiated factor analysis allows accurate determination of the time-activity curves and spatial distributions for tissues that exhibit significant radiotracer concentration at any stage of the emission scan, including the arterial input function. We used this approach in the analysis of PET images obtained using (11)C-Pittsburgh Compound B in which specific binding reflects the presence of β-amyloid. The fraction of the specific binding tissues determined using our approach correlated with that computed using the Logan graphical analysis. We believe that CIFA can be an accurate and convenient tool for measuring specific binding tissue concentration and for analyzing tracer kinetics from dynamic images for a variety of PET tracers. As an illustration, we show that four-factor CIFA allows extraction of two blood curves and the corresponding distributions of arterial and venous blood from PET images even with a coarse temporal resolution.

A review on segmentation of positron emission tomography images

Positron Emission Tomography (PET), a non-invasive functional imaging method at the molecular level, images the distribution of biologically targeted radiotracers with high sensitivity. PET imaging provides detailed quantitative information about many diseases and is often used to evaluate inflammation, infection, and cancer by detecting emitted photons from a radiotracer localized to abnormal cells. In order to differentiate abnormal tissue from surrounding areas in PET images, image segmentation methods play a vital role; therefore, accurate image segmentation is often necessary for proper disease detection, diagnosis, treatment planning, and follow-ups. In this review paper, we present state-of-the-art PET image segmentation methods, as well as the recent advances in image segmentation techniques. In order to make this manuscript self-contained, we also briefly explain the fundamentals of PET imaging, the challenges of diagnostic PET image analysis, and the effects of these challenges on the segmentation results.

Image-derived input function derived from a supervised clustering algorithm: methodology and validation in a clinical protocol using [11C](R)-rolipram

Image-derived input function (IDIF) obtained by manually drawing carotid arteries (manual-IDIF) can be reliably used in [¹¹C](R)-rolipram positron emission tomography (PET) scans. However, manual-IDIF is time consuming and subject to inter- and intra-operator variability. To overcome this limitation, we developed a fully automated technique for deriving IDIF with a supervised clustering algorithm (SVCA). To validate this technique, 25 healthy controls and 26 patients with moderate to severe major depressive disorder (MDD) underwent T1-weighted brain magnetic resonance imaging (MRI) and a 90-minute [¹¹C](R)-rolipram PET scan. For each subject, metabolite-corrected input function was measured from the radial artery. SVCA templates were obtained from 10 additional healthy subjects who underwent the same MRI and PET procedures. Cluster-IDIF was obtained as follows: 1) template mask images were created for carotid and surrounding tissue; 2) parametric image of weights for blood were created using SVCA; 3) mask images to the individual PET image were inversely normalized; 4) carotid and surrounding tissue time activity curves (TACs) were obtained from weighted and unweighted averages of each voxel activity in each mask, respectively; 5) partial volume effects and radiometabolites were corrected using individual arterial data at four points. Logan-distribution volume (V_T/f_P) values obtained by cluster-IDIF were similar to reference results obtained using arterial data, as well as those obtained using manual-IDIF; 39 of 51 subjects had a V_T/f_P error of <5%, and only one had error >10%. With automatic voxel selection, cluster-IDIF curves were less noisy than manual-IDIF and free of operator-related variability. Cluster-IDIF showed widespread decrease of about 20% [¹¹C](R)-rolipram binding in the MDD group. Taken together, the results suggest that cluster-IDIF is a good alternative to full arterial input function for estimating Logan-V_T/f_P in [¹¹C](R)-rolipram PET clinical scans. This technique enables fully automated extraction of IDIF and can be applied to other radiotracers with similar kinetics.

Non-local means denoising of dynamic PET images

Objective

Dynamic positron emission tomography (PET), which reveals information about both the spatial distribution and temporal kinetics of a radiotracer, enables quantitative interpretation of PET data. Model-based interpretation of dynamic PET images by means of parametric fitting, however, is often a challenging task due to high levels of noise, thus necessitating a denoising step. The objective of this paper is to develop and characterize a denoising framework for dynamic PET based on non-local means (NLM).

Theory

NLM denoising computes weighted averages of voxel intensities assigning larger weights to voxels that are similar to a given voxel in terms of their local neighborhoods or patches. We introduce three key modifications to tailor the original NLM framework to dynamic PET. Firstly, we derive similarities from less noisy later time points in a typical PET acquisition to denoise the entire time series. Secondly, we use spatiotemporal patches for robust similarity computation. Finally, we use a spatially varying smoothing parameter based on a local variance approximation over each spatiotemporal patch.

Methods

To assess the performance of our denoising technique, we performed a realistic simulation on a dynamic digital phantom based on the Digimouse atlas. For experimental validation, we denoised PET images from a mouse study and a hepatocellular carcinoma patient study. We compared the performance of NLM denoising with four other denoising approaches – Gaussian filtering, PCA, HYPR, and conventional NLM based on spatial patches.

Results

The simulation study revealed significant improvement in bias-variance performance achieved using our NLM technique relative to all the other methods. The experimental data analysis revealed that our technique leads to clear improvement in contrast-to-noise ratio in Patlak parametric images generated from denoised preclinical and clinical dynamic images, indicating its ability to preserve image contrast and high intensity details while lowering the background noise variance.

Single-scan rest∕stress imaging (18)F-labeled flow tracers

PURPOSE

The authors report a novel measurement strategy to obtain both rest and stress blood flow during a single, relatively short, scan session.

METHODS

Measurement of rest-stress myocardial blood flow with long-lived tracers usually requires separate scan sessions to remove the confounding effects of residual radioactivity concentration in the blood and tissue. The innovation of this method is to treat the rest-stress scan as a single entity in which the flow parameters change due to pharmacological challenge. With this approach the fate of a tracer molecule is naturally accounted for, no matter if it was introduced during the rest or stress phase of the study. Two new dual-injection kinetic models are considered that represent the response to pharmacological stress as a transitional or transient increase of myocardial blood flow. The authors present the theory of the method followed by the specific application of the theory to (18)F-Flurpiridaz, a new myocardial flow-imaging agent.

RESULTS

Myocardial blood flow was accurately and precisely estimated from a single-scan rest∕stress study for the long half-lived tracer (18)F-Flurpiridaz. By accounting for the time-dependence of the kinetic parameters, the proposed models achieved good accuracy and precision (5%) under different vasodilators and different ischemic states.

CONCLUSIONS

Detailed simulations predict that accurate and precise rest-stress blood flow measurements can be obtained in 20-30 min.

3.5D dynamic PET image reconstruction incorporating kinetics-based clusters

Standard 3D dynamic positron emission tomographic (PET) imaging consists of independent image reconstructions of individual frames followed by application of appropriate kinetic model to the time activity curves at the voxel or region-of-interest (ROI). The emerging field of 4D PET reconstruction, by contrast, seeks to move beyond this scheme and incorporate information from multiple frames within the image reconstruction task. Here we propose a novel reconstruction framework aiming to enhance quantitative accuracy of parametric images via introduction of priors based on voxel kinetics, as generated via clustering of preliminary reconstructed dynamic images to define clustered neighborhoods of voxels with similar kinetics. This is then followed by straightforward maximum a posteriori (MAP) 3D PET reconstruction as applied to individual frames; and as such the method is labeled '3.5D' image reconstruction. The use of cluster-based priors has the advantage of further enhancing quantitative performance in dynamic PET imaging, because: (a) there are typically more voxels in clusters than in conventional local neighborhoods, and (b) neighboring voxels with distinct kinetics are less likely to be clustered together. Using realistic simulated (11)C-raclopride dynamic PET data, the quantitative performance of the proposed method was investigated. Parametric distribution-volume (DV) and DV ratio (DVR) images were estimated from dynamic image reconstructions using (a) maximum-likelihood expectation maximization (MLEM), and MAP reconstructions using (b) the quadratic prior (QP-MAP), (c) the Green prior (GP-MAP) and (d, e) two proposed cluster-based priors (CP-U-MAP and CP-W-MAP), followed by graphical modeling, and were qualitatively and quantitatively compared for 11 ROIs. Overall, the proposed dynamic PET reconstruction methodology resulted in substantial visual as well as quantitative accuracy improvements (in terms of noise versus bias performance) for parametric DV and DVR images. The method was also tested on a 90 min (11)C-raclopride patient study performed on the high-resolution research tomography. The proposed method was shown to outperform the conventional method in visual as well as quantitative accuracy improvements (in terms of noise versus regional DVR value performance).

