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• To predict the precision of its predictions, brain relies on its own beliefs; that is to say about the confidence of its prior predictions. • Fluency—the subjective experience associated with any cognitive treatment—plays a key role in prediction because it reflects the precision of (i.e., confidence placed in) predictions. • It is not fluency itself that is perceived but rather changes in fluency. • Changes in fluency orient attentional selection in response to violations and unexplained prediction errors. • Fluency can be read as recognising and contextualising unfelt fluency; where unfelt fluency optimises predictions of the precision of sensory processing. For a growing number of researchers, it is now accepted that the brain is a predictive organ that predicts the content of the sensorium and crucially the precision of—or confidence in—its own predictions. In order to predict the precision of its predictions, the brain has to infer the reliability of its own beliefs. This means that our brains have to recognise the precision of their predictions or, at least, their accuracy. In this paper, we argue that fluency is product of this recognition process. In short, to recognise fluency is to infer that we have a precise 'grip' on the unfolding processes that generate our sensations. More specifically, we propose that it is changes in fluency — from unfelt to felt — that are both recognised and realised when updating predictions about precision. Unfelt fluency orients attention to unpredicted sensations, while felt fluency supervenes on—and contextualises—unfelt fluency; thereby rendering certain attentional processes, phenomenologically opaque. As such, fluency underwrites the precision we place in our predictions and therefore acts upon our perceptual inferences. Hence, the causes of conscious subjective inference have unconscious perceptual precursors. [ABSTRACT FROM AUTHOR]

• Variational Laplace (VL) is a scheme for Bayesian modelling. • VL is widely used in neuroimaging, in particular DCM. • This paper provides a tutorial explanation of the math and algorithms. • New standalone code is provided to enable re-implementation. • The supplementary materials provide worked derivations. This article details a scheme for approximate Bayesian inference, which has underpinned thousands of neuroimaging studies since its introduction 15 years ago. Variational Laplace (VL) provides a generic approach to fitting linear or non-linear models, which may be static or dynamic, returning a posterior probability density over the model parameters and an approximation of log model evidence, which enables Bayesian model comparison. VL applies variational Bayesian inference in conjunction with quadratic or Laplace approximations of the evidence lower bound (free energy). Importantly, update equations do not need to be derived for each model under consideration, providing a general method for fitting a broad class of models. This primer is intended for experimenters and modellers who may wish to fit models to data using variational Bayesian methods, without assuming previous experience of variational Bayes or machine learning. Accompanying code demonstrates how to fit different kinds of model using the reference implementation of the VL scheme in the open-source Statistical Parametric Mapping (SPM) software package. In addition, we provide a standalone software function that does not require SPM, in order to ease translation to other fields, together with detailed pseudocode. Finally, the supplementary materials provide worked derivations of the key equations. [ABSTRACT FROM AUTHOR]

Although the relationship between resting-state functional connectivity and task-related activity has been addressed, the relationship between task and resting-state directed or effective connectivity – and its behavioral concomitants – remains elusive. We evaluated effective connectivity under an N-back working memory task in 24 participants using stochastic dynamic causal modelling (DCM) of 7 T fMRI data. We repeated the analysis using resting-state data, from the same subjects, to model connectivity among the same brain regions engaged by the N-back task. This allowed us to: (i) examine the relationship between intrinsic (task-independent) effective connectivity during resting (A rest ) and task states (A task ), (ii) cluster phenotypes of task-related changes in effective connectivity (B task ) across participants, (iii) identify edges (B task ) showing high inter-individual effective connectivity differences and (iv) associate reaction times with the similarity between B task and A rest in these edges. We found a strong correlation between A rest and A task over subjects but a marked difference between B task and A rest . We further observed a strong clustering of individuals in terms of B task , which was not apparent in A rest . The task-related effective connectivity B task varied highly in the edges from the parietal to the frontal lobes across individuals, so the three groups were clustered mainly by the effective connectivity within these networks. The similarity between B task and A rest at the edges from the parietal to the frontal lobes was positively correlated with 2-back reaction times. This result implies that a greater change in context-sensitive coupling – from resting-state connectivity – is associated with faster reaction times. In summary, task-dependent connectivity endows resting-state connectivity with a context sensitivity, which predicts the speed of information processing during the N-back task. [ABSTRACT FROM AUTHOR]

Many analysis methods exist to extract graphs of functional connectivity from neuronal networks. Confidence in the results is limited because, (i) different methods give different results, (ii) parameter setting directly influences the final result, and (iii) systematic evaluation of the results is not always performed. Here, we introduce MULAN (MULtiple method ANalysis), which assumes an ensemble based approach combining multiple analysis methods and fuzzy logic to extract graphs with the most probable structure. In order to reduce the dependency on parameter settings, we determine the best set of parameters using a genetic algorithm on simulated datasets, whose temporal structure is similar to the experimental one. After a validation step, the selected set of parameters is used to analyze experimental data. The final step cross-validates experimental subsets of data and provides a direct estimate of the most likely graph and our confidence in the proposed connectivity. A systematic evaluation validates our strategy against empirical stereotactic electroencephalography (SEEG) and functional magnetic resonance imaging (fMRI) data. [ABSTRACT FROM AUTHOR]

The neural substrate of bodily ownership can be disclosed by the rubber hand illusion (RHI); namely, the illusory self-attribution of an artificial hand that is induced by synchronous tactile stimulation of the subject's hand that is hidden from view. Previous studies have pointed to the premotor cortex (PMC) as a pivotal area in such illusions. To investigate the effective connectivity between – and within – sensory and premotor areas involved in bodily perceptions, we used dynamic causal modeling of touch-evoked responses in 13 healthy subjects. Each subject's right hand was stroked while viewing their own hand (“REAL”), or an artificial hand presented in an anatomically plausible (“CONGRUENT”) or implausible (“INCONGRUENT”) position. Bayesian model comparison revealed strong evidence for a differential involvement of the PMC in the generation of touch-evoked responses under the three conditions, confirming a crucial role of PMC in bodily self-attribution. In brief, the extrinsic (forward) connection from left occipital cortex to left PMC was stronger for CONGRUENT and INCONGRUENT as compared to REAL, reflecting the augmentation of bottom-up visual input when multisensory integration is challenged. Crucially, intrinsic connectivity in the primary somatosensory cortex (S1) was attenuated in the CONGRUENT condition, during the illusory percept. These findings support predictive coding models of the functional architecture of multisensory integration (and attenuation) in bodily perceptual experience. [ABSTRACT FROM AUTHOR]

