Technical NoteDynamic causal modelling of evoked responses: The role of intrinsic connections
Introduction
In dynamic causal modelling, one views the brain as a dynamic network that produces observable output. This perspective is useful for constructing fully spatiotemporal, generative or forward models for evoked responses as measured with M/EEG (David et al., 2005, Friston et al., 2003). The aim of DCM is to make inferences about effective connections and their changes in different experimental contexts. This is an important advance over conventional analyses of evoked responses, and allows one to test mechanistic hypotheses about distributed responses derived from cognitive or physiological theories. In brief, DCM entails specification of a plausible model of electrodynamic responses. This model is inverted by optimising a variational free-energy bound on the model’s evidence to provide the conditional density of the model parameters and the evidence itself for model comparison. Bayesian model comparison allows one to select the best model without the risk of ‘over-fitting’ when using classical ‘goodness-of-fit’ approaches (Penny et al., 2004).
In DCM for M/EEG, a network usually consists of a few sources (between two and eight), which communicate via directed extrinsic connections. Sensory input enters at primary sources, after passing through thalamic structures. The dynamics are described quantitatively by ordinary differential equations using a state–space description. The spatial expression of each source, at the sensors, is described by the lead field, whose free parameters (e.g., dipole locations and moments) are parameters of the DCM. We use a neural mass model to describe the neuronal dynamics of each source (Jansen and Rit, 1995) and established principles for extrinsic connections among sources (David et al., 2005). Although a clear simplification, the ensuing network model is based on anatomical and physiological features of the brain. These neurobiological constraints furnish spatiotemporal priors for model inversion and enforce a biological parameterisation, which distinguishes DCM from conventional inversion techniques.
In the original application of DCM to ERPs, the difference between two evoked responses was attributed exclusively to changes in extrinsic (between-sources) connectivity (David et al., 2006). Extrinsic connections are mediated by axons that leave grey matter and connect to other sources via the white matter (DeFelipe et al., 2002, Peters, 2002). Conversely, intrinsic connections use axons that do not leave grey matter, i.e., they connect neuronal populations horizontally or vertically within or between cortical layers. To test hypotheses about local adaptation of neuronal populations, this paper extends the original formulation and allows changes in intrinsic connections to explain ERP differences.
We use synthetic data to validate our extension and show that DCM can disambiguate between data generated by changes in intrinsic or extrinsic connections. Furthermore, we will illustrate the use of the ensuing DCM in a multi-subject mismatch negativity (MMN) study (Garrido et al., 2006). The MMN has been studied extensively (Naatanen et al., 2005). In brief, it is the differential response to an unexpected (rare) auditory stimulus relative to an expected (standard) stimulus. The conventional understanding of its genesis rests on an auditory network of change-sensitive populations. In this note, we will consider two recently described MMN hypotheses, which explain the MMN either by adaptation or within a predictive coding framework (Friston, 2005, Garrido et al., 2006, Jaaskelainen et al., 2004). We will show that both these hypotheses can be formulated and tested using DCM. This paper focuses on the methodology and motivation for DCM of intrinsic changes; consequently, we will focus on the grand mean average of the multi-subject study. A subsequent paper will present a full ERP analysis of each subject and discuss the neurobiological implications of the results from a cognitive neuroscience perspective.
In what follows, we first review the DCM approach to ERPs, with a special focus on the experimental modulation of intrinsic parameters. We then briefly review the MMN hypotheses to be tested. In the results section, we will establish face-validity of the model using synthetic data. Finally, we illustrate the approach using real ERP data.
Section snippets
Dynamic causal modelling of evoked responses
For completeness, we review the current DCM for evoked responses. Chapter 6 of Friston et al. (2006) provides a comprehensive summary of the larger research context embedding the DCM approach. Intuitively, the DCM scheme regards an experiment as a designed perturbation of neuronal dynamics that are promulgated and distributed throughout a system of coupled anatomical sources to produce region-specific responses. This system is modelled using a dynamic input–state–output system with multiple
Mismatch negativity: Hypotheses and models
In this section, we briefly review three hypotheses about the genesis of the mismatch negativity (MMN), the ‘traditional’, ‘adaptation’, and ‘predictive coding’ hypotheses. Here, we use the ‘adaptation’ and ‘predictive coding’ hypotheses to motivate the potential importance of both intrinsic and extrinsic mechanisms for the MMN that can be expressed formally as a DCM.
Simulations
In this section, we motivate and validate the extension of DCM using simulated data in which the true parameters and their changes are known. With these simulations we establish face-validity, i.e., we check whether the model inversion is veridical, given data that have been generated from the same class of models. We performed three sets of simulations. In the first, we compared four potential mechanisms of intrinsic adaptation. These were modelled as gains on parameters (i) γ1, (ii) γ2, (iii)
Discussion
We have complemented the original DCM (David et al., 2006) by allowing changes in within-source or intrinsic connectivity. These intrinsic changes can be used to test hypotheses which postulate local neuronal adaptation as a mechanism for the genesis of evoked responses. We have demonstrated the usefulness of this extension using the grand mean of a multi-subject mismatch ERP study. We anticipate that similar intrinsic adaptation models will be useful in testing hypotheses about other ERP/ERF
Conclusion
We have shown that the modulation of intrinsic connectivity is a useful extension of DCM for evoked responses. Mechanistic theories that invoke local adaptation of neuronal populations can be explicitly tested and compared with competing hypotheses.
Software note
All procedures described in this note have been implemented as Matlab (MathWorks) code. The source code is freely available as the ‘DCM for evoked responses’ toolbox of the Statistical Parametric Mapping package (SPM5) under http://www.fil.ion.ucl.ac.uk/spm/.
Acknowledgments
The Wellcome Trust funded this work. We thank Nikolaus Weiskopf for helpful discussions.
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