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Published on: May 7, 2017
Excitable neurons, firing threshold manifolds and canards
John Mitry1, Michelle McCarthy, Nancy Kopell
1School of Mathematics and Statistics, University of Sydney, Sydney, NSW, Australia. J.Mitry@maths.usyd.edu.au.
Journal of Mathematical Neuroscience
|August 16, 2013
Summary
This study reveals how propofol anesthesia affects neuron firing. Geometric analysis identifies "canards" as key structures determining rebound spiking, showing anesthesia
Area of Science:
- Computational Neuroscience
- Mathematical Biology
- Anesthesiology
Background:
- Propofol anesthesia induces post-inhibitory rebound spiking in excitable neurons.
- This phenomenon is linked to modulations in inhibitory GABAa synaptic currents.
- Understanding these dynamics is crucial for anesthesia mechanisms.
Purpose of the Study:
- To investigate firing threshold manifolds in a mathematical model of neuronal excitability.
- To elucidate the role of propofol-induced changes in synaptic currents on rebound spiking.
- To analyze the geometric structures underlying these dynamic firing patterns.
Main Methods:
- Utilized a mathematical model of an excitable neuron adapted from McCarthy et al.
- Employed geometric singular perturbation theory to identify firing threshold manifolds.
- Analyzed the impact of propofol-modulated GABAa synaptic current decay time-scales.
Main Results:
- Identified canards of folded saddle-type as the firing threshold manifolds.
- Demonstrated that the canard separatrix's position and orientation are propofol-dependent.
- Showed that static inhibitory current step protocols fail to capture dynamic behaviors.
Conclusions:
- Firing threshold manifolds, characterized by canards, encode synaptic process speeds.
- Propofol dose directly influences these geometric structures, controlling rebound spiking.
- Dynamic analysis is essential for fully understanding anesthesia-induced neuronal responses.
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