This technical note describes some Bayesian procedures for the analysis of group studies that use nonlinear models at the first (within-subject) level – e.g., dynamic causal models – and linear models at subsequent (between-subject) levels. Its focus is on using Bayesian model reduction to finesse the inversion of multiple models of a single dataset or a single (hierarchical or empirical Bayes) model of multiple datasets. These applications of Bayesian model reduction allow one to consider parametric random effects and make inferences about group effects very efficiently (in a few seconds). We provide the relatively straightforward theoretical background to these procedures and illustrate their application using a worked example. This example uses a simulated mismatch negativity study of schizophrenia. We illustrate the robustness of Bayesian model reduction to violations of the (commonly used) Laplace assumption in dynamic causal modelling and show how its recursive application can facilitate both classical and Bayesian inference about group differences. Finally, we consider the application of these empirical Bayesian procedures to classification and prediction. [ABSTRACT FROM AUTHOR]

In this technical note, we derive two MCMC (Markov chain Monte Carlo) samplers for dynamic causal models (DCMs). Specifically, we use (a) Hamiltonian MCMC (HMC-E) where sampling is simulated using Hamilton’s equation of motion and (b) Langevin Monte Carlo algorithm (LMC-R and LMC-E) that simulates the Langevin diffusion of samples using gradients either on a Euclidean (E) or on a Riemannian (R) manifold. While LMC-R requires minimal tuning, the implementation of HMC-E is heavily dependent on its tuning parameters. These parameters are therefore optimised by learning a Gaussian process model of the time-normalised sample correlation matrix. This allows one to formulate an objective function that balances tuning parameter exploration and exploitation, furnishing an intervention-free inference scheme. Using neural mass models (NMMs)—a class of biophysically motivated DCMs—we find that HMC-E is statistically more efficient than LMC-R (with a Riemannian metric); yet both gradient-based samplers are far superior to the random walk Metropolis algorithm, which proves inadequate to steer away from dynamical instability. [ABSTRACT FROM AUTHOR]

This paper considers communication in terms of inference about the behaviour of others (and our own behaviour). It is based on the premise that our sensations are largely generated by other agents like ourselves. This means, we are trying to infer how our sensations are caused by others, while they are trying to infer our behaviour: for example, in the dialogue between two speakers. We suggest that the infinite regress induced by modelling another agent – who is modelling you – can be finessed if you both possess the same model. In other words, the sensations caused by others and oneself are generated by the same process. This leads to a view of communication based upon a narrative that is shared by agents who are exchanging sensory signals. Crucially, this narrative transcends agency – and simply involves intermittently attending to and attenuating sensory input. Attending to sensations enables the shared narrative to predict the sensations generated by another (i.e. to listen), while attenuating sensory input enables one to articulate the narrative (i.e. to speak). This produces a reciprocal exchange of sensory signals that, formally, induces a generalised synchrony between internal (neuronal) brain states generating predictions in both agents. We develop the arguments behind this perspective, using an active (Bayesian) inference framework and offer some simulations (of birdsong) as proof of principle. [ABSTRACT FROM AUTHOR]

In this technical note we compare the performance of four gradient-free MCMC samplers (random walk Metropolis sampling, slice-sampling, adaptive MCMC sampling and population-based MCMC sampling with tempering) in terms of the number of independent samples they can produce per unit computational time. For the Bayesian inversion of a single-node neural mass model, both adaptive and population-based samplers are more efficient compared with random walk Metropolis sampler or slice-sampling; yet adaptive MCMC sampling is more promising in terms of compute time. Slice-sampling yields the highest number of independent samples from the target density — albeit at almost 1000% increase in computational time, in comparison to the most efficient algorithm (i.e., the adaptive MCMC sampler). [ABSTRACT FROM AUTHOR]

Human faces may signal relevant information and are therefore analysed rapidly and effectively by the brain. However, the precise mechanisms and pathways involved in rapid face processing are unclear. One view posits a role for a subcortical connection between early visual sensory regions and the amygdala, while an alternative account emphasises cortical mediation. To adjudicate between these functional architectures, we recorded magnetoencephalographic (MEG) evoked fields in human subjects to presentation of faces with varying emotional valence. Early brain activity was better explained by dynamic causal models containing a direct subcortical connection to the amygdala irrespective of emotional modulation. At longer latencies, models without a subcortical connection had comparable evidence. Hence, our results support the hypothesis that a subcortical pathway to the amygdala plays a role in rapid sensory processing of faces, in particular during early stimulus processing. This finding contributes to an understanding of the amygdala as a behavioural relevance detector. [ABSTRACT FROM AUTHOR]

This technical paper offers a critical re-evaluation of (spectral) Granger causality measures in the analysis of biological timeseries. Using realistic (neural mass) models of coupled neuronal dynamics, we evaluate the robustness of parametric and nonparametric Granger causality. Starting from a broad class of generative (state-space) models of neuronal dynamics, we show how their Volterra kernels prescribe the second-order statistics of their response to random fluctuations; characterised in terms of cross-spectral density, cross-covariance, autoregressive coefficients and directed transfer functions. These quantities in turn specify Granger causality — providing a direct (analytic) link between the parameters of a generative model and the expected Granger causality. We use this link to show that Granger causality measures based upon autoregressive models can become unreliable when the underlying dynamics is dominated by slow (unstable) modes — as quantified by the principal Lyapunov exponent. However, nonparametric measures based on causal spectral factors are robust to dynamical instability. We then demonstrate how both parametric and nonparametric spectral causality measures can become unreliable in the presence of measurement noise. Finally, we show that this problem can be finessed by deriving spectral causality measures from Volterra kernels, estimated using dynamic causal modelling. [ABSTRACT FROM AUTHOR]

