Laminar fMRI and computational theories of brain function.

Recently developed methods for functional MRI at the resolution of cortical layers (laminar fMRI) offer a novel window into neurophysiological mechanisms of cortical activity. Beyond physiology, laminar fMRI also offers an unprecedented opportunity to test influential theories of brain function. Specifically, hierarchical Bayesian theories of brain function, such as predictive coding, assign specific computational roles to different cortical layers. Combined with computational models, laminar fMRI offers a unique opportunity to test these proposals noninvasively in humans. This review provides a brief overview of predictive coding and related hierarchical Bayesian theories, summarises their predictions with regard to layered cortical computations, examines how these predictions could be tested by laminar fMRI, and considers methodological challenges. We conclude by discussing the potential of laminar fMRI for clinically useful computational assays of layer-specific information processing.

Computational neuroimaging strategies for single patient predictions.

Neuroimaging increasingly exploits machine learning techniques in an attempt to achieve clinically relevant single-subject predictions. An alternative to machine learning, which tries to establish predictive links between features of the observed data and clinical variables, is the deployment of computational models for inferring on the (patho)physiological and cognitive mechanisms that generate behavioural and neuroimaging responses. This paper discusses the rationale behind a computational approach to neuroimaging-based single-subject inference, focusing on its potential for characterising disease mechanisms in individual subjects and mapping these characterisations to clinical predictions. Following an overview of two main approaches - Bayesian model selection and generative embedding - which can link computational models to individual predictions, we review how these methods accommodate heterogeneity in psychiatric and neurological spectrum disorders, help avoid erroneous interpretations of neuroimaging data, and establish a link between a mechanistic, model-based approach and the statistical perspectives afforded by machine learning.

Bayesian model selection for group studies - revisited.

In this paper, we revisit the problem of Bayesian model selection (BMS) at the group level. We originally addressed this issue in Stephan et al. (2009), where models are treated as random effects that could differ between subjects, with an unknown population distribution. Here, we extend this work, by (i) introducing the Bayesian omnibus risk (BOR) as a measure of the statistical risk incurred when performing group BMS, (ii) highlighting the difference between random effects BMS and classical random effects analyses of parameter estimates, and (iii) addressing the problem of between group or condition model comparisons. We address the first issue by quantifying the chance likelihood of apparent differences in model frequencies. This leads to the notion of protected exceedance probabilities. The second issue arises when people want to ask "whether a model parameter is zero or not" at the group level. Here, we provide guidance as to whether to use a classical second-level analysis of parameter estimates, or random effects BMS. The third issue rests on the evidence for a difference in model labels or frequencies across groups or conditions. Overall, we hope that the material presented in this paper finesses the problems of group-level BMS in the analysis of neuroimaging and behavioural data.

Multi-site reproducibility of prefrontal-hippocampal connectivity estimates by stochastic DCM.

This study examined the reproducibility of prefrontal-hippocampal connectivity estimates obtained by stochastic dynamic causal modeling (sDCM). 180 healthy subjects were measured by functional magnetic resonance imaging (fMRI) during a standard working memory N-Back task at three different sites (Mannheim, Bonn, Berlin; each with 60 participants). The reproducibility of regional activations in key regions for working memory (dorsolateral prefrontal cortex, DLPFC; hippocampal formation, HF) was evaluated using conjunction analyses across locations. These analyses showed consistent activation of right DLPFC and deactivation of left HF across all three different sites. The effective connectivity between DLPFC and HF was analyzed using a simple two-region sDCM. For each subject, we evaluated sixty-seven alternative sDCMs and compared their relative plausibility using Bayesian model selection (BMS). Across all locations, BMS consistently revealed the same winning model, with the 2-Back working memory condition as driving input to both DLPFC and HF and with a connection from DLPFC to HF. Statistical tests on the sDCM parameter estimates did not show any significant differences across the three sites. The consistency of both the BMS results and model parameter estimates indicates the reliability of sDCM in our paradigm. This provides a basis for future genetic and clinical studies using this approach.

Stochastic dynamic causal modelling of fMRI data: should we care about neural noise?

