Maximum likelihood estimation for second level fMRI data analysis with expectation trust region algorithm

The trust region method which originated from the Levenberg–Marquardt (LM) algorithm for mixed effect model estimation are considered in the context of second level functional magnetic resonance imaging (fMRI) data analysis. We first present the mathematical and optimization details of the method for the mixed effect model analysis, then we compare the proposed methods with the conventional expectation-maximization (EM) algorithm based on a series of datasets (synthetic and real human fMRI datasets). From simulation studies, we found a higher damping factor for the LM algorithm is better than lower damping factor for the fMRI data analysis. More importantly, in most cases, the expectation trust region algorithm is superior to the EM algorithm in terms of accuracy if the random effect variance is large. We also compare these algorithms on real human datasets which comprise repeated measures of fMRI in phased-encoded and random block experiment designs. We observed that the proposed method is faster in computation and robust to Gaussian noise for the fMRI analysis. The advantages and limitations of the suggested methods are discussed.     

Functional MR imaging in the awake monkey: effects of motion on dynamic off-resonance and processing strategies

Functional MR imaging of the alert, behaving monkey is being used more and more often to detect activation patterns and guide electrophysiological research investigating the neural basis of behavior. Several labs have reported fMRI data from the awake monkey, but none of them has studied and systematically corrected the effects of monkeys' motion on fMRI time series. In this study, a significant refinement of acquisition and correction strategies is reported that can be used to minimize magnetic susceptibility artifacts induced by respiration and by jaw and body movement. Real-time acquisition of sensor signals (e.g., signals induced by jaw and body movement) and MR navigator data were combined to optimize fMRI signal-correction strategies. Within trials, the artifact-induced off-resonance changes were small and mainly reflected the effects of respiration; between trials, movements caused major changes of global frequency and shim (>20 Hz/cm). Several methods were used to assess the stability of the fMRI series: k-space analysis ('dynamic intensity and off-resonance changes in k-space', dubbed DICK and DORK) and image analysis using a Laplace operator and a center-of-mass metric. The variability between trials made it essential to correct for inter-trial variations. On the other hand, images were sufficiently stable with our approach to perform fMRI evaluations on single trials before averaging of trials. Different motion correction strategies were compared: DORK, McFLIRT (rigid body model with three translations and three rotations) and 2D image alignment based on a center-of-mass detection (in-plane translation). The latter yielded the best results and proved to be fast and robust for intra- and inter-trial alignment. Finally, fMRI in the behaving monkey was tested for spatial and temporal reproducibility on a trial-to-trial basis. Highly activated voxels also displayed good reproducibility between trials. On average, the BOLD amplitude response to a short 3-s visual stimulus was close to 2%.     

Comprehensive mathematical simulation of functional magnetic resonance imaging time series including motion-related image distortion and spin saturation effect

There has been vast interest in determining the feasibility of functional magnetic resonance imaging (fMRI) as an accurate method of imaging brain function for patient evaluations. The assessment of fMRI as an accurate tool for activation localization largely depends on the software used to process the time series data. The performance evaluation of different analysis tools is not reliable unless truths in motion and activation are known. Lack of valid truths has been the limiting factor for comparisons of different algorithms. Until now, currently available phantom data do not include comprehensive accounts of head motion. While most fMRI studies assume no interslice motion during the time series acquisition in fMRI data acquired using a multislice and single-shot echo-planar imaging sequence, each slice is subject to a different set of motion parameters. In this study, in addition to known three-dimensional motion parameters applied to each slice, included in the time series computation are geometric distortion from field inhomogeneity and spin saturation effect as a result of out-of-plane head motion. We investigated the effect of these head motion-related artifacts and present a validation of the mapping slice-to-volume (MSV) algorithm for motion correction and activation detection against the known truths. MSV was evaluated, and showed better performance in comparison with other widely used fMRI data processing software, which corrects for head motion with a volume-to-volume realignment method. Furthermore, improvement in signal detection was observed with the implementation of the geometric distortion correction and spin saturation effect compensation features in MSV.     