This paper examines intrinsic brain networks in light of recent developments in the characterisation of resting state fMRI timeseries -- and simulations of neuronal fluctuations based upon the connectome. Its particular focus is on patterns or modes of distributed activity that underlie functional connectivity. We first demonstrate that the eigenmodes of functional connectivity - or covariance among regions or nodes - are the same as the eigenmodes of the underlying effective connectivity, provided we limit ourselves to symmetrical connections. This symmetry constraint is motivated by appealing to proximity graphs based upon multidimensional scaling. Crucially, the principal modes of functional connectivity correspond to the dynamically unstable modes of effective connectivity that decay slowly and show long term memory. Technically, these modes have small negative Lyapunov exponents that approach zero from below. Interestingly, the superposition of modes - whose exponents are sampled from a power law distribution - produces classical 1/f (scale free) spectra. We conjecture that the emergence of dynamical instability - that underlies intrinsic brain networks - is inevitable in any system that is separated from external states by a Markov blanket. This conjecture appeals to a free energy formulation of nonequilibrium steady-state dynamics. The common theme that emerges from these theoretical considerations is that endogenous fluctuations are dominated by a small number of dynamically unstable modes. We use this as the basis of a dynamic causal model (DCM) of resting state fluctuations -- as measured in terms of their complex cross spectra. In this model, effective connectivity is parameterised in terms of eigenmodes and their Lyapunov exponents -- that can also be interpreted as locations in a multidimensional scaling space. Model inversion provides not only estimates of edges or connectivity but also the topography and dimensionality of the underlying scaling space. Here, we focus on conceptual issues with simulated fMRI data and provide an illustrative application using an empirical multi-region timeseries. [ABSTRACT FROM AUTHOR]

Abstract: This technical note introduces a dynamic causal model (DCM) for resting state fMRI time series based upon observed functional connectivity—as measured by the cross spectra among different brain regions. This DCM is based upon a deterministic model that generates predicted crossed spectra from a biophysically plausible model of coupled neuronal fluctuations in a distributed neuronal network or graph. Effectively, the resulting scheme finds the best effective connectivity among hidden neuronal states that explains the observed functional connectivity among haemodynamic responses. This is because the cross spectra contain all the information about (second order) statistical dependencies among regional dynamics. In this note, we focus on describing the model, its relationship to existing measures of directed and undirected functional connectivity and establishing its face validity using simulations. In subsequent papers, we will evaluate its construct validity in relation to stochastic DCM and its predictive validity in Parkinson's and Huntington's disease. [Copyright &y& Elsevier]

Abstract: Reward outcome signalling in the sensory cortex is held as important for linking stimuli to their consequences and for modulating perceptual learning in response to incentives. Evidence for reward outcome signalling has been found in sensory regions including the visual, auditory and somatosensory cortices across a range of different paradigms, but it is unknown whether the population of neurons signalling rewarding outcomes are the same as those processing predictive stimuli. We addressed this question using a multivariate analysis of high-resolution functional magnetic resonance imaging (fMRI), in a task where subjects were engaged in instrumental learning with visual predictive cues and auditory signalled reward feedback. We found evidence that outcome signals in sensory regions localise to the same areas involved in stimulus processing. These outcome signals are non-specific and we show that the neuronal populations involved in stimulus representation are not their exclusive target, in keeping with theoretical models of value learning. Thus, our results reveal one likely mechanism through which rewarding outcomes are linked to predictive sensory stimuli, a link that may be key for both reward and perceptual learning. [Copyright &y& Elsevier]

Abstract: Lohmann et al. (this issue) make three unremarkable observations about model selection and use them to critique dynamic causal modelling—a Bayesian model selection procedure based on causal models of dynamical systems (Marreiros et al., 2010). In this response, we unpack their misconceptions and try to answer their questions. [Copyright &y& Elsevier]

Abstract: In this work, we address the problem of using dynamic causal modelling (DCM) to estimate the coupling parameters (effective connectivity) of large models with many regions. This is a potentially important problem because meaningful graph theoretic analyses of effective connectivity rest upon the statistics of the connections (edges). This calls for characterisations of networks with an appreciable number of regions (nodes). The problem here is that the number of coupling parameters grows quadratically with the number of nodes—leading to severe conditional dependencies among their estimates and a computational load that quickly becomes unsustainable. Here, we describe a simple solution, in which we use functional connectivity to provide prior constraints that bound the effective number of free parameters. In brief, we assume that priors over connections between individual nodes can be replaced by priors over connections between modes (patterns over nodes). By using a small number of modes, we can reduce the dimensionality of the problem in an informed way. The modes we use are the principal components or eigenvectors of the functional connectivity matrix. However, this approach begs the question of how many modes to use. This question can be addressed using Bayesian model comparison to optimise the number of modes. We imagine that this form of prior – over the extrinsic (endogenous) connections in large DCMs – may be useful for people interested in applying graph theory to distributed networks in the brain or to characterise connectivity beyond the subgraphs normally examined in DCM. [Copyright &y& Elsevier]

Abstract: Estimating the precision or uncertainty associated with sensory signals is an important part of perception. Based on a previous computational model, we tested the hypothesis that increasing visual contrast increased the precision encoded in early visual areas by the gain or excitability of superficial pyramidal cells. This hypothesis was investigated using electroencephalography and dynamic causal modelling (DCM); a biologically constrained modelling of the cortical processes underlying EEG activity. Source localisation identified the electromagnetic sources of visually evoked responses and DCM was used to characterise the coupling among these sources. Bayesian model selection was used to select the most likely connectivity pattern and contrast-dependent changes in connectivity. As predicted, the model with the highest evidence entailed increased superficial pyramidal cell gain in higher-contrast trials. As predicted theoretically, contrast-dependent increases were reduced at higher levels of the hierarchy. These results demonstrate that increased signal-to-noise ratio in sensory signals produce (or are represented by) increased superficial pyramidal cell gain, and that synaptic parameters encoding statistical properties like sensory precision can be quantified using EEG and dynamic causal modelling. [Copyright &y& Elsevier]

Abstract: The slight perversion of the original title of this piece (The Future of the Bayesian Brain) reflects my attempt to write prospectively about ‘Science and Stories’ over the past 20years. I will meet this challenge by dealing with the future and then turning to its history. The future of the Bayesian brain (in neuroimaging) is clear: it is the application of dynamic causal modeling to understand how the brain conforms to the free energy principle. In this context, the Bayesian brain is a corollary of the free energy principle, which says that any self organizing system (like a brain or neuroimaging community) must maximize the evidence for its own existence, which means it must minimize its free energy using a model of its world. Dynamic causal modeling involves finding models of the brain that have the greatest evidence or the lowest free energy. In short, the future of imaging neuroscience is to refine models of the brain to minimize free energy, where the brain refines models of the world to minimize free energy. This endeavor itself minimizes free energy because our community is itself a self organizing system. I cannot imagine an alternative future that has the same beautiful self consistency as mine. Having dispensed with the future, we can now focus on the past, which is much more interesting: [Copyright &y& Elsevier]

