A Stochastic Mean Field Model for an Excitatory and Inhibitory Synaptic Drive Cortical Neuronal Network

作者：Hui Qing^*; Haddad Wassim M; Bailey James M; Hayakawa Tomohisa

来源：IEEE Transactions on Neural Networks and Learning Systems, 2014, 25(4): 751-763.

DOI：10.1109/TNNLS.2013.2281065

• Brownian motion
• excitatory and inhibitory neurons
• general anesthesia
• mean field model
• multiplicative white noise
• spiking neuron models
• stochastic multistability
• uncertainty modeling
• Wiener process

With the advances in biochemistry, molecular biology, and neurochemistry there has been impressive progress in understanding the molecular properties of anesthetic agents. However, there has been little focus on how the molecular properties of anesthetic agents lead to the observed macroscopic property that defines the anesthetic state, that is, lack of responsiveness to noxious stimuli. In this paper, we develop a mean field synaptic drive firing rate cortical neuronal model and demonstrate how the induction of general anesthesia can be explained using multistability; the property whereby the solutions of a dynamical system exhibit multiple attracting equilibria under asymptotically slowly changing inputs or system parameters. In particular, we demonstrate multistability in the mean when the system initial conditions or the system coefficients of the neuronal connectivity matrix are random variables. Uncertainty in the system coefficients is captured by representing system uncertain parameters by a multiplicative white noise model wherein stochastic integration is interpreted in the sense of Ito. Modeling a priori system parameter uncertainty using a multiplicative white noise model is motivated by means of the maximum entropy principle of Jaynes and statistical analysis.

• 出版日期2014-4