Statistical mechanics of neocortical interactions: Training and testing canonical momenta indicators of EEG

A latent state space model for estimating brain dynamics from electroencephalogram (EEG) data

Modern neuroimaging technologies have substantially advanced the measurement of brain activity. Electroencephalogram (EEG) as a noninvasive neuroimaging technique measures changes in electrical voltage on the scalp induced by brain cortical activity. With its high temporal resolution, EEG has emerged as an increasingly useful tool to study brain connectivity. Challenges with modeling EEG signals of complex brain activity include interactions among unknown sources, low signal-to-noise ratio, and substantial between-subject heterogeneity. In this work, we propose a state space model that jointly analyzes multichannel EEG signals and learns dynamics of different sources corresponding to brain cortical activity. Our model borrows strength from spatially correlated measurements and uses low-dimensional latent states to explain all observed channels. The model can account for patient heterogeneity and quantify the effect of a subject's covariates on the latent space. The EM algorithm, Kalman filtering, and bootstrap resampling are used to fit the state space model and provide comparisons between patient diagnostic groups. We apply the developed approach to a case-control study of alcoholism and reveal significant attenuation of brain activity in response to visual stimuli in alcoholic subjects compared to healthy controls.

Sparse algorithms for EEG source localization

Source localization using EEG is important in diagnosing various physiological and psychiatric diseases related to the brain. The high temporal resolution of EEG helps medical professionals assess the internal physiology of the brain in a more informative way. The internal sources are obtained from EEG by an inversion process. The number of sources in the brain outnumbers the number of measurements. In this article, a comprehensive review of the state-of-the-art sparse source localization methods in this field is presented. A recently developed method, certainty-based-reduced-sparse-solution (CARSS), is implemented and is examined. A vast comparative study is performed using a sixty-four-channel setup involving two source spaces. The first source space has 5004 sources and the other has 2004 sources. Four test cases with one, three, five, and seven simulated active sources are considered. Two noise levels are also being added to the noiseless data. The CARSS is also evaluated. The results are examined. A real EEG study is also attempted. Graphical Abstract.

Exploring individual and group differences in latent brain networks using cross-validated simultaneous component analysis

Component models such as PCA and ICA are often used to reduce neuroimaging data into a smaller number of components, which are thought to reflect latent brain networks. When data from multiple subjects are available, the components are typically estimated simultaneously (i.e., for all subjects combined) using either tensor ICA or group ICA. As we demonstrate in this paper, neither of these approaches is ideal if one hopes to find latent brain networks that cross-validate to new samples of data. Specifically, we note that the tensor ICA model is too rigid to capture real-world heterogeneity in the component time courses, whereas the group ICA approach is too flexible to uniquely identify latent brain networks. For multi-subject component analysis, we recommend comparing a hierarchy of simultaneous component analysis (SCA) models. Our proposed model hierarchy includes a flexible variant of the SCA framework (the Parafac2 model), which is able to both (i) model heterogeneity in the component time courses, and (ii) uniquely identify latent brain networks. Furthermore, we propose cross-validation methods to tune the relevant model parameters, which reduces the potential of over-fitting the observed data. Using simulated and real data examples, we demonstrate the benefits of the proposed approach for finding credible components that reveal interpretable individual and group differences in latent brain networks.

Robust nonparametric tests of general linear model coefficients: A comparison of permutation methods and test statistics

Statistical inference in neuroimaging research often involves testing the significance of regression coefficients in a general linear model. In many applications, the researcher assumes a model of the form Y=α+Xβ+Zγ+ε, where Y is the observed brain signal, and X and Z contain explanatory variables that are thought to be related to the brain signal. The goal is to test the null hypothesis H₀:β=0 with the nuisance parameters γ included in the model. Several nonparametric (permutation) methods have been proposed for this problem, and each method uses some variant of the F ratio as the test statistic. However, recent research suggests that the F ratio can produce invalid permutation tests of H₀:β=0 when the ε terms are heteroscedastic (i.e., have non-constant variance), which can occur for a variety of reasons. This study compares the classic F test statistic to the robust W (Wald) test statistic using eight different permutation methods. The results reveal that permutation tests using the F ratio can produce accurate results when the errors are homoscedastic, but high false positive rates when the errors are heteroscedastic. In contrast, permutation tests using the W test statistic produced valid results when the errors were homoscedastic, and asymptotically valid results when the errors were heteroscedastic. In the situation with homoscedastic errors, permutation tests using the W statistic showed slightly reduced power compared to the F statistic, but the difference disappeared as the sample size n increased. Consequently, the W test statistic is recommended for robust nonparametric hypothesis tests of regression coefficients in neuroimaging research.