Abstract: As an expert reviewer, it is sometimes necessary to ensure a paper is rejected. This can sometimes be achieved by highlighting improper statistical practice. This technical note provides guidance on how to critique the statistical analysis of neuroimaging studies to maximise the chance that the paper will be declined. We will review a series of critiques that can be applied universally to any neuroimaging paper and consider responses to potential rebuttals that reviewers might encounter from authors or editors. [Copyright &y& Elsevier]

Abstract: After more than twenty years busily mapping the human brain, what have we learned from neuroimaging? This review (coda) considers this question from the point of view of structure–function relationships and the two cornerstones of functional neuroimaging; functional segregation and integration. Despite remarkable advances and insights into the brain''s functional architecture, the earliest and simplest challenge in human brain mapping remains unresolved: We do not have a principled way to map brain function onto its structure in a way that speaks directly to cognitive neuroscience. Having said this, there are distinct clues about how this might be done: First, there is a growing appreciation of the role of functional integration in the distributed nature of neuronal processing. Second, there is an emerging interest in data-driven cognitive ontologies, i.e., that are internally consistent with functional anatomy. We will focus this review on the growing momentum in the fields of functional connectivity and distributed brain responses and consider this in the light of meta-analyses that use very large data sets to disclose large-scale structure–function mappings in the human brain. [Copyright &y& Elsevier]

Abstract: Normal ageing is associated with a decline in episodic memory, and neuroimaging studies in older adults have shown reduced activity in prefrontal cortex and other regions critical for memory function in the young. However, older adults also activate additional regions, suggesting a degree of functional reorganisation that has been attributed variously to detrimental and adaptive changes. Evaluation of these competing hypotheses depends critically upon inferences about the relative location and distribution of activity that are not well supported by current univariate or multivariate analyses. Here, we employed a recently developed model-based multivariate ‘decoding’ approach (Friston et al., 2008) to re-analyse a rich episodic encoding dataset and examine directly how the patterns of activity change in ageing. We assessed which spatial activity patterns, within lateral prefrontal cortex, best predict successful memory formation. Bayesian model comparison showed that the older adults had more distributed and bilateral (fragmented) predictive patterns of activity in anterior inferior frontal gyrus and middle frontal gyrus. With this direct multivariate test for changes in patterns of activity, we replicate and extend earlier findings of reduced prefrontal lateralisation in ageing. These findings extend conclusions based on conventional analyses, and support the notion that ageing alters the spatial deployment of neuronal activity, to render it less spatially coherent and regionally specific. This greater distribution of activity in older adults was also linked to poorer individual memory performance, suggesting that it reflects neural ageing, rather than adaptive compensatory responses. [Copyright &y& Elsevier]

Abstract: Exact timing is essential for functional MRI data analysis. Datasets are commonly measured using repeated 2D imaging methods, resulting in a temporal offset between slices. To compensate for this timing difference, slice-timing correction (i.e. temporal data interpolation) has been used as an fMRI pre-processing step for more than fifteen years. However, there has been an ongoing debate about the effectiveness and applicability of this method. This paper presents the first elaborated analysis of the impact of the slice-timing effect on simulated data for different fMRI paradigms and measurement parameters, taking into account data noise and smoothing effects. Here we show, depending on repetition time and paradigm design, slice-timing effects can significantly impair fMRI results and slice-timing correction methods can successfully compensate for these effects and therefore increase the robustness of the data analysis. In addition, our results from simulated data were supported by empirical in vivo datasets. Our findings suggest that slice-timing correction should be included in the fMRI pre-processing pipeline. [Copyright &y& Elsevier]

Abstract: This paper presents a new approach to inverting (fitting) models of coupled dynamical systems based on state-of-the-art (cubature) Kalman filtering. Crucially, this inversion furnishes posterior estimates of both the hidden states and parameters of a system, including any unknown exogenous input. Because the underlying generative model is formulated in continuous time (with a discrete observation process) it can be applied to a wide variety of models specified with either ordinary or stochastic differential equations. These are an important class of models that are particularly appropriate for biological time-series, where the underlying system is specified in terms of kinetics or dynamics (i.e., dynamic causal models). We provide comparative evaluations with generalized Bayesian filtering (dynamic expectation maximization) and demonstrate marked improvements in accuracy and computational efficiency. We compare the schemes using a series of difficult (nonlinear) toy examples and conclude with a special focus on hemodynamic models of evoked brain responses in fMRI. Our scheme promises to provide a significant advance in characterizing the functional architectures of distributed neuronal systems, even in the absence of known exogenous (experimental) input; e.g., resting state fMRI studies and spontaneous fluctuations in electrophysiological studies. Importantly, unlike current Bayesian filters (e.g. DEM), our scheme provides estimates of time-varying parameters, which we will exploit in future work on the adaptation and enabling of connections in the brain. [Copyright &y& Elsevier]

Abstract: This note describes a Bayesian model selection or optimization procedure for post hoc inferences about reduced versions of a full model. The scheme provides the evidence (marginal likelihood) for any reduced model as a function of the posterior density over the parameters of the full model. It rests upon specifying models through priors on their parameters, under the assumption that the likelihood remains the same for all models considered. This provides a quick and efficient scheme for scoring arbitrarily large numbers of models, after inverting a single (full) model. In turn, this enables the selection among discrete models that are distinguished by the presence or absence of free parameters, where free parameters are effectively removed from the model using very precise shrinkage priors. An alternative application of this post hoc model selection considers continuous model spaces, defined in terms of hyperparameters (sufficient statistics) of the prior density over model parameters. In this instance, the prior (model) can be optimized with respect to its evidence. The expressions for model evidence become remarkably simple under the Laplace (Gaussian) approximation to the posterior density. Special cases of this scheme include Savage–Dickey density ratio tests for reduced models and automatic relevance determination in model optimization. We illustrate the approach using general linear models and a more complicated nonlinear state-space model. [Copyright &y& Elsevier]

