Synchronisation and propagation in human cortical networks

将大脑建模为一个复杂网络的想法现在已经很好地建立起来了。然而，功能性大脑状态的出现，通过大型互联神经元群体的相互作用，仍然知之甚少。这阻碍了对病理性大脑状态及其治疗操作的理解。该项目旨在采用计算和数学技术来阐明结构与功能之间的关系，并特别应用于经颅磁刺激（TMS），这是一种非侵入性治疗抑郁症，精神分裂症和慢性疼痛的方法，其神经机制仍然未知。为了实现这一目标，我们将利用神经质量模型的直接模拟（提供神经群体行为的粗粒度描述），以及一系列互补的数学方法，这些方法将建立结构-功能关系的图像。数学技术包括：研究引起神经振荡的平衡的网络不稳定性，弱耦合振荡器分析以描述振荡开始后的锁相状态，考虑假分叉（网络极限环振荡的形状发生质的变化）和结构-功能网络的图论询问，包括多路复用方法。从这些研究的见解将告知如何在TMS输送参数（频率，振幅，目标区域等）的变化。影响所产生的功能网络，以帮助理解优化TMS治疗的治疗设计。

The idea of modelling the brain as a complex network is now well established. However, the emergence of functional brain states, via the interaction of large interconnected neuronal populations, remains poorly understood. This hinders understanding of pathological brain states, and their therapeutic manipulation. This project aims to employ computational and mathematical techniques to shed light on the relationship between structure and function, and with particular application to Transcranial Magnetic Stimulation (TMS), a non-invasive treatment for depression, schizophrenia and chronic pain, whose neurological mechanism remains unknown. To achieve this, we will utilise direct simulation of neural mass models (that provide a coarse-grained description of neural population behaviour) posed on physiological brain networks, together with a range of complementary mathematical approaches that will build up a picture of the structure-function relationship. Mathematical techniques include: study of the network instabilities of equilibria that give rise to neural oscillations, weakly coupled oscillator analyses to describe phase-locked states beyond the onset of oscillations, consideration of false bifurcations (where the shape of network limit-cycle oscillations undergoes a qualitative change) and graph theoretical interrogation of structure-function networks, including multiplex approaches. Insights from these studies will inform how changes in the parameters of TMS delivery (frequency, amplitude, target region etc.) affect resultant functional networks to help understand treatment design for optimisation of TMS therapy.