Quantum Calcium-Ion Interactions with EEG

Background: Previous papers have developed a statistical mechanics of neocortical interactions (SMNI) fit to short-term memory and EEG data. Adaptive Simulated Annealing (ASA) has been developed to perform fits to such nonlinear stochastic systems. An N-dimensional path-integral algorithm for quantum systems, qPATHINT, has been developed from classical PATHINT. Both fold short-time propagators (distributions or wave functions) over long times. Previous papers applied qPATHINT to two systems, in neocortical interactions and financial options. Objective: In this paper the quantum path-integral for Calcium ions is used to derive a closed-form analytic solution at arbitrary time that is used to calculate interactions with classical-physics SMNI interactions among scales. Using fits of this SMNI model to EEG data, including these effects, will help determine if this is a reasonable approach. Method: Methods of mathematical-physics for optimization and for path integrals in classical and quantum spaces are used for this project. Studies using supercomputer resources tested various dimensions for their scaling limits. In this paper the quantum path-integral is used to derive a closed-form analytic solution at arbitrary time that is used to calculate interactions with classical-physics SMNI interactions among scales. Results: The mathematical-physics and computer parts of the study are successful, in that there is modest improvement of cost/objective functions used to fit EEG data using these models. Conclusions: This project points to directions for more detailed calculations using more EEG data and qPATHINT at each time slice to propagate quantum calcium waves, synchronized with PATHINT propagation of classical SMNI.

Dynamical Hurst analysis identifies EEG channel differences between PTSD and healthy controls

We employ a time-dependent Hurst analysis to identify EEG signals that differentiate between healthy controls and combat-related PTSD subjects. The Hurst exponents, calculated using a rescaled range analysis, demonstrate a significant differential response between healthy and PTSD samples which may lead to diagnostic applications. To overcome the non-stationarity of EEG data, we apply an appropriate window length wherein the EEG data displays stationary behavior. We then use the Hurst exponents for each channel as hypothesis test statistics to identify differences between PTSD cases and controls. Our study included a cohort of 12 subjects with half healthy controls. The Hurst exponent of the PTSD subjects is found to be significantly smaller than the healthy controls in channel F3. Our results indicate that F3 may be a useful channel for diagnostic applications of Hurst exponents in distinguishing PTSD and healthy subjects.

Statistical mechanics of neocortical interactions: Large-scale EEG influences on molecular processes

Calculations further support the premise that large-scale synchronous firings of neurons may affect molecular processes. The context is scalp electroencephalography (EEG) during short-term memory (STM) tasks. The mechanism considered is Π=p+qA (SI units) coupling, where p is the momenta of free Ca(2+) waves, q the charge of Ca(2+) in units of the electron charge, and A the magnetic vector potential of current I from neuronal minicolumnar firings considered as wires, giving rise to EEG. Data has processed using multiple graphs to identify sections of data to which spline-Laplacian transformations are applied, to fit the statistical mechanics of neocortical interactions (SMNI) model to EEG data, sensitive to synaptic interactions subject to modification by Ca(2+) waves.