Abstract: This paper is about inferring or discovering the functional architecture of distributed systems using Dynamic Causal Modelling (DCM). We describe a scheme that recovers the (dynamic) Bayesian dependency graph (connections in a network) using observed network activity. This network discovery uses Bayesian model selection to identify the sparsity structure (absence of edges or connections) in a graph that best explains observed time-series. The implicit adjacency matrix specifies the form of the network (e.g., cyclic or acyclic) and its graph-theoretical attributes (e.g., degree distribution). The scheme is illustrated using functional magnetic resonance imaging (fMRI) time series to discover functional brain networks. Crucially, it can be applied to experimentally evoked responses (activation studies) or endogenous activity in task-free (resting state) fMRI studies. Unlike conventional approaches to network discovery, DCM permits the analysis of directed and cyclic graphs. Furthermore, it eschews (implausible) Markovian assumptions about the serial independence of random fluctuations. The scheme furnishes a network description of distributed activity in the brain that is optimal in the sense of having the greatest conditional probability, relative to other networks. The networks are characterised in terms of their connectivity or adjacency matrices and conditional distributions over the directed (and reciprocal) effective connectivity between connected nodes or regions. We envisage that this approach will provide a useful complement to current analyses of functional connectivity for both activation and resting-state studies. [Copyright &y& Elsevier]

Abstract: This paper presents a nonlinear image registration algorithm based on the setting of Large Deformation Diffeomorphic Metric Mapping (LDDMM), but with a more efficient optimisation scheme — both in terms of memory required and the number of iterations required to reach convergence. Rather than perform a variational optimisation on a series of velocity fields, the algorithm is formulated to use a geodesic shooting procedure, so that only an initial velocity is estimated. A Gauss–Newton optimisation strategy is used to achieve faster convergence. The algorithm was evaluated using freely available manually labelled datasets, and found to compare favourably with other inter-subject registration algorithms evaluated using the same data. [Copyright &y& Elsevier]

Abstract: This article reviews the substantial impact computational neuroscience has had on neuroimaging over the past years. It builds on the distinction between models of the brain as a computational machine and computational models of neuronal dynamics per se; i.e., models of brain function and biophysics. Both sorts of model borrow heavily from computational neuroscience, and both have enriched the analysis of neuroimaging data and the type of questions we address. To illustrate the role of functional models in imaging neuroscience, we focus on optimal control and decision (game) theory; the models used here provide a mechanistic account of neuronal computations and the latent (mental) states represent by the brain. In terms of biophysical modelling, we focus on dynamic causal modelling, with a special emphasis on recent advances in neural-mass models for hemodynamic and electrophysiological time series. Each example emphasises the role of generative models, which embed our hypotheses or questions, and the importance of model comparison (i.e., hypothesis testing). We will refer to this theme, when trying to contextualise recent trends in relation to each other. [Copyright &y& Elsevier]

Abstract: This note presents a framework for generating tissue probability maps that represent the average shape of a number of subjects'' brain images. The procedure is formulated as finding maximum a posteriori estimates within a probabilistic generative model. Estimating the parameters involves alternating between estimating the deformations that match tissue class images of individual subjects to template, and updating the template according to the latest estimates of the deformations. A multinomial matching criterion is used, such that multiple tissue class images (e.g. grey and white matter) are registered simultaneously with the current template estimate. In order to generalise the resulting template to a broader range of subjects, a template blurriness prior is included within the model. [Copyright &y& Elsevier]

Abstract: We describe the use of spatial and temporal constraints in dynamic causal modelling (DCM) of magneto- and electroencephalography (M/EEG) data. DCM for M/EEG is based on a spatiotemporal, generative model of electromagnetic brain activity. The temporal dynamics are described by neural-mass models of equivalent current dipole (ECD) sources and their spatial expression is modelled by parameterized lead-field functions. Often, in classical ECD models, symmetry constraints are used to model homologous pairs of dipoles in both hemispheres. These constraints are motivated by assumptions about symmetric activation of bilateral sensory sources. In classical approaches, these constraints are ‘hard’; i.e. the parameters of homologous dipoles are shared. Here, in the context of DCM, we illustrate the use of informed Bayesian priors to implement ‘soft’ symmetry constraints that are expressed in the posterior estimates only when supported by the data. Critically, with DCM one can deploy symmetry constraints in either the temporal or spatial components of the model. This enables one to test for symmetry in temporal (neural-mass) parameters in the presence of non-symmetric spatial expressions of homologous sources (and vice versa). Furthermore, we demonstrate that Bayesian model comparison can be used to identify the best models among a range of symmetric and non-symmetric variants. Our main finding is that the use of ‘soft’ symmetry priors is recommended for evoked responses to bilateral sensory input. We illustrate the use of symmetry constraints in DCM on synthetic and real EEG data. [Copyright &y& Elsevier]

Abstract: In this note, we revisit earlier work on false discovery rate (FDR) and evaluate it in relation to topological inference in statistical parametric mapping. We note that controlling the false discovery rate of voxels is not equivalent to controlling the false discovery rate of activations. This is a problem that is unique to inference on images, in which the underlying signal is continuous (i.e., signal which does not have a compact support). In brief, inference based on conventional voxel-wise FDR procedures is not appropriate for inferences on the topological features of a statistical parametric map (SPM), such as peaks or regions of activation. We describe the nature of the problem, illustrate it with some examples and suggest a simple solution based on controlling the false discovery rate of connected excursion sets within an SPM, characterised by their volume. [Copyright &y& Elsevier]

Abstract: The aim of this paper is to describe a simple procedure for electromagnetic (EEG or MEG) source reconstruction, in the context of group studies. This entails a simple extension of existing source reconstiruction techniques based upon the inversion of hierarchical models. The extension ensures that evoked or induced responses are reconstructed in the same subset of sources, over subjects. Effectively, the procedure aligns the deployment of reconstructed activity over subjects and increases, substantially, the detection of differences between evoked or induced responses at the group or between-subject level. [Copyright &y& Elsevier]

