Bayesian model averaging in EEG/MEG imaging

Abstract

In this paper, the Bayesian Theory is used to formulate the Inverse Problem (IP) of the EEG/MEG. This formulation offers a comparison framework for the wide range of inverse methods available and allows us to address the problem of model uncertainty that arises when dealing with different solutions for a single data. In this case, each model is defined by the set of assumptions of the inverse method used, as well as by the functional dependence between the data and the Primary Current Density (PCD) inside the brain. The key point is that the Bayesian Theory not only provides for posterior estimates of the parameters of interest (the PCD) for a given model, but also gives the possibility of finding posterior expected utilities unconditional on the models assumed. In the present work, this is achieved by considering a third level of inference that has been systematically omitted by previous Bayesian formulations of the IP. This level is known as Bayesian model averaging (BMA). The new approach is illustrated in the case of considering different anatomical constraints for solving the IP of the EEG in the frequency domain. This methodology allows us to address two of the main problems that affect linear inverse solutions (LIS): (a) the existence of ghost sources and (b) the tendency to underestimate deep activity. Both simulated and real experimental data are used to demonstrate the capabilities of the BMA approach, and some of the results are compared with the solutions obtained using the popular lowresolution electromagnetic tomography (LORETA) and its anatomically constraint version (cLORETA). IntroductionOur interest lies in the identification of electro/magnetoencephalogram (EEG/MEG) generators, that is, the distribution of current sources inside the brain that generate the voltage -magnetic field measured over an array of sensors distributed on the scalp surface. This is known as the Inverse Problem (IP) of the EEG/ MEG.Much literature has been devoted to the solution of this problem. The main difficulty stems from its ill-posed character due to the nonuniqueness of the solution, which is caused by the existence of silent sources that cannot be measured over the scalp surface. Additional complications that arise when dealing with actual data are related to the limited number of sensors available, making the problem highly underdetermined, as well as to the numerical instability of the solution, given by its high sensitivity to measurement noise.The usual way to deal with these difficulties has been to include additional information or constraints about the physical and mathematical properties of the current sources inside the head, which limit the space of possible solutions. This has resulted in the emergence of a great variety of methods, each depending on the kind of information that has been introduced and resulting consequently in many different unique solutions.Some methods handle the many-to-one nature of the problem by characterizing the sources in terms of a limited number of current dipoles that are...

DEM: A variational treatment of dynamic systems

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Fusing EEG and fMRI based on a bottom-up model: inferring activation and effective connectivity in neural masses

“…However, even at present, these techniques are being used independently to explore some aspects of both activations and effective connectivity maps during particular experimental paradigms (see Carew et al 2003;Friston et al 2003;Marrelec et al 2003;Galka et al 2004;Miwakeichi et al 2004;Penny et al 2004;Trujillo-Barreto et al 2004;Yamashita et al 2004). There have been few attempts to develop methods that make use of the complementary potentialities of EEG and fMRI data that have recently emerged (Dale et al 2000;Kruggel et al 2001;Goldman et al 2002;Martinez-Montes et al 2004).…”

An evaluation of EEG scanner's dependence on the imaging technique, forward model computation method, and array dimensionality

“…For example l 2 -norm approaches, like the weighted minimum norm method [2] and low resolution electromagnetic tomography (LORETA) [3], assume sources to be diffuse and highly distributed. On the other hand models based on the l 1 -norm [4], l p -norms [5], minimum variance beamformer [6], Bayesian model averaging [7], multiple priors models [8], and automatic relevance determination methods [9], [10] While the recent EEG imaging literature mainly have focused on the source reconstruction performance using high density EEG equipment we here draw the attention to quantify the performance of EEG brain imaging using few electrodes as we are interested in mobile EEG equipment. We have previously, demonstrated the feasibility of performing online brain imaging on a smartphone device [11] allowing for experiments in more naturalistic settings.…”