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A set of nonlinear continuum field equations is presented which describes the dynamics of neural activity in cortex. These take into account the most pertinent anatomical and physiological features found in cortex with all parameter values obtainable from independent experiment. Derivation of a white noise fluctuation spectrum from a linearized set of(More)
Changes to the electroencephalogram (EEG) observed during general anesthesia are modeled with a physiological mean field theory of electrocortical activity. To this end a parametrization of the postsynaptic impulse response is introduced which takes into account pharmacological effects of anesthetic agents on neuronal ligand-gated ionic channels. Parameter(More)
We present a model for the dynamics of a cerebral cortex in which inputs to neuronal assemblies are treated as random Gaussian fluctuations about a mean value. We incorporate the effect of general anesthetic agents on the cortex as a modulation of the inhibitory neurotransmitter rate constant. Stochastic differential equations are derived for the state(More)
A method is outlined for estimating the the average number of synapses forming between cortical neurons as a function of their intercellular separation and the geometry of their dendritic and axonal arboriration. Consideration is confined to the formation of local intracortical connections and to the case where the distribution of axonal and dendritic(More)
A set of non-linear continuum field equations are presented which describe the macroscopic dynamics of neural activity in cortex. Numerical solutions of the coupled non-linear system of partial differential equations show properties analogous to cortical evoked potentials, oscillations at the frequency of the mammalian alpha rhythm and non-stationary(More)
A central difficulty in modeling epileptogenesis using biologically plausible computational and mathematical models is not the production of activity characteristic of a seizure, but rather producing it in response to specific and quantifiable physiologic change or pathologic abnormality. This is particularly problematic when it is considered that the(More)
Neural field models of firing rate activity typically take the form of integral equations with space-dependent axonal delays. Under natural assumptions on the synaptic connectivity we show how one can derive an equivalent partial differential equation (PDE) model that properly treats the axonal delay terms of the integral formulation. Our analysis avoids(More)
Conical pyramidal and stellate neurons were simulated using the GENESIS simulation package. Model neurons were leaky integrate-and-fire and consisted of from four to nine passive compartments. Neurophysiological measurements, based on single-cell recordings and patch-clamp experiments, provided estimations for the simulation of cortical neurons:(More)