Generation and control of cortical gamma: findings from simulation at two scales. J. J. Wright Liggins Institute, and Department of Psychological Medicine, University of Auckland, Auckland, New Zealand. Brain Dynamics Centre, University of Sydney, Sydney, Australia. ______________________________________________________________________________ Abstract. A continuum model of electrocortical activity was applied separately at centimetric and macrocolumnar scales, permitting analysis of interaction between scales. State equations included effects of retrograde action potential propagation in dendritic trees, and kinetics of AMPA, GABA and NMDA receptors. Parameter values were provided from independent physiological and anatomical estimates. Realistic field potentials and pulse rates were obtained, including resonances in the alpha/theta and gamma ranges, 1/ background activity, and autonomous gamma activity. Zero- lag synchrony and travelling waves occurred as complementary aspects of cortical transmission, and lead/lag relations between excitatory and inhibitory cell populations varied systematically around transition to autonomous gamma oscillation. f 2 Properties of the simulations can account for generation and control of gamma activity. All factors acting on excitatory/inhibitory balance controlled the onset and offset of gamma oscillation. Autonomous gamma was initiated by focal excitation of excitatory cells, and suppressed by laterally spreading trans-cortical excitation, which acted on both excitatory and inhibitory cell populations. Consequently, although spatially extensive non-specific reticular activation tended to suppress autonomous gamma, spatial variation of reticular activation could preferentially select fields of synchrony. Keywords: Gamma activity; Synchronous oscillation; Cortical self-regulation; EEG. _______________________________________________________________________________ 1. Introduction This paper specifies continuum state equations for simulation of local field potentials and population pulse rates in the cerebral cortex. The model thus obtained is used to help explain the origin and control of gamma synchrony in relation to global electrocortical activity. In the attempt to capture essential aspects of cortical dynamics, models of neuronal interactions range from very detailed simulations of individual neurons then studied in interacting networks (e.g. Bower & Beeman,1998; Traub, Whittington, Stanford & Jefferies, 1996), to classical approaches utilizing highly simplified neurons (e.g. Amit, 1989; Arbib, 1995; Buzsaki & Draguhn, 2004). Problems of numerical complexity and loss of analytical advantage, versus loss of physiological realism, arise at either end of this spectrum. A further, and complementary, approach has been motivated by studies of electroencephalogram (EEG) and local field potentials, and is variously described as mean-field, continuum, or population approximation (Freeman, 1975; Haken, 1976; Nunez, 1981, 1995; van Rotterdam, Lopes da Silva, van den Ende, Viergever & Hermans, 1982; Wilson & Cowan, 1973). Continuum models treat the cortical medium as a continuous field, and offer the possibility that the field equations might be applied at different spatial scale and resolution, by appropriate adjustment of parameters and connections. In the present work, for the first time, a single parameter set obtained a priori is applied to continuum simulations to test whether the results exhibit appropriate scale-dependent effects. Also for the first time, action potential retrograde propagation into the dendritic tree is included within continuum state equations – an inclusion