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Ingber L.,Lester Ingber Research | Nunez P.L.,Tulane University
Mathematical Biosciences | Year: 2011

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. © 2010 Elsevier Inc. Source


Ingber L.,Lester Ingber Research
Journal of Theoretical Biology | Year: 2016

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 Ca2+ waves, q the charge of Ca2+ 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 Ca2+ waves. © 2016 Elsevier Ltd. Source


Ingber L.,Lester Ingber Research
Cognitive Computation | Year: 2012

A statistical mechanics of neocortical interactions of columnar activity and the vector potential of minicolumnar electromagnetic activity provide a context to explore neocortical information processes and influences on cognitive processing at multiple scales, i. e., mesoscopic (columnar scales), macroscopic (mesoscopic influences at regional scales), and microscopic (mesoscopic influences of ions affecting interactions between and among neurons and astrocytes). Even within this confined context, a case has been made that it should not be expected that the proposed Holy Grail of neuroscience, i. e., to ultimately explain all brain processing in terms of a nonlinear science at molecular scales, is at all realistic. As with many Crusades for some truths, other truths can be trampled. © 2011 Springer Science+Business Media, LLC. Source


Ingber L.,Lester Ingber Research | Pappalepore M.,Lester Ingber Research | Stesiak R.R.,Lester Ingber Research
Journal of Theoretical Biology | Year: 2014

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 Ca2+ 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 Ca2+ momentum, p. The canonical momentum of a charged particle in an electromagnetic field, Π = p + qA (SI units), is calculated, where the charge of Ca2+ 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 Ca2+ ions, in both classical and quantum mechanics. Molecular scales of Ca2+ 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 Ca2+ 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. © 2013 Elsevier Ltd. Source

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