Abstract
Ongoing changes in attention and cognition depend upon cortical/subcortical interactions, which select sequences of different spatial patterns of activation in the cortex.
It is proposed that each pattern of cortical activation permits evolution of electrocortical wave activity toward statistically stationary states, analogous to thermodynamic equilibrium. In each steady-state, neurons fire with an intrinsic Poisson spike probability and also with a bursting pattern related to network oscillations. Excitatory cell dendrites act as a regenerative reservoir in which pulse generation is balanced against dissipations.
Equilibria exhibit contrasting limits. One limit, at high cortical activation, generates widespread zero-lag synchrony among excitatory cells, with partial suppression of noise. Excitatory and inhibitory cells approach zero-lag local correlation, with 1/4 cycle lag-correlation at greater distances of separation. The high-activation limit defines a correlated system of attractor basins, capable of co-ordinating synaptic modifications and intracortical signal generation. Suppression of noise would enhance convergence about attractor basins in the manner of simulated annealing, while, conversely, the persistence of some noise prevents network paralysis by phase locking. At the opposite limit—that of low activation—spikes and waves have low cross- and auto-correlation, but have wide-spectrum sensitivity to inputs. It is hypothesised that cortical regions, transiently at equilibrium near these extremes, engage in interaction with each other and with subcortical systems, to generate ongoing sequences of attention and cognition.
This account is compatible with classical and recently observed experimental phenomena. The principle features inferred from a simplified linear mathematical account are reproduced in a more physiologically realistic and non-linear numerical simulation.
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References
Alexander, G. E., Crutcher, M. D., & DeLong, M. R. (1990). Basal ganglia-thalamocortical circuits: parallel substrates for motor, oculomotor, ‘prefrontal’ and ‘limbic’ functions. In Progress in brain research. Amsterdam: Elsevier.
Amari, S.-I. (1974). A method of statistical neurodynamics. Kybernetik, 14, 201–215.
Amari, S.-I., & Maginu, K. (1988). Statistical neurodynamics of associative memory. Neural Netw., 1, 63–73.
Amari, S.-I., Yoshida, K., & Kanatani, K.-I. (1977). A mathematical foundation for statistical neurodynamics. SIAM J. Appl. Math., 33, 95–126.
Amit, D. J. (1989). Modelling brain function. Cambridge: Cambridge University Press.
Arbib, M. A. (Ed.) (1995). The handbook of brain theory and neural networks. Cambridge: MIT Press.
Barrie, J. M., Freeman, W. J., & Lenhart, M. D. (1996). Spatiotemporal analysis of prepyriform, visual, auditory, and somesthetic surface EEGs in trained rabbits. J. Neurophysiol., 76, 520–539.
beim Graben, P., Barrett, A., & Atmanspacher, H. (2009). Stability criteria for contextual emergence of macrostates in neural networks. Netw. Comput. Neural Syst., 20, 178–196.
Braitenberg, V., & Schüz, A. (1991). Anatomy of the cortex: statistics and geometry. Berlin, New York: Springer.
Bressler, S. L., Coppola, R., & Nakamura, R. (1993). Episodic multiregional cortical coherence at multiple frequencies during visual task performance. Nature, 366, 153–156.
Chapman, C. L., Bourke, P. D., & Wright, J. J. (2002). Spatial eigenmodes and synchronous oscillation: coincidence detection in simulated cerebral cortex. J. Math. Biol., 45, 57–78.
Eckhorn, R., Bauer, R., Jordon, W., Brosch, M., Kruse, W., Monk, M., & Reitboeck, H. J. (1988). Coherent oscillations: a mechanism of feature linking in the in the visual cortex? Biol. Cybern., 60, 121–130.
Freeman, W. J. (1975). Mass action in the nervous system. San Diego: Academic Press.
Freeman, W. J. (1991). Predictions on neocortical dynamics derived from studies on paleocortex. In Induced rhythms of the brain. Boston: Birkhäuser.
Freeman, W. J. (2003). The wave packet: an action potential for the 21st Century. J. Integr. Neurosci., 2, 3–30.
Freeman, W. J. (2004a). Origin, structure and role of background EEG activity. Part 1. Analytic amplitude. Clin. Neurophysiol., 115, 2077–2088.
Freeman, W. J. (2004b). Origin, structure and role of background EEG activity. Part 2. Analytic phase. Clin. Neurophysiol., 115, 2089–2107.
Freeman, W. J. (2005). Origin, structure and role of background EEG activity. Part 3. Neural frame classification. Clin. Neurophysiol., 116, 1118–1129.
