John A. D. Aston

A GENERAL STATISTICAL ANALYSIS FOR FMRI DATA

We propose a method for the statistical analysis of fMRI data that seeks a compromise between efficiency, generality, validity, simplicity, and execution speed. The main differences between this analysis and previous ones are: a simple bias reduction and regularization for voxel-wise autoregressive model parameters; the combination of effects and their estimated standard deviations across different runs/sessions/subjects via a hierarchical random effects analysis using the EM algorithm; overcoming the problem of a small number of runs/session/subjects using a regularized variance ratio to increase the degrees of freedom.

Positron emission tomography compartmental models: a basis pursuit strategy for kinetic modeling.

A kinetic modeling approach for the quantification of in vivo tracer studies with dynamic positron emission tomography (PET) is presented. The approach is based on a general compartmental description of the tracers fate in vivo and determines a parsimonious model consistent with the measured data. The technique involves the determination of a sparse selection of kinetic basis functions from an overcomplete dictionary using the method of basis pursuit denoising. This enables the characterization of the systems impulse response function from which values of the systems macro parameters can be estimated. These parameter estimates can be obtained from a region of interest analysis or as parametric images from a voxel-based analysis. In addition, model order estimates are returned that correspond to the number of compartments in the estimated compartmental model. Validation studies evaluate the methods performance against two preexisting data led techniques, namely, graphical analysis and spectral analysis. Application of this technique to measured PET data is demonstrated using [11C]diprenorphine (opiate receptor) and [11C]WAY-100635 (5-HT1A receptor). Although the method is presented in the context of PET neuroreceptor binding studies, it has general applicability to the quantification of PET/SPECT radiotracer studies in neurology, oncology, and cardiology.

Positron emission tomography Partial volume correction: estimation and algorithms

Partial volume effects in positron emission tomography (PET) lead to quantitative under- and over-estimations of the regional concentrations of radioactivity in reconstructed images and corresponding errors in derived functional or parametric images. The limited resolution of PET leads to “tissue-fraction” effects, reflecting underlying tissue heterogeneity, and “spillover” effects between regions. Addressing the former problem in general requires supplementary data, for example, coregistered high-resolution magnetic resonance images, whereas the latter effect can be corrected for with PET data alone if the point-spread function of the tomograph has been characterized. Analysis of otherwise homogeneous region-of-interest data ideally requires a combination of tissue classification and correction for the point-spread function. The formulation of appropriate algorithms for partial volume correction (PVC) is dependent on both the distribution of the signal and the distribution of the underlying noise. A mathematical framework has therefore been developed to accommodate both of these factors and to facilitate the development of new PVC algorithms based on the description of the problem. Several methodologies and algorithms have been proposed and implemented in the literature in order to address these problems. These methods do not, however, explicitly consider the noise model while differing in their underlying assumptions. The general theory for estimation of regional concentrations, associated error estimation, and inhomogeneity tests are presented in a weighted least squares framework. The analysis has been validated using both simulated and real PET data sets. The relations between the current algorithms and those published previously are formulated and compared. The incorporation of tensors into the formulation of the problem has led to the construction of computationally rapid algorithms taking into account both tissue-fraction and spillover effects. The suitability of their application to dynamic and static images is discussed.

Dynamic functional changes associated with cognitive skill learning of an adapted version of the Tower of London task.

In this study, we used a modified version of the Tower of London (TOL) planning task, in conjunction with positron emission tomography, to examine the neural substrates mediating cognitive skill learning. Twelve healthy, right-handed participants solved a total of 90 different TOL problems. They were scanned on four occasions during the fast learning stage as well as in a condition designed to control for internally guided movements. Practice of the TOL task resulted in a significant decrease in planning, execution, and total time taken to solve the problems. Consistent with the results of previous studies, early performance of the TOL task was associated with increased blood flow activity in the dorsolateral prefrontal, orbitofrontal, and parietal cortices on the left, as well as in the caudate nucleus, cerebellum, and premotor cortex, bilaterally. Interestingly, however, activity in the left caudate nucleus was maintained from the beginning to the end of the learning process, suggesting that this structure plays a role in this type of cognitive skill learning. In addition, correlational analyses revealed that improved performance on the TOL task was associated with a significant decrease of activity in the medial orbitofrontal and frontopolar cortices over the course of learning, areas thought to be involved in decision making, guessing, and monitoring of feedback information. In sum, the results lend further support to the idea that the learning of cognitive skills requiring planning and working memory capacities is mediated through a fronto-striatal network.

Estimating the delay of the fMRI response.

We propose a fast, efficient, general, simple, valid, and robust method of estimating and making inference about the delay of the fMRI response modeled as a temporal shift of the hemodynamic response function (HRF). We estimate the shift unbiasedly using two optimally chosen basis functions for a spectrum of time shifted HRFs. This is done at every voxel, to create an image of estimated delays and their standard deviations. This can be used to compare delays for the same stimulus at different voxels, or for different stimuli at the same voxel. Our method is compared to other alternatives and validated on an fMRI data set from an experiment in pain perception.

