Modelling the spatial effects of the anaesthetic-induced phase-transition in the cerebral cortex

Whiting, David Robin

Modelling the spatial effects of the anaesthetic-induced phase-transition in the cerebral cortex

dc.contributor.advisor	Steyn-Ross, Moira L.
dc.contributor.advisor	Steyn-Ross, D. Alistair
dc.contributor.advisor	Sleigh, James W.
dc.contributor.author	Whiting, David Robin
dc.date.accessioned	2013-11-22T02:59:16Z
dc.date.available	2013-11-22T02:59:16Z
dc.date.issued	2003
dc.date.updated	2013-11-22T02:48:37Z
dc.description.abstract	In this thesis I investigate the theoretical stochastic behaviour of a one-dimensional model of the cerebral cortex, exposed to varying concentrations of a general anaesthetic agent. The model is that of Steyn-Ross et al. (2003). Theirs is a continuum theory based on the electrical response of a neural mass known as the macrocolum. The model predicts that as anaethetic concentration is increased the cortex will undergo a sudden electrical phase transition corresponding to loss of consciousness (LOC). Similarly, at return of consciousness (ROC) a second distinct phase transition is predicted. Spatial variability is incorporated into the original homogeneous cortical model of Steyn-Ross et al. (1999). This is done by including the possibility of spatial variation in distant excitatory and inhibitory inputs. By modelling the cortex in this way, we hope to gain an understanding of how the cortex functions, and how anaethestic agents “shut-down” the brain. I simulate the one-dimensional system numerically in order to verify analytical predictions. Both analytical and numerical results show an increase in the coherence (spatial-correlation) of the electrical activity along the one-dimensional rod on approach to both LOC and ROC. Theory and simulations also show that the electrical ﬂuctuations in the unconscious cortex should have a larger correlation length than for the cortex in the conscious state, suggesting that the unconscious state is the more ordered. I derive the theoretical power spectrum and discuss some of its properties. By expanding the model to include spatial variability, we discover the possibility of self-organized structures forming spontaneously in the one-dimensional cortex. These “Turing” or dissipative structures are stationary in time, showing giant DC voltage variations along the cortical rod. Although the dissipative structures can from a rich variety of pseudo-periodic patterns, the physiological signiﬁcance of such stationary neural structures is not yet clear.
dc.format.mimetype	application/pdf
dc.identifier.citation	Whiting, D. R. (2003). Modelling the spatial effects of the anaesthetic-induced phase-transition in the cerebral cortex (Thesis, Master of Science (MSc)). University of Waikato, Hamilton, New Zealand. Retrieved from https://hdl.handle.net/10289/8222	en
dc.identifier.uri	https://hdl.handle.net/10289/8222
dc.language.iso	en
dc.publisher	University of Waikato
dc.rights	All items in Research Commons are provided for private study and research purposes and are protected by copyright with all rights reserved unless otherwise indicated.
dc.subject	anaesthesia
dc.subject	cerebral cortex
dc.subject	phase transition
dc.subject	macrocolumn
dc.subject	mean-field cortical model
dc.subject	Turing bifurcation
dc.title	Modelling the spatial effects of the anaesthetic-induced phase-transition in the cerebral cortex
dc.type	Thesis
pubs.place-of-publication	Hamilton, New Zealand	en_NZ
thesis.degree.discipline	Physics
thesis.degree.grantor	University of Waikato
thesis.degree.level	Masters
thesis.degree.name	Master of Science (MSc)