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...

This article describes a new method for 3D QEEG tomography in the frequency domain. A variant of Statistical Parametric Mapping is presented for source log spectra. Sources are estimated by means of a Discrete Spline EEG inverse solution known as Variable Resolution Electromagnetic Tomography (VARETA). Anatomical constraints are incorporated by the use of the Montreal Neurological Institute (MNI) probabilistic brain atlas. Efficient methods are developed for frequency domain VARETA in order to estimate the source spectra for the set of 10(3)-10(5) voxels that comprise an EEG/MEG inverse solution. High resolution source Z spectra are then defined with respect to the age dependent mean and standard deviations of each voxel, which are summarized as regression equations calculated from the Cuban EEG normative database. The statistical issues involved are addressed by the use of extreme value statistics. Examples are shown that illustrate the potential clinical utility of the methods herein developed.

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The Cuban Human Brain Mapping Project (CHBMP) repository is an open multimodal neuroimaging and cognitive dataset from 282 young and middle age healthy participants (31.9 ± 9.3 years, age range 18–68 years). This dataset was acquired from 2004 to 2008 as a subset of a larger stratified random sample of 2,019 participants from La Lisa municipality in La Habana, Cuba. The exclusion criteria included the presence of disease or brain dysfunctions. Participant data that is being shared comprises i) high-density (64–120 channels) resting-state electroencephalograms (EEG), ii) magnetic resonance images (MRI), iii) psychological tests (MMSE, WAIS-III, computerized go-no go reaction time), as well as iv,) demographic information (age, gender, education, ethnicity, handedness, and weight). The EEG data contains recordings with at least 30 minutes in duration including the following conditions: eyes closed, eyes open, hyperventilation, and subsequent recovery. The MRI consists of anatomical T1 as well as diffusion-weighted (DWI) images acquired on a 1.5 Tesla system. The dataset presented here is hosted by Synapse.org and available at https://chbmp-open.loris.ca.

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The Tomographic Quantitative Electroencephalography (qEEGt) toolbox is integrated with the Montreal Neurological Institute (MNI) Neuroinformatics Ecosystem as a docker into the Canadian Brain Imaging Research Platform (CBRAIN). qEEGt produces age-corrected normative Statistical Parametric Maps of EEG log source spectra testing compliance to a normative database. This toolbox was developed at the Cuban Neuroscience Center as part of the first wave of the Cuban Human Brain Mapping Project (CHBMP) and has been validated and used in different health systems for several decades. Incorporation into the MNI ecosystem now provides CBRAIN registered users access to its full functionality and is accompanied by a public release of the source code on GitHub and Zenodo repositories. Among other features are the calculation of EEG scalp spectra, and the estimation of their source spectra using the Variable Resolution Electrical Tomography (VARETA) source imaging. Crucially, this is completed by the evaluation of z spectra by means of the built-in age regression equations obtained from the CHBMP database (ages 5–87) to provide normative Statistical Parametric Mapping of EEG log source spectra. Different scalp and source visualization tools are also provided for evaluation of individual subjects prior to further post-processing. Openly releasing this software in the CBRAIN platform will facilitate the use of standardized qEEGt methods in different research and clinical settings. An updated precis of the methods is provided in Appendix I as a reference for the toolbox. qEEGt/CBRAIN is the first installment of instruments developed by the neuroinformatic platform of the Cuba-Canada-China (CCC) project.

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The curtain of technical limitations impeding rat multichannel non-invasive electroencephalography (EEG) has risen. Given the importance of this preclinical model, development and validation of EEG source imaging (ESI) is essential. We investigate the validity of well-known human ESI methodologies in rats which individual tissue geometries have been approximated by those extracted from an MRI template, leading also to imprecision in electrode localizations. With the half and fifth sensitivity volumes we determine both the theoretical minimum electrode separation for non-redundant scalp EEG measurements and the electrode sensitivity resolution, which vary over the scalp because of the head geometry. According to our results, electrodes should be at least ~3 to 3.5 mm apart for an optimal configuration. The sensitivity resolution is generally worse for electrodes at the boundaries of the scalp measured region, though, by analogy with human montages, concentrates the sensitivity enough to localize sources. Cramér-Rao lower bounds of source localization errors indicate it is theoretically possible to achieve ESI accuracy at the level of anatomical structures, such as the stimulus-specific somatosensory areas, using the template. More validation for this approximation is provided through the comparison between the template and the individual lead field matrices, for several rats. Finally, using well-accepted inverse methods, we demonstrate that somatosensory ESI is not only expected but also allows exploring unknown phenomena related to global sensory integration. Inheriting the advantages and pitfalls of human ESI, rat ESI will boost the understanding of brain pathophysiological mechanisms and the evaluation of ESI methodologies, new pharmacological treatments and ESI-based biomarkers.