Surface-based functional magnetic resonance imaging analysis of partial brain echo planar imaging data at 1.5 T

Surface-based functional magnetic resonance imaging (fMRI) analysis is more sensitive and accurate than volume-based analysis for detecting neural activation. However, these advantages are less important in practical fMRI experiments with commonly used 1.5-T magnetic resonance devices because of the resolution gap between the echo planar imaging data and the cortical surface models. We expected high-resolution segmented partial brain echo planar imaging (EPI) data to overcome this problem, and the activation patterns of the high-resolution data could be different from the low-resolution data. For the practical applications of surface-based fMRI analysis using segmented EPI techniques, the effects of some important factors (e.g., activation patterns, registration and local distortions) should be intensively evaluated because the results of surface-based fMRI analyses could be influenced by them. In this study, we demonstrated the difference between activations detected from low-resolution EPI data, which were covering whole brain, and high-resolution segmented EPI data covering partial brain by volume- and surface-based analysis methods. First, we compared the activation maps of low- and high-resolution EPI datasets detected by volume- and surface-based analyses, with the spatial patterns of activation clusters, and analyzed the distributions of activations in occipital lobes. We also analyzed the high-resolution EPI data covering motor areas and fusiform gyri of human brain, and presented the differences of activations detected by volume- and surface-based methods.     

A two-compartment gel phantom for optimization and quality assurance in clinical BOLD fMRI

Clinical applications of blood oxygen level-dependent (BOLD) functional magnetic resonance imaging (fMRI) depend heavily on robust paradigms, imaging methods and analysis procedures. In this work, as a means to optimize and perform quality assurance of the entire imaging and analysis chain, a phantom that provides a well known and reproducible signal change similar to a block type fMRI experiment is presented. It consists of two gel compartments with slightly different T2 that dynamically enter and leave the imaged volume. The homogeneous gel in combination with a cylindrical geometry results in a well-defined T*2 difference causing a signal difference between the two compartments in T*2-weighted MR images. From time series data obtained with the phantom, maps of percent signal change (PSC) and t-values are calculated. As an example of image parameter optimisation, the phantom is demonstrated to be useful for accurate determination of the influence of echo time (TE) on BOLD fMRI results, taking the t-value as a measure of sensitivity. In addition, the phantom is proposed as a tool for quality assurance (QA) since reproducible time series and t-maps are obtained in a series of independent repeat experiments. The phantom is relatively simple to build and can therefore be used by any clinical fMRI center.     

Bayesian wavelet-based analysis of functional magnetic resonance time series

Wavelet methods for image regularization offer a data-driven alternative to Gaussian smoothing in functional magnetic resonance (fMRI) analysis. Their impact has been limited by the difficulties in integrating regularization in the wavelet domain and inference in the image domain, precluding the probabilistic decision on which areas are activated by a task. Here we present an integrated framework for Bayesian estimation and regularization in wavelet space that allows the usual voxelwise hypothesis testing. This framework is flexible, being an adaptation to fMRI time series of a more general wavelet-based functional mixed-effect model. Through testing on a combination of simulated and real fMRI data, we show evidence of improved signal recovery, without compromising test accuracy in image space.     

Elimination of k-space spikes in fMRI data

The subtle signal changes in functional magnetic resonance imaging (fMRI) can be easily overwhelmed by noise of various origins. Spikes in the collected fMRI raw data often arise from high-duty usage of the scanner hardware and can introduce significant noise in the image and thereby in the image time series. Consequently, the spikes will corrupt the functional data and degrade the result of functional mapping. In this work, a simple method based on processing the time course of the k-space data are introduced and implemented to remove the spikes in the acquired data. Application of the method to experimental data shows that the methods are robust and effective for eliminating of spike-related noise in fMRI time series.     