Abstract: Using dynamic causal modelling (DCM), we have presented provisional evidence to suggest: (i) the mismatch negativity (MMN) is generated by self-organised interactions within a hierarchy of cortical sources [Garrido, M.I., Kilner, J.M., Kiebel, S.J., Stephan, K.E., Friston, K.J., 2007. Dynamic causal modelling of evoked potentials: a reproducibility study. NeuroImage 36, 571–580] and (ii) the MMN rests on plastic change in both extrinsic (between-source) and intrinsic (within source) connections (Garrido et al., under review). In this work we re-visit these two key issues in the context of the roving paradigm. Critically, this paradigm allows us to discount any differential response to differences in the stimuli per se, because the standards and oddballs are physically identical. We were able to confirm both the hierarchical nature of the MMN generation and the conjoint role of changes in extrinsic and intrinsic connections. These findings are consistent with a predictive coding account of repetition–suppression and the MMN, which gracefully accommodates two important mechanistic perspectives; the model-adjustment hypothesis [Winkler, I., Karmos, G., Näätänen, R., 1996. Adaptive modelling of the unattended acoustic environment reflected in the mismatch negativity event-related potential. Brain Res. 742, 239–252; Näätänen, R., Winkler, I., 1999. The concept of auditory stimulus representation in cognitive neuroscience. Psychol Bull 125, 826–859; Sussman, E., Winkler, I., 2001. Dynamic sensory updating in the auditory system. Brain Res. Cogn Brain Res. 12, 431–439] and the adaptation hypothesis [May, P., Tiitinen, H., Ilmoniemi, R.J., Nyman, G., Taylor, J.G., Näätänen, R., 1999. Frequency change detection in human auditory cortex. J. Comput. Neurosci. 6, 99–120; Jääskeläinen, I.P., Ahveninen, J., Bonmassar, G., Dale, A.M., Ilmoniemi, R.J., Levänen, S., Lin, F.H., May, P., Melcher, J., Stufflebeam, S., Tiitinen, H., Belliveau, J.W., 2004. Human posterior auditory cortex gates novel sounds to consciousness. Proc. Natl. Acad. Sci. U. S. A. 101, 6809–6814]. [Copyright &y& Elsevier]

Abstract: This paper describes an application of hierarchical or empirical Bayes to the distributed source reconstruction problem in electro- and magnetoencephalography (EEG and MEG). The key contribution is the automatic selection of multiple cortical sources with compact spatial support that are specified in terms of empirical priors. This obviates the need to use priors with a specific form (e.g., smoothness or minimum norm) or with spatial structure (e.g., priors based on depth constraints or functional magnetic resonance imaging results). Furthermore, the inversion scheme allows for a sparse solution for distributed sources, of the sort enforced by equivalent current dipole (ECD) models. This means the approach automatically selects either a sparse or a distributed model, depending on the data. The scheme is compared with conventional applications of Bayesian solutions to quantify the improvement in performance. [Copyright &y& Elsevier]

Abstract: This paper introduces a multivariate Bayesian (MVB) scheme to decode or recognise brain states from neuroimages. It resolves the ill-posed many-to-one mapping, from voxel values or data features to a target variable, using a parametric empirical or hierarchical Bayesian model. This model is inverted using standard variational techniques, in this case expectation maximisation, to furnish the model evidence and the conditional density of the model’s parameters. This allows one to compare different models or hypotheses about the mapping from functional or structural anatomy to perceptual and behavioural consequences (or their deficits). We frame this approach in terms of decoding measured brain states to predict or classify outcomes using the rhetoric established in pattern classification of neuroimaging data. However, the aim of MVB is not to predict (because the outcomes are known) but to enable inference on different models of structure–function mappings; such as distributed and sparse representations. This allows one to optimise the model itself and produce predictions that outperform standard pattern classification approaches, like support vector machines. Technically, the model inversion and inference uses the same empirical Bayesian procedures developed for ill-posed inverse problems (e.g., source reconstruction in EEG). However, the MVB scheme used here extends this approach to include a greedy search for sparse solutions. It reduces the problem to the same form used in Gaussian process modelling, which affords a generic and efficient scheme for model optimisation and evaluating model evidence. We illustrate MVB using simulated and real data, with a special focus on model comparison; where models can differ in the form of the mapping (i.e., neuronal representation) within one region, or in the (combination of) regions per se. [Copyright &y& Elsevier]

Abstract: Dynamic causal modelling (DCM) is a modelling framework used to describe causal interactions in dynamical systems. It was developed to infer the causal architecture of networks of neuronal populations in the brain [Friston, K.J., Harrison, L, Penny, W., 2003. Dynamic causal modelling. NeuroImage. Aug; 19 (4): 1273–302]. In current formulations of DCM, the mean structure of the likelihood is a nonlinear and numerical function of the parameters, which precludes exact or analytic Bayesian inversion. To date, approximations to the posterior depend on the assumption of normality (i.e., the Laplace assumption). In particular, two arguments have been used to motivate normality of the prior and posterior distributions. First, Gaussian priors on the parameters are specified carefully to ensure that activity in the dynamic system of neuronal populations converges to a steady state (i.e., the dynamic system is dissipative). Secondly, normality of the posterior is an approximation based on general asymptotic results, regarding the form of the posterior under infinite data [Friston, K.J., Harrison, L, Penny, W., 2003. Dynamic causal modelling. NeuroImage. Aug; 19 (4): 1273–302]. Here, we provide a critique of these assumptions and evaluate them numerically. We use a Bayesian inversion scheme (the Metropolis–Hastings algorithm) that eschews both assumptions. This affords an independent route to the posterior and an external means to assess the performance of conventional schemes for DCM. It also allows us to assess the sensitivity of the posterior to different priors. First, we retain the conventional priors and compare the ensuing approximate posterior (Laplace) to the exact posterior (MCMC). Our analyses show that the Laplace approximation is appropriate for practical purposes. In a second, independent set of analyses, we compare the exact posterior under conventional priors with an exact posterior under newly defined uninformative priors. Reassuringly, we observe that the posterior is, for all practical purposes, insensitive of the choice of prior. [Copyright &y& Elsevier]

Abstract: We present a multi-scale generative model for EEG, that entails a minimum number of assumptions about evoked brain responses, namely: (1) bioelectric activity is generated by a set of distributed sources, (2) the dynamics of these sources can be modelled as random fluctuations about a small number of mesostates, (3) mesostates evolve in a temporal structured way and are functionally connected (i.e. influence each other), and (4) the number of mesostates engaged by a cognitive task is small (e.g. between one and a few). A Variational Bayesian learning scheme is described that furnishes the posterior density on the models parameters and its evidence. Since the number of meso-sources specifies the model, the model evidence can be used to compare models and find the optimum number of meso-sources. In addition to estimating the dynamics at each cortical dipole, the mesostate-space model and its inversion provide a description of brain activity at the level of the mesostates (i.e. in terms of the dynamics of meso-sources that are distributed over dipoles). The inclusion of a mesostate level allows one to compute posterior probability maps of each dipole being active (i.e. belonging to an active mesostate). Critically, this model accommodates constraints on the number of meso-sources, while retaining the flexibility of distributed source models in explaining data. In short, it bridges the gap between standard distributed and equivalent current dipole models. Furthermore, because it is explicitly spatiotemporal, the model can embed any stochastic dynamical causal model (e.g. a neural mass model) as a Markov process prior on the mesostate dynamics. The approach is evaluated and compared to standard inverse EEG techniques, using synthetic data and real data. The results demonstrate the added-value of the mesostate-space model and its variational inversion. [Copyright &y& Elsevier]

