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Calcium imaging has been used as a promising technique to monitor the dynamic activity of neuronal populations. However, the calcium trace is temporally smeared which restricts the extraction of quantities of interest such as spike trains of individual neurons. To address this issue, spike reconstruction algorithms have been introduced. One limitation of such reconstructions is that the underlying models are not informed about the biophysics of spike and burst generations. Such existing prior knowledge might be useful for constraining the possible solutions of spikes. Here we describe, in a novel Bayesian approach, how principled knowledge about neuronal dynamics can be employed to infer biophysical variables and parameters from fluorescence traces. By using both synthetic and in vitro recorded fluorescence traces, we demonstrate that the new approach is able to reconstruct different repetitive spiking and/or bursting patterns with accurate single spike resolution. Furthermore, we show that the high inference precision of the new approach is preserved even if the fluorescence trace is rather noisy or if the fluorescence transients show slow rise kinetics lasting several hundred milliseconds, and inhomogeneous rise and decay times. In addition, we discuss the use of the new approach for inferring parameter changes, e.g. due to a pharmacological intervention, as well as for inferring complex characteristics of immature neuronal circuits.

The olfactory information that is received by the insect brain is encoded in the form of spatiotemporal patterns in the projection neurons of the antennal lobe. These dense and overlapping patterns are transformed into a sparse code in Kenyon cells in the mushroom body. Although it is clear that this sparse code is the basis for rapid categorization of odors, it is yet unclear how the sparse code in Kenyon cells is computed and what information it represents. Here we show that this computation can be modeled by sequential firing rate patterns using Lotka-Volterra equations and Bayesian online inference. This new model can be understood as an 'intelligent coincidence detector', which robustly and dynamically encodes the presence of specific odor features. We found that the model is able to qualitatively reproduce experimentally observed activity in both the projection neurons and the Kenyon cells. In particular, the model explains mechanistically how sparse activity in the Kenyon cells arises from the dense code in the projection neurons. The odor classification performance of the model proved to be robust against noise and time jitter in the observed input sequences. As in recent experimental results, we found that recognition of an odor happened very early during stimulus presentation in the model. Critically, by using the model, we found surprising but simple computational explanations for several experimental phenomena.

Even for simple perceptual decisions, the mechanisms that the brain employs are still under debate. Although current consensus states that the brain accumulates evidence extracted from noisy sensory information, open questions remain about how this simple model relates to other perceptual phenomena such as flexibility in decisions, decision-dependent modulation of sensory gain, or confidence about a decision. We propose a novel approach of how perceptual decisions are made by combining two influential formalisms into a new model. Specifically, we embed an attractor model of decision making into a probabilistic framework that models decision making as Bayesian inference. We show that the new model can explain decision making behaviour by fitting it to experimental data. In addition, the new model combines for the first time three important features: First, the model can update decisions in response to switches in the underlying stimulus. Second, the probabilistic formulation accounts for top-down effects that may explain recent experimental findings of decision-related gain modulation of sensory neurons. Finally, the model computes an explicit measure of confidence which we relate to recent experimental evidence for confidence computations in perceptual decision tasks.

Accumulating empirical evidence suggests a role of Bayesian inference and learning for shaping neural responses in auditory and visual perception. However, its relevance for somatosensory processing is unclear. In the present study we test the hypothesis that cortical somatosensory processing exhibits dynamics that are consistent with Bayesian accounts of brain function. Specifically, we investigate the cortical encoding of Bayesian surprise, a recently proposed marker of Bayesian perceptual learning, using EEG data recorded from 15 subjects. Capitalizing on a somatosensory mismatch roving paradigm, we performed computational single-trial modeling of evoked somatosensory potentials for the entire peri-stimulus time period in source space. By means of Bayesian model selection, we find that, at 140 ms post-stimulus onset, secondary somatosensory cortex represents Bayesian surprise rather than stimulus change, which is the conventional marker of EEG mismatch responses. In contrast, at 250 ms, right inferior frontal cortex indexes stimulus change. Finally, at 360 ms, our analyses indicate additional perceptual learning attributable to medial cingulate cortex. In summary, the present study provides novel evidence for anatomical-temporal/functional segregation in human somatosensory processing that is consistent with the Bayesian brain hypothesis., (Copyright © 2012 Elsevier Inc. All rights reserved.)