Imaging detailed glucose metabolism in the brain using MAP estimation in Positron Emission Tomography

In this study, maximize a posterior approach (MAP) was applied for detailed imaging of the glucose metabolism in the brain using PET and ¹⁸F-FDG. FDG is a glucose analog and it can investigate a glucose metabolism. In PET studies, glucose metabolism can be measured to estimate a compartment model which describes the behavior of glucose in the brain. We applied the MAP approach to a voxel-by-voxel compartment model estimation in order to visualize a net amount of glucose, glucose transportation, and glucose phosphorylation because a MAP approach is advantageous for robust model estimation against noise existence. When the algorithm was applied to Alzheimer patients, the images had different patterns depending on severity of the disease. We conclude that the proposed MAP-based algorithm is useful for detail imaging of glucose metabolism in the brain.

Gaussian process models of dynamic PET for functional volume definition in radiation oncology

In routine oncologic positron emission tomography (PET), dynamic information is discarded by time-averaging the signal to produce static images of the "standardised uptake value" (SUV). Defining functional volumes of interest (VOIs) in terms of SUV is flawed, as values are affected by confounding factors and the chosen time window, and SUV images are not sensitive to functional heterogeneity of pathological tissues. Also, SUV iso-contours are highly affected by the choice of threshold and no threshold, or other SUV-based segmentation method, is universally accepted for a given VOI type. Gaussian Process (GP) time series models describe macro-scale dynamic behavior arising from countless interacting micro-scale processes, as is the case for PET signals from heterogeneous tissue. We use GPs to model time-activity curves (TACs) from dynamic PET and to define functional volumes for PET oncology. Probabilistic methods of tissue discrimination are presented along with novel contouring methods for functional VOI segmentation. We demonstrate the value of GP models for voxel classification and VOI contouring of diseased and metastatic tissues with functional heterogeneity in prostate PET. Classification experiments reveal superior sensitivity and specificity over SUV calculation and a TAC-based method proposed in recent literature. Contouring experiments reveal differences in shape between gold-standard and GP VOIs and correlation with kinetic models shows that the novel VOIs contain extra clinically relevant information compared to SUVs alone. We conclude that the proposed models offer a principled data analysis technique that improves on SUVs for oncologic VOI definition. Continuing research will generalize GP models for different oncology tracers and imaging protocols with the ultimate goal of clinical use including treatment planning.

Parametric mapping of [18F]fluoromisonidazole positron emission tomography using basis functions

In this study, we show a basis function method (BAFPIC) for voxelwise calculation of kinetic parameters (K(1), k(2), k(3), K(i)) and blood volume using an irreversible two-tissue compartment model. BAFPIC was applied to rat ischaemic stroke micro-positron emission tomography data acquired with the hypoxia tracer [(18)F]fluoromisonidazole because irreversible two-tissue compartmental modelling provided good fits to data from both hypoxic and normoxic tissues. Simulated data show that BAFPIC produces kinetic parameters with significantly lower variability and bias than nonlinear least squares (NLLS) modelling in hypoxic tissue. The advantage of BAFPIC over NLLS is less pronounced in normoxic tissue. K(i) determined from BAFPIC has lower variability than that from the Patlak-Gjedde graphical analysis (PGA) by up to 40% and lower bias, except for normoxic tissue at mid-high noise levels. Consistent with the simulation results, BAFPIC parametric maps of real data suffer less noise-induced variability than do NLLS and PGA. Delineation of hypoxia on BAFPIC k(3) maps is aided by low variability in normoxic tissue, which matches that in K(i) maps. BAFPIC produces K(i) values that correlate well with those from PGA (r(2)=0.93 to 0.97; slope 0.99 to 1.05, absolute intercept <0.00002 mL/g per min). BAFPIC is a computationally efficient method of determining parametric maps with low bias and variance.

Segmentation of mouse dynamic PET images using a multiphase level set method

Image segmentation plays an important role in medical diagnosis. Here we propose an image segmentation method for four-dimensional mouse dynamic PET images. We consider that voxels inside each organ have similar time activity curves. The use of tracer dynamic information allows us to separate regions that have similar integrated activities in a static image but with different temporal responses. We develop a multiphase level set method that utilizes both the spatial and temporal information in a dynamic PET data set. Different weighting factors are assigned to each image frame based on the noise level and activity difference among organs of interest. We used a weighted absolute difference function in the data matching term to increase the robustness of the estimate and to avoid over-partition of regions with high contrast. We validated the proposed method using computer simulated dynamic PET data, as well as real mouse data from a microPET scanner, and compared the results with those of a dynamic clustering method. The results show that the proposed method results in smoother segments with the less number of misclassified voxels.

