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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.


Bifurcation diagram of (11) and (12) for , , , , , , , , and  with  as a bifurcation parameter. The solid line represents asymptotically stable equilibrium point, whereas the dashed line represents unstable equilibrium point. A supercritical Hopf bifurcation occurs at  where the single asymptotically stable equilibrium point becomes unstable and gives rise to a stable limit cycle. At , the unstable equilibrium point reverts to an asymptotically stable equilibrium point and the stable limit cycle disappears
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Fig5: Bifurcation diagram of (11) and (12) for , , , , , , , , and with as a bifurcation parameter. The solid line represents asymptotically stable equilibrium point, whereas the dashed line represents unstable equilibrium point. A supercritical Hopf bifurcation occurs at where the single asymptotically stable equilibrium point becomes unstable and gives rise to a stable limit cycle. At , the unstable equilibrium point reverts to an asymptotically stable equilibrium point and the stable limit cycle disappears

Mentions: Next, we illustrate the effect of the excitatory sensory input on the mean excitatory and mean inhibitory synaptic drives. Here, we fix the parameters to be as in the simulation shown in Fig. 3 and vary . It can be seen from Fig. 5 that, for the value of below , (11) and (12) have exactly one asymptotically stable equilibrium point. As increases to , the equilibrium point becomes unstable. At this point, a supercritical Hopf bifurcation occurs, giving rise to a stable limit cycle. As increases beyond , the unstable equilibrium point reverts to an asymptotically stable equilibrium point and the stable limit cycle disappears. The value of and increases as increases; see Fig. 5. The effect of on the mean firing rates and mean synaptic drives of the excitatory and the inhibitory neurons is shown in Figs. 6 and 7, respectively. As increases, the mean firing rates and mean synaptic drives for the excitatory and the inhibitory neurons increase for the chosen parameter values. Fig. 5


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)

Bifurcation diagram of (11) and (12) for , , , , , , , , and  with  as a bifurcation parameter. The solid line represents asymptotically stable equilibrium point, whereas the dashed line represents unstable equilibrium point. A supercritical Hopf bifurcation occurs at  where the single asymptotically stable equilibrium point becomes unstable and gives rise to a stable limit cycle. At , the unstable equilibrium point reverts to an asymptotically stable equilibrium point and the stable limit cycle disappears
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

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

Fig5: Bifurcation diagram of (11) and (12) for , , , , , , , , and with as a bifurcation parameter. The solid line represents asymptotically stable equilibrium point, whereas the dashed line represents unstable equilibrium point. A supercritical Hopf bifurcation occurs at where the single asymptotically stable equilibrium point becomes unstable and gives rise to a stable limit cycle. At , the unstable equilibrium point reverts to an asymptotically stable equilibrium point and the stable limit cycle disappears
Mentions: Next, we illustrate the effect of the excitatory sensory input on the mean excitatory and mean inhibitory synaptic drives. Here, we fix the parameters to be as in the simulation shown in Fig. 3 and vary . It can be seen from Fig. 5 that, for the value of below , (11) and (12) have exactly one asymptotically stable equilibrium point. As increases to , the equilibrium point becomes unstable. At this point, a supercritical Hopf bifurcation occurs, giving rise to a stable limit cycle. As increases beyond , the unstable equilibrium point reverts to an asymptotically stable equilibrium point and the stable limit cycle disappears. The value of and increases as increases; see Fig. 5. The effect of on the mean firing rates and mean synaptic drives of the excitatory and the inhibitory neurons is shown in Figs. 6 and 7, respectively. As increases, the mean firing rates and mean synaptic drives for the excitatory and the inhibitory neurons increase for the chosen parameter values. Fig. 5

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.