Respiratory noise correction using phase information

Respiratory noise is a confounding factor in functional magnetic resonance imaging (MRI) data analysis. A novel method called Respiratory noise Correction using Phase information is proposed to retrospectively correct for the respiratory noise in functional MRI (fMRI) time series. It is demonstrated that the respiratory movement and the phase of functional MRI images are highly correlated in time. The signal fluctuation due to respiratory movements can be effectively estimated from the phase variation and removed from the functional MRI time series using a Wiener filtering technique. In our experiments, this new method is compared with RETROICOR, which requires recording respiration signal simultaneously in an fMRI experiment. The two techniques show comparable performance with respect to the respiratory noise correction for fMRI time series. However, this technique is more advantageous because there is no need for monitoring the subjects’ respiration or changing functional MRI protocols. This technique is also potentially useful for correcting respiratory noise from abnormal breathing or when the respiration is not periodic.     

Artificial neural network for suppression of banding artifacts in balanced steady-state free precession MRI

The balanced steady-state free precession (bSSFP) MR sequence is frequently used in clinics, but is sensitive to off-resonance effects, which can cause banding artifacts. Often multiple bSSFP datasets are acquired at different phase cycling (PC) angles and then combined in a special way for banding artifact suppression. Many strategies of combining the datasets have been suggested for banding artifact suppression, but there are still limitations in their performance, especially when the number of phase-cycled bSSFP datasets is small. The purpose of this study is to develop a learning-based model to combine the multiple phase-cycled bSSFP datasets for better banding artifact suppression. Multilayer perceptron (MLP) is a feedforward artificial neural network consisting of three layers of input, hidden, and output layers. MLP models were trained by input bSSFP datasets acquired from human brain and knee at 3T, which were separately performed for two and four PC angles. Banding-free bSSFP images were generated by maximum-intensity projection (MIP) of 8 or 12 phase-cycled datasets and were used as targets for training the output layer. The trained MLP models were applied to another brain and knee datasets acquired with different scan parameters and also to multiple phase-cycled bSSFP functional MRI datasets acquired on rat brain at 9.4T, in comparison with the conventional MIP method. Simulations were also performed to validate the MLP approach. Both the simulations and human experiments demonstrated that MLP suppressed banding artifacts significantly, superior to MIP in both banding artifact suppression and SNR efficiency. MLP demonstrated superior performance over MIP for the 9.4T fMRI data as well, which was not used for training the models, while visually preserving the fMRI maps very well. Artificial neural network is a promising technique for combining multiple phase-cycled bSSFP datasets for banding artifact suppression.     

Principal component analysis of the dynamic response measured by fMRI: a generalized linear systems framework.

Principal component analysis (PCA) is one of several structure-seeking multivariate statistical techniques, exploratory as well as inferential, that have been proposed recently for the characterization and detection of activation in both PET and fMRI time series data. In particular, PCA is data driven and does not assume that the neural or hemodynamic response reaches some steady state, nor does it involve correlation with any pre-defined or exogenous experimental design template. In this paper, we present a generalized linear systems framework for PCA based on the singular value decomposition (SVD) model for representation of spatio-temporal fMRI data sets. Statistical inference procedures for PCA, including point and interval estimation will be introduced without the constraint of explicit hypotheses about specific task-dependent effects. The principal eigenvectors capture both the spatial and temporal aspects of fMRI data in a progressive fashion; they are inherently matched to unique and uncorrelated features and are ranked in order of the amount of variance explained. PCA also acts as a variation reduction technique, relegating most of the random noise to the trailing components while collecting systematic structure into the leading ones. Features summarizing variability may not directly be those that are the most useful. Further analysis is facilitated through linear subspace methods involving PC rotation and strategies of projection pursuit utilizing a reduced, lower-dimensional natural basis representation that retains most of the information. These properties will be illustrated in the setting of dynamic time-series response data from fMRI experiments involving pharmacological stimulation of the dopaminergic nigro-striatal system in primates.     

False positive control of activated voxels in single fMRI analysis using bootstrap resampling in comparison to spatial smoothing

Functional magnetic resonance imaging (fMRI) is an effective tool for the measurement of brain neuronal activities. To date, several statistical methods have been proposed for analyzing fMRI datasets to select true active voxels among all the voxels appear to be positively activated. Finding a reliable and valid activation map is very important and becomes more crucial in clinical and neurosurgical investigations of single fMRI data, especially when pre-surgical planning requires accurate lateralization index as well as a precise localization of activation map.Defining a proper threshold to determine true activated regions, using common statistical processes, is a challenging task. This is due to a number of variation sources such as noise, artifacts, and physiological fluctuations in time series of fMRI data which affect spatial distribution of noise in an expected uniform activated region. Spatial smoothing methods are frequently used as a preprocessing step to reduce the effect of noise and artifacts. The smoothing may lead to a shift and enlargement of activation regions, and in some extend, unification of distinct regions.In this article, we propose a bootstrap resampling technique for analyzing single fMRI dataset with the aim of finding more accurate and reliable activated regions. This method can remove false positive voxels and present high localization accuracy in activation map without any spatial smoothing and statistical threshold setting.     

Microcanonical and Canonical Ensembles for fMRI Brain Networks in Alzheimer’s Disease

This paper seeks to advance the state-of-the-art in analysing fMRI data to detect onset of Alzheimer’s disease and identify stages in the disease progression. We employ methods of network neuroscience to represent correlation across fMRI data arrays, and introduce novel techniques for network construction and analysis. In network construction, we vary thresholds in establishing BOLD time series correlation between nodes, yielding variations in topological and other network characteristics. For network analysis, we employ methods developed for modelling statistical ensembles of virtual particles in thermal systems. The microcanonical ensemble and the canonical ensemble are analogous to two different fMRI network representations. In the former case, there is zero variance in the number of edges in each network, while in the latter case the set of networks have a variance in the number of edges. Ensemble methods describe the macroscopic properties of a network by considering the underlying microscopic characterisations which are in turn closely related to the degree configuration and network entropy. When applied to fMRI data in populations of Alzheimer’s patients and controls, our methods demonstrated levels of sensitivity adequate for clinical purposes in both identifying brain regions undergoing pathological changes and in revealing the dynamics of such changes.     

Functional magnetic resonance imaging of awake monkeys: some approaches for improving imaging quality

Functional magnetic resonance imaging (fMRI) at high magnetic field strength can suffer from serious degradation of image quality because of motion and physiological noise, as well as spatial distortions and signal losses due to susceptibility effects. Overcoming such limitations is essential for sensitive detection and reliable interpretation of fMRI data. These issues are particularly problematic in studies of awake animals. As part of our initial efforts to study functional brain activations in awake, behaving monkeys using fMRI at 4.7 T, we have developed acquisition and analysis procedures to improve image quality with encouraging results.We evaluated the influence of two main variables on image quality. First, we show how important the level of behavioral training is for obtaining good data stability and high temporal signal-to-noise ratios. In initial sessions, our typical scan session lasted 1.5 h, partitioned into short (<10 min) runs. During reward periods and breaks between runs, the monkey exhibited movements resulting in considerable image misregistrations. After a few months of extensive behavioral training, we were able to increase the length of individual runs and the total length of each session. The monkey learned to wait until the end of a block for fluid reward, resulting in longer periods of continuous acquisition. Each additional 60 training sessions extended the duration of each session by 60 min, culminating, after about 140 training sessions, in sessions that last about 4 h. As a result, the average translational movement decreased from over 500 μm to less than 80 μm, a displacement close to that observed in anesthetized monkeys scanned in a 7-T horizontal scanner.Another major source of distortion at high fields arises from susceptibility variations. To reduce such artifacts, we used segmented gradient-echo echo-planar imaging (EPI) sequences. Increasing the number of segments significantly decreased susceptibility artifacts and image distortion. Comparisons of images from functional runs using four segments with those using a single-shot EPI sequence revealed a roughly twofold improvement in functional signal-to-noise-ratio and 50% decrease in distortion. These methods enabled reliable detection of neural activation and permitted blood-oxygenation-level-dependent-based mapping of early visual areas in monkeys using a volume coil.In summary, both extensive behavioral training of monkeys and application of segmented gradient-echo EPI sequence improved signal-to-noise ratio and image quality. Understanding the effects these factors have is important for the application of high field imaging methods to the detection of submillimeter functional structures in the awake monkey brain.     