Neuronal responses exhibit two stimulus or task-related components: evoked and induced. The functional role of induced responses has been ascribed to 'top-down' modulation through backward connections and lateral interactions; as opposed to the bottom-up driving processes that may predominate in evoked components. The implication is that evoked and induced components may reflect different neuronal processes. The conventional way of separating evoked and induced responses assumes that they can be decomposed linearly; in that induced responses are the average of the power minus the power of the average (the evoked component). However, this decomposition may not hold if both components are generated by nonlinear processes. In this work, we propose a Dynamic Causal Model that models evoked and induced responses at the same time. This allows us to explain both components in terms of shared mechanisms (coupling) and changes in coupling that are necessary to explain any induced components. To establish the face validity of our approach, we used Bayesian Model Selection to show that the scheme can disambiguate between models of synthetic data that did and did not contain induced components. We then repeated the analysis using MEG data during a hand grip task to ask whether induced responses in motor control circuits are mediated by 'top-down' or backward connections. Our result provides empirical evidence that induced responses are more likely to reflect backward message passing in the brain, while evoked and induced components share certain characteristics and mechanisms., (Copyright © 2011 Elsevier Inc. All rights reserved.)

The neuronal system underlying learning, generation and recognition of song in birds is one of the best-studied systems in the neurosciences. Here, we use these experimental findings to derive a neurobiologically plausible, dynamic, hierarchical model of birdsong generation and transform it into a functional model of birdsong recognition. The generation model consists of neuronal rate models and includes critical anatomical components like the premotor song-control nucleus HVC (proper name), the premotor nucleus RA (robust nucleus of the arcopallium), and a model of the syringeal and respiratory organs. We use Bayesian inference of this dynamical system to derive a possible mechanism for how birds can efficiently and robustly recognize the songs of their conspecifics in an online fashion. Our results indicate that the specific way birdsong is generated enables a listening bird to robustly and rapidly perceive embedded information at multiple time scales of a song. The resulting mechanism can be useful for investigating the functional roles of auditory recognition areas and providing predictions for future birdsong experiments.

Neural mass models (NMMs) explain dynamics of neuronal populations and were designed to strike a balance between mathematical simplicity and biological plausibility. They are currently widely used as generative models for noninvasive electrophysiological brain measurements; that is, magneto- and electroencephalography (M/EEG). Here, we systematically describe the oscillatory regimes which a NMM of a single cortical source with extrinsic input from other cortical and subcortical areas to each subpopulation can explain. For this purpose, we used bifurcation analysis to describe qualitative changes in system behavior in response to quantitative input changes. This approach allowed us to describe sequences of oscillatory regimes, given some specific input trajectory. We systematically classified these sequential phenomena and mapped them into parameter space. Our analysis suggests a principled scheme of how complex M/EEG phenomena can be modeled parsimoniously on two time scales: While the system displays fast oscillations, it slowly traverses phase space to another qualitatively different oscillatory regime, depending on the input dynamics. The resulting scheme is useful for applications where one needs to model an ordered sequence of switching between qualitatively different oscillatory regimes, for example, in pharmacological interventions, epilepsy, sleep, or context-induced state changes., (Copyright (c) 2009 Elsevier Inc. All rights reserved.)

In this paper, we compare mean-field and neural-mass models of electrophysiological responses using Bayesian model comparison. In previous work, we presented a mean-field model of neuronal dynamics as observed with magnetoencephalography and electroencephalography. Unlike neural-mass models, which consider only the mean activity of neuronal populations, mean-field models track the distribution (e.g., mean and dispersion) of population activity. This can be important if the mean affects the dispersion or vice versa. Here, we introduce a dynamical causal model based on mean-field (i.e., population density) models of neuronal activity, and use it to assess the evidence for a coupling between the mean and dispersion of hidden neuronal states using observed electromagnetic responses. We used Bayesian model comparison to compare homologous mean-field and neural-mass models, asking whether empirical responses support a role for population variance in shaping neuronal dynamics. We used the mismatch negativity (MMN) and somatosensory evoked potentials (SEP) as representative neuronal responses in physiological and non-physiological paradigms respectively. Our main conclusion was that although neural-mass models may be sufficient for cognitive paradigms, there is clear evidence for an effect of dispersion at the high levels of depolarization evoked in SEP paradigms. This suggests that (i) the dispersion of neuronal states within populations generating evoked brain signals can be manifest in observed brain signals and that (ii) the evidence for their effects can be accessed with dynamic causal model comparison., (Copyright (c) 2010 Elsevier Inc. All rights reserved.)