Freeman, W. J. (2006). Origin, structure and role of background EEG activity. Part 4. Neural frame simulation. Clin. Neurophysiol., 117, 572–589.
Freeman, W. J. (2009). Freeman’s mass action. www.scholarpedia.org/article/Freeman%27s_mass_action_#.
Freeman, W. J., & Barrie, J. M. (2000). Analysis of spatial patterns of phase in neocortical gamma EEGs in rabbit. J. Neurophysiol., 84, 1266–1278.
Fukushima, Y., Tsukada, M., Tsuda, I., Yamaguti, Y., & Kuroda, S. (2007). Spatial clustering property and self-similarity in membrane potentials of hippocampal CA1 neurons for spatio-temporal input sequence. Cogn. Neurodyn., 1, 305–316.
Gray, C. M., & Singer, W. (1989). Stimulus-specific neuronal oscillations in orientation columns of cat visual cortex. Proc. Nat. Acad. Sci., 86, 1698–1702.
Gray, C. M., Konig, P., Engel, A. K., & Singer, W. (1989). Oscillatory responses in cat visual cortex exhibit intercolumnar synchronisation which reflects global stimulus properties. Nature, 388, 334–337.
Gray, C. M., Engel, A. K., Konig, P., & Singer, W. (1992). Synchronization of oscillatory neuronal responses in cat striate cortex: temporal properties. Vis. Neurosci., 8, 337–347.
Grossberg, S. (1980). How does a brain build a cognitive code? Psychol. Rev., 87, 1–51.
Haken, H. (1976). Principles of brain functioning. Berlin: Springer.
Hasenstaub, A., Shu, Y., Haider, B., Kraushaar, U., Duque, A., & McCormick, D. A. (2005). Inhibitory postsynaptic potentials carry synchronized frequency information in active cortical networks. Neuron, 47, 423–435.
Hebb, D. O. (1949). The organization of behavior. New York: Wiley.
Hopfield, J. J. (1982). Neural networks and physical systems with emergent collective computational abilities. Proc. Nat. Acad. Sci., 79, 2554–2558.
Jirsa, V. K., & Haken, H. (1996). Field theory of electromagnetic brain activity. Phys. Rev. Lett., 77, 960–963.
Jirsa, V. K., & Stefanescu, R. A. (2010). Neural population codes capture biologically realistic large scale network dynamics. This Special Issue, BMB.
Kandel, E. R., Schwartz, J. H., & Jessell, T. M. (1991). Principles of neural science (3rd edn.). Englewood Cliffs: Prentice-Hall International (p. 276 and assoc.).
Kay, J. W., & Phillips, W. A. (2010). Coherent infomax as a computational goal for neural systems. This Special Issue, BMB.
Kirkpatrick, S., Gellatt, C. D., & Vecchi, M. P. (1983). Optimization by simulated annealing. Science, 220, 671–680.
Liley, D. T. J., & Wright, J. J. (1994). Intracortical connectivity of pyramidal and stellate cells: estimates of synaptic densities and coupling symmetry. Netw. Comput. Neural Syst., 5, 175–189.
Mathworld (2009). http://mathworld.wolfram.com/DifferentialEntropy.html.
Miltner, W. H., Braun, C., Arnold, M., Witte, H., & Taube, E. (1999). Coherence of gamma-band EEG activity as a basis for associative learning. Nature, 397, 434–436.
Mizraji, E., & Lin, J. (2010). Logic in a dynamic brain. This Special Issue, BMB.
Neuenschwander, S., & Singer, W. (1996). Long range synchronisation of oscillatory light responses in the cat retina and lateral geniculate nucleus. Nature, 379, 728–733.
Nunez, P. L. (1981). Electric fields of the brain. London: Oxford University Press.
Nunez, P. L. (1995). Neocortical dynamics and human EEG rhythms. London: Oxford University Press.
Pitts, W., & McCulloch, W. S. (1943). A logical calculus of the ideas immanent in nervous activity. Bull. Math. Biophys., 5, 115–133.
Potthast, R. P., beim Graben, P., & Wright, J. J. (2010). Emergence of cortical maps through synaptic competition and cooperation dynamics. This Special Issue, BMB.
Rennie, C. J., Wright, J. J., & Robinson, P. A. (2000). Mechanisms of cortical electrical activity and the emergence of gamma rhythm. J. Theor. Biol., 205, 17–35.
Rennie, C. J., Robinson, P. A., & Wright, J. J. (2002). Unified neurophysical model of EEG spectra and evoked potentials. Biol. Cybern., 86, 457–471.