Dynamic causal modelling (DCM) was introduced to study the effective connectivity among brain regions using neuroimaging data. Until recently, DCM relied on deterministic models of distributed neuronal responses to external perturbation (e.g., sensory stimulation or task demands). However, accounting for stochastic fluctuations in neuronal activity and their interaction with task-specific processes may be of particular importance for studying state-dependent interactions. Furthermore, allowing for random neuronal fluctuations may render DCM more robust to model misspecification and finesse problems with network identification. In this article, we examine stochastic dynamic causal models (sDCM) in relation to their deterministic counterparts (dDCM) and highlight questions that can only be addressed with sDCM. We also compare the network identification performance of deterministic and stochastic DCM, using Monte Carlo simulations and an empirical case study of absence epilepsy. For example, our results demonstrate that stochastic DCM can exploit the modelling of neural noise to discriminate between direct and mediated connections. We conclude with a discussion of the added value and limitations of sDCM, in relation to its deterministic homologue.

An electrophysiological validation of stochastic DCM for fMRI.

In this note, we assess the predictive validity of stochastic dynamic causal modeling (sDCM) of functional magnetic resonance imaging (fMRI) data, in terms of its ability to explain changes in the frequency spectrum of concurrently acquired electroencephalography (EEG) signal. We first revisit the heuristic model proposed in Kilner et al. (2005), which suggests that fMRI activation is associated with a frequency modulation of the EEG signal (rather than an amplitude modulation within frequency bands). We propose a quantitative derivation of the underlying idea, based upon a neural field formulation of cortical activity. In brief, dense lateral connections induce a separation of time scales, whereby fast (and high spatial frequency) modes are enslaved by slow (low spatial frequency) modes. This slaving effect is such that the frequency spectrum of fast modes (which dominate EEG signals) is controlled by the amplitude of slow modes (which dominate fMRI signals). We then use conjoint empirical EEG-fMRI data-acquired in epilepsy patients-to demonstrate the electrophysiological underpinning of neural fluctuations inferred from sDCM for fMRI.

DCM for complex-valued data: cross-spectra, coherence and phase-delays.

This note describes an extension of Bayesian model inversion procedures for the Dynamic Causal Modeling (DCM) of complex-valued data. Modeling complex data can be particularly useful in the analysis of multivariate ergodic (stationary) time-series. We illustrate this with a generalization of DCM for steady-state responses that models both the real and imaginary parts of sample cross-spectra. DCM allows one to infer underlying biophysical parameters generating data (like synaptic time constants, connection strengths and conduction delays). Because transfer functions and complex cross-spectra can be generated from these parameters, one can also describe the implicit system architecture in terms of conventional (linear systems) measures; like coherence, phase-delay or cross-correlation functions. Crucially, these measures can be derived in both sensor and source-space. In other words, one can examine the cross-correlation or phase-delay functions between hidden neuronal sources using non-invasive data and relate these functions to synaptic parameters and neuronal conduction delays. We illustrate these points using local field potential recordings from the subthalamic nucleus and globus pallidus, with a special focus on the relationship between conduction delays and the ensuing phase relationships and cross-correlation time lags between population activities.

Dynamic causal modelling: a critical review of the biophysical and statistical foundations.

The goal of dynamic causal modelling (DCM) of neuroimaging data is to study experimentally induced changes in functional integration among brain regions. This requires (i) biophysically plausible and physiologically interpretable models of neuronal network dynamics that can predict distributed brain responses to experimental stimuli and (ii) efficient statistical methods for parameter estimation and model comparison. These two key components of DCM have been the focus of more than thirty methodological articles since the seminal work of Friston and colleagues published in 2003. In this paper, we provide a critical review of the current state-of-the-art of DCM. We inspect the properties of DCM in relation to the most common neuroimaging modalities (fMRI and EEG/MEG) and the specificity of inference on neural systems that can be made from these data. We then discuss both the plausibility of the underlying biophysical models and the robustness of the statistical inversion techniques. Finally, we discuss potential extensions of the current DCM framework, such as stochastic DCMs, plastic DCMs and field DCMs.

Ten simple rules for dynamic causal modeling.

Dynamic causal modeling (DCM) is a generic Bayesian framework for inferring hidden neuronal states from measurements of brain activity. It provides posterior estimates of neurobiologically interpretable quantities such as the effective strength of synaptic connections among neuronal populations and their context-dependent modulation. DCM is increasingly used in the analysis of a wide range of neuroimaging and electrophysiological data. Given the relative complexity of DCM, compared to conventional analysis techniques, a good knowledge of its theoretical foundations is needed to avoid pitfalls in its application and interpretation of results. By providing good practice recommendations for DCM, in the form of ten simple rules, we hope that this article serves as a helpful tutorial for the growing community of DCM users.

