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Neural Field Dynamics on Curved Cortical Geometries S&T37

  • School: School of Science and Technology
  • Study mode(s): Full-time / Part-time
  • Starting: 2022
  • Funding: UK student / EU student (non-UK) / International student (non-EU) / Fully-funded

Overview

NTU's Fully-funded PhD Studentship Scheme 2022

Project ID: S&T37

The human cortex is composed of an enormous number of neurons (of the order 100 billion) which via their synaptic connections (of the order 1000 trillion) enable the brain to perform a myriad of complex cognitive processes. Mathematical modelling of the brain at this scale, however, is typically constrained by a lack of connectivity data describing detailed synaptic interactions, as well as several daunting technical obstacles. To circumvent these issues, mathematicians study so-called neural field models that provide a continuous, and crucially mathematically tractable, approach for modelling large-scale behaviour of large populations of neurons. Such models have been used to interpret brain imaging data from different modalities (e.g. EEG and fMRI) as well as to investigate neural phenomena such as hallucinogenic patterns.

Despite the highly convoluted nature of the human brain, neural field models typically treat the cortex as a planar one- or two-dimensional sheet of neurons, and so the role cortical geometry plays in non-local models of brain activity is poorly understood. The aim of this project is to extend current research on neural field models to more physiologically realistic cortical domains, and to implement novel numerical schemes to investigate the role that surface curvature (arising through cortical gyri and sulci) has on the properties of observed neural activity patterns. This will require techniques from dynamical systems theory (including linear stability analysis and bifurcation theory), numerical analysis and scientific computing.

Importantly, such an approach provides a means by which to investigate the influence of cortical geometry upon the formation and transmission of spatially localised neural activity and beyond, and thus promises to provide model-based insights into disorders like epilepsy, or spreading depression, as well as healthy cognitive processes like working memory or attention.

The ideal candidate for this project will have a passion for numerical methods (numerical analysis, numerical bifurcation analysis, scientific computing) and a willingness to learn about mathematical neuroscience. Working closely with Dr Crofts, Dr Chappell and Dr Smith, the student will develop robust and efficient algorithms for simulating neural field models on cortical geometries obtained from the Human Connectome Project, and perform numerical bifurcation analyses on these generic folded domains.

School strategic research priority

This project aligns with the CHAUD research priorities: the improved modelling capabilities resulting from this study will advance understanding of neural activity

Entry qualifications

For the eligibility criteria, visit our studentship application page.

How to apply

For guidance and to make an application, please visit our studentship application page. The application deadline is Friday 14 January 2022.

Fees and funding

This is part of NTU's 2022 fully-funded PhD Studentship Scheme.

Guidance and support

Download our full applicant guidance notes for more information.

Still need help?

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