We have previously tried to explain perceptual inference and learning under a free-energy principle that pursues Helmholtz's agenda to understand the brain in terms of energy minimization. It is fairly easy to show that making inferences about the causes of sensory data can be cast as the minimization of a free-energy bound on the likelihood of sensory inputs, given an internal model of how they were caused. In this article, we consider what would happen if the data themselves were sampled to minimize this bound. It transpires that the ensuing active sampling or inference is mandated by ergodic arguments based on the very existence of adaptive agents. Furthermore, it accounts for many aspects of motor behavior; from retinal stabilization to goal-seeking. In particular, it suggests that motor control can be understood as fulfilling prior expectations about proprioceptive sensations. This formulation can explain why adaptive behavior emerges in biological agents and suggests a simple alternative to optimal control theory. We illustrate these points using simulations of oculomotor control and then apply to same principles to cued and goal-directed movements. In short, the free-energy formulation may provide an alternative perspective on the motor control that places it in an intimate relationship with perception.

In this note, we describe a variant of dynamic causal modelling for evoked responses as measured with electroencephalography or magnetoencephalography (EEG and MEG). We depart from equivalent current dipole formulations of DCM, and extend it to provide spatiotemporal source estimates that are spatially distributed. The spatial model is based upon neural-field equations that model neuronal activity on the cortical manifold. We approximate this description of electrocortical activity with a set of local standing-waves that are coupled though their temporal dynamics. The ensuing distributed DCM models source as a mixture of overlapping patches on the cortical mesh. Time-varying activity in this mixture, caused by activity in other sources and exogenous inputs, is propagated through appropriate lead-field or gain-matrices to generate observed sensor data. This spatial model has three key advantages. First, it is more appropriate than equivalent current dipole models, when real source activity is distributed locally within a cortical area. Second, the spatial degrees of freedom of the model can be specified and therefore optimised using model selection. Finally, the model is linear in the spatial parameters, which finesses model inversion. Here, we describe the distributed spatial model and present a comparative evaluation with conventional equivalent current dipole (ECD) models of auditory processing, as measured with EEG.

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.

We present a review of dynamic causal modeling (DCM) for magneto- and electroencephalography (M/EEG) data. DCM is based on a spatiotemporal model, where the temporal component is formulated in terms of neurobiologically plausible dynamics. Following an intuitive description of the model, we discuss six recent studies, which use DCM to analyze M/EEG and local field potentials. These studies illustrate how DCM can be used to analyze evoked responses (average response in time), induced responses (average response in time-frequency), and steady-state responses (average response in frequency). Bayesian model comparison plays a critical role in these analyses, by allowing one to compare equally plausible models in terms of their model evidence. This approach might be very useful in M/EEG research; where correlations among spatial and neuronal model parameter estimates can cause uncertainty about which model best explains the data. Bayesian model comparison resolves these uncertainties in a principled and formal way. We suggest that DCM and Bayesian model comparison provides a useful way to test hypotheses about distributed processing in the brain, using electromagnetic data., ((c) 2009 Wiley-Liss, Inc.)

This article describes the use of dynamic causal modeling to test hypotheses about the genesis of evoked responses. Specifically, we consider the mismatch negativity (MMN), a well-characterized response to deviant sounds and one of the most widely studied evoked responses. There have been several mechanistic accounts of how the MMN might arise. It has been suggested that the MMN results from a comparison between sensory input and a memory trace of previous input, although others have argued that local adaptation, due to stimulus repetition, is sufficient to explain the MMN. Thus the precise mechanisms underlying the generation of the MMN remain unclear. This study tests some biologically plausible spatiotemporal dipole models that rest on changes in extrinsic top-down connections (that enable comparison) and intrinsic changes (that model adaptation). Dynamic causal modeling suggested that responses to deviants are best explained by changes in effective connectivity both within and between cortical sources in a hierarchical network of distributed sources. Our model comparison suggests that both adaptation and memory comparison operate in concert to produce the early (N1 enhancement) and late (MMN) parts of the response to frequency deviants. We consider these mechanisms in the light of predictive coding and hierarchical inference in the brain.

