Kinetic modeling of dynamic PET data requires knowledge of tracer concentration in blood plasma, described by the arterial input function (AIF). Arterial blood sampling is the gold standard for AIF measurement, but is invasive and labour intensive. A number of methods have been proposed to accurately estimate the AIF directly from blood sampling and/or imaging data. Here we consider fitting a patient-adaptive mixture of historical population time course profiles to estimate individual AIFs. Travel time of a tracer atom from the injection site to the right ventricle of the heart is modeled as a realization from a Gamma distribution, and the time this atom spends in circulation before being sampled is represented by a subject-specific linear mixture of population profiles. These functions are estimated from independent population data. Individual AIFs are obtained by projection onto this basis of population profile components. The model incorporates knowledge of injection duration into the fit, allowing for varying injection protocols. Analyses of arterial sampling data from 18F-FDG, 15O-H2O and 18F-FLT clinical studies show that the proposed model can outperform reference techniques. The statistically significant gain achieved by using population data to train the basis components, instead of fitting these from the single individual sampling data, is measured on the FDG cohort. Kinetic analyses of simulated data demonstrate the reliability and potential benefit of this approach in estimating physiological parameters. These results are further supported by numerical simulations that demonstrate convergence and stability of the proposed technique under varying training population sizes and noise levels.

When a scanner is installed and begins to be used operationally, its actual performance may deviate somewhat from the predictions made at the design stage. Thus it is recommended that routine quality assurance (QA) measurements be used to provide an operational understanding of scanning properties. While QA data are primarily used to evaluate sensitivity and bias patterns, there is a possibility to also make use of such data sets for a more refined understanding of the 3-D scanning properties. Building on some recent work on analysis of the distributional characteristics of iteratively reconstructed PET data, we construct an auto-regression model for analysis of the 3-D spatial auto-covariance structure of iteratively reconstructed data, after normalization. Appropriate likelihood-based statistical techniques for estimation of the auto-regression model coefficients are described. The fitted model leads to a simple process for approximate simulation of scanner performance-one that is readily implemented in an R script. The analysis provides a practical mechanism for evaluating the operational error characteristics of iteratively reconstructed PET images. Simulation studies are used for validation. The approach is illustrated on QA data from an operational clinical scanner and numerical phantom data. We also demonstrate the potential for use of these techniques, as a form of model-based bootstrapping, to provide assessments of measurement uncertainties in variables derived from clinical FDG-PET scans. This is illustrated using data from a clinical scan in a lung cancer patient, after a 3-minute acquisition has been re-binned into three consecutive 1-minute time-frames. An uncertainty measure for the tumor SUVmax value is obtained. The methodology is seen to be practical and could be a useful support for quantitative decision making based on PET data.

The basic emission process associated with positron emission tomography (PET) imaging is Poisson in nature. Reconstructed images inherit some aspects of this-regional variability is typically proportional to the regional mean. Iterative reconstruction using expectation-maximization (EM), widely used in clinical imaging now, imposes positivity constraints that impact noise properties. This paper is motivated by the analysis of data from a physical phantom study of a PET/CT scanner in routine clinical use. Both traditional filtered back-projection (FBP) and EM reconstructions of the images are considered. FBP images are quite Gaussian, but the EM reconstructions exhibit Gamma-like skewness. The Gamma structure has implications for how reconstructed PET images might be processed statistically. Post-reconstruction inference-model fitting and diagnostics for regions of interest are of particular interest. Although the relevant Gamma parameterization is not within the framework of generalized linear models (GLM), iteratively re-weighted least squares (IRLS) techniques, which are often used to find the maximum likelihood estimates of a GLM, can be adapted for analysis in this setting. This paper highlights the use of a Gamma-based probability transform in producing normalized residuals as model diagnostics. The approach is demonstrated for quality assurance analyses associated with physical phantom studies-recovering estimates of local bias and variance characteristics in an operational scanner. Numerical simulations show that when the Gamma assumption is reasonable, gains in efficiency are obtained. This paper shows that the adaptation of standard analysis methods to accommodate the Gamma structure is straightforward and beneficial.

In a positron emission tomography (PET) study, the local uptake of the tracer is dependent on vascular delivery and retention. For dynamic studies the measured uptake time-course information can be best interpreted when knowledge of the time-course of tracer in the blood is available. This is certainly true for the most established tracers such as 18F-Fluorodeoxyglucose (FDG) and 15O-Water (H2O). Since direct sampling of blood as part of PET studies is increasingly impractical, there is ongoing interest in image-extraction of blood time-course information. But analysis of PET-measured blood pool signals is complicated because they will typically involve a combination of arterial, venous and tissue information. Thus, a careful appreciation of these components is needed to interpret the available data. To facilitate this process, we propose a novel Markov chain model for representation of the circulation of a tracer atom in the body. The model represents both arterial and venous time-course patterns. Under reasonable conditions equilibration of tracer activity in arterial and venous blood is achieved by the end of the PET study-consistent with empirical measurement. Statistical inference for Markov model parameters is a challenge. A penalized nonlinear least squares process, incorporating a generalized cross-validation score, is proposed. Random effects analysis is used to adaptively specify the structure of the penalty function based on historical samples of directly measured blood data. A collection of arterially sampled data from PET studies with FDG and H2O is used to illustrate the methodology. These data analyses are highly supportive of the overall modeling approach. An adaptation of the model to the problem of extraction of arterial blood signals from imaging data is also developed and promising preliminary results for cerebral and thoracic imaging studies with FDG and H2O are obtained.

MOTIVATION: Array comparative genomic hybridization (aCGH) provides a genome-wide technique to screen for copy number alteration. The existing segmentation approaches for analyzing aCGH data are based on modeling data as a series of discrete segments with unknown boundaries and unknown heights. Although the biological process of copy number alteration is discrete, in reality a variety of biological and experimental factors can cause the signal to deviate from a stepwise function. To take this into account, we propose a smooth segmentation (smoothseg) approach. METHODS: To achieve a robust segmentation, we use a doubly heavy-tailed random-effect model. The first heavy-tailed structure on the errors deals with outliers in the observations, and the second deals with possible jumps in the underlying pattern associated with different segments. We develop a fast and reliable computational procedure based on the iterative weighted least-squares algorithm with band-limited matrix inversion. RESULTS: Using simulated and real data sets, we demonstrate how smoothseg can aid in identification of regions with genomic alteration and in classification of samples. For the real data sets, smoothseg leads to smaller false discovery rate and classification error rate than the circular binary segmentation (CBS) algorithm. In a realistic simulation setting, smoothseg is better than wavelet smoothing and CBS in identification of regions with genomic alterations and better than CBS in classification of samples. For comparative analyses, we demonstrate that segmenting the t-statistics performs better than segmenting the data. AVAILABILITY: The R package smoothseg to perform smooth segmentation is available from http://www.meb.ki.se/~yudpaw.