Synchronisation and propagation in human cortical networks

将大脑建模为复杂网络的想法现在已经很成熟了。然而，大脑功能状态的出现，通过大量相互联系的神经元群体的相互作用，仍然知之甚少。这阻碍了对大脑病理状态及其治疗操作的理解。该项目旨在利用计算和数学技术阐明结构和功能之间的关系，并特别应用于经颅磁刺激(TMS)，这是一种治疗抑郁症、精神分裂症和慢性疼痛的非侵入性治疗方法，其神经机制尚不清楚。为了实现这一点，我们将利用对生理性大脑网络上提出的神经质量模型(提供对神经种群行为的粗粒度描述)的直接模拟，以及一系列互补的数学方法，来构建结构-功能关系的图景。数学方法包括：研究引起神经振荡的平衡点的网络不稳定性，用弱耦合振子分析来描述振荡开始后的锁相态，考虑虚假分叉(其中网络极限环振荡的形状经历了质的变化)，以及结构-功能网络的图论询问，包括多重方法。来自这些研究的见解将告知TMS传递参数(频率、幅度、目标区域等)如何变化。影响由此产生的功能网络，以帮助理解治疗设计，以优化TMS治疗。

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.