A statistical method for the analysis of positron emission tomography neuroreceptor ligand data.

A method for voxel by voxel statistical inference of PET radioligand receptor studies is presented. This method is aimed at detecting differences in radioligand binding between baseline and activation scans. It uses nonlinear least squares theory to estimate the ligand-receptor model parameters and utilizes the residuals to calculate their associated variance. The approach both increases the degrees of freedom for statistical testing and produces more accurate estimates of the standard deviation of the parameters. This technique is applicable to any ligand with a validated compartmental model, whether reversibly or irreversibly bound. The method was investigated and compared with a simple voxel-wise t test. Both simulated and real PET data for the dopamine D(1) receptor ligand [(11)C]SCH 23390 were used to assess the method. The assumptions implicit in the residuals methods were validated. The residuals method was found to be more sensitive than a simple t test, while not producing false-positive results. In addition, we showed that this method reliably differentiates changes in radioligand binding from the effects of changes in cerebral blood flow.

A linear wavelet filter for parametric imaging with dynamic PET

Describes a new filter for parametric images obtained from dynamic positron emission tomography (PET) studies. The filter is based on the wavelet transform following the heuristics of a previously published method that are here developed into a rigorous theoretical framework. It is shown that the space-time problem of modeling a dynamic PET sequence reduces to the classical one of estimation of a normal multivariate vector of independent wavelet coefficients that, under least-squares risk, can be solved by straightforward application of well established theory. From the study of the distribution of wavelet coefficients of PET images, it is inferred that a James-Stein linear estimator is more suitable for the problem than traditional nonlinear procedures that are incorporated in standard wavelet filters. This is confirmed by the superior performance of the James-Stein filter in simulation studies compared to a state-of-the-art nonlinear wavelet filter and a nonstationary filter selected from literature. Finally, the formal framework is interpreted for the practitioners point of view and advantages and limitations of the method are discussed.

MR Image Segmentation Using a Power Transformation Approach

This study proposes a segmentation method for brain MR images using a distribution transformation approach. The method extends traditional Gaussian mixtures expectation-maximization segmentation to a power transformed version of mixed intensity distributions, which includes Gaussian mixtures as a special case. As MR intensities tend to exhibit non-Gaussianity due to partial volume effects, the proposed method is designed to fit non-Gaussian tissue intensity distributions. One advantage of the method is that it is intuitively appealing and computationally simple. To avoid performance degradation caused by intensity inhomogeneity, different methods for correcting bias fields were applied prior to image segmentation, and their correction effects on the segmentation results were examined in the empirical study. The partitions of brain tissues (i.e., gray and white matter) resulting from the method were validated and evaluated against manual segmentation results based on 38 real T1-weighted image volumes from the Internet brain segmentation repository, and 18 simulated image volumes from BrainWeb. The Jaccard and Dice similarity indexes were computed to evaluate the performance of the proposed approach relative to the expert segmentations. Empirical results suggested that the proposed segmentation method yielded higher similarity measures for both gray matter and white matter as compared with those based on the traditional segmentation using the Gaussian mixtures approach.

Multi-resolution Bayesian regression in PET dynamic studies using wavelets

In the kinetic analysis of dynamic PET data, one usually posits that the variation of the data through one dimension, time, can be described by a mathematical model encapsulating the relevant physiological features of the radioactive tracer. In this work, we posit that the remaining dimension, space, can also be modeled as a physiological feature, and we introduce this concept into a new computational procedure for the production of parametric maps. An organ and, in the instance considered here, the brain presents similarities in the physiological properties of its elements across scales: computationally, this similarity can be implemented in two stages. Firstly, a multi-scale decomposition of the dynamic frames is created through the wavelet transform. Secondly, kinetic analysis is performed in wavelet space and the kinetic parameters estimated at low resolution are used as priors to inform estimates at higher resolutions. Kinetic analysis in the above scheme is achieved by extension of the Patlak analysis through Bayesian linear regression that retains the simplicity and speed of the original procedure. Application to artificial and real data (FDG and FDOPA) demonstrates the ability of the procedure to reduce remarkably the variance of parametric maps (up to 4-fold reduction) without introducing sizeable bias. Significance of the methodology and extension of the procedure to other data (fMRI) and models are discussed.

Modeling Dynamic PET-SPECT Studies in the Wavelet Domain

This work develops a theoretical framework and corresponding algorithms for the modeling of dynamic PET-SPECT studies both in time and space. The problem of estimating the spatial dimension is solved by applying the wavelet transform to each scan of the dynamic sequence and then performing the kinetic modeling and statistical analysis in the wavelet domain. On reconstruction through the inverse wavelet transform, one obtains parametric images that are consistent estimates of the spatial patterns of the kinetic parameter of interest. The theoretical setup allows the use of linear techniques currently used in PET-SPECT for kinetic analysis. The method is applied to artificial and real data sets. The application to dynamic PET-SPECT studies was performed both for validation purposes, when the spatial patterns are known, and for illustration of the advantages offered by the technique in case of tracers with an unknown pattern of distribution.