Multi-area neural mass modeling of EEG and MEG signals

Abstract

We previously proposed an integrated electroencephalography (EEG), magnetoencephalography (MEG), and functional Magnetic Resonance Imaging (fMRI) model based on an extended neural mass model (ENMM) within a single cortical area. In the ENMM, a cortical area contains several minicolumns where strengths of their connections diminish exponentially with their distances. The ENMM was derived based on the physiological principles of the cortical minicolumns and their connections within a single cortical area to generate EEG, MEG, and fMRI signals. The purpose of this paper is to further extend the ENMM model from a single-area to a multi-area model to develop a neural mass model of the entire brain that generates EEG and MEG signals. For multi-area modeling, two connection types are considered: short-range connections (SRCs) and long-range connections (LRCs). The intra-area SRCs among the minicolumns within the areas were previously modeled in the ENMM. To define inter-area LRCs among the cortical areas, we consider that the cell populations of all minicolumns in the destination area are affected by the excitatory afferent of the pyramidal cells of all minicolumns in the source area. The state-space representation of the multi-area model is derived considering the intra-minicolumn, SRCs', and LRCs' parameters. Using simulations, we evaluate effects of parameters of the model on its dynamics and, based on stability analysis, find valid ranges for parameters of the model. In addition, we evaluate reducing redundancy of the model parameters using simulation results and conclude that the parameters of the model can be limited to the LRCs and SRCs while the intra-minicolumn parameters stay at their physiological mean values. The proposed multi-area integrated E/MEG model provides an efficient neuroimaging technique for effective connectivity analysis in healthy subjects as well as neurological and psychiatric patients.

Introduction

Function of the brain is the consequence of the interaction among several cortical regions, which are reciprocally interconnected. Knowledge of connectivity facilitates our understanding of how the brain works, and helps us to assess the role of different areas in the success of specific cognitive functions. Connectivity can be defined in the following three ways: structural, functional, and effective connectivity (Lee et al., 2003a, Lee et al., 2003b, Wendling et al., 2002). The anatomical layout of axons and synaptic connections can be considered as the structural connectivity that shows the direct interaction among neural units (Zeki and Shipp, 1988). The functional connectivity in the analysis of neuroimaging time-series is defined as the temporal correlations between spatially remote neurophysiological events (Friston, 1994). The influence that one neural system exerts on another one has been defined as effective connectivity which requires a causal model connecting several brain regions (Friston, 1994, Friston et al., 1993, Friston et al., 2003).

Two main classes of models have been proposed for the effective connectivity: detailed models, which are at the level of a single neuron (Makarov et al., 2005), and macroscopic models in which the state variables represent the dynamics of entire neural populations. In detailed models, due to the very large number of parameters involved and the strong dependencies between them, it is usually impossible to fit them to empirical data. However, they can be used for simulations (Deco et al., 2004, Husain et al., 2004). The macroscopic models such as the neural mass model (NMM) and the mean-field model were originally developed to simulate activity in the olfactory cortex (Freeman, 1987) and the spontaneous alpha rhythms (Lopes da Silva et al., 1974). These models have subsequently been improved and extended (Jansen and Rit, 1995, Wendling et al., 2002, Wendling et al., 2000). They use a few state variables to represent the mean activity of a large neuronal population. In recent years, the NMM has been used in neuroimaging applications to generate spontaneous rhythms in various frequency bands (Babiloni et al., 2003, David and Friston, 2003), to study generation of the epileptic activities (Wendling et al., 2002, Wendling et al., 2000), to analyze the connectivity and coherence on electroencephalography (EEG) rhythms (Zavaglia et al., 2008), and to generate the event related responses (David et al., 2005, Rennie et al., 2002). The NMM has also been used to simulate positron emission tomography (PET) imaging (Horwitz et al., 1999, Tagamets and Horwitz, 1998, Tagamets and Horwitz, 2000) as well as for integrated modeling of EEG, magnetoencephalography (MEG), and functional magnetic resonance imaging (fMRI) (Babajani and Soltanian-Zadeh, 2006, Daunizeau et al., 2007, Riera et al., 2005, Riera et al., 2007, Riera et al., 2006, Sotero and Trujillo-Barreto, 2008).

Friston et al. (2003) and Stephan et al. (2007a) developed Dynamic Causal Modeling (DCM), a general framework for the effective connectivity that makes inferences about processes at the neural level given measured imaging data. DCM is represented by state-space equations whose state equation is deterministic (noise-free) and thus the noise model is limited to the measurement noise. Parameters of the DCM are estimated from measured data using variational Bayesian inversion. DCM has been used separately for fMRI (Allen et al., 2008, Booth et al., 2008, Booth et al., 2007, Brazdil et al., 2007, Cao et al., 2008, Ethofer et al., 2006, Grefkes et al., 2008, Kasess et al., 2008, Kiebel et al., 2007b, Kim et al., 2007, Marreiros et al., 2008, Mechelli et al., 2003, Schlosser et al., 2008, Sonty et al., 2007, Stephan et al., 2008a, Stephan et al., 2007b) and EEG/MEG (Chen et al., 2008, David et al., 2005, David et al., 2006, David et al., 2008, Fastenrath et al., 2009, Garrido et al., 2007, Kiebel et al., 2006, Kiebel et al., 2007a, Lee et al., 2006). For EEG/MEG data, DCM is based on Jansen's NMM (Jansen and Rit, 1995) where long-range cortico-cortical connections are embodied by considering forward, backward, and lateral connections among remote areas (David et al., 2006). DCM is used for investigating a wide range of functional neuroimaging applications at different temporal and spatial scales (David and Friston, 2003, Moran et al., 2007, Moran et al., 2008, Stephan et al., 2008b). There are alternative approaches for characterizing effective connectivity, e.g., proposed methods in Riera et al. (2006) and Valdes-Sosa et al. (2005), however, DCM is used in a variety of studies for broad neuroimaging purposes.