To smooth or not to smooth? ROC analysis of perfusion fMRI data

Blood oxygenation level dependent (BOLD) contrast has been widely used for visualizing regional neural activation. Temporal filtering and parameter estimation algorithms are generally used to account for the intrinsic temporal autocorrelation present in BOLD data. Arterial spin labeling perfusion imaging is an emerging methodology for visualizing regional brain function both at rest and during activation. Perfusion contrast manifests different noise properties compared with BOLD contrast, represented by the even distribution of noise power and spatial coherence across the frequency spectrum. Consequently, different strategies are expected to be employed in the statistical analysis of functional magnetic resonance imaging (fMRI) data based on perfusion contrast. In this study, the effect of different analysis methods upon signal detection efficacy, as assessed by receiver operator characteristic (ROC) measures, was examined for perfusion fMRI data. Simulated foci of neural activity of varying amplitude and spatial extent were added to resting perfusion data, and the accuracy of each analysis was evaluated by comparing the results with the known distribution of pseudo-activation. In contrast to the BOLD fMRI, temporal smoothing or filtering reduces the power of perfusion fMRI data analyses whereas spatial smoothing is beneficial to the efficacy of analyses.     

Cortex-based independent component analysis of fMRI time series

The cerebral cortex is the main target of analysis in many functional magnetic resonance imaging (fMRI) studies. Since only about 20% of the voxels of a typical fMRI data set lie within the cortex, statistical analysis can be restricted to the subset of the voxels obtained after cortex segmentation. While such restriction does not influence conventional univariate statistical tests, it may have a substantial effect on the performance of multivariate methods.

Here, we describe a novel approach for data-driven analysis of single-subject fMRI time series that combines techniques for the segmentation and reconstruction of the cortical surface of the brain and the spatial independent component analysis (sICA) of the functional time courses (TCs). We use the mesh of the white matter/gray matter boundary, automatically reconstructed from high-spatial-resolution anatomical MR images, to limit the sICA decomposition of a coregistered functional time series to those voxels which are within a specified region with respect to the cortical sheet (cortex-based ICA, or cbICA). We illustrate our analysis method in the context of fMRI blocked and event-related experimental designs and in an fMRI experiment with perceptually ambiguous stimulation, in which an a priori specification of the stimulation protocol is not possible.

A comparison between cbICA and conventional hypothesis-driven statistical methods shows that cortical surface maps and component TCs blindly obtained with cbICA reliably reflect task-related spatiotemporal activation patterns. Furthermore, the advantages of using cbICA when the specification of a temporal model of the expected hemodynamic response is not straightforward are illustrated and discussed. A comparison between cbICA and anatomically unconstrained ICA reveals that — beside reducing computational demand — the cortex-based approach improves the fitting of the ICA model in the gray matter voxels, the separation of cortical components and the estimation of their TCs, particularly in the case of fMRI data sets with a complex spatiotemporal statistical structure.     

Performance of blind source separation algorithms for fMRI analysis using a group ICA method

Independent component analysis (ICA) is a popular blind source separation technique that has proven to be promising for the analysis of functional magnetic resonance imaging (fMRI) data. A number of ICA approaches have been used for fMRI data analysis, and even more ICA algorithms exist; however, the impact of using different algorithms on the results is largely unexplored. In this paper, we study the performance of four major classes of algorithms for spatial ICA, namely, information maximization, maximization of non-Gaussianity, joint diagonalization of cross-cumulant matrices and second-order correlation-based methods, when they are applied to fMRI data from subjects performing a visuo-motor task. We use a group ICA method to study variability among different ICA algorithms, and we propose several analysis techniques to evaluate their performance. We compare how different ICA algorithms estimate activations in expected neuronal areas. The results demonstrate that the ICA algorithms using higher-order statistical information prove to be quite consistent for fMRI data analysis. Infomax, FastICA and joint approximate diagonalization of eigenmatrices (JADE) all yield reliable results, with each having its strengths in specific areas. Eigenvalue decomposition (EVD), an algorithm using second-order statistics, does not perform reliably for fMRI data. Additionally, for iterative ICA algorithms, it is important to investigate the variability of estimates from different runs. We test the consistency of the iterative algorithms Infomax and FastICA by running the algorithm a number of times with different initializations, and we note that they yield consistent results over these multiple runs. Our results greatly improve our confidence in the consistency of ICA for fMRI data analysis.     