Robinson, P. A., Wright, J. J., & Rennie, C. J. (1998). Synchronous oscillations in the cerebral cortex. Phys. Rev. E, 57, 4578–4588.
Saddy, D., beim Graben, P., Drenhaus, H., & Frisch, S. (2004). Distinguishing process from content in language processing: a new answer to an old question. In Proceedings of the 8th experimental chaos conference, American Institute of Physics. ISBN 0-7354-0226-4.
Scheibel, M. E., & Scheibel, B. A. (1970). Elementary processes in selected thalamic and cortical subsystems—the structural substrates. In Schmitt, F. O. (Ed.), The neurosciences: 2nd study program (pp. 443–457). New York: Rockefeller University Press.
Schillen, T. B., & Konig, P. (1994). Binding by temporal structure in multiple feature domains of an oscillatory neural network. Biol. Cybern., 70, 397–405.
Scholl, D. A. (1956). The organization of the cerebral cortex. New York: Wiley.
Singer, W. (1994). Putative functions of temporal correlations in neocortical processing. In Large scale neuronal theories of the brain. Cambridge: MIT Press.
Singer, W., & Gray, C. M. (1995). Visual feature integration and the temporal correlation hypothesis. Ann. Rev. Neurosci., 18, 555–586.
Steriade, M., Timofeev, I., & Grenier, F. (2001). Natural waking and sleep states: a view from inside cortical neurons. J. Neurophysiol., 85, 1969–1985.
Steyn-Ross, D. A., & Steyn-Ross, M. L. (Eds.) (2009). Modeling phase transitions in the brain. Berlin: Springer. ISBN: 978-1-4419-0795-0 (in press).
Steyn-Ross, M. L., Steyn-Ross, D. A., Sleigh, J. W., & Wilson, M. T. (2010). A mechanism for ultra-slow oscillations in the cortical default network. This Special Issue, BMB.
Stryker, M. P. (1989). Is grandmother an oscillation? Nature, 388, 297–298.
Traub, R. D., Whittington, M. A., Stanford, I. M., & Jefferys, J. G. R. (1996). A mechanism for generation of long-range synchronous fast oscillations in the cortex. Nature, 383, 621–624.
Tsuda, I., & Kuroda, S. (2004). A complex systems approach to an interpretation of dynamic brain activity II: does Cantor coding provide a dynamic model for the formation of episodic memory? In Erdi, P. et al. (Eds.), LCNS : Vol. 3146. Cortical dynamics. Berlin: Springer.
Tsukada, M., & Fukushima, Y. (2010). A context sensitive mechanism in hippocampal CA1 networks. This Special Issue, BMB.
van Rotterdam, A., Lopes da Silva, F. H., van den Ende, J., Viergever, M. A., & Hermans, A. J. (1982). A model of the spatio-temporal characteristics of the alpha rhythm. Bull. Math. Biol., 44, 283–305.
von der Malsburg, C. (1983). How are nervous structures organised? In Basar, E., Flohr, H., Haken, H., & Mandell, A. J. (Eds.), Synergetics of the brain. Berlin, Heidelberg, New York: Springer.
Whittington, M. A., Faulkner, H. J., Doheny, H. C., & Traub, R. D. (2000). Neuronal fast oscillations as a target site for psychoactive drugs. Pharmacol. Ther., 86, 171–190.
Wilson, H. R., & Cowan, J. D. (1973). A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue. Kybernetik, 13, 55–80.
Wright, J. J. (2009a). Generation and control of cortical gamma: findings from simulation at two scales. Neural Netw., 22, 373–384.
Wright, J. J. (2009b). Cortical phase transitions: properties demonstrated in continuum simulations at mesocopic and macroscopic scales. New Math. Nat. Comput., 5, 159–183.
Wright, J. J., & Liley, D. T. J. (1996). Dynamics of the brain at global and microscopic scales. Neural networks and the EEG. Behav. Brain Sci., 19, 285–320.
Wright, J. J., Bourke, P. D., & Chapman, C. L. (2000). Synchronous oscillation in the cerebral cortex and object coherence: simulation of basic electrophysiological findings. Biol. Cybern., 83, 341–353.
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An erratum to this article can be found at http://dx.doi.org/10.1007/s11538-011-9639-3
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Wright, J.J. Attractor Dynamics and Thermodynamic Analogies in the Cerebral Cortex: Synchronous Oscillation, the Background EEG, and the Regulation of Attention. Bull Math Biol 73, 436–457 (2011). https://doi.org/10.1007/s11538-010-9562-z
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DOI: https://doi.org/10.1007/s11538-010-9562-z