We proposed two integrated E/MEG and fMRI models for the effective connectivity Babajani et al. (2005). In the first model, we introduced a stochastic model based on the conditions of the postsynaptic potentials (PSPs) that generate MEG and fMRI signals. Here, directions and strengths of PSPs are modeled using several physiological parameters which are treated as random variables. The expected values of the direction and strength of the current flow of PSPs in active voxels are calculated and used to generate the corresponding MEG and fMRI signals. We estimated the parameters of the model in a real condition using MEG and fMRI datasets from seven normal subjects gathered using a simple auditory stimulus (Babajani-Feremi et al., 2008). For the auditory tone stimulus, we illustrated the capability of the proposed integrated analysis method to generate high-resolution spatiotemporal activation map.

In the second integrated E/MEG and fMRI model which is the base of this paper, we proposed an extended neural mass model (ENMM) in a single cortical area (Babajani and Soltanian-Zadeh, 2006). In the ENMM, the area contains several minicolumns where the intra-minicolumn dynamics are modeled by the Jansen's NMM using the intra-minicolumn parameters (Jansen and Rit, 1995). Using the physiological principles of the cortical minicolumns and their connections according to the previous studies (Buxhoeveden and Casanova, 2002, Mountcastle, 1997), we considered short-range inter-column connections and extended the Jansen's model to the ENMM. In the model, the EEG and MEG signals are generated by synaptic activations of the pyramidal cells in the minicolumns. We extracted the fMRI signal from the proposed ENMM by calculating the relationship between the stimulus and the overall neural activity and using it as the input of the extended Balloon model (Friston et al., 2000). We validated the proposed model by comparing the simulations with the experimental results.

In this paper, we further extend our proposed ENMM from a single-area model to the entire brain containing all active cortical areas related to a specific external stimulus. For multi-area modeling, two connection types are considered: short-range connections (SRCs) and long-range connections (LRCs). The SRCs among intra-area minicolumns were previously modeled in the ENMM (Babajani and Soltanian-Zadeh, 2006). The LRCs characterize configuration of the multi-area model with describing the connections among the cortical areas. To define LRCs among the cortical areas, we consider that the three cell populations (stellate cells, pyramidal cells, inhibitory interneurons) of all minicolumns in the destination area are affected by the excitatory afferent of the pyramidal cells of all minicolumns in the source area. The state-space representation of the multi-area model is derived considering the SRCs' and LRCs' parameters. Here, we focus on the EEG and the MEG signals in the model to verify the effects of the parameters of the model on its dynamics and find valid ranges for the parameters. In future, we will extend the proposed model to a multi-area integrated E/MEG and fMRI model.

DCM uses the variational Bayesian approach to estimate the parameters of the model based on the assumption that the state equation is noise-free and the system noise is limited to the measurement noise. Therefore, DCM is a deterministic state-space model (SSM) stated in terms of ordinary differential equations. Stochastic extension of the DCM is recently proposed where both of the state noise and the observation noise are considered in the model (Daunizeau et al., 2009). Similar to stochastic DCM, both of the state noise and the observation noise are considered in our proposed multi-area model. In future, we will introduce a variational Bayesian expectation maximization (VBEM) method to estimate the sufficient statistics of the parameters and the hidden state variables as well as the precisions (inverse variances) of the state and observation noises of the proposed multi-area model. The VBEM method will be based on the proposed method in Beal and Ghahramani, 2001a, Beal, 2003, Ghahramani and Beal, 2000, Ghahramani and Beal, 2001, and Ghahramani and Hinton (1996) for the linear SSM. The performance and excellent capability of the VBEM method for linear SSM are illustrated in Beal (2003). We will extend the proposed method in Beal and Ghahramani, 2001a, Beal, 2003, Ghahramani and Beal, 2000, Ghahramani and Beal, 2001, and Ghahramani and Hinton (1996) from a linear SSM to our multi-area ENMM which is a nonlinear SSM. The VBEM algorithm leads to analytically tractable forms and has the capability to outperform the Laplace approximation method which is used in the deterministic or stochastic versions of the DCM (see Discussions). It should be noted that a combination of the proposed multi-area ENMM and an inversion method to estimate its parameters, e.g., VBEM method, is expected to improve solution of the inverse problem of E/MEG. This is because the multi-area ENMM can realistically model the interactions among the active cortical areas.

Our proposed approach will generate several improvements compared to the DCM which has been widely used for the effective connectivity. First advantage of our proposed multi-area NMM is to use more realistic model compared to the DCM. Each cortical area in the DCM is modeled by the Jansen's NMM which is a simplified model and is unable to generate complicated dynamics of the cortical area. However, our proposed model uses the ENMM in each area which has superior performance compared to the Jansen's model, as we illustrated in Babajani and Soltanian-Zadeh (2006). Therefore, our model more realistically and comprehensively models the dynamics of the cortical areas. The DCM can separately analyze E/MEG and fMRI signals but our proposed multi-area model has the capability of integrated E/MEG and fMRI modeling and analysis that enables us to exploit complementary spatio-temporal aspects of these techniques.

The organization of the paper is as follows. In the next section, the multi-are model is presented considering the SRCs as well as LRCs in the model and the state-space representation of the model is derived. In the Simulation results section, effects of the parameters of the model on its dynamics are explored to find valid ranges of variations of the parameters based on a stability analysis. Discussions and Conclusions are presented at the end of the paper.