A hybrid clustering method for ROI delineation in small-animal dynamic PET images: application to the automatic estimation of FDG input functions

Tracer kinetic modeling with dynamic positron emission tomography (PET) requires a plasma time-activity curve (PTAC) as an input function. Several image-derived input function (IDIF) methods that rely on drawing the region of interest (ROI) in large vascular structures have been proposed to overcome the problems caused by the invasive approach for obtaining the PTAC, especially for small-animal studies. However, the manual placement of ROIs for estimating IDIF is subjective and labor-intensive, making it an undesirable and unreliable process. In this paper, we propose a novel hybrid clustering method (HCM) that objectively delineates ROIs in dynamic PET images for the estimation of IDIFs, and demonstrate its application to the mouse PET studies acquired with [ (18)F]Fluoro-2-deoxy-2-D-glucose (FDG). We begin our HCM using k-means clustering for background removal. We then model the time-activity curves using polynomial regression mixture models in curve clustering for heart structure detection. The hierarchical clustering is finally applied for ROI refinements. The HCM achieved accurate ROI delineation in both computer simulations and experimental mouse studies. In the mouse studies, the predicted IDIF had a high correlation with the gold standard, the PTAC derived from the invasive blood samples. The results indicate that the proposed HCM has a great potential in ROI delineation for automatic estimation of IDIF in dynamic FDG-PET studies.

Smoothing dynamic positron emission tomography time courses using functional principal components

A functional smoothing approach to the analysis of PET time course data is presented. By borrowing information across space and accounting for this pooling through the use of a nonparametric covariate adjustment, it is possible to smooth the PET time course data thus reducing the noise. A new model for functional data analysis, the Multiplicative Nonparametric Random Effects Model, is introduced to more accurately account for the variation in the data. A locally adaptive bandwidth choice helps to determine the correct amount of smoothing at each time point. This preprocessing step to smooth the data then allows subsequent analysis by methods such as Spectral Analysis to be substantially improved in terms of their mean squared error.

Clustering dynamic PET images on the Gaussian distributed sinogram domain

Segmentation of dynamic PET images is an important preprocessing step for kinetic parameter estimation. The time activity curve (TAC) of individual pixels has very low signal-to-noise ratio (SNR). Therefore, the kinetic parameters estimated from the TAC of an individual pixel may not be accurate, and these estimations may have very high spatial variance. To alleviate this problem, pixels with similar kinetic characteristics are clustered into regions, and TACs of pixels within each region are averaged to increase SNR. It has recently been shown that clustering dynamic PET images in the sinogram domain is better than clustering them in the reconstructed image domain [M.E. Kamasak, B. Bayraktar, Clustering dynamic PET images on the projection domain, IEEE Trans. Nucl. Sci. 54 (3) (June 2007) 496-503.]. In that study, the sinograms are assumed to have Poisson distribution. The clusters and TACs of the clusters are then chosen to maximize the posterior probability of the measured sinograms. Although the raw sinogram data are Poisson distributed, the sinogram data corrected for scatter, randoms, attenuation etc. are not Poisson distributed anymore. In this paper, we describe how to cluster dynamic PET images on the sinogram domain when the sinograms are Gaussian distributed.

A robust method for estimating regional pulmonary parameters in presence of noise

RATIONALE AND OBJECTIVES

Estimation of regional lung function parameters from hyperpolarized gas magnetic resonance images can be very sensitive to presence of noise. Clustering pixels and averaging over the resulting groups is an effective method for reducing the effects of noise in these images, commonly performed by grouping proximal pixels together, thus creating large groups called "bins." This method has several drawbacks, primarily that it can group dissimilar pixels together, and it degrades spatial resolution. This study presents an improved approach to simplifying data via principal component analysis (PCA) when noise level prohibits a pixel-by-pixel treatment of data, by clustering them based on similarity to one another rather than spatial proximity. The application to this technique is demonstrated in measurements of regional lung oxygen tension using hyperpolarized (3)He magnetic resonance imaging (MRI).

MATERIALS AND METHODS

A synthetic dataset was generated from an experimental set of oxygen tension measurements by treating the experimentally derived parameters as "true" values, and then solving backwards to generate "noiseless" images. Artificial noise was added to the synthetic data, and both traditional binning and PCA-based clustering were performed. For both methods, the root-mean-square (RMS) error between each pixel's "estimated" and "true" parameters was computed and the resulting effects were compared.

