Statistical analysis of functional images (signals) allows the assessment of neural connectivity patterns at mesoscopic scale. Scalp fields, recorded with Magneto-Electro Encephalography MEEG, strongly correlate to the average effect of synaptic activity, i.e. Primary Current Density (PCD) at the Gray Matter space. Nevertheless, what is observed at the sensor space with either technique is a superposition of projected fields, from the whole Gray-Matter PCD. That is the reason for a major pitfall of MEEG analysis methods, distorted reconstruction of source activity and its connectivity or "Leakage". There has been a quest for the modelling to counterattack Leakage of both activation and connectivity. It has been proven that current methods produce incorrect connectomes , also related to incorrect connectivity modelling : they disregard either System Theory and Bayesian Formalism . We introduce a system theoretic formalism of MEEG connectivity alongside its Bayesian inference: Hidden Hermitian Gaussian Graphical Model (H-HGGM). This is a source (state) GGM hidden by the MEEG observation equation , i. e. equivalent to a frequency domain Linear State Space Model (LSSM) . It is unhidden due to the Type II Likelihood approximated representation: Expected Log-Likelihood (ELL). The essential contributions here are a theory for HGGM solvers, and its implementation for the subsequent Maximization step of the H-HGGM ELL. Its efficacy is demonstrated in high resolution EEG simulations and a Steady State Visual Evoked potential. Open source packages  , to reproduce the results presented in this paper and to analyze external MEEG databases , are freely available online .
The noninvasive procedures for neural connectivity are under questioning. Theoretical models sustain that the electromagnetic field registered at external sensors is elicited by currents at neural space. Nevertheless, what we observe at the sensor space is a superposition of projected fields, from the whole gray-matter. This is the reason for a major pitfall of noninvasive Electrophysiology methods: distorted reconstruction of neural activity and its connectivity or leakage. It has been proven that current methods produce incorrect connectomes . Somewhat related to the incorrect connectivity modelling , they disregard either Systems Theory and Bayesian Information Theory . We introduce a new formalism that attains for it, Hidden Gaussian Graphical State-Model (HIGGS). A neural Gaussian Graphical Model (GGM) hidden by the observation equation of Magneto-encephalographic (MEEG) signals. HIGGS is equivalent to a frequency domain Linear State Space Model (LSSM) but with sparse connectivity prior. The mathematical contribution here is the theory for high-dimensional and frequency-domain HIGGS solvers. We demonstrate that HIGGS can attenuate the leakage effect in the most critical case: the distortion EEG signal due to head volume conduction heterogeneities. Its application in EEG is illustrated with retrieved connectivity patterns from human Steady State Visual Evoked Potentials (SSVEP). We provide for the first time confirmatory evidence for noninvasive procedures of neural connectivity: concurrent EEG and Electrocorticography (ECoG) recordings on monkey. Open source packages are freely available online , to reproduce the results presented in this paper and to analyze external MEEG databases .
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Statistical analysis of functional images (signals) allows the assessment of neural connectivity patterns at mesoscopic scale. Scalp fields, recorded with Magneto-Electro Encephalography MEEG, strongly correlate to the average effect of synaptic activity, i.e. Primary Current Density (PCD) at the Gray Matter
The noninvasive procedures for neural connectivity are under questioning. Theoretical models sustain that the electromagnetic field registered at external sensors is elicited by currents at neural
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we observe
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with either technique
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Gray-Matter PCD. That
gray-matter. This
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MEEG analysis methods,
noninvasive Electrophysiology methods:
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source
neural
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"Leakage". There has been a quest for the modelling to counterattack Leakage of both activation and connectivity.
leakage.
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System
Systems
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Formalism
Information Theory
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system theoretic formalism of MEEG connectivity alongside its Bayesian inference: Hidden Hermitian Gaussian Graphical Model (H-HGGM). This is a source (state) GGM
new formalism that attains for it, Hidden Gaussian Graphical State-Model (HIGGS). A neural Gaussian Graphical Model (GGM)
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MEEG observation equation , i. e.
observation equation of Magneto-encephalographic (MEEG) signals. HIGGS is
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. It is unhidden due to the Type II Likelihood approximated representation: Expected Log-Likelihood (ELL). The essential contributions here are a theory for HGGM solvers, and its implementation for the subsequent Maximization step of the H-HGGM ELL. Its efficacy is demonstrated in high resolution EEG simulations and a
but with sparse connectivity prior. The mathematical contribution here is the theory for high-dimensional and frequency-domain HIGGS solvers. We demonstrate that HIGGS can attenuate the leakage effect in the most critical case: the distortion EEG signal due to head volume conduction heterogeneities. Its application in EEG is illustrated with retrieved connectivity patterns from human
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potential.
Potentials (SSVEP). We provide for the first time confirmatory evidence for noninvasive procedures of neural connectivity: concurrent EEG and Electrocorticography (ECoG) recordings on monkey.
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are freely available online
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, are freely available online