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Measuring functional connectivity in MEG: a multivariate approach insensitive to linear source leakage.
A number of recent studies have begun to show the promise of magnetoencephalography (MEG) as a means to non-invasively measure functional connectivity within distributed networks in the human brain. However, a number of problems with the methodology still remain--the biggest of these being how to deal with the non-independence of voxels in source space, often termed signal leakage. In this paper we demonstrate a method by which non-zero lag cortico-cortical interactions between the power envelopes of neural oscillatory processes can be reliably identified within a multivariate statistical framework. The method is spatially unbiased, moderately conservative in false positive rate and removes linear signal leakage between seed and target voxels. We demonstrate this methodology in simulation and in real MEG data. The multivariate method offers a powerful means to capture the high dimensionality and rich information content of MEG signals in a single imaging statistic. Given a significant interaction between two areas, we go on to show how classical statistical tests can be used to quantify the importance of the data features driving the interaction.
Investigating the electrophysiological basis of resting state networks using magnetoencephalography
In recent years the study of resting state brain networks (RSNs) has become an important area of neuroimaging. The majority of studies have used functional magnetic resonance imaging (fMRI) to measure temporal correlation between blood-oxygenation- level–dependent (BOLD) signals from different brain areas. How- ever, BOLD is an indirect measure related to hemodynamics, and the electrophysiological basis of connectivity between spatially separate network nodes cannot be comprehensively assessed using this technique. In this paper we describe a means to charac- terize resting state brain networks independently using magneto- encephalography (MEG), a neuroimaging modality that bypasses the hemodynamic response and measures the magnetic fields as- sociated with electrophysiological brain activity. The MEG data are analyzed using a unique combination of beamformer spatial filter- ing and independent component analysis (ICA) and require no prior assumptions about the spatial locations or patterns of the net- works. This method results in RSNs with significant similarity in their spatial structure compared with RSNs derived independently using fMRI. This outcome confirms the neural basis of hemody- namic networks and demonstrates the potential of MEG as a tool for understanding the mechanisms that underlie RSNs and the na- ture of connectivity that binds network nodes.
The danger of systematic bias in group-level FMRI-lag-based causality estimation.
Schippers, Renken and Keysers (NeuroImage, 2011) present a simulation of multi-subject lag-based causality estimation. We fully agree that single-subject evaluations (e.g., Smith et al., 2011) need to be revisited in the context of multi-subject studies, and Schippers' paper is a good example, including detailed multi-level simulation and cross-subject statistical modelling. The authors conclude that "the average chance to find a significant Granger causality effect when no actual influence is present in the data stays well below the p-level imposed on the second level statistics" and that "when the analyses reveal a significant directed influence, this direction was accurate in the vast majority of the cases". Unfortunately, we believe that the general meaning that may be taken from these statements is not supported by the paper's results, as there may in reality be a systematic (group-average) difference in haemodynamic delay between two brain areas. While many statements in the paper (e.g., the final two sentences) do refer to this problem, we fear that the overriding message that many readers may take from the paper could cause misunderstanding.
Bayesian inference in FMRI.
Bayesian inference has taken FMRI methods research into areas that frequentist statistics have struggled to reach. In this article we will consider some of the early forays into Bayes and what motivated its use. We shall see the impact that Bayes has had on haemodynamic modelling, spatial modelling, group analysis, model selection and brain connectivity analysis; and consider how these advancements have spun-off into related areas of neuroscience and some of the challenges that remain. Bayes has brought to the table inference flexibility, incorporation of prior information, adaptive regularisation and model selection. But perhaps more important than these things, is the ability of Bayes to empower the methods researcher with a mathematically principled framework for inferring on any model.
FSL.
FSL (the FMRIB Software Library) is a comprehensive library of analysis tools for functional, structural and diffusion MRI brain imaging data, written mainly by members of the Analysis Group, FMRIB, Oxford. For this NeuroImage special issue on "20 years of fMRI" we have been asked to write about the history, developments and current status of FSL. We also include some descriptions of parts of FSL that are not well covered in the existing literature. We hope that some of this content might be of interest to users of FSL, and also maybe to new research groups considering creating, releasing and supporting new software packages for brain image analysis.
MEG beamforming using Bayesian PCA for adaptive data covariance matrix regularization.
Beamformers are a commonly used method for doing source localization from magnetoencephalography (MEG) data. A key ingredient in a beamformer is the estimation of the data covariance matrix. When the noise levels are high, or when there is only a small amount of data available, the data covariance matrix is estimated poorly and the signal-to-noise ratio (SNR) of the beamformer output degrades. One solution to this is to use regularization whereby the diagonal of the covariance matrix is amplified by a pre-specified amount. However, this provides improvements at the expense of a loss in spatial resolution, and the parameter controlling the amount of regularization must be chosen subjectively. In this paper, we introduce a method that provides an adaptive solution to this problem by using a Bayesian Principle Component Analysis (PCA). This provides an estimate of the data covariance matrix to give a data-driven, non-arbitrary solution to the trade-off between the spatial resolution and the SNR of the beamformer output. This also provides a method for determining when the quality of the data covariance estimate maybe under question. We apply the approach to simulated and real MEG data, and demonstrate the way in which it can automatically adapt the regularization to give good performance over a range of noise and signal levels.
Combined spatial and non-spatial prior for inference on MRI time-series.
When modelling FMRI and other MRI time-series data, a Bayesian approach based on adaptive spatial smoothness priors is a compelling alternative to using a standard generalized linear model (GLM) on presmoothed data. Another benefit of the Bayesian approach is that biophysical prior information can be incorporated in a principled manner; however, this requirement for a fixed non-spatial prior on a parameter would normally preclude using spatial regularization on that same parameter. We have developed a Gaussian-process-based prior to apply adaptive spatial regularization while still ensuring that the fixed biophysical prior is correctly applied on each voxel. A parameterized covariance matrix provides separate control over the variance (the diagonal elements) and the between-voxel correlation (due to off-diagonal elements). Analysis proceeds using evidence optimization (EO), with variational Bayes (VB) updates used for some parameters. The method can also be applied to non-linear forward models by using a linear Taylor expansion centred on the latest parameter estimates. Applying the method to FMRI with a constrained haemodynamic response function (HRF) shape model shows improved fits in simulations, compared to using either the non-spatial or spatial-smoothness prior alone. We also analyse multi-inversion arterial spin labelling data using a non-linear perfusion model to estimate cerebral blood flow and bolus arrival time. By combining both types of prior information, this new prior performs consistently well across a wider range of situations than either prior alone, and provides better estimates when both types of prior information are relevant.
Multiple-subjects connectivity-based parcellation using hierarchical Dirichlet process mixture models.
We propose a hierarchical infinite mixture model approach to address two issues in connectivity-based parcellations: (i) choosing the number of clusters, and (ii) combining data from different subjects. In a Bayesian setting, we model voxel-wise anatomical connectivity profiles as an infinite mixture of multivariate Gaussian distributions, with a Dirichlet process prior on the cluster parameters. This type of prior allows us to conveniently model the number of clusters and estimate its posterior distribution directly from the data. An important benefit of using Bayesian modelling is the extension to multiple subjects clustering via a hierarchical mixture of Dirichlet processes. Data from different subjects are used to infer on class parameters and the number of classes at individual and group level. Such a method accounts for inter-subject variability, while still benefiting from combining different subjects data to yield more robust estimates of the individual clusterings.
Associative learning of social value.
Our decisions are guided by information learnt from our environment. This information may come via personal experiences of reward, but also from the behaviour of social partners. Social learning is widely held to be distinct from other forms of learning in its mechanism and neural implementation; it is often assumed to compete with simpler mechanisms, such as reward-based associative learning, to drive behaviour. Recently, neural signals have been observed during social exchange reminiscent of signals seen in studies of associative learning. Here we demonstrate that social information may be acquired using the same associative processes assumed to underlie reward-based learning. We find that key computational variables for learning in the social and reward domains are processed in a similar fashion, but in parallel neural processing streams. Two neighbouring divisions of the anterior cingulate cortex were central to learning about social and reward-based information, and for determining the extent to which each source of information guides behaviour. When making a decision, however, the information learnt using these parallel streams was combined within ventromedial prefrontal cortex. These findings suggest that human social valuation can be realized by means of the same associative processes previously established for learning other, simpler, features of the environment.
How green is the grass on the other side? Frontopolar cortex and the evidence in favor of alternative courses of action.
Behavioral flexibility is the hallmark of goal-directed behavior. Whereas a great deal is known about the neural substrates of behavioral adjustment when it is explicitly cued by features of the external environment, little is known about how we adapt our behavior when such changes are made on the basis of uncertain evidence. Using a Bayesian reinforcement-learning model and fMRI, we show that frontopolar cortex (FPC) tracks the relative advantage in favor of switching to a foregone alternative when choices are made voluntarily. Changes in FPC functional connectivity occur when subjects finally decide to switch to the alternative behavior. Moreover, interindividual variation in the FPC signal predicts interindividual differences in effectively adapting behavior. By contrast, ventromedial prefrontal cortex (vmPFC) encodes the relative value of the current decision. Collectively, these findings reveal complementary prefrontal computations essential for promoting short- and long-term behavioral flexibility.
Modeling dispersion in arterial spin labeling: validation using dynamic angiographic measurements.
A major assumption in arterial spin labeling (ASL) MRI perfusion quantification is the time course of the signal on arrival in the capillary network. The normally assumed square label profile is not preserved during transit of the label through the vasculature. This change in profile can be attributed to a number of effects collectively denoted as dispersion. A number of models for this effect have been proposed, but they have been difficult to validate. In this study ASL data acquired whilst the label was still within larger arteries was used to compare models of label dispersion. Models were fit using a probabilistic algorithm and evaluated according to their ability to fit the data. Data from an elderly population were considered including both healthy controls and patients with a variety of vascular disease. The authors conclude that modeling ASL dispersion using a convolution of the ideal ASL label profile with a dispersion kernel is most appropriate, where the kernel itself takes the form of a gamma distribution. This model provided a best fit to the data considered, was consistent with the measured flow profile in arteries and was sufficiently mathematically simple to make it practical for ASL tissue perfusion quantification.
Relationship between physiological measures of excitability and levels of glutamate and GABA in the human motor cortex.
Magnetic resonance spectroscopy (MRS) allows measurement of neurotransmitter concentrations within a region of interest in the brain. Inter-individual variation in MRS-measured GABA levels have been related to variation in task performance in a number of regions. However, it is not clear how MRS-assessed measures of GABA relate to cortical excitability or GABAergic synaptic activity. We therefore performed two studies investigating the relationship between neurotransmitter levels as assessed by MRS and transcranial magnetic stimulation (TMS) measures of cortical excitability and GABA synaptic activity in the primary motor cortex. We present uncorrected correlations, where the P value should therefore be considered with caution. We demonstrated a correlation between cortical excitability, as assessed by the slope of the TMS input-output curve and MRS-assessed glutamate levels (r = 0.803, P = 0.015) but no clear relationship between MRS-assessed GABA levels and TMS-assessed synaptic GABA(A) activity (2.5 ms inter-stimulus interval (ISI) short-interval intracortical inhibition (SICI); Experiment 1: r = 0.33, P = 0.31; Experiment 2: r = -0.23, P = 0.46) or GABA(B) activity (long-interval intracortical inhibition (LICI); Experiment 1: r = -0.47, P = 0.51; Experiment 2: r = 0.23, P = 0.47). We demonstrated a significant correlation between MRS-assessed GABA levels and an inhibitory TMS protocol (1 ms ISI SICI) with distinct physiological underpinnings from the 2.5 ms ISI SICI (r = -0.79, P = 0.018). Interpretation of this finding is challenging as the mechanisms of 1 ms ISI SICI are not well understood, but we speculate that our results support the possibility that 1 ms ISI SICI reflects a distinct GABAergic inhibitory process, possibly that of extrasynaptic GABA tone.
Bayesian deconvolution of [corrected] fMRI data using bilinear dynamical systems.
In Penny et al. [Penny, W., Ghahramani, Z., Friston, K.J. 2005. Bilinear dynamical systems. Philos. Trans. R. Soc. Lond. B Biol. Sci. 360(1457) 983-993], a particular case of the Linear Dynamical Systems (LDSs) was used to model the dynamic behavior of the BOLD response in functional MRI. This state-space model, called bilinear dynamical system (BDS), is used to deconvolve the fMRI time series in order to estimate the neuronal response induced by the different stimuli of the experimental paradigm. The BDS model parameters are estimated using an expectation-maximization (EM) algorithm proposed by Ghahramani and Hinton [Ghahramani, Z., Hinton, G.E. 1996. Parameter Estimation for Linear Dynamical Systems. Technical Report, Department of Computer Science, University of Toronto]. In this paper we introduce modifications to the BDS model in order to explicitly model the spatial variations of the haemodynamic response function (HRF) in the brain using a non-parametric approach. While in Penny et al. [Penny, W., Ghahramani, Z., Friston, K.J. 2005. Bilinear dynamical systems. Philos. Trans. R. Soc. Lond. B Biol. Sci. 360(1457) 983-993] the relationship between neuronal activation and fMRI signals is formulated as a first-order convolution with a kernel expansion using basis functions (typically two or three), in this paper, we argue in favor of a spatially adaptive GLM in which a local non-parametric estimation of the HRF is performed. Furthermore, in order to overcome the overfitting problem typically associated with simple EM estimates, we propose a full Variational Bayes (VB) solution to infer the BDS model parameters. We demonstrate the usefulness of our model which is able to estimate both the neuronal activity and the haemodynamic response function in every voxel of the brain. We first examine the behavior of this approach when applied to simulated data with different temporal and noise features. As an example we will show how this method can be used to improve interpretability of estimates from an independent component analysis (ICA) analysis of fMRI data. We finally demonstrate its use on real fMRI data in one slice of the brain.
