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A Mechanistic Neural Field Theory of How Anesthesia Suppresses Consciousness: Synaptic Drive Dynamics, Bifurcations, Attractors, and Partial State Equipartitioning.

Hou SP, Haddad WM, Meskin N, Bailey JM - J Math Neurosci (2015)

Bottom Line: Furthermore, we address the more general question of synchronization and partial state equipartitioning of neural activity without mean field assumptions.This is done by focusing on a postulated subset of inhibitory neurons that are not themselves connected to other inhibitory neurons.Finally, several numerical experiments are presented to illustrate the different aspects of the proposed theory.

View Article: PubMed Central - PubMed

Affiliation: A*STAR, Singapore Institute of Manufacturing Technology, Singapore, 638075, Singapore. house@SIMTech.a-star.edu.sg.

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 use dynamical system theory to develop a mechanistic mean field model for neural activity to study the abrupt transition from consciousness to unconsciousness as the concentration of the anesthetic agent increases. The proposed synaptic drive firing-rate model predicts the conscious-unconscious transition as the applied anesthetic concentration increases, where excitatory neural activity is characterized by a Poincaré-Andronov-Hopf bifurcation with the awake state transitioning to a stable limit cycle and then subsequently to an asymptotically stable unconscious equilibrium state. Furthermore, we address the more general question of synchronization and partial state equipartitioning of neural activity without mean field assumptions. This is done by focusing on a postulated subset of inhibitory neurons that are not themselves connected to other inhibitory neurons. Finally, several numerical experiments are presented to illustrate the different aspects of the proposed theory.

No MeSH data available.


Solutions to (25) and (26) with initial conditions ,  for , , and . The synaptic drive of the excitatory neurons  to  do not converge to zero
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Fig14: Solutions to (25) and (26) with initial conditions , for , , and . The synaptic drive of the excitatory neurons to do not converge to zero

Mentions: Next, we apply Theorem 3 to the connectivity matrix given by (126). Here, we assume that , , , , and the activation functions , , are given by (52) with . As can be seen from Fig. 14, the synaptic drives of the excitatory neurons to do not converge to zero. However, when the time constants of the inhibitory neurons are increased to , the synaptic drives of the excitatory neurons to converge to zero; see Fig. 15. Fig. 14


A Mechanistic Neural Field Theory of How Anesthesia Suppresses Consciousness: Synaptic Drive Dynamics, Bifurcations, Attractors, and Partial State Equipartitioning.

Hou SP, Haddad WM, Meskin N, Bailey JM - J Math Neurosci (2015)

Solutions to (25) and (26) with initial conditions ,  for , , and . The synaptic drive of the excitatory neurons  to  do not converge to zero
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4593994&req=5

Fig14: Solutions to (25) and (26) with initial conditions , for , , and . The synaptic drive of the excitatory neurons to do not converge to zero
Mentions: Next, we apply Theorem 3 to the connectivity matrix given by (126). Here, we assume that , , , , and the activation functions , , are given by (52) with . As can be seen from Fig. 14, the synaptic drives of the excitatory neurons to do not converge to zero. However, when the time constants of the inhibitory neurons are increased to , the synaptic drives of the excitatory neurons to converge to zero; see Fig. 15. Fig. 14

Bottom Line: Furthermore, we address the more general question of synchronization and partial state equipartitioning of neural activity without mean field assumptions.This is done by focusing on a postulated subset of inhibitory neurons that are not themselves connected to other inhibitory neurons.Finally, several numerical experiments are presented to illustrate the different aspects of the proposed theory.

View Article: PubMed Central - PubMed

Affiliation: A*STAR, Singapore Institute of Manufacturing Technology, Singapore, 638075, Singapore. house@SIMTech.a-star.edu.sg.

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 use dynamical system theory to develop a mechanistic mean field model for neural activity to study the abrupt transition from consciousness to unconsciousness as the concentration of the anesthetic agent increases. The proposed synaptic drive firing-rate model predicts the conscious-unconscious transition as the applied anesthetic concentration increases, where excitatory neural activity is characterized by a Poincaré-Andronov-Hopf bifurcation with the awake state transitioning to a stable limit cycle and then subsequently to an asymptotically stable unconscious equilibrium state. Furthermore, we address the more general question of synchronization and partial state equipartitioning of neural activity without mean field assumptions. This is done by focusing on a postulated subset of inhibitory neurons that are not themselves connected to other inhibitory neurons. Finally, several numerical experiments are presented to illustrate the different aspects of the proposed theory.

No MeSH data available.