DocumentCode :
31392
Title :
A Stochastic Mean Field Model for an Excitatory and Inhibitory Synaptic Drive Cortical Neuronal Network
Author :
Qing Hui ; Haddad, Wassim M. ; Bailey, James M. ; Hayakawa, Takeshi
Author_Institution :
Dept. of Mech. Eng., Texas Tech Univ., Lubbock, TX, USA
Volume :
25
Issue :
4
fYear :
2014
fDate :
Apr-14
Firstpage :
751
Lastpage :
763
Abstract :
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 Itô. 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.
Keywords :
biochemistry; drugs; maximum entropy methods; molecular biophysics; neural nets; neurophysiology; statistical analysis; stochastic processes; white noise; Jaynes maximum entropy principle; anesthetic agents; anesthetic state; asymptotically slowly changing input; biochemistry; dynamical system; excitatory cortical neuronal network; general anesthesia; inhibitory synaptic drive cortical neuronal network; macroscopic property; mean field synaptic drive firing rate cortical neuronal model; molecular biology; molecular properties; multiplicative white noise model; multistability; neurochemistry; neuronal connectivity matrix; noxious stimuli; random variables; statistical analysis; stochastic integration; stochastic mean field model; system coefficient uncertainty; system coefficients; system uncertain parameters; Anesthesia; Biological neural networks; Biomembranes; Electric potential; Mathematical model; Neurons; Stochastic processes; Brownian motion; Wiener process; excitatory and inhibitory neurons; general anesthesia; mean field model; multiplicative white noise; spiking neuron models; stochastic multistability; uncertainty modeling;
fLanguage :
English
Journal_Title :
Neural Networks and Learning Systems, IEEE Transactions on
Publisher :
ieee
ISSN :
2162-237X
Type :
jour
DOI :
10.1109/TNNLS.2013.2281065
Filename :
6615921
Link To Document :
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