Dynamic Causal Modeling with Neural Population Models
KeywordsNeuronal State Neural Mass Model Dynamic Causal Model Bayesian Inversion Average Membrane Potential
Dynamic causal models with neural populations are state-space models that impose a specified dynamical systems form to the generation of neuroimaging and electrophysiological data. The forms of these models constitute neurobiologically motivated and identifiable parameterizations, where empirical observations offer conditional descriptions of parameter space following application of a Bayesian inversion scheme. They comprise separate generative processes at the neuronal level and at the observation level through a set of deterministic or stochastic differential equations and an observer functional, respectively.
Dynamic causal models were first invented in 2003 for the purpose of estimating human brain connectivity and task-dependent functional integration using functional magnetic resonance imaging (fMRI) (Friston et al. 2003). The framework was extended for electrophysiological domains including noninvasive electroencephalography (EEG) and magnetoencephalography (MEG) and later for invasive local field potential recordings. Application domains share a common generative and inversion framework (Stephan et al. 2010). At the neuronal level, a network of “nodes” are connected with intrinsic (within-region) and extrinsic (region-to-region) connections. These effective or model-based connections constrain the output of a set of differential equations and can be modulated by experimental perturbation. These are modality-dependent, mesoscale descriptions of neuronal ensemble activity and are summarized through mean-field reductions. Different connectivity architectures can be considered as different models, embodying competing hypotheses to be formally tested. At the observation level, contributing neuronal states form inputs to a second dynamic process or static function (lead field), transforming neuronal activity to the required measurement space, e.g., blood oxygen level dependent – BOLD fMRI responses. Together, these form a complete forward model that is inverted, given real data, using Bayesian approaches.
Modality-Dependent Population Models
Together with the neuronal state space, these transforms produce a full generative model with which mechanistic hypotheses regarding the physiological processes underlying empirical data observations can be performed.
Bayesian Inversion, Parameter Estimation, and Model Selection
Applications of DCM
The DCM approach has been applied to many experimental preparations and imaging modalities (a PubMed search reveals ~400 articles associated with dynamic causal modeling). As well as offering insights into the fundamental role of effective brain connections, e.g., how callosal connections support interhemispheric integration in a task-dependent manner (Stephan et al. 2005) or how feedback loops are necessary to support prototypical event-related potentials (Garrido et al. 2007), specific network topologies have been elucidated for cognitive and motor phenomena in health and disease. DCM for fMRI was used in one study to ascertain which regions in a prefrontal-subcortical network drive the so-called “status quo” motor-bias behavior (Fleming et al. 2010), finding a prefrontal-causality the most likely. During learning, similar networks have been shown to adapt along bottom-up axes, with changes in connections that support motor responsivity driven by modulation from subcortical structures (den Ouden et al. 2010). In disease, support for disconnection-related mechanisms has been observed in patients with schizophrenia (Dima et al. 2009) but also in neurological disorders more traditionally associated with focal lesions, such as Parkinson’s disease (Marreiros et al. 2012). As a “mathematical microscope,” electrophysiological DCMs have been applied to small, one-node networks to uncover particular synapses and receptors subtending memory performance (Moran et al. 2011). Overall, the methodology provides a principled Bayesian framework to address the mechanisms of functional brain architectures that support our mental repertoire.
- Šmídl V, Quinn AP (2006) The variational Bayes method in signal processing. Springer, New YorkGoogle Scholar