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Open Access Highly Accessed Research article

Zwanzig-Mori projection operators and EEG dynamics: deriving a simple equation of motion

David Hsu* and Murielle Hsu

Author Affiliations

Department of Neurology, University of Wisconsin, Madison WI, USA

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PMC Biophysics 2009, 2:6  doi:10.1186/1757-5036-2-6

Published: 13 July 2009


We present a macroscopic theory of electroencephalogram (EEG) dynamics based on the laws of motion that govern atomic and molecular motion. The theory is an application of Zwanzig-Mori projection operators. The result is a simple equation of motion that has the form of a generalized Langevin equation (GLE), which requires knowledge only of macroscopic properties. The macroscopic properties can be extracted from experimental data by one of two possible variational principles. These variational principles are our principal contribution to the formalism. Potential applications are discussed, including applications to the theory of critical phenomena in the brain, Granger causality and Kalman filters.

PACS code: 87.19.lj