In this paper, we describe a generic approach to modelling dynamics in neuronal populations. This approach models a full density on the states of neuronal populations but finesses this high-dimensional problem by re-formulating density dynamics in terms of ordinary differential equations on the sufficient statistics of the densities considered (c.f., the method of moments). The particular form for the population density we adopt is a Gaussian density (c.f., the Laplace assumption). This means population dynamics are described by equations governing the evolution of the population's mean and covariance. We derive these equations from the Fokker-Planck formalism and illustrate their application to a conductance-based model of neuronal exchanges. One interesting aspect of this formulation is that we can uncouple the mean and covariance to furnish a neural-mass model, which rests only on the populations mean. This enables us to compare equivalent mean-field and neural-mass models of the same populations and evaluate, quantitatively, the contribution of population variance to the expected dynamics. The mean-field model presented here will form the basis of a dynamic causal model of observed electromagnetic signals in future work.

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.

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].

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.

This paper demonstrates how the sigmoid activation function of neural-mass models can be understood in terms of the variance or dispersion of neuronal states. We use this relationship to estimate the probability density on hidden neuronal states, using non-invasive electrophysiological (EEG) measures and dynamic casual modelling. The importance of implicit variance in neuronal states for neural-mass models of cortical dynamics is illustrated using both synthetic data and real EEG measurements of sensory evoked responses.

Dynamical causal modelling (DCM) for functional magnetic resonance imaging (fMRI) is a technique to infer directed connectivity among brain regions. These models distinguish between a neuronal level, which models neuronal interactions among regions, and an observation level, which models the hemodynamic responses each region. The original DCM formulation considered only one neuronal state per region. In this work, we adopt a more plausible and less constrained neuronal model, using two neuronal states (populations) per region. Critically, this gives us an explicit model of intrinsic (between-population) connectivity within a region. In addition, by using positivity constraints, the model conforms to the organization of real cortical hierarchies, whose extrinsic connections are excitatory (glutamatergic). By incorporating two populations within each region we can model selective changes in both extrinsic and intrinsic connectivity. Using synthetic data, we show that the two-state model is internal consistent and identifiable. We then apply the model to real data, explicitly modelling intrinsic connections. Using model comparison, we found that the two-state model is better than the single-state model. Furthermore, using the two-state model we find that it is possible to disambiguate between subtle changes in coupling; we were able to show that attentional gain, in the context of visual motion processing, is accounted for sufficiently by an increased sensitivity of excitatory populations of neurons in V5, to forward afferents from earlier visual areas.

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.

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.

Dynamic causal modelling (DCM) has been applied recently to event-related responses (ERPs) measured with EEG/MEG. DCM attempts to explain ERPs using a network of interacting cortical sources and waveform differences in terms of coupling changes among sources. The aim of this work was to establish the validity of DCM by assessing its reproducibility across subjects. We used an oddball paradigm to elicit mismatch responses. Sources of cortical activity were modelled as equivalent current dipoles, using a biophysical informed spatiotemporal forward model that included connections among neuronal subpopulations in each source. Bayesian inversion provided estimates of changes in coupling among sources and the marginal likelihood of each model. By specifying different connectivity models we were able to evaluate three different hypotheses: differences in the ERPs to rare and frequent events are mediated by changes in forward connections (F-model), backward connections (B-model) or both (FB-model). The results were remarkably consistent over subjects. In all but one subject, the forward model was better than the backward model. This is an important result because these models have the same number of parameters (i.e., the complexity). Furthermore, the FB-model was significantly better than both, in 7 out of 11 subjects. This is another important result because it shows that a more complex model (that can fit the data more accurately) is not necessarily the most likely model. At the group level the FB-model supervened. We discuss these findings in terms of the validity and usefulness of DCM in characterising EEG/MEG data and its ability to model ERPs in a mechanistic fashion.

Dynamic causal modelling is an approach to characterising evoked responses as measured by magneto/electroencephalography (M/EEG). A dynamic causal model (DCM) is a spatiotemporal, generative network model for event-related fields/responses (ERP/ERF) data. Using Bayesian model inversion, one can compute the posterior distributions of the DCM's physiological parameters and its marginal likelihood for model comparison. Model comparison can be used to test mechanistic hypotheses about how electrophysiological data were generated. In this work, we look at the relative importance of changes in intrinsic (within source) and extrinsic (between sources) connections in generating mismatch responses. In short, we introduce the modulation of intrinsic connectivity to the DCM framework. This is useful for testing hypotheses about adaptation of neuronal responses to local influences, in relation to influences that are mediated by long-range extrinsic connections (forward, backward, and lateral) from other sources. We illustrate this extension using synthetic data and empirical data from an oddball ERP experiment.