Changing meaning causes coupling changes within higher levels of the cortical hierarchy.

Processing of speech and nonspeech sounds occurs bilaterally within primary auditory cortex and surrounding regions of the superior temporal gyrus; however, the manner in which these regions interact during speech and nonspeech processing is not well understood. Here, we investigate the underlying neuronal architecture of the auditory system with magnetoencephalography and a mismatch paradigm. We used a spoken word as a repeating "standard" and periodically introduced 3 "oddball" stimuli that differed in the frequency spectrum of the word's vowel. The closest deviant was perceived as the same vowel as the standard, whereas the other 2 deviants were perceived as belonging to different vowel categories. The neuronal responses to these vowel stimuli were compared with responses elicited by perceptually matched tone stimuli under the same paradigm. For both speech and tones, deviant stimuli induced coupling changes within the same bilateral temporal lobe system. However, vowel oddball effects increased coupling within the left posterior superior temporal gyrus, whereas perceptually equivalent nonspeech oddball effects increased coupling within the right primary auditory cortex. Thus, we show a dissociation in neuronal interactions, occurring at both different hierarchal levels of the auditory system (superior temporal versus primary auditory cortex) and in different hemispheres (left versus right). This hierarchical specificity depends on whether auditory stimuli are embedded in a perceptual context (i.e., a word). Furthermore, our lateralization results suggest left hemisphere specificity for the processing of phonological stimuli, regardless of their elemental (i.e., spectrotemporal) characteristics.

Forward and backward connections in the brain: a DCM study of functional asymmetries.

In this paper, we provide evidence for functional asymmetries in forward and backward connections that define hierarchical architectures in the brain. We exploit the fact that modulatory or nonlinear influences of one neuronal system on another (i.e., effective connectivity) entail coupling between different frequencies. Functional asymmetry in forward and backward connections was addressed by comparing dynamic causal models of MEG responses induced by visual processing of normal and scrambled faces. We compared models with and without nonlinear (between-frequency) coupling in both forward and backward connections. Bayesian model comparison indicated that the best model had nonlinear forward and backward connections. Using the best model we then quantified frequency-specific causal influences mediating observed spectral responses. We found a striking asymmetry between forward and backward connections; in which high (gamma) frequencies in higher cortical areas suppressed low (alpha) frequencies in lower areas. This suppression was significantly greater than the homologous coupling in the forward connections. Furthermore, exactly the asymmetry was observed when we examined face-selective coupling (i.e., coupling under faces minus scrambled faces). These results highlight the importance of nonlinear coupling among brain regions and point to a functional asymmetry between forward and backward connections in the human brain that is consistent with anatomical and physiological evidence from animal studies. This asymmetry is also consistent with functional architectures implied by theories of perceptual inference in the brain, based on hierarchical generative models.

Dynamic causal models of steady-state responses.

In this paper, we describe a dynamic causal model (DCM) of steady-state responses in electrophysiological data that are summarised in terms of their cross-spectral density. These spectral data-features are generated by a biologically plausible, neural-mass model of coupled electromagnetic sources; where each source comprises three sub-populations. Under linearity and stationarity assumptions, the model's biophysical parameters (e.g., post-synaptic receptor density and time constants) prescribe the cross-spectral density of responses measured directly (e.g., local field potentials) or indirectly through some lead-field (e.g., electroencephalographic and magnetoencephalographic data). Inversion of the ensuing DCM provides conditional probabilities on the synaptic parameters of intrinsic and extrinsic connections in the underlying neuronal network. This means we can make inferences about synaptic physiology, as well as changes induced by pharmacological or behavioural manipulations, using the cross-spectral density of invasive or non-invasive electrophysiological recordings. In this paper, we focus on the form of the model, its inversion and validation using synthetic and real data. We conclude with an illustrative application to multi-channel local field potential data acquired during a learning experiment in mice.

Do patients with schizophrenia exhibit aberrant salience?