Electroencephalographic field influence on calcium momentum waves

Macroscopic electroencephalographic (EEG) fields can be an explicit top-down neocortical mechanism that directly drives bottom-up processes that describe memory, attention, and other neuronal processes. The top-down mechanism considered is macrocolumnar EEG firings in neocortex, as described by a statistical mechanics of neocortical interactions (SMNI), developed as a magnetic vector potential A. The bottom-up process considered is Ca(2+) waves prominent in synaptic and extracellular processes that are considered to greatly influence neuronal firings. Here, the complimentary effects are considered, i.e., the influence of A on Ca(2+) momentum, p. The canonical momentum of a charged particle in an electromagnetic field, Π=p+qA (SI units), is calculated, where the charge of Ca(2+) is q=-2e, e is the magnitude of the charge of an electron. Calculations demonstrate that macroscopic EEG A can be quite influential on the momentum p of Ca(2+) ions, in both classical and quantum mechanics. Molecular scales of Ca(2+) wave dynamics are coupled with A fields developed at macroscopic regional scales measured by coherent neuronal firing activity measured by scalp EEG. The project has three main aspects: fitting A models to EEG data as reported here, building tripartite models to develop A models, and studying long coherence times of Ca(2+) waves in the presence of A due to coherent neuronal firings measured by scalp EEG. The SMNI model supports a mechanism wherein the p+qA interaction at tripartite synapses, via a dynamic centering mechanism (DCM) to control background synaptic activity, acts to maintain short-term memory (STM) during states of selective attention.

Neocortical dynamics at multiple scales: EEG standing waves, statistical mechanics, and physical analogs

The dynamic behavior of scalp potentials (EEG) is apparently due to some combination of global and local processes with important top-down and bottom-up interactions across spatial scales. In treating global mechanisms, we stress the importance of myelinated axon propagation delays and periodic boundary conditions in the cortical-white matter system, which is topologically close to a spherical shell. By contrast, the proposed local mechanisms are multiscale interactions between cortical columns via short-ranged non-myelinated fibers. A mechanical model consisting of a stretched string with attached nonlinear springs demonstrates the general idea. The string produces standing waves analogous to large-scale coherent EEG observed in some brain states. The attached springs are analogous to the smaller (mesoscopic) scale columnar dynamics. Generally, we expect string displacement and EEG at all scales to result from both global and local phenomena. A statistical mechanics of neocortical interactions (SMNI) calculates oscillatory behavior consistent with typical EEG, within columns, between neighboring columns via short-ranged non-myelinated fibers, across cortical regions via myelinated fibers, and also derives a string equation consistent with the global EEG model.

Quantifying electrode position effects in EEG data with Lempel-Ziv complexity

Complexity measurement using Lempel and Ziv algorithm (LZ) has been used to analyze physiological data. This work shows that the Lempel and Ziv complexity measurement of EEG signals using wavelets transforms is independent of electrode position and dependent on cognitive tasks and brain activity. EEG database with 122 subjects from the public EEG dataset was used in this study. This database have spontaneous EEG and evoked potential (EP) data from a 64-multielectrode array under a variety of conditions collected at several centers in the United States, sponsored by the National Institute on Alcohol Abuse and Alcoholism (NIAAA) project. Two experiments were performed with this database. The first experiment was to test the dependency of electrode positions into LZ complexity measures and the second experiment was to analyze if the LZ complexity was sensitive to the EEG acquired from control and alcoholic subjects. The results show that the complexity measurement is dependent on the changes of the pattern of brain dynamics and not dependent on electrode position.

Nonlinear feature extraction using kernel principal component analysis with non-negative pre-image

The inherent physical characteristics of many real-life phenomena, including biological and physiological aspects, require adapted nonlinear tools. Moreover, the additive nature in some situations involve solutions expressed as positive combinations of data. In this paper, we propose a nonlinear feature extraction method, with a non-negativity constraint. To this end, the kernel principal component analysis is considered to define the most relevant features in the reproducing kernel Hilbert space. These features are the nonlinear principal components with high-order correlations between input variables. A pre-image technique is required to get back to the input space. With a non-negative constraint, we show that one can solve the pre-image problem efficiently, using a simple iterative scheme. Furthermore, the constrained solution contributes to the stability of the algorithm. Experimental results on event-related potentials (ERP) illustrate the efficiency of the proposed method.