Critical dynamics of Hopf bifurcations in the corticothalamic system: Transitions from normal arousal states to epileptic seizures

Physical Review. E
Dong-Ping Yang, Peter A Robinson

Abstract

A physiologically based corticothalamic model of large-scale brain activity is used to analyze critical dynamics of transitions from normal arousal states to epileptic seizures, which correspond to Hopf bifurcations. This relates an abstract normal form quantitatively to underlying physiology that includes neural dynamics, axonal propagation, and time delays. Thus, a bridge is constructed that enables normal forms to be used to interpret quantitative data. The normal form of the Hopf bifurcations with delays is derived using Hale's theory, the center manifold theorem, and normal form analysis, and it is found to be explicitly expressed in terms of transfer functions and the sensitivity matrix of a reduced open-loop system. It can be applied to understand the effect of each physiological parameter on the critical dynamics and determine whether the Hopf bifurcation is supercritical or subcritical in instabilities that lead to absence and tonic-clonic seizures. Furthermore, the effects of thalamic and cortical nonlinearities on the bifurcation type are investigated, with implications for the roles of underlying physiology. The theoretical predictions about the bifurcation type and the onset dynamics are confirmed by numerical simu...Continue Reading

References

Apr 20, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·P A RobinsonD L Rowe
Apr 20, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·P A RobinsonC J Rennie
May 15, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·P A RobinsonD L Rowe
Jun 23, 2004·Neuroscience·P SuffczynskiF H Lopes Da Silva
Jul 29, 2004·Human Brain Mapping·P A RobinsonS C O'Connor
Aug 10, 2005·Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences·P A RobinsonE Gordon
Aug 11, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·P A Robinson
May 16, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·J W Kim, P A Robinson
Sep 5, 2008·PLoS Computational Biology·Gustavo DecoKarl Friston
Feb 19, 2010·Epilepsy & Behavior : E&B·Stiliyan N KalitzinFernando H Lopes da Silva
Jun 2, 2012·NeuroImage·J A Roberts, P A Robinson
Aug 23, 2012·PLoS Computational Biology·Frank FreyerMichael Breakspear
Sep 7, 2012·Frontiers in Physiology·Matthew J AburnMichael Breakspear
Sep 26, 2012·Physical Review Letters·Kiyoshi KotaniG Bard Ermentrout
Jun 15, 2015·Journal of Neuroscience Methods·R G AbeysuriyaP A Robinson
Feb 16, 2016·Scientific Reports·Yoko SuzukiJosé N Onuchic
Sep 24, 2016·Physical Review Letters·Takashi Nishikawa, Adilson E Motter

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Citations

Aug 23, 2018·PLoS Computational Biology·Paula Sanz-LeonXuelong Zhao
Feb 10, 2019·Journal of Computational Neuroscience·Yue LiuSue Ann Campbell
Oct 3, 2019·Physical Review. E·F DeebaP A Robinson
Jul 25, 2019·Physical Review. E·K N MuktaP A Robinson
Feb 20, 2020·Physical Review. E·Daniele DainiViktor Jirsa

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