BACKGROUND: It has been suggested that some psychotic symptoms reflect 'aberrant salience', related to dysfunctional reward learning. To test this hypothesis we investigated whether patients with schizophrenia showed impaired learning of task-relevant stimulus-reinforcement associations in the presence of distracting task-irrelevant cues. METHOD: We tested 20 medicated patients with schizophrenia and 17 controls on a reaction time game, the Salience Attribution Test. In this game, participants made a speeded response to earn money in the presence of conditioned stimuli (CSs). Each CS comprised two visual dimensions, colour and form. Probability of reinforcement varied over one of these dimensions (task-relevant), but not the other (task-irrelevant). Measures of adaptive and aberrant motivational salience were calculated on the basis of latency and subjective reinforcement probability rating differences over the task-relevant and task-irrelevant dimensions respectively. RESULTS: Participants rated reinforcement significantly more likely and responded significantly faster on high-probability-reinforced relative to low-probability-reinforced trials, representing adaptive motivational salience. Patients exhibited reduced adaptive salience relative to controls, but the two groups did not differ in terms of aberrant salience. Patients with delusions exhibited significantly greater aberrant salience than those without delusions, and aberrant salience also correlated with negative symptoms. In the controls, aberrant salience correlated significantly with 'introvertive anhedonia' schizotypy. CONCLUSIONS: These data support the hypothesis that aberrant salience is related to the presence of delusions in medicated patients with schizophrenia, but are also suggestive of a link with negative symptoms. The relationship between aberrant salience and psychotic symptoms warrants further investigation in unmedicated patients.

Bayesian estimation of synaptic physiology from the spectral responses of neural masses.

We describe a Bayesian inference scheme for quantifying the active physiology of neuronal ensembles using local field recordings of synaptic potentials. This entails the inversion of a generative neural mass model of steady-state spectral activity. The inversion uses Expectation Maximization (EM) to furnish the posterior probability of key synaptic parameters and the marginal likelihood of the model itself. The neural mass model embeds prior knowledge pertaining to both the anatomical [synaptic] circuitry and plausible trajectories of neuronal dynamics. This model comprises a population of excitatory pyramidal cells, under local interneuron inhibition and driving excitation from layer IV stellate cells. Under quasi-stationary assumptions, the model can predict the spectral profile of local field potentials (LFP). This means model parameters can be optimised given real electrophysiological observations. The validity of inferences about synaptic parameters is demonstrated using simulated data and experimental recordings from the medial prefrontal cortex of control and isolation-reared Wistar rats. Specifically, we examined the maximum a posteriori estimates of parameters describing synaptic function in the two groups and tested predictions derived from concomitant microdialysis measures. The modelling of the LFP recordings revealed (i) a sensitization of post-synaptic excitatory responses, particularly marked in pyramidal cells, in the medial prefrontal cortex of socially isolated rats and (ii) increased neuronal adaptation. These inferences were consistent with predictions derived from experimental microdialysis measures of extracellular glutamate levels.

A neural mass model of spectral responses in electrophysiology.

We present a neural mass model of steady-state membrane potentials measured with local field potentials or electroencephalography in the frequency domain. This model is an extended version of previous dynamic causal models for investigating event-related potentials in the time-domain. In this paper, we augment the previous formulation with parameters that mediate spike-rate adaptation and recurrent intrinsic inhibitory connections. We then use linear systems analysis to show how the model's spectral response changes with its neurophysiological parameters. We demonstrate that much of the interesting behaviour depends on the non-linearity which couples mean membrane potential to mean spiking rate. This non-linearity is analogous, at the population level, to the firing rate-input curves often used to characterize single-cell responses. This function depends on the model's gain and adaptation currents which, neurobiologically, are influenced by the activity of modulatory neurotransmitters. The key contribution of this paper is to show how neuromodulatory effects can be modelled by adding adaptation currents to a simple phenomenological model of EEG. Critically, we show that these effects are expressed in a systematic way in the spectral density of EEG recordings. Inversion of the model, given such non-invasive recordings, should allow one to quantify pharmacologically induced changes in adaptation currents. In short, this work establishes a forward or generative model of electrophysiological recordings for psychopharmacological studies.

Extra-classical receptive field effects measured in striate cortex with fMRI.

The aim of this study was to measure the contextual influence of globally coherent motion on visual cortical responses using functional magnetic resonance imaging. Our motivation was to test a prediction from representational theories of perception (i.e. predictive coding) that primary visual responses should be suppressed by top-down influences during coherent motion. We used a sparse stimulus array such that each element could not fall within the same classical receptive field of primary visual cortex neurons (i.e. precluding lateral interactions within V1). This enabled us to attribute differences, in striate cortex responses, to extra-classical receptive field effects mediated by backward connections. In accord with theoretical predictions we were able to demonstrate suppression of striate cortex activations to coherent relative to incoherent motion. These results suggest that suppression of primary visual cortex responses to coherent motion reflect extra-classical effects mediated by backward connections.