A Bayesian framework for global tractography.
We readdress the diffusion tractography problem in a global and probabilistic manner. Instead of tracking through local orientations, we parameterise the connexions between brain regions at a global level, and then infer on global and local parameters simultaneously in a Bayesian framework. This approach offers a number of important benefits. The global nature of the tractography reduces sensitivity to local noise and modelling errors. By constraining tractography to ensure a connexion is found, and then inferring on the exact location of the connexion, we increase the robustness of connectivity-based parcellations, allowing parcellations of connexions that were previously invisible to tractography. The Bayesian framework allows a direct comparison of the evidence for connecting and non-connecting models, to test whether the connexion is supported by the data. Crucially, by explicit parameterisation of the connexion between brain regions, we infer on a parameter that is shared with models of functional connectivity. This model is a first step toward the joint inference on functional and anatomical connectivity.
Probabilistic inference of regularisation in non-rigid registration.
A long-standing issue in non-rigid image registration is the choice of the level of regularisation. Regularisation is necessary to preserve the smoothness of the registration and penalise against unnecessary complexity. The vast majority of existing registration methods use a fixed level of regularisation, which is typically hand-tuned by a user to provide "nice" results. However, the optimal level of regularisation will depend on the data which is being processed; lower signal-to-noise ratios require higher regularisation to avoid registering image noise as well as features, and different pairs of images require registrations of varying complexity depending on their anatomical similarity. In this paper we present a probabilistic registration framework that infers the level of regularisation from the data. An additional benefit of this proposed probabilistic framework is that estimates of the registration uncertainty are obtained. This framework has been implemented using a free-form deformation transformation model, although it would be generically applicable to a range of transformation models. We demonstrate our registration framework on the application of inter-subject brain registration of healthy control subjects from the NIREP database. In our results we show that our framework appropriately adapts the level of regularisation in the presence of noise, and that inferring regularisation on an individual basis leads to a reduction in model over-fitting as measured by image folding while providing a similar level of overlap.
Knowing when to stop: the brain mechanisms of chasing losses.
BACKGROUND: Continued gambling to recover previous losses ("loss-chasing") is central to pathological gambling. However, very little is known about the neural mechanisms that mediate this behavior. METHODS: We used functional magnetic resonance imaging (fMRI) to examine neural activity while healthy adult participants decided to chase losses or decided to quit gambling to prevent further losses. RESULTS: Chasing losses was associated with increased activity in cortical areas linked to incentive-motivation and an expectation of reward. By contrast, quitting was associated with decreased activity in these areas but increased activity in areas associated with anxiety and conflict monitoring. Activity within the anterior cingulate cortex associated with the experience of chasing and then losing predicted decisions to stop chasing losses at the next opportunity. CONCLUSIONS: Excessive loss-chasing behavior in pathological gambling might involve a failure to appropriately balance activity within neural systems coding conflicting motivational states. Similar mechanisms might underlie the loss-of-control over appetitive behaviors in other impulse control disorders.
Meaningful design and contrast estimability in FMRI.
Optimising the efficiency of an experimental design is known to be of great importance. However, existing methods for calculating design rank deficiency and contrast estimability (an important aspect of experimental design) relate to computational precision rather than image noise and are therefore not very meaningful. For example, a contrast between two experimental conditions may be mathematically "estimable" while requiring a huge differential BOLD response for statistical significance to be reached. In this paper we formulate standard efficiency equations in terms of required BOLD effect, and use this to generate measures of rank/estimability which are meaningful. This takes into account the strength and smoothness of the timeseries noise and is applicable to complex contrasts; we show how to re-express several regressors and an associated contrast vector as a single equivalent regressor, so that we can calculate the contrast's effective peak-peak height unambiguously. We also present some example results on typical designs, and characterise noise results from a range of typical FMRI acquisitions, in order to allow experimenters to apply efficiency estimation in advance of acquiring data.
Probabilistic diffusion tractography with multiple fibre orientations: What can we gain?
We present a direct extension of probabilistic diffusion tractography to the case of multiple fibre orientations. Using automatic relevance determination, we are able to perform online selection of the number of fibre orientations supported by the data at each voxel, simplifying the problem of tracking in a multi-orientation field. We then apply the identical probabilistic algorithm to tractography in the multi- and single-fibre cases in a number of example systems which have previously been tracked successfully or unsuccessfully with single-fibre tractography. We show that multi-fibre tractography offers significant advantages in sensitivity when tracking non-dominant fibre populations, but does not dramatically change tractography results for the dominant pathways.