Dynamic causal modeling (DCM) of functional magnetic resonance imaging (fMRI) data allows one to make inferences about the architecture of distributed networks in the brain, in terms of effective connectivity. fMRI data are usually acquired using echo planar imaging (EPI). EPI sequences typically acquire slices at different times over a few seconds. DCM, in its original inception, was not informed about these slice timings and assumed that all slices were acquired simultaneously. It has been shown that DCM can cope with slice timing differences of up to 1 s. However, many fMRI studies employ a repetition time (TR) of 3 to 5 s, which precludes a straightforward DCM of these data. We show that this limitation can be overcome easily by including slice timing in the DCM. Using synthetic data we show that the extended DCM furnishes veridical posterior means, even if there are large slice-timing differences. Model comparisons show that, in general, the extended DCM out-performs the original model. We contrast the modeling of slice timing, in the context of DCM, with the less effective approach of 'slice-timing correction', prior to modeling. We apply our procedure to real data and show that slice timings are important parameters. We conclude that, generally, one should use DCM with slice timing.

Complex processes resulting from interaction of multiple elements can rarely be understood by analytical scientific approaches alone; additional, mathematical models of system dynamics are required. This insight, which disciplines like physics have embraced for a long time already, is gradually gaining importance in the study of cognitive processes by functional neuroimaging. In this field, causal mechanisms in neural systems are described in terms of effective connectivity. Recently, dynamic causal modelling (DCM) was introduced as a generic method to estimate effective connectivity from neuroimaging data in a Bayesian fashion. One of the key advantages of DCM over previous methods is that it distinguishes between neural state equations and modality-specific forward models that translate neural activity into a measured signal. Another strength is its natural relation to Bayesian model selection (BMS) procedures. In this article, we review the conceptual and mathematical basis of DCM and its implementation for functional magnetic resonance imaging data and event-related potentials. After introducing the application of BMS in the context of DCM, we conclude with an outlook to future extensions of DCM. These extensions are guided by the long-term goal of using dynamic system models for pharmacological and clinical applications, particularly with regard to synaptic plasticity.

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.

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.

This paper introduces the general framework, concepts, and procedures of anatomically informed basis functions (AIBF), a new method for the analysis of functional magnetic resonance imaging (fMRI) data. In contradistinction to existing voxel-based univariate or multivariate methods the approach described here can incorporate various forms of prior anatomical knowledge to specify sophisticated spatiotemporal models for fMRI time-series. In particular, we focus on anatomical prior knowledge, based on reconstructed gray matter surfaces and assumptions about the location and spatial smoothness of the blood oxygenation level dependent (BOLD) effect. After reconstruction of the grey matter surface from an individual's high-resolution T1-weighted MRI, we specify a set of anatomically informed basis functions, fit the model parameters for a single time point, using a regularized solution, and finally make inferences about the estimated parameters over time. Significant effects, induced by the experimental paradigm, can then be visualized in the native voxel-space or on the reconstructed folded, inflated, or flattened cortical surface. As an example, we apply the approach to a fMRI study (finger opposition task) and compare the results to those of a voxel-based analysis as implemented in the Statistical Parametric Mapping package (SPM99). Additionally, we show, using simulated data, that the approach offers several desirable features particularly in terms of superresolution and localization., (Copyright 2000 Academic Press.)

The assessment of significant activations in functional imaging using voxel-based methods often relies on results derived from the theory of Gaussian random fields. These results solve the multiple comparison problem and assume that the spatial correlation or smoothness of the data is known or can be estimated. End results (i. e., P values associated with local maxima, clusters, or sets of clusters) critically depend on this assessment, which should be as exact and as reliable as possible. In some earlier implementations of statistical parametric mapping (SPM) (SPM94, SPM95) the smoothness was assessed on Gaussianized t-fields (Gt-f) that are not generally free of physiological signal. This technique has two limitations. First, the estimation is not stable (the variance of the estimator being far from negligible) and, second, physiological signal in the Gt-f will bias the estimation. In this paper, we describe an estimation method that overcomes these drawbacks. The new approach involves estimating the smoothness of standardized residual fields which approximates the smoothness of the component fields of the associated t-field. Knowing the smoothness of these component fields is important because it allows one to compute corrected P values for statistical fields other than the t-field or the Gt-f (e.g., the F-map) and eschews bias due to deviation from the null hypothesis. We validate the method on simulated data and demonstrate it using data from a functional MRI study., (Copyright 1999 Academic Press.)