The left parietal cortex and motor intention: an event-related functional magnetic resonance imaging study.

Traditionally the posterior parietal cortex was believed to be a sensory structure. More recently, however, its important role in sensory-motor integration has been recognized. One of its functions suggested in this context is the forming of intentions, i.e. high-level cognitive plans for movements. The selection and planning of a specific movement defines motor intention. In this study we used rapid event-related functional magnetic resonance imaging of healthy human subjects to investigate the involvement of posterior parietal cortex in motor intention in response to valid imperative cues. Subjects were provided with either neutral, motor or spatial cues. Neutral cues simply alerted, motor cues indicated which hand to use for response, and spatial cues indicated on which side the target would appear. Importantly, identical targets and responses followed these cues. Therefore any differential neural effects observed are independent from the actual movement performed. Differential blood oxygen level dependent signal changes for motor vs. neutral as well as motor vs. spatial cue trials were found in the left supramarginal gyrus, as hypothesized. The results demonstrate that neural activity in the left supramarginal gyrus underlies motor plans independent from the execution of the movement and thus extend previous neuropsychological and functional imaging data on the role of the left supramarginal gyrus in higher motor cognition.

CoCoDat: a database system for organizing and selecting quantitative data on single neurons and neuronal microcircuitry.

We present a novel database system for organizing and selecting quantitative experimental data on single neurons and neuronal microcircuitry that has proven useful for reference-keeping, experimental planning and computational modelling. Building on our previous experience with large neuroscientific databases, the system takes into account the diversity and method-dependence of single cell and microcircuitry data and provides tools for entering and retrieving published data without a priori interpretation or summarizing. Data representation is based on the framework suggested by biophysical theory and enables flexible combinations of data on membrane conductances, ionic and synaptic currents, morphology, connectivity and firing patterns. Innovative tools have been implemented for data retrieval with optional relaxation of search criteria along the conceptual dimensions of brain region, cortical layer, cell type and subcellular compartment. The relaxation procedures help to overcome the traditional trade-off between exact, non-interpreted data representation in the original nomenclature and convenient data retrieval. We demonstrate the use of these tools for the construction, tuning and validation of a multicompartmental model of a layer V pyramidal cell from the rat barrel cortex. CoCoDat is freely available at . Its application is scalable from offline use by individual researchers via local laboratory networks to a federation of distributed web sites in platform-independent XML format using Axiope tools.

Mixed-effects and fMRI studies.

This note concerns mixed-effect (MFX) analyses in multisession functional magnetic resonance imaging (fMRI) studies. It clarifies the relationship between mixed-effect analyses and the two-stage "summary statistics" procedure (Holmes, A.P., Friston, K.J., 1998. Generalisability, random effects and population inference. NeuroImage 7, S754) that has been adopted widely for analyses of fMRI data at the group level. We describe a simple procedure, based on restricted maximum likelihood (ReML) estimates of covariance components, that enables full mixed-effects analyses in the context of statistical parametric mapping. Using this procedure, we compare the results of a full mixed-effects analysis with those obtained from the simpler two-stage procedure and comment on the situations when the two approaches may give different results.

Modelling functional integration: a comparison of structural equation and dynamic causal models.

The brain appears to adhere to two fundamental principles of functional organisation, functional integration and functional specialisation, where the integration within and among specialised areas is mediated by effective connectivity. In this paper, we review two different approaches to modelling effective connectivity from fMRI data, structural equation models (SEMs) and dynamic causal models (DCMs). In common to both approaches are model comparison frameworks in which inferences can be made about effective connectivity per se and about how that connectivity can be changed by perceptual or cognitive set. Underlying the two approaches, however, are two very different generative models. In DCM, a distinction is made between the 'neuronal level' and the 'hemodynamic level'. Experimental inputs cause changes in effective connectivity expressed at the level of neurodynamics, which in turn cause changes in the observed hemodynamics. In SEM, changes in effective connectivity lead directly to changes in the covariance structure of the observed hemodynamics. Because changes in effective connectivity in the brain occur at a neuronal level DCM is the preferred model for fMRI data. This review focuses on the underlying assumptions and limitations of each model and demonstrates their application to data from a study of attention to visual motion.