An unsupervised deep learning technique for susceptibility artifact correction in reversed phase-encoding EPI images

Echo planar imaging (EPI) is a fast and non-invasive magnetic resonance imaging technique that supports data acquisition at high spatial and temporal resolutions. However, susceptibility artifacts, which cause the misalignment to the underlying structural image, are unavoidable distortions in EPI. Traditional susceptibility artifact correction (SAC) methods estimate the displacement field by optimizing an objective function that involves one or more pairs of reversed phase-encoding (PE) images. The estimated displacement field is then used to unwarp the distorted images and produce the corrected images. Since this conventional approach is time-consuming, we propose an end-to-end deep learning technique, named S-Net, to correct the susceptibility artifacts the reversed-PE image pair. The proposed S-Net consists of two components: (i) a convolutional neural network to map a reversed-PE image pair to the displacement field; and (ii) a spatial transform unit to unwarp the input images and produce the corrected images. The S-Net is trained using a set of reversed-PE image pairs and an unsupervised loss function, without ground-truth data. For a new image pair of reversed-PE images, the displacement field and corrected images are obtained simultaneously by evaluating the trained S-Net directly. Evaluations on three different datasets demonstrate that S-Net can correct the susceptibility artifacts in the reversed-PE images. Compared with two state-of-the-art SAC methods (TOPUP and TISAC), the proposed S-Net runs significantly faster: 20 times faster than TISAC and 369 times faster than TOPUP, while achieving a similar correction accuracy. Consequently, S-Net accelerates the medical image processing pipelines and makes the real-time correction for MRI scanners feasible. Our proposed technique also opens up a new direction in learning-based SAC.     

Functional Magnetic Resonance Imaging Data Analysis by Autoregressive Estimator

The autoregressive (AR) estimator, a non-parametric method, is used to analyze functional magnetic resonance imaging (fMRI) data. The same method has been used, with success, in several other time series data analysis. It uses exclusively the available experimental data points to estimate the most plausible power spectra compatible with the experimental data and there is no need to make any assumption about non-measured points. The time series, obtained from fMRI block paradigm data, is analyzed by the AR method to determine the brain active regions involved in the processing of a given stimulus. This method is considerably more reliable than the fast Fourier transform or the parametric methods. The time series corresponding to each image pixel is analyzed using the AR estimator and the corresponding poles are obtained. The pole distribution gives the shape of power spectra, and the pixels with poles at the stimulation frequency are considered as the active regions. The method was applied in simulated and real data, its superiority is shown by the receiver operating characteristic curves which were obtained using the simulated data.     

Comparison of pattern recognition methods in classifying high-resolution BOLD signals obtained at high magnetic field in monkeys

Pattern recognition methods have shown that functional magnetic resonance imaging (fMRI) data can reveal significant information about brain activity. For example, in the debate of how object categories are represented in the brain, multivariate analysis has been used to provide evidence of a distributed encoding scheme [Science 293:5539 (2001) 2425–2430]. Many follow-up studies have employed different methods to analyze human fMRI data with varying degrees of success [Nature reviews 7:7 (2006) 523–534]. In this study, we compare four popular pattern recognition methods: correlation analysis, support-vector machines (SVM), linear discriminant analysis (LDA) and Gaussian naïve Bayes (GNB), using data collected at high field (7 Tesla) with higher resolution than usual fMRI studies. We investigate prediction performance on single trials and for averages across varying numbers of stimulus presentations. The performance of the various algorithms depends on the nature of the brain activity being categorized: for several tasks, many of the methods work well, whereas for others, no method performs above chance level. An important factor in overall classification performance is careful preprocessing of the data, including dimensionality reduction, voxel selection and outlier elimination.