ingber@umiacs.umd.edu (04/26/91)
Below is the Abstract and Conclusion of a 100+ page paper submitted to Physical Review. Comments are welcome, and I will fulfill reprint requests after publication of this paper. ============================================================================== Statistical mechanics of neocortical interactions: A scaling paradigm applied to electroencephalography Lester Ingber Science Transfer Corporation, P.O. Box 857, McLean, VA 22101 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) systemat- ics. The necessity of including nonlinear and stochastic struc- tures in this development has been stressed. In this paper, a more stringent test is placed on SMNI: The algebraic and numeri- cal algorithms previously developed in this and similar systems are brought to bear to fit large sets of EEG/evoked potential data being collected to investigate genetic predispositions to alcoholism and to extract brain "signatures" of short-term memory. 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 discrim- inate between high-risk and low-risk populations genetically predisposed to alcoholism. Since this first study is a control to include relatively long time epochs, similar to earlier attempts to establish such correlations, this discrimination is inconclusive. However, the model is shown to be consistent with EEG data and with neocortical mechanisms 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/physics mechanisms that scale across quite disparate spatial scales and functional/behavioral phenomena, i.e., describing interactions among neurons, columns of neurons, and regional masses of neurons. PACS Nos.: 87.10.+e, 05.40.+j, 02.50.+s, 02.70.+d VI. CONCLUSION We have outlined in some detail a reasonable approach to extract more ``signal'' out of the ``noise'' in EEG data, in terms of physical dynamical variables, than by merely performing regression statistical analyses on collateral variables. To learn more about complex systems, we inevitably must form func- tional models to represent huge sets of data. Indeed, modeling phenomena is as much a cornerstone of 20th century science as is collection of empirical data. We have been able to fit these sets of EEG data, using parameters either set to experimentally observed values, or being fitted within experimentally observed values. The ranges of columnar firings are consistent with a centering mechanism derived in earlier papers. The ability to fit data to these particular SMNI functional forms goes beyond nonlinear statistical modeling of data. The plausibility of the SMNI model, as emphasized in this and previ- ous SMNI papers, as spanning several important neuroscientific phenomena, suggests that the fitted functional forms may yet help to explicate some underlying biophysical mechanisms responsible for the normal and abnormal behavioral states being investigated, e.g., excitatory and/or inhibitory influences, background elec- tromagnetic influences from nearby firing states (by using SMNI synaptic conductivity parameter in the fits). There is much more work to be done. We have not yet addressed the "renormalization" issues raised, based on the nature of EEG data collection, and which are amenable to this framework. While the fitting of these distributions certainly compacts the experimental data onto a reasonable algebraic model, a prime task of most physical theory, in order to be useful to clinicians (and therefore to give more feedback to theory) more data reduction must be performed. We are experimenting with path-integral calculations and some methods of "scientific visu- alization" to determine what minimal, or at least small, set of "signatures" might suffice to be faithful to the data yet useful to clinicians. We also are examining the gains that might be made by putting these codes onto a parallel processor, which might enable real-time diagnoses based on non-invasive EEG recordings. In order to detail such a model of EEG phenomena we found it useful to seek guidance from ``top-down'' models, e.g., the non- linear string model representing nonlinear dipoles of neuronal columnar activity. In order to construct a more detailed ``bottom-up'' model that could give us reasonable algebraic func- tions with physical parameters to be fit by data, we then needed to bring together a wealth of empirical data and modern tech- niques of mathematical physics across multiple scales of neocort- ical activity. At each of these scales, we had to derive and establish reasonable procedures and sub-models for climbing from scale to scale. Each of these sub-models could then be tested against some experimental data to see if we were on the right track. For example, at the mesoscopic scale we checked con- sistency of SMNI with known aspects of visual and auditory short-term memory; at the macroscopic scale we checked con- sistency with known aspects of EEG and propagation of information across neocortex. Here, we have demonstrated that the currently accepted dipole EEG model can be derived as the Euler-Lagrange equations of an electric-potential Lagrangian. The theoretical and experimental importance of specific scaling of interactions in neocortex has been quantitatively demonstrated: We have shown that the explicit algebraic form of the probability distribution for mesoscopic columnar interactions is driven by a nonlinear threshold factor of the same form taken to describe microscopic neuronal interactions, in terms of electrical-chemical synaptic and neuronal parameters all lying within their experimentally observed ranges; these threshold fac- tors largely determine the nature of the drifts and diffusions of the system. This mesoscopic probability distribution has suc- cessfully described STM phenomena and, when used as a basis to derive most likely trajectories using the Euler-Lagrange varia- tional equations, it also has described the systematics of EEG phenomena. In this paper, we have taken the mesoscopic form of the full probability distribution more seriously for macroscopic interactions, deriving macroscopic drifts and diffusions linearly related to sums of their (nonlinear) mesoscopic counterparts, scaling its variables to describe interactions among regional interactions correlated with observed electrical activities meas- ured by electrode recordings of scalp EEG, with apparent success. These results give strong quantitative support for an accurate intuitive picture, portraying neocortical interactions as having common algebraic/physics mechanisms that scale across quite disparate spatial scales and functional/behavioral phenomena, i.e., describing interactions among neurons, columns of neurons, and regional masses of neurons. It seems reasonable to speculate on the evolutionary desira- bility of developing Gaussian-Markovian statistics at the mesos- copic columnar scale from microscopic neuronal interactions, and maintaining this type of system up to the macroscopic regional scale. I.e., this permits maximal processing of information. There is much work to be done, but we believe that modern methods of statistical mechanics have helped to point the way to promising approaches. -- Domain: curtiss@umiacs.umd.edu Phillip Curtiss UUCP: uunet!mimsy!curtiss UMIACS - Univ. of Maryland Phone: +1-301-405-6710 College Park, Md 20742