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A general framework for the analysis of vessel encoded arterial spin labeling for vascular territory mapping.
Vessel encoded arterial spin labeling provides a way to perform non-invasive vascular territory imaging. By uniquely encoding the blood within feeding arteries over a number of images, the territories of each can be identified. Here, a new approach for the analysis of vessel encoded arterial spin labeling data is presented. The method includes a full description of how the geometry of arteries and spatial label modulation affects the measured signal. It also incorporates an artery-based classification that considers multiple arteries in each class, explicitly permitting a voxel to be supplied by multiple arteries. The developed framework is cast within a Bayesian inference procedure allowing both flow contributions and the locations of the arteries in the labeling plane to be inferred. By using simulated data, the method was shown to provide more accurate estimates of blood contribution in areas of mixed supply, such as would be found in watershed regions, than conventional methods. It was also able to estimate the location of arteries within the labeling plane, accounting for motion between sequence prescription and acquisition. Similar performance was found for data acquired using a pseudo-continuous labeling scheme both in the neck and above the Circle of Willis.
Characterization and propagation of uncertainty in diffusion-weighted MR imaging.
A fully probabilistic framework is presented for estimating local probability density functions on parameters of interest in a model of diffusion. This technique is applied to the estimation of parameters in the diffusion tensor model, and also to a simple partial volume model of diffusion. In both cases the parameters of interest include parameters defining local fiber direction. A technique is then presented for using these density functions to estimate global connectivity (i.e., the probability of the existence of a connection through the data field, between any two distant points), allowing for the quantification of belief in tractography results. This technique is then applied to the estimation of the cortical connectivity of the human thalamus. The resulting connectivity distributions correspond well with predictions from invasive tracer methods in nonhuman primate.
Bayesian inference of hemodynamic changes in functional arterial spin labeling data.
The study of brain function using MRI relies on acquisition techniques that are sensitive to different aspects of the hemodynamic response contiguous to areas of neuronal activity. For this purpose different contrasts such as arterial spin labeling (ASL) and blood oxygenation level dependent (BOLD) functional MRI techniques have been developed to investigate cerebral blood flow (CBF) and blood oxygenation, respectively. Analysis of such data typically proceeds by separate, linear modeling of the appropriate CBF or BOLD time courses. In this work an approach is developed that provides simultaneous inference on hemodynamic changes via a nonlinear physiological model of ASL data acquired at multiple echo times. Importantly, this includes a significant contribution by changes in the static magnetization, M, to the ASL signal. Inference is carried out in a Bayesian framework. This is able to extract, from dual-echo ASL data, probabilistic estimates of percentage changes of CBF, R(2) (*), and the static magnetization, M. This approach provides increased sensitivity in inferring CBF changes and reduced contamination in inferring BOLD changes when compared with general linear model approaches on single-echo ASL data. We also consider how the static magnetization, M, might be related to changes in CBV by assuming the same mechanism for water exchange as in vascular space occupancy.
Variational Bayes inference of spatial mixture models for segmentation.
Mixture models are commonly used in the statistical segmentation of images. For example, they can be used for the segmentation of structural medical images into different matter types, or of statistical parametric maps into activating and nonactivating brain regions in functional imaging. Spatial mixture models have been developed to augment histogram information with spatial regularization using Markov random fields (MRFs). In previous work, an approximate model was developed to allow adaptive determination of the parameter controlling the strength of spatial regularization. Inference was performed using Markov Chain Monte Carlo (MCMC) sampling. However, this approach is prohibitively slow for large datasets. In this work, a more efficient inference approach is presented. This combines a variational Bayes approximation with a second-order Taylor expansion of the components of the posterior distribution, which would otherwise be intractable to Variational Bayes. This provides inference on fully adaptive spatial mixture models an order of magnitude faster than MCMC. We examine the behavior of this approach when applied to artificial data with different spatial characteristics, and to functional magnetic resonance imaging statistical parametric maps.
Motor practice promotes increased activity in brain regions structurally disconnected after subcortical stroke.
BACKGROUND: Motor practice is an important component of neurorehabilitation. Imaging studies in healthy individuals show that dynamic brain activation changes with practice. Defining patterns of functional brain plasticity associated with motor practice following stroke could guide rehabilitation. OBJECTIVE: The authors aimed to test whether practice-related changes in brain activity differ after stroke and to explore spatial relationships between activity changes and patterns of structural degeneration. METHODS: They studied 10 patients at least 6 months after left-hemisphere subcortical strokes and 18 healthy controls. Diffusion-weighted magnetic resonance imaging (MRI) was acquired at baseline, and functional MRI (fMRI) was acquired during performance of a visuomotor tracking task before and after a 15-day period of practice of the same task. RESULTS: Smaller short-term practice effects at baseline correlated with lower fractional anisotropy in the posterior limbs of the internal capsule (PLIC) bilaterally in patients (t > 3; cluster P < .05). After 15 days of motor practice a Group × Time interaction (z > 2.3; cluster P < .05) was found in the basal ganglia, thalamus, inferior frontal gyrus, superior temporal gyrus, and insula. In these regions, healthy controls showed decreases and patients showed increases in activity with practice. Some regions of interest had a loss of white matter connectivity at baseline. CONCLUSIONS: Performance gains with motor practice can be associated with increased activity in regions that have been either directly or indirectly impaired by loss of connectivity. These results suggest that neurorehabilitation interventions may be associated with compensatory adaptation of intact brain regions as well as enhanced activity in regions with impaired structural connectivity.
Learning the value of information in an uncertain world.
Our decisions are guided by outcomes that are associated with decisions made in the past. However, the amount of influence each past outcome has on our next decision remains unclear. To ensure optimal decision-making, the weight given to decision outcomes should reflect their salience in predicting future outcomes, and this salience should be modulated by the volatility of the reward environment. We show that human subjects assess volatility in an optimal manner and adjust decision-making accordingly. This optimal estimate of volatility is reflected in the fMRI signal in the anterior cingulate cortex (ACC) when each trial outcome is observed. When a new piece of information is witnessed, activity levels reflect its salience for predicting future outcomes. Furthermore, variations in this ACC signal across the population predict variations in subject learning rates. Our results provide a formal account of how we weigh our different experiences in guiding our future actions.
Non-invasive mapping of connections between human thalamus and cortex using diffusion imaging.
Evidence concerning anatomical connectivities in the human brain is sparse and based largely on limited post-mortem observations. Diffusion tensor imaging has previously been used to define large white-matter tracts in the living human brain, but this technique has had limited success in tracing pathways into gray matter. Here we identified specific connections between human thalamus and cortex using a novel probabilistic tractography algorithm with diffusion imaging data. Classification of thalamic gray matter based on cortical connectivity patterns revealed distinct subregions whose locations correspond to nuclei described previously in histological studies. The connections that we found between thalamus and cortex were similar to those reported for non-human primates and were reproducible between individuals. Our results provide the first quantitative demonstration of reliable inference of anatomical connectivity between human gray matter structures using diffusion data and the first connectivity-based segmentation of gray matter.
Tools of the trade: psychophysiological interactions and functional connectivity.
Psychophysiological interactions (PPIs) analysis is a method for investigating task-specific changes in the relationship between activity in different brain areas, using functional magnetic resonance imaging (fMRI) data. Specifically, PPI analyses identify voxels in which activity is more related to activity in a seed region of interest (seed ROI) in a given psychological context, such as during attention or in the presence of emotive stimuli. In this tutorial, we aim to give a simple conceptual explanation of how PPI analysis works, in order to assist readers in planning and interpreting their own PPI experiments.
Robust group analysis using outlier inference.
Neuroimaging group studies are typically performed with the assumption that subjects used are randomly drawn from a population of subjects. The population of subjects is assumed to have a distribution of effect sizes associated with it that are Gaussian distributed. However, in practice, group studies can include "outlier" subjects whose effect sizes are completely at odds with the general population for reasons that are not of experimental interest. If ignored, these outliers can dramatically affect the inference results. To solve this problem, we propose a group inference approach which includes inference of outliers using a robust general linear model (GLM) approach. This approach models the errors as being a mixture of two Gaussian distributions, one for the normal population and one for the outliers. Crucially the robust GLM is part of a traditional hierarchical group model which uses GLMs at each level of the hierarchy. This combines the benefits of outlier inference with the benefits of using variance information from lower levels in the hierarchy. A Bayesian inference framework is used to infer on the robust GLM, while using the lower level variance information. The performance of the method is demonstrated on simulated and fMRI data and is compared with iterative reweighted least squares and permutation testing.
Automated single-trial measurement of amplitude and latency of laser-evoked potentials (LEPs) using multiple linear regression.
OBJECTIVE: Laser stimulation of Adelta-fibre nociceptors in the skin evokes nociceptive-specific brain responses (laser-evoked potentials, LEPs). The largest vertex complex (N2-P2) is widely used to assess nociceptive pathways in physiological and clinical studies. The aim of this study was to develop an automated method to measure amplitudes and latencies of the N2 and P2 peaks on a single-trial basis. METHODS: LEPs were recorded after Nd:YAP laser stimulation of the left hand dorsum in 7 normal volunteers. For each subject, a basis set of 4 regressors (the N2 and P2 waveforms and their respective temporal derivatives) was derived from the time-averaged data and regressed against every single-trial LEP response. This provided a separate quantitative estimate of amplitude and latency for the N2 and P2 components of each trial. RESULTS: All estimates of LEP parameters correlated significantly with the corresponding measurements performed by a human expert (N2 amplitude: R2=0.70; P2 amplitude: R2=0.70; N2 latency: R2=0.81; P2 latency: R2=0.59. All P<0.0001). Furthermore, regression analysis was able to extract an LEP response from a subset of the trials that had been classified by the human expert as without response. CONCLUSIONS: This method provides a simple, fast and unbiased measurement of different components of single-trial LEP responses. SIGNIFICANCE: This method is particularly desirable in several experimental conditions (e.g. drug studies, correlations with experimental variables, simultaneous EEG/fMRI and low signal-to-noise ratio data) and in clinical practice. The described multiple linear regression approach can be easily implemented for measuring evoked potentials in other sensory modalities.
A fast analysis method for non-invasive imaging of blood flow in individual cerebral arteries using vessel-encoded arterial spin labelling angiography.
Arterial spin labelling (ASL) MRI offers a non-invasive means to create blood-borne contrast in vivo for dynamic angiographic imaging. By spatial modulation of the ASL process it is possible to uniquely label individual arteries over a series of measurements, allowing each to be separately identified in the resulting angiographic images. This separation requires appropriate analysis for which a general Bayesian framework has previously been proposed. Here this framework is adapted for clinical dynamic angiographic imaging. This specifically addresses the issues of computational speed of the algorithm and the robustness required to deal with real patient data. An algorithm is proposed that can incorporate planning information about the arteries being imaged whilst adapting for subsequent patient movement. A fast maximum a posteriori solution is adopted and shown to be only marginally less accurate than Monte Carlo sampling under simulation. The final algorithm is demonstrated on in vivo data with analysis on a time scale of the order of 10min, from both a healthy control and a patient with a vertebro-basilar occlusion.
Separation of macrovascular signal in multi-inversion time arterial spin labelling MRI.
Arterial spin labeling (ASL) provides a noninvasive method to measure brain perfusion and is becoming an increasingly viable alternative to more invasive MR methods due to improvements in acquisition, such as the use of a three-dimensional GRASE readout. A potential source of error in ASL measurements is signal arising from intravascular blood that is destined for more distal tissue. This is typically suppressed using diffusion gradients in many ASL sequences. However, several problems exist with this approach, such as the choice of cutoff velocity and gradient direction and incompatibility with certain readout modules. An alternative approach is to explicitly model the intravascular signal. This study exploits this approach by using multi-inversion time ASL data with a recently developed model-fitting method. The method employed permits the intravascular contribution to be discarded in voxels where there is no support in the data for its inclusion, thereby addressing the issue of overfitting. It is shown by comparing data with and without flow suppression, and by comparing the intravascular contribution in GRASE ASL data to MR angiographic images, that the model-fitting approach can provide a viable alternative to flow suppression in ASL where suppression is either not feasible or not desirable.
Applying FSL to the FIAC data: model-based and model-free analysis of voice and sentence repetition priming.
This article presents results obtained from applying various tools from FSL (FMRIB Software Library) to data from the repetition priming experiment used for the HBM'05 Functional Image Analysis Contest. We present analyses from the model-based General Linear Model (GLM) tool (FEAT) and from the model-free independent component analysis tool (MELODIC). We also discuss the application of tools for the correction of image distortions prior to the statistical analysis and the utility of recent advances in functional magnetic resonance imaging (FMRI) time series modeling and inference such as the use of optimal constrained HRF basis function modeling and mixture modeling inference. The combination of hemodynamic response function (HRF) and mixture modeling, in particular, revealed that both sentence content and speaker voice priming effects occurred bilaterally along the length of the superior temporal sulcus (STS). These results suggest that both are processed in a single underlying system without any significant asymmetries for content vs. voice processing.
Partial volume correction of multiple inversion time arterial spin labeling MRI data.
The accuracy of cerebral blood flow (CBF) estimates from arterial spin labeling (ASL) is affected by the presence of both gray matter (GM) and white matter within any voxel. Recently a partial volume (PV) correction method for ASL has been demonstrated (Asllani et al. Magn Reson Med 2008; 60:1362-1371), where PV estimates were used with a local linear regression to separate the GM and white matter ASL signal. Here a new PV correction method for multi-inversion time ASL is proposed that exploits PV estimates within a spatially regularized kinetic curve model analysis. The proposed method exploits both PV estimates and the different kinetics of the ASL signal arising from GM and white matter. The new correction method is shown, on both simulated and real data, to provide correction of GM CBF comparable to a linear regression approach, whilst preserving greater spatial detail in the CBF image. On real data corrected GM CBF values were found to be largely independent of GM PV, implying that the correction had been successful. Increases of mean GM CBF after correction of 69-80% were observed.
Constrained linear basis sets for HRF modelling using Variational Bayes.
FMRI modelling requires flexible haemodynamic response function (HRF) modelling, with the HRF being allowed to vary spatially and between subjects. To achieve this flexibility, voxelwise parameterised HRFs have been proposed; however, inference on such models is very slow. An alternative approach is to use basis functions allowing inference to proceed in the more manageable General Linear Model (GLM) framework. However, a large amount of the subspace spanned by the basis functions produces nonsensical HRF shapes. In this work we propose a technique for choosing a basis set, and then the means to constrain the subspace spanned by the basis set to only include sensible HRF shapes. Penny et al. showed how Variational Bayes can be used to infer on the GLM for FMRI. Here we extend the work of Penny et al. to give inference on the GLM with constrained HRF basis functions and with spatial Markov Random Fields on the autoregressive noise parameters. Constraining the subspace spanned by the basis set allows for far superior separation of activating voxels from nonactivating voxels in FMRI data. We use spatial mixture modelling to produce final probabilities of activation and demonstrate increased sensitivity on an FMRI dataset.
Multilevel linear modelling for FMRI group analysis using Bayesian inference.
Functional magnetic resonance imaging studies often involve the acquisition of data from multiple sessions and/or multiple subjects. A hierarchical approach can be taken to modelling such data with a general linear model (GLM) at each level of the hierarchy introducing different random effects variance components. Inferring on these models is nontrivial with frequentist solutions being unavailable. A solution is to use a Bayesian framework. One important ingredient in this is the choice of prior on the variance components and top-level regression parameters. Due to the typically small numbers of sessions or subjects in neuroimaging, the choice of prior is critical. To alleviate this problem, we introduce to neuroimage modelling the approach of reference priors, which drives the choice of prior such that it is noninformative in an information-theoretic sense. We propose two inference techniques at the top level for multilevel hierarchies (a fast approach and a slower more accurate approach). We also demonstrate that we can infer on the top level of multilevel hierarchies by inferring on the levels of the hierarchy separately and passing summary statistics of a noncentral multivariate t distribution between them.
Advances in functional and structural MR image analysis and implementation as FSL.
The techniques available for the interrogation and analysis of neuroimaging data have a large influence in determining the flexibility, sensitivity, and scope of neuroimaging experiments. The development of such methodologies has allowed investigators to address scientific questions that could not previously be answered and, as such, has become an important research area in its own right. In this paper, we present a review of the research carried out by the Analysis Group at the Oxford Centre for Functional MRI of the Brain (FMRIB). This research has focussed on the development of new methodologies for the analysis of both structural and functional magnetic resonance imaging data. The majority of the research laid out in this paper has been implemented as freely available software tools within FMRIB's Software Library (FSL).
Comparing model-based and model-free analysis methods for QUASAR arterial spin labeling perfusion quantification.
Amongst the various implementations of arterial spin labeling MRI methods for quantifying cerebral perfusion, the QUASAR method is unique. By using a combination of labeling with and without flow suppression gradients, the QUASAR method offers the separation of macrovascular and tissue signals. This permits local arterial input functions to be defined and "model-free" analysis, using numerical deconvolution, to be used. However, it remains unclear whether arterial spin labeling data are best treated using model-free or model-based analysis. This work provides a critical comparison of these two approaches for QUASAR arterial spin labeling in the healthy brain. An existing two-component (arterial and tissue) model was extended to the mixed flow suppression scheme of QUASAR to provide an optimal model-based analysis. The model-based analysis was extended to incorporate dispersion of the labeled bolus, generally regarded as the major source of discrepancy between the two analysis approaches. Model-free and model-based analyses were compared for perfusion quantification including absolute measurements, uncertainty estimation, and spatial variation in cerebral blood flow estimates. Major sources of discrepancies between model-free and model-based analysis were attributed to the effects of dispersion and the degree to which the two methods can separate macrovascular and tissue signal.