Statistical mechanics of neocortical interactions: A scaling paradigm applied to electroencephalography

Abstract

A series of papers has developed a statistical mechanics of neocortical interactions (SMNI), deriving aggregate behavior of experimentally observed columns of neurons from statistical electrical-chemical properties of synaptic interactions. While not useful to yield insights at the single neuron level, SMNI has demonstrated its capability in describing large-scale properties of short-term memory and electroencephalographic (EEG) systematics. The necessity of including nonlinear and stochastic structures in this development has been stressed. In this paper, a more stringent test is placed on SMNI: The algebraic and numerical algorithms previously developed in this and similar systems are brought to bear to fit large sets of EEG and evoked potential data being collected to investigate genetic predispositions to alcoholism and to extract brain "signatures" of short-term memory. Using the numerical algorithm of Very Fast Simulated Re-Annealing, it is demonstrated that SMNI can indeed fit this data within experimentally observed ranges of its underlying neuronal-synaptic parameters, and use the quantitative modeling results to examine physical neocortical mechanisms to discriminate between high-risk and low-risk populations genetically predisposed to alcoholism. Since this first study is a control to span relatively long time epochs, similar to earlier attempts to establish such correlations, this discrimination is inconclusive because of other neuronal activity which can mask such effects. However, the SMNI model is shown to be consistent with EEG data during selective attention tasks and with neocortical mechanisms describing short-term memory previously published using this approach. This paper explicitly identifies similar nonlinear stochastic mechanisms of interaction at the microscopic-neuronal, mesoscopic-columnar and macroscopic-regional scales of neocortical interactions. These results give strong quantitative support for an accurate intuitive picture, portraying neocortical interactions as having common algebraic or physics mechanisms that scale across quite disparate spatial scales and functional or behavioral phenomena, i.e., describing interactions among neurons, columns of neurons, and regional masses of neurons.PA

Natural world physical, brain operational, and mind phenomenal space–time

“…3), forming a much coarser structure of neuronal assembly [169,170]. A macrocolumn has a spatial extent of about a few millimeters [98,171,172]. It is argued that typically only several macrocolumns, that fire coherently, produce neuronal assembly's electric potentials (Fig.…”

Statistical mechanics of neocortical interactions: Path-integral evolution of short-term memory

“…Section II gives a short description of SMNI as it has been focused to EEG analyses [13] and generic algorithms for nonlinear systems [14]. Section III gives a short description of that part of the SMNI algebra of the mesoscopic scale relevant to this paper, where confirmation of experimental data was obtained with systematics of STM phenomena.…”

“…In nature, complex systems often present different phenomena at different scales. In this context, a plausible model of statistical mechanics of neocortical interactions (SMNI) has been developed over the past decade [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. Some recent experimental work further justifies the SMNI mathematical development of the microscopic scale into mesocolumns [17].…”

“…In this paper, to place all calculations in this context, it is helpful to consider the utility of SMNI as directed towards phenomena such as measured by electroencephalography (EEG). For example, fitted SMNI functional forms to EEG data may help to explicate some underlying biophysical mechanisms responsible for the normal and abnormal behavioral states being investigated [13,15].…”

“…Section IV presents a path-integral algorithm, PATHINT, applied to SMNI, with detailed calculations of the evolution of STM. Section V concludes with a brief outlook to future work that now can be reasonably accomplished given the PATHINT algorithm together with the adaptive simulated annealing (ASA) code [19], previously called very fast simulated reannealing (VFSR) [20], which was used to fit EEG data [13].…”