MathsNet: Research Student Directory

Name Byrne, Áine
Group Mathematical Medicine and Biology
Room A14, Math Sci
Telephone +44 (0) 115 82 32068 [direct dial]
Thesis Title Next Generation neural activity models: Bridging the gap between mesoscopic and microscopic brain scales
Thesis Abstract Modern non-invasive probes of human brain activity such as Magneto-encephalography (MEG) give high temporal resolution (and increasingly improved spatial resolution). With this more detailed picture of the workings of the brain, we will use mathematical and statistical modelling to establish more complete mechanistic theories of spatio-temporal neuroimaging signals. These arise both from the non-local nature of the brain connections (via long range axonal fibres) and the patterns of synaptic currents across dendritic trees (the branching extensions of brain cells). Perhaps the most definitive model of brain activity to date is that of Paul Nunez, which has culminated in the brain-wave equation. Indeed this, and more general neural mass and neural field models, are the major frameworks for the forward generation of neuroimaging signals. We shall adapt these models for the generation of MEG (via modelling of appropriate trans-membrane currents and the use of Maxwell’s equations) and develop computational models. To facilitate state and parameter estimation (e.g. of parameters for anatomical connectivity, synaptic currents and firing rates) we will use novel and state-of-the-art statistical methods. By focusing on realistic representations of synaptic currents within a neural mass model for MEG brain dynamics we will be able to assess the action of pharmacological agents (and in particular neurotransmitter agonists and antagonists commonly used in psychiatric treatments) on brain states and allow the very real world application of techniques from physics and mathematics to the clinical sciences.
School contact information School of Mathematical Sciences
University of Nottingham
University Park
Nottingham, NG7 2RD
Tel: +44 (0) 115 951 4949
Fax: +44 (0) 115 951 4951
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