Modelling Complex-Valued Diffusion Tensor Imaging Data and Efficient Methods for Inference

该项目的主要重点是使用扩散张量成像（DTI）测量对大脑结构进行建模和分析。DTI是一种基于磁共振成像（MRI）技术的体内医学成像技术，可捕获水分子在组织中的扩散。神经对该扩散过程的阻碍使得能够表征白色物质结构和测量白色物质完整性的定量描述。DTI已经确定了白色物质改变的大量条件，包括阿尔茨海默氏病，帕金森氏病，精神分裂症，神经系统并发症的艾滋病毒感染，自闭症，多发性硬化症等DTI的潜力，以产生成像生物标志物的疾病进展打开了大门，在制药行业的应用，药物发现和开发。DTI是最重要的新技术之一，它将帮助我们提高对大脑复杂结构的理解。DTI数据采用复值量的形式，但目前分析这种数据的实践涉及简单地将复值数据转换为实值数据集。这个过程在分析非常嘈杂的数据集时尤其有害，并且可能产生非常差的分析方法。为了改进估计，应该对复值数据的幅度和相位进行建模和使用。一旦复值数据得到适当处理，估计可能会得到很大的改进。通过开发更好的估计程序，可以减少发现治疗组之间统计学显著变化所需的受试者数量。开发更强大的推理程序，具有更好的灵敏度和特异性的估计，可以帮助，例如，在早期识别减少萎缩使用DTI数据，并用于常规表征疾病进展。现代信号处理方法也将在两个不同的层面上使用，即在给定位置（体素）的局部，以及区域性地估计跨位置的结构。在本地，多尺度方法的使用将使得能够在方向偏好方面没有人为约束的情况下对扩散进行建模：在观察到的数据中，脑纤维可能在给定的体素处交叉、接触和/或分叉，并且这必须被结合到模型中。将开发区域性方法来描述在脑中观察到的结构特征，例如通过设计纤维字典，即结合了脑纤维和神经特征的局部分解。这些分解可用于估计高度特异性特征的存在，并且即使在非常低的信噪比下也能够实现良好的估计。此外，由于结构特征在该框架中被自然地表示，因此可以直接测试纵向测量中的潜在结构退化，特别是与理解表现出退化的疾病（例如阿尔茨海默氏症）的发展相关。然后，所提出的方法是研究计划的高潮，从对给定方向上的DTI测量的幅度和相位建模的基本问题开始，建立幅度和相位的相干似然性，对局部结构进行建模，同时允许复杂的纤维结构，并最终产生跨体素的整个大脑结构的模型，其中后者可用于回答人类外貌的问题。完整的工具包方法代表了信号处理，统计学和MRI的最新发展的综合，并将有助于回答人类疾病进展的重要生理问题。

The main focus of this project is the modelling and analysis of brain structure using Diffusion Tensor Imaging (DTI) measurements. DTI is an in vivo medical imaging technique, based on Magnetic Resonance Imaging (MRI) technology, that captures the diffusion of water molecules in tissue. The impediment of this diffusion process by nerves enables the characterisation of white matter structure and the measurement of quantitative descriptions of white matter integrity. DTI has identified white matter alterations for a large number of conditions including Alzheimer's disease, Parkinson's disease, schizophrenia, neurological complications of HIV infection, autism, multiple sclerosis etc. The potential of DTI to generate imaging biomarkers for disease progression opens the door to applications in the pharmaceutical industry for drug discovery and development. DTI stands as one of the most important new technologies that will help us to improve our understanding of the complex structure of the brain. DTI data takes the form of a complex-valued quantity but current practice in the analysis of such data involves naively converting the complex-valued data into a real-valued data set. This procedure is especially detrimental in the analysis of very noisy data sets, and may yield very poor analysis methods. To improve estimation both the amplitude and phase of the complex-valued data should be modelled and used. Once the complex-valued data is treated appropriately, estimation may be very much improved upon.By developing better estimation procedures the number of subjects required to find statistically significant changes between treatment groups, may be reduced. The development of more powerful inferential procedures with estimators that have better sensitivity and specificity may aid, for example, in the early identification of a reduction in atrophy using DTI data, and be utilised for routine characterisation of disease progression. Modern signal processing methods will also be used at two different levels, namely locally at a given location (voxel), and regionally to estimate structure across locations. Locally, the usage of multiscale methods will enable modelling the diffusion without artificial constraints in terms directional preference: in observed data brain fibres may cross, kiss and/or fork at a given voxel, and this must be incorporated in the model.Regionally methods will be developed to characterise structural features observed in the brain, for instance by designing fibre dictionaries, i.e. local decompositions that incorporate the characteristics of brain fibres and nerves. These decompositions can be used to estimate the presence of highly specific features, and enable good estimation even at very low signal to noise ratios. Furthermore as structural features are naturally represented in this framework, it is straightforward to test for potential structural degradation in longitudinal measurements, especially relevant for understanