Dynamic causal modelling of evoked responses in EEG/MEG with lead field parameterization
Introduction
In David et al. (2006), we described dynamic causal modeling (DCM) for event-related fields (ERFs) and potentials (ERPs). This new approach is grounded on a neuronally plausible, generative model that can be used to estimate and make inferences about category- or context-specific coupling among cortical regions. Context-specific coupling changes as a function of condition (i.e., experimental context such as “new” vs. “old” in memory paradigms) or stimulus-bound attributes (i.e., “house” vs. “face”). These changes can reconfigure neuronal interactions and produce different evoked responses for each category or context. The coupling parameters embody bottom-up, top-down, and lateral connections among remote cortical regions. Parameters are estimated with a Bayesian procedure using empirical data (ERPs/ERFs). With Bayesian model selection, one can use model evidences to compare competing models and identify the model that best explains the data.
In David et al. (2006), we constructed the spatial forward model using distributed dipole modeling on the grey matter surface. This procedure has the advantage of using the precise anatomical structure of the head. The subject's anatomy was derived from the high-resolution structural magnetic resonance imaging (sMRI). Critically, each area's lead field was predetermined so that each area had a fixed spatial expression in the sensors. Although this approach provides spatially precise expressions in the sensors, the true spatial configuration of an area may be different from our model and lead to biased conditional estimates of other [e.g., coupling] parameters. For example, the spatial model can be wrong because its parameters like location, orientation, or extent are specified inaccurately.
Alternatively, each lead field or its underlying spatial parameters can be regarded as a parameter of the model. In a Bayesian context, the above procedure is equivalent to using zero prior variance (i.e., infinite precision which expresses our belief that the specified lead field mediated the sensor data). If this belief is not supported by the data, the optimization algorithm will, at worst, fail to provide a good solution and compensate for the mis-specified spatial model by biasing conditional estimates of other parameters like coupling. A way to avoid this is to decrease our strong belief in a specific lead field and use finite precision priors on the lead field parameters. There are several ways to parameterize the lead field. Although we could employ a surface-based forward model, we use equivalent current dipoles (ECDs). This has distinct advantages over other models. First, ECDs' spatial expression is analytic, i.e., the forward model computation is fast (Mosher et al., 1999). Secondly, the model is based on electrode positions only and does not need information from a structural MRI. Thirdly, many authors reported ECD location and orientation for specific ERP/ERF experiments in the peer-reviewed literature (e.g., Valeriani et al., 2001): Within our approach, these locations and orientations could be employed as prior expectations on ECD parameters. Finally, ECDs are a natural way to specify nodes in the probabilistic graphs that DCMs represent.
One can also view DCM for evoked responses as a source reconstruction approach with temporal, physiologically informed constraints imposed by our assumption that a hierarchical network of discrete areas generated the data. The reconstructed source activities over time fall out naturally as the system's states. Typically, most current source reconstruction approaches for EEG/MEG data are based exclusively on constraints given by the spatial forward model (Darvas et al., 2004). However, recently models have been proposed which use (spatio-) temporal constraints to invert the model (Darvas et al., 2001, Galka et al., 2004). These spatiotemporal approaches are closer to DCM but use generic constraints derived from temporal smoothness considerations and autoregressive modeling.
This paper is structured as follows. In the Theory section, we will describe briefly the temporal generative model for ERP/ERFs (for a detailed description, see David et al., 2005). This is followed by a description of the spatial forward model, its parameterization and typical prior distributions we adopt for ERP data. In the Results section, we illustrate the operational details of the procedures on two ERP datasets. In the first ERP experiment, we repeat the analysis of an auditory oddball dataset (David et al., 2006) to show that the mismatch negativity can be explained by changes in connectivity to and from the primary auditory cortex. This analysis shows that biologically meaningful results can be obtained in terms of the parameters governing the neuronal architectures generating ERPs. In the second experiment, we establish face validity in terms of the spatial parameters; we analyze sensory-evoked potentials (SEPs) elicited by unilateral median nerve stimulation and measured with EEG. With this model, we can explain the observed SEP to 200 ms. We find strong connectivity among areas during the course of the SEP. The estimated orientations of these sources conform almost exactly to classical estimates in the literature. Furthermore, we observe short transmission delays among sources within the contralateral hemisphere (∼6 ms) but long delays (∼50 ms) between homologous sources in both hemispheres. Finally, using synthetic data, we show that finite precision priors on lead field parameters result in models with greater evidence and more accurate and robust conditional estimates, in relation to models with infinitely precise priors.
Section snippets
Theory
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 modeled using a dynamic input–state–output system with multiple inputs and outputs. Responses are evoked by deterministic inputs that correspond to experimental manipulations (i.e., presentation of stimuli). Experimental factors (i.e., stimulus attributes or
Results
In this section, we illustrate the use of DCM using two real ERP datasets. Furthermore, we use two synthetic ERP datasets to show that DCM with a parameterized lead field can furnish more accurate and robust coupling estimates and models with greater evidence. This rest on using synthetic data where one knows the true model and true parameters. We use the first real dataset to address the face validity of the neuronal (i.e., coupling) parameter estimates and the second to look at the spatial
Discussion
In this paper, we have presented dynamical causal modeling (DCM) for event-related potentials and fields using equivalent current dipole models. We have shown that this Bayesian approach can be used to estimate parameters for a generative ERP model. Importantly, one can estimate, simultaneously, source activity, extrinsic connectivity, its modulation by context, and spatial lead field parameters from the data. An alternative view of DCM for ERP/ERF is to consider it a source reconstruction
Conclusion
DCM is useful for estimating connectivity in a hierarchical network based on evoked responses measured with EEG and MEG data. The parameterization of the lead field using equivalent current dipoles results in an accurate and robust estimation of both connectivity and dipole parameters. One can view DCM for evoked responses as a source reconstruction approach with temporal, physiologically informed constraints.
Acknowledgments
This work was supported by the Wellcome Trust. We thank Akaysha Tang and Felix Blankenburg for their valuable discussions and Robert Oostenveld for providing us with his Matlab implementation of ECD forward models.
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