Spatiotemporal models of brain electrophysiology

现代的二维(2D)多电极阵列可以同时记录大量神经元的细胞外活动，并已被用于收集来自视觉皮质、假体运动皮质以及一维(1D)硅探针等的数据。这项工作的大部分工作使用阵列通过关注相关的尖峰频率来提取单个神经元的动作电位。因此，许多数据特征被有效地浪费。该项目的目标是(I)使用先进的数学方法从2D多电极阵列(以及源重建的脑电数据)中提取新的信息，以及(Ii)开发新的神经元质量模型来模拟空间扩展的神经活动。目前，确定电流源和电流汇分布的方法是所谓的电流源-密度(CSD)法。这种方法没有提供相关来源的任何详细的空间特征。该项目的第一个目标是开发从局部场势估计电流源密度的新方法，该方法将详细考虑电流源和汇的空间分布。在更大的空间尺度上，目前的神经质量模型虽然相当成功，但没有考虑神经组织中电流源和电流汇的空间分布。该项目的第二个目标是通过使用偏微分方程组(PDE)将电流通量建模为大脑皮层上的连续过程，来构建LFP和EEG数据的广义动态因果模型。此外，我们将使用它们的模型证据(针对不同类型的经验数据)来评估这些模型相对于它们的ODE同源物的改进。这样的努力将对管理皮质活动的空间参数的估计产生重要影响，例如大脑内在联系的空间范围。

Modern two-dimensional (2D) multi-electrode arrays allow for the simultaneous recording of extracellular activity from a large number of neurons and have been used to collect data among others from the visual cortex, the motor cortex for prosthetics, along with one dimensional (1D) silicon probes etc. Most of this work uses arrays to extract the action potentials of single neurons by focusing on the relevant spike rates. Thus, many data-features are effectively wasted.The goals of this project are (i) to use advanced mathematical methods to extract new information from 2D multi-electrode arrays (and sources reconstructed EEG data) and (ii) to develop novel neural mass models which model spatially extended neural activity. At present, the determination of the distribution of current sources and sinks is carried out using the so-called Current Source-Density (CSD) method. This method does not provide any detailed spatial characterisation of the relevant sources. The first aim of this project is to develop new methods for the estimation of the current source density from local field potentials, which will take into detailed consideration the spatial distribution of the current sources and sinks. At a larger spatial scale, current neural mass models, although quite successful, do not consider the spatial distribution of current sources and sinks in the neural tissue. The second aim of this project is to construct generalised dynamic causal models of LFP and EEG data by modelling current fluxes as continuous processes on the cortical sheet using partial differential equations (PDE). Furthermore, we will evaluate the improvement in these models, over their ODE homologues, using their model evidence (for different sorts of empirical data). Such an endeavour will have important implications regarding the estimation of spatial parameters that govern cortical activity, such as the spatial extent of intrinsic connections in the brain.