RESULTS

At high signal-to-noise ratios (SNRs), clustering did not enhance accuracy. Clustering did, however, improve parameter estimations for moderate SNR values (below 100). For SNR values between 100 and 20, the PCA-based K-means clustering analysis yielded greater accuracy than Cartesian binning. In extreme cases (SNR<5), Cartesian binning can be more accurate.

CONCLUSIONS

The reliability of parameters estimation in imaging-based regional functional measurements can be improved in the presence of noise by utilizing principal component analysis-based clustering without sacrificing spatial resolution compared to Cartesian binning. Results suggest that this approach has a great potential for robust grouping of pixels in hyperpolarized (3)He MRI maps of lung oxygen tension.

Improving PET receptor binding estimates from Logan plots using principal component analysis

This work reports a principal component analysis (PCA)-based approach for reducing bias in distribution volume ratio (DVR) estimates from Logan plots in positron emission tomography (PET). Comparison has been made of all existing bias-removal methods with the proposed PCA method, for both single-estimate PET studies and intervention studies where pre- and post-intervention estimates are made. Bias in Logan-based DVR estimates is because of the noise in the PET time-activity curves (TACs) that propagates as correlated errors in dependent and independent variables of the Logan equation. Intervention studies show this same bias but also higher variance in DVR estimates. In this work, noise in the TACs was reduced by fitting the curves to a low-dimension PCA-based linear model, leading to reduced bias and variance in DVR. For validating the approach, TACs with realistic noise were simulated for a 11C-labeled tracer with carfentanil (CFN)-like kinetics for both single-measurement and intervention studies. Principal component analysis and existing methods were applied to the simulated data and their performance was compared by statistical analysis. The results indicated that existing methods either removed only part of the bias or reduced bias at the expense of precision. The proposed method removed approximately 90% of the bias while also improving precision in both single- and dual-measurement simulations. After validation of the proposed method in simulations, PCA, along with the existing methods, was applied to human [11C]CFN data acquired for both single estimation of DVR and dual-estimation intervention studies. Similar results were observed in human scans as were seen in the simulation studies.

Segmentation of rodent whole-body dynamic PET images: an unsupervised method based on voxel dynamics

Positron emission tomography (PET) is a useful tool for pharmacokinetics studies in rodents during the preclinical phase of drug and tracer development. However, rodent organs are small as compared to the scanner's intrinsic resolution and are affected by physiological movements. We present a new method for the segmentation of rodent whole-body PET images that takes these two difficulties into account by estimating the pharmacokinetics far from organ borders. The segmentation method proved efficient on whole-body numerical rat phantom simulations, including 3-14 organs, together with physiological movements (heart beating, breathing, and bladder filling). The method was resistant to spillover and physiological movements, while other methods failed to obtain a correct segmentation. The radioactivity concentrations calculated with this method also showed an excellent correlation with the manual delineation of organs in a large set of preclinical images. In addition, it was faster, detected more organs, and extracted organs' mean time activity curves with a better confidence on the measure than manual delineation.

Supervised clustering approach to form functional images in positron emission tomography

The aim of this study is to investigate the availability of supervised statistical clustering algorithm for image-based model analysis in positron emission tomography or nuclear medicine to form a functional image. Voxel-by-voxel model analysis can derive functional images, but bad statistic property in voxel-based PET data and huge number of voxels prevent to realize practical algorithm to form parametric images. In this study, supervised clustering is applied to categorized PET data. The shape of tTAC is projected in multidimensional feature space, and noise propagation is modeled as multivariate Gaussian in the space. Simulation study shows that the estimates by the proposed algorithm was identical to the true values. And a clinical image of has physiologically acceptable aspect. We can conclude that supervised clustering sachem has potential to realize practical algorithm for voxel-based model analysis in PET.

