Impacts of noise on a field theoretical model of the human brain

Salient properties of the spatio-temporal patterns in MEG recordings of hum an brain activity, such as macroscopic coherence of a limited number of mod es and the occurrence of phase transitions, have been successfully describe d with the help of field theoretical models for the dendritic currents in t he cortex. So far, however, these models have ignored the effects of noise which play an important role in the emergence of such properties. The prese nt article provides a formal treatment of the effects of stochastic fluctua tions in the vicinity of the phase transitions that were observed by Kelso in his so-called Julliard experiment [Fuchs et al., Phase transition in the human brain: spatial mode dynamics, Int. J. Bifurcation and Chaos 2 (1992) 917-939; H. Haken, Principles of Brain Functioning, Springer, Berlin, 1996 ; J.A.S. Kelso, Dynamic Patterns - The Self-organization of Brain and Behav ior, MIT Press, Cambridge, 1995]. To describe and examine these effects, th e field theoretical model proposed by Jirsa and Haken [A field theory of el ectromagnetic brain activity, Phys. Rev. Lett. 77 (1996) 960-963; A derivat ion of a macroscopic field theory of the brain from the quasi-microscopic n eural dynamics, Physica D 99 (1997) 503-526] was extended by incorporating Gaussian white noise. The extended model describes the stochastic propertie s of the most dominant spatio-temporal components, including stochastic var iations of the amplitudes of the extracted spatial modes. Furthermore, the model captures critical phenomena such as critical slowing down and critica l fluctuations, which are derived analytically. These theoretical results a re generalized by means of numerical simulations of amplitude and phase dyn amics. (C) 1998 Elsevier Science B.V. All rights reserved.