Abstract: Inter-subject variability in evoked brain responses is attracting attention because it may reflect important variability in structure–function relationships over subjects. This variability could be a signature of degenerate (many-to-one) structure–function mappings in normal subjects or reflect changes that are disclosed by brain damage. In this paper, we describe a non-iterative fuzzy clustering algorithm (FCP: fuzzy clustering with fixed prototypes) for characterizing inter-subject variability in between-subject or second-level analyses of fMRI data. The approach identifies the contribution of each subject to response profiles in voxels surviving a classical F-statistic criterion. The output identifies subjects who drive activation in specific cortical regions (local effects) or in voxels distributed across neural systems (global effects). The sensitivity of the approach was assessed in 38 normal subjects performing an overt naming task. FCP revealed that several subjects had either abnormally high or abnormally low responses. FCP may be particularly useful for characterizing outlier responses in rare patients or heterogeneous populations. In these cases, atypical activations may not be detected by standard tests, under parametric assumptions. The advantage of using FCP is that it searches all voxels systematically and can identify atypical activation patterns in a quantitative and unsupervised manner. [Copyright &y& Elsevier]

Abstract: Recently, pattern recognition methods (e.g., support vector machines (SVM)) have been used to analyze fMRI data. In these applications the fMRI scans are treated as spatial patterns and statistical learning methods are used to identify statistical properties of the data that discriminate between brain states (e.g., task 1 vs. task 2) or group of subjects (e.g., patients and controls). We propose an extension of these approaches using temporal embedding. This makes the dynamic aspect of fMRI time series an explicit part of the classification. The proposed pattern recognition approach uses both spatial and temporal information. Temporal embedding was implemented by defining spatiotemporal fMRI observations and applying a support vector machine to these temporally extended observations. This produces a discriminating weight vector encompassing both voxels and time. The resulting vector furnishes discriminating responses, at each voxel without imposing any constraints on their temporal form. [Copyright &y& Elsevier]

Abstract: This note derives the variational free energy under the Laplace approximation, with a focus on accounting for additional model complexity induced by increasing the number of model parameters. This is relevant when using the free energy as an approximation to the log-evidence in Bayesian model averaging and selection. By setting restricted maximum likelihood (ReML) in the larger context of variational learning and expectation maximisation (EM), we show how the ReML objective function can be adjusted to provide an approximation to the log-evidence for a particular model. This means ReML can be used for model selection, specifically to select or compare models with different covariance components. This is useful in the context of hierarchical models because it enables a principled selection of priors that, under simple hyperpriors, can be used for automatic model selection and relevance determination (ARD). Deriving the ReML objective function, from basic variational principles, discloses the simple relationships among Variational Bayes, EM and ReML. Furthermore, we show that EM is formally identical to a full variational treatment when the precisions are linear in the hyperparameters. Finally, we also consider, briefly, dynamic models and how these inform the regularisation of free energy ascent schemes, like EM and ReML. [Copyright &y& Elsevier]

Abstract: Perfusion weighted MRI has proven very useful for deriving hemodynamic parameters such as CBF, CBV and MTT. These quantities are important diagnostically, e.g. in acute stroke, where they are used to delineate ischemic regions. Yet the standard method for estimating CBF based on singular value decomposition (SVD) has been demonstrated to underestimate (especially high) flow components and to be sensitive to delays in the arterial input function (AIF). Furthermore, the estimated residue functions often oscillate. This compromises their physiological interpretation/basis and makes estimation of related measures such as flow heterogeneity difficult. In this study, we estimate perfusion parameters based on a vascular model (VM) which represents heterogeneous capillary flow and explicitly leads to monotonically decreasing residue functions. We use a fully Bayesian approach to obtain posterior probability distributions for all parameters. In simulation studies, we show that the VM method has less bias in CBF estimates than the SVD based method for realistic SNRs. This also applies to cases where the AIF is delayed. We employ our method to estimate perfusion maps using data from (i) a healthy volunteer and (ii) from a stroke patient. [Copyright &y& Elsevier]

Abstract: Dynamic causal modelling (DCM) is a method for estimating and making inferences about the coupling among small numbers of brain areas, and the influence of experimental manipulations on that coupling [Friston, K.J., Harrison, L., Penny, W., 2003 Dynamic causal modelling. Neuroimage 19, 1273–1302]. Large-scale neural modelling aims to construct neurobiologically grounded computational models with emergent behaviours that inform our understanding of neuronal systems. One such model has been used to simulate region-specific BOLD time-series [Horwitz, B., Friston, K.J., Taylor, J.G., 2000. Neural modeling and functional brain imaging: an overview. Neural Netw. 13, 829–846]. DCM was used to make inferences about effective connectivity using data generated by a model implementing a visual delayed match-to-sample task [Tagamets, M.A., Horwitz, B., 1998. Integrating electrophysiological and anatomical experimental data to create a large-scale model that simulates a delayed match-to-sample human brain imaging study. Cereb. Cortex 8, 310–320]. The aim was to explore the validity of inferences made using DCM about the connectivity structure and task-dependent modulatory effects, in a system with a known connectivity structure. We also examined the effects of misspecifying regions of interest. Models with hierarchical connectivity and reciprocal connections were examined using DCM and Bayesian Model Comparison [Penny, W.D., Stephan, K.E., Mechelli, A., Friston, K.J., 2004. Comparing dynamic causal models. Neuroimage 22, 1157–1172]. This approach revealed strong evidence for those models with correctly specified anatomical connectivity. Furthermore, Bayesian model comparison favoured those models when bilinear effects corresponded to their implementation in the neural model. These findings generalised to an extended model with two additional areas and reentrant circuits. The conditional uncertainty of coupling parameter estimates increased in proportion to the number of incorrectly specified regions. These results highlight the role of neural models in establishing the validity of estimation and inference schemes. Specifically, Bayesian model comparison confirms the validity of DCM in relation to a well-characterised and comprehensive neuronal model. [Copyright &y& Elsevier]

Abstract: A probabilistic framework is presented that enables image registration, tissue classification, and bias correction to be combined within the same generative model. A derivation of a log-likelihood objective function for the unified model is provided. The model is based on a mixture of Gaussians and is extended to incorporate a smooth intensity variation and nonlinear registration with tissue probability maps. A strategy for optimising the model parameters is described, along with the requisite partial derivatives of the objective function. [Copyright &y& Elsevier]

Abstract: The aim of this note is to revisit the analysis of conjunctions in imaging data. We review some conceptual issues that have emerged from recent discussion (Nichols, T., Brett, M., Andersson, J., Wager, T., Poline, J.-B., 2004. Valid Conjunction Inference with the Minimum Statistic.) and reformulate the conjunction of null hypotheses as a conjunction of k or more effects. Analyses based on minimum statistics have typically used the null hypothesis that k = 0. This enables inferences about one or more effects (k > 0). However, this does not provide control over false-positive rates (FPR) for inferences about a conjunction of k = n effects, over n tests. This is the key point made by Nichols et al., who suggest a procedure based on supremum P values that provides an upper bound on FPR for k = n. Although valid, this is a very conservative procedure, particularly in the context of multiple comparisons. We suggest that an inference on a conjunction of k = n effects is generally unnecessary and distinguish between congruent contrasts that test for the same treatment and incongruent contrasts of the sort used in cognitive conjunctions. For congruent contrasts, the usual inference, k > 0, is sufficient. With incongruent contrasts it is sufficient to infer a conjunction of k >u effects, where u is the number of contrasts that share some uninteresting effect. The issues highlighted by Nichols et al., have important implications for the design and analysis of cognitive conjunction studies and have motivated a change to the SPM software, that affords a test for the more general hypothesis k >u. This more general conjunction test is described. [Copyright &y& Elsevier]

In this paper, we describe a temporal model for event-related potentials (ERP) in the context of statistical parametric mapping (SPM). In brief, we project channel data onto a two-dimensional scalp surface or into three-dimensional brain space using some appropriate inverse solution. We then treat the spatiotemporal data in a mass-univariate fashion. This implicitly factorises the model into spatial and temporal components. The key contribution of this paper is the use of observation models that afford an explicit distinction between observation error and variation in the expression of ERPs. This distinction is created by employing a two-level hierarchical model, in which the first level models the ERP effects within-subject and trial type, while the second models differences in ERP expression among trial types and subjects. By bringing the analysis of ERP data into a classical hierarchical (i.e., mixed effects) framework, many apparently disparate approaches (e.g., conventional P300 analyses and time-frequency analyses of stimulus-locked oscillations) can be reconciled within the same estimation and inference procedure. Inference proceeds in the normal way using t or F statistics to test for effects that are localised in peristimulus time or in some time–frequency window. The use of F statistics is an important generalisation of classical approaches, because it allows one to test for effects that lie in a multidimensional subspace (i.e., of unknown but constrained form). We describe the analysis procedures, the underlying theory and compare its performance to established techniques. [Copyright &y& Elsevier]

In this paper, we frame the strategy and motivations behind developments in statistical parametric mapping (SPM) for the analysis of electroencephalogram (EEG) data. This work deals specifically with SPM procedures for the analysis of event-related potentials (ERP). We place these developments in the larger context of integrating electrophysiological and hemodynamic measurements of evoked brain responses through the fusion of EEG and fMRI data. In this paper, we consider some fundamental issues when selecting an appropriate statistical model that enables diverse questions to be asked of the data and at the same time retains maximum sensitivity. The three key issues addressed in this paper are as follows: (i) should multivariate or mass univariate analyses be adopted, (ii) should time be treated as an experimental factor or as a dimension of the measured response variable, and (iii) how to form appropriate explanatory variables in a hierarchical observation model. We review the relative merits of the different options and explain the rationale for our choices. In brief, we motivate a mass univariate approach in terms of sensitivity to region-specific responses. This involves modeling responses at each voxel or space bin separately. In contradistinction, we treat time as an experimental factor to enable inferences about temporally distributed responses that encompass multiple time bins.In a companion paper, we develop statistical models of ERPs in the time domain that follow from the heuristics established here and illustrate the approach using simulated and real data. [Copyright &y& Elsevier]

Although MEG/EEG signals are highly variable, systematic changes in distinct frequency bands are commonly encountered. These frequency-specific changes represent robust neural correlates of cognitive or perceptual processes (for example, alpha rhythms emerge on closing the eyes). However, their functional significance remains a matter of debate. Some of the mechanisms that generate these signals are known at the cellular level and rest on a balance of excitatory and inhibitory interactions within and between populations of neurons. The kinetics of the ensuing population dynamics determine the frequency of oscillations. In this work we extended the classical nonlinear lumped-parameter model of alpha rhythms, initially developed by Lopes da Silva and colleagues [Kybernetik 15 (1974) 27], to generate more complex dynamics. We show that the whole spectrum of MEG/EEG signals can be reproduced within the oscillatory regime of this model by simply changing the population kinetics. We used the model to examine the influence of coupling strength and propagation delay on the rhythms generated by coupled cortical areas. The main findings were that (1) coupling induces phase-locked activity, with a phase shift of 0 or π when the coupling is bidirectional, and (2) both coupling and propagation delay are critical determinants of the MEG/EEG spectrum. In forthcoming articles, we will use this model to (1) estimate how neuronal interactions are expressed in MEG/EEG oscillations and establish the construct validity of various indices of nonlinear coupling, and (2) generate event-related transients to derive physiologically informed basis functions for statistical modelling of average evoked responses. [Copyright &y& Elsevier]

The prefrontal cortex may exert cognitive control by a general mechanism of attentional selection of neuronal representations. We used functional magnetic resonance imaging to test this hypothesis in the motor system. Normal volunteers were scanned during performance of a simple motor task, with their attention either directed towards their actions, or diverted towards a visual search task, or neither. Attention to action increased activity in prefrontal, premotor and parietal cortex, compared with unattended performance of the same movements. Analysis of cortical activity by structural equation modelling of regional fMRI time series was used to measure effective connectivity among prefrontal, premotor and parietal cortices. Attention to action enhanced effective connectivity between dorsal prefrontal cortex and premotor cortex, whereas non-motor attention diminished it. These effects were not attributable to common inputs from parietal cortex to the prefrontal and premotor cortex. The results suggest a supra-modal role for the dorsal prefrontal cortex in attentional selection, operating within the motor system as well as sensory and mnemonic domains. [Copyright &y& Elsevier]