Fast and reliable estimation of multiple parametric images using an integrated method for dynamic SPECT

Dynamic single photon emission computed tomography (SPECT) has demonstrated the potential to quantitatively estimate physiological parameters in the brain and the heart. The generalized linear least square (GLLS) method is a well-established method for solving linear compartment models with fast computational speed. However, the high level of noise intrinsic in the SPECT data leads to reliability and instability problems of GLLS for generating parametric images. An integrated method is proposed to restrict the noise in both the temporal and spatial domains to estimate multiple parametric images for dynamic SPECT. This method comprises three steps which are optimum image sampling schedule in the projection space, cluster analysis applied postreconstruction and parametric image generation with GLLS. The simulation and experimental studies for the neuronal nicotine acetylcholine receptor tracer of 5-[123I]-iodo-A-85380 were employed to evaluate the performance of the proposed method. The results of influx rate of K1 and volume of distribution of Vd demonstrated that the integrated method was successful in generating low noise parametric images for high noise SPECT data without enhancing the partial volume effect. Furthermore, the integrated method is computationally efficient for potential clinical applications.

Segmentation of VOI from multidimensional dynamic PET images by integrating spatial and temporal features

Segmentation of multidimensional dynamic positron emission tomography (PET) images into volumes of interest (VOIs) exhibiting similar temporal behavior and spatial features is a challenging task due to inherently poor signal-to-noise ratio and spatial resolution. In this study, we propose VOI segmentation of dynamic PET images by utilizing both the three-dimensional (3-D) spatial and temporal domain information in a hybrid technique that integrates two independent segmentation techniques of cluster analysis and region growing. The proposed technique starts with a cluster analysis that partitions the image based on temporal similarities. The resulting temporal partitions, together with the 3-D spatial information are utilized in the region growing segmentation. The technique was evaluated with dynamic 2-[18F] fluoro-2-deoxy-D-glucose PET simulations and clinical studies of the human brain and compared with the k-means and fuzzy c-means cluster analysis segmentation methods. The quantitative evaluation with simulated images demonstrated that the proposed technique can segment the dynamic PET images into VOIs of different kinetic structures and outperforms the cluster analysis approaches with notable improvements in the smoothness of the segmented VOIs with fewer disconnected or spurious segmentation clusters. In clinical studies, the hybrid technique was only superior to the other techniques in segmenting the white matter. In the gray matter segmentation, the other technique tended to perform slightly better than the hybrid technique, but the differences did not reach significance. The hybrid technique generally formed smoother VOIs with better separation of the background. Overall, the proposed technique demonstrated potential usefulness in the diagnosis and evaluation of dynamic PET neurological imaging studies.

Visualizing lung function with positron emission tomography

Positron emission tomography (PET) provides three-dimensional images of the distributions of radionuclides that have been inhaled or injected into the lungs. By using radionuclides with short half-lives, the radiation exposure of the subject can be kept small. By following the evolution of the distributions of radionuclides in gases or compounds that participate in lung function, information about such diverse lung functions as regional ventilation, perfusion, shunt, gas fraction, capillary permeability, inflammation, and gene expression can be inferred. Thus PET has the potential to provide information about the links between cellular function and whole lung function in vivo. In this paper, recent advancements in PET methodology and techniques and information about lung function that have been obtained with these techniques are reviewed.

MAP-based kinetic analysis for voxel-by-voxel compartment model estimation: Detailed imaging of the cerebral glucose metabolism using FDG

We propose a novel algorithm for voxel-by-voxel compartment model analysis based on a maximum a posteriori (MAP) algorithm. Voxel-by-voxel compartment model analysis can derive functional images of living tissues, but it suffers from high noise statistics in voxel-based PET data and extended calculation times. We initially set up a feature space of the target radiopharmaceutical composed of a measured plasma time activity curve and a set of compartment model parameters, and measured the noise distribution of the PET data. The dynamic PET data were projected onto the feature space, and then clustered using the Mahalanobis distance. Our method was validated using simulation studies, and compared with ROI-based ordinary kinetic analysis for FDG. The parametric images exhibited an acceptable linear relation with the simulations and the ROI-based results, and the calculation time took about 10 min. We therefore concluded that our proposed MAP-based algorithm is practical.

Parametric image of myocardial blood flow generated from dynamic H2(15)O PET using factor analysis and cluster analysis

Algorithm-based parametric imaging of myocardial blood flow (MBF), as measured by H2(15)O PET, has been the goal of many research efforts. A method for generating parametric images of regional MBF by factor and cluster analysis on H2(15)O dynamic myocardial PET was validated by its comparison with gold-standard MBF values determined invasively using radiolabelled microspheres. Right and left ventricular blood pool activities and their factor images were obtained by the application of factor analysis to dynamic frames. By subtraction of the factor images multiplied by their corresponding values on the factors from the original dynamic images for each frame, pure tissue dynamic images were obtained, from which arterial blood activities were excluded. Cluster analysis that averaged pixels having time-activity curves with the same shape was applied to pure tissue images to generate parametric MBF images. The usefulness of this method for quantifying regional MBF was evaluated using canine experiment data. H2(15)O PET scans and microsphere studies were performed on seven dogs at rest and after pharmacological stress. The image qualities and the contrast of parametric images obtained using the proposed method were significantly improved over either the tissue factor images or the parametric images obtained using a conventional method. Regional MBFs obtained using the proposed method correlated well with those obtained by the region of interest method (r = 0.94) and by the microsphere technique (r = 0.90). A non-invasive method is presented for generating parametric images of MBF from H2(15)O PET, using factor and cluster analysis.

Evaluation of objective functions for estimation of kinetic parameters

There is growing interest in quantitatively analyzing in vivo image data, as this facilitates objective comparisons and measurement of effect. In this regard, people increasingly turn to pharmacokinetic models and estimation of parameters of such models. In this work several parameter estimation methodologies were compared within the context of the most common pharmacokinetic model used in positron emission tomography imaging to describe glucose metabolism and receptor-ligand interactions at tracer concentrations. Simulated data were generated with 1000 realizations at each of 5 different noise levels. Estimates of the kinetic parameters were made for each realization using seven iterative, nonlinear estimation methodologies: ordinary least squares (OLS), weighted least squares (WLS), penalized weighted least squares (PWLS), iteratively reweighted least squares (IRLS), and variations of extended least squares (ELS0, ELS1, ELS3). Additionally, generalized linear least squares (GLLS) was also used. With relatively noise-free data, the iterative nonlinear estimation methods generally produced low-bias, high-precision parameter estimates, whereas with GLLS the bias was more prominent. Greater distinction between the estimation methods was seen at the higher, more realistic noise levels, with ELS and IRLS methods generally achieving better precision than the other methods. At the high noise levels WLS, GLLS, and PWLS yielded parameter estimates with large bias (>200%) for some kinetic parameters. In general, there are more favorable estimator methodologies than the frequently employed WLS. Methods that determine values of weights based on model output--IRLS, ELS0, ELS1 and ELS3--generally perform better than methods that determine values of weights based directly on the experimental data.

Locally constrained mixture representation of dynamic imaging data from PET and MR studies

Dynamic positron emission tomography (PET) studies provide measurements of the kinetics of radiotracers in living tissue. This is a powerful technology which can play a major role in the study of biological processes, potentially leading to better understanding and treatment of disease. Dynamic PET data relate to complex spatiotemporal processes and its analysis poses significant challenges. In previous work, mixture models that expressed voxel-level PET time course data as a convex linear combination of a finite number of dominant time course characteristics (called sub-TACs) were introduced. This paper extends that mixture model formulation to allow for a weighted combination of scaled sub-TACs and also considers the imposition of local constraints in the number of sub-TACs that can be active at any one voxel. An adaptive 3D scaled segmentation algorithm is developed for model initialization. Increases in the weighted residual sums of squares is used to guide the choice of the number of segments and the number of sub-TACs in the final mixture model. The methodology is applied to five data sets from representative PET imaging studies. The methods are also applicable to other contexts in which dynamic image data are acquired. To illustrate this, data from an echo-planar magnetic resonance (MR) study of cerebral hemodynamics are considered. Our analysis shows little indication of departure from a locally constrained mixture model representation with at most two active components at any voxel. Thus, the primary sources of spatiotemporal variation in representative dynamic PET and MR imaging studies would appear to be accessible to a substantially simplified representation in terms of the generalized locally constrained mixture model introduced.

Enhanced parameter estimation from noisy PET data: Part I--methodology

RATIONALE AND OBJECTIVES

The reliability of positron emission tomographic (PET) images depends on the number of annihilation events that are detected. Short image durations are required to capture rapid tracer dynamics, and the resultant images are noisy. Consequently, direct parameter estimation from time-activity curves at high resolution often is unreliable. If adjacent voxels are combined into larger regions of interest the reliability of parameter estimation may be improved, but at the expense of decreased spatial resolution. In this report, a method is presented that provides an alternative to degrading image resolution.

MATERIALS AND METHODS

Following the approach of Kimura et al, voxels are grouped not by spatial proximity, but by the similarity of their kinetics. Parameter estimation is performed on these groups, and derived parameters are assigned to all members of the group. Spatial information thus is preserved, but at the expense of parametric discretization. An improvement to the method of Kimura et al is described, in which data are grouped using principal components derived from artificial data.

RESULTS

The application of the method is demonstrated by analysis of PET images of human lungs obtained by the nitrogen-13 infusion-washout technique. In a comparison of the accuracy of parameter estimates, the enhanced method is shown to outperform the original method at all noise levels, with the difference increasing as the amount of noise increases. The robustness of this parameter estimation method in the presence of noise is described in part II of this report in this issue of Academic Radiology.

CONCLUSION

A method is described that provides demonstrably robust parameter estimates from noisy PET data, while not compromising image resolution.

Use of reference tissue models for quantification of histamine H1 receptors in human brain by using positron emission tomography and [11C]doxepin

The aim of the present study is to evaluate the validity of the simplified reference tissue model (SRTM) and of Logan graphical analysis with reference tissue (LGAR) for quantification of histamine H1 receptors (H1Rs) by using positron emission tomography (PET) with [11C]doxepin. These model-based analytic methods (SRTM and LGAR) are compared to Logan graphical analysis (LGA) and to the one-tissue model (1TM), using complete datasets obtained from 5 healthy volunteers. Since HIR concentration in the cerebellum can be regarded as negligibly small, the cerebellum was selected as the reference tissue in the present study. The comparison of binding potential (BP) values estimated by LGAR and 1TM showed good agreement; on the other hand, SRTM turned out to be unstable concerning parameter estimation in several regions of the brain. By including the results of noise analysis, LGAR became a reliable method for parameter estimation of [11C]doxepin data in the cortical regions.

Direct reconstruction of kinetic parameter images from dynamic PET data

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.

Clustering huge data sets for parametric PET imaging

A new preprocessing clustering technique for quantification of kinetic PET data is presented. A two-stage clustering process, which combines a precluster and a classic hierarchical cluster analysis, provides data which are clustered according to a distance measure between time activity curves (TACs). The resulting clustered mean TACs can be used directly for estimation of kinetic parameters at the cluster level, or to span a vector space that is used for subsequent estimation of voxel level kinetics. The introduction of preclustering significantly reduces the overall time for clustering of multiframe kinetic data. The efficiency and superiority of the preclustering scheme combined with thresholding is validated by comparison of the results for clustering both with and without preclustering for FDG-PET brain data of 13 healthy subjects.

Linear regression with spatial constraint to generate parametric images of ligand-receptor dynamic PET studies with a simplified reference tissue model

For the quantitative analysis of ligand-receptor dynamic positron emission tomography (PET) studies, it is often desirable to apply reference tissue methods that eliminate the need for arterial blood sampling. A common technique is to apply a simplified reference tissue model (SRTM). Applications of this method are generally based on an analytical solution of the SRTM equation with parameters estimated by nonlinear regression. In this study, we derive, based on the same assumptions used to derive the SRTM, a new set of operational equations of integral form with parameters directly estimated by conventional weighted linear regression (WLR). In addition, a linear regression with spatial constraint (LRSC) algorithm is developed for parametric imaging to reduce the effects of high noise levels in pixel time activity curves that are typical of PET dynamic data. For comparison, conventional weighted nonlinear regression with the Marquardt algorithm (WNLRM) and nonlinear ridge regression with spatial constraint (NLRRSC) were also implemented using the nonlinear analytical solution of the SRTM equation. In contrast to the other three methods, LRSC reduces the percent root mean square error of the estimated parameters, especially at higher noise levels. For estimation of binding potential (BP), WLR and LRSC show similar variance even at high noise levels, but LRSC yields a smaller bias. Results from human studies demonstrate that LRSC produces high-quality parametric images. The variance of R(1) and k(2) images generated by WLR, WNLRM, and NLRRSC can be decreased 30%-60% by using LRSC. The quality of the BP images generated by WLR and LRSC is visually comparable, and the variance of BP images generated by WNLRM can be reduced 10%-40% by WLR or LRSC. The BP estimates obtained using WLR are 3%-5% lower than those estimated by LRSC. We conclude that the new linear equations yield a reliable, computationally efficient, and robust LRSC algorithm to generate parametric images of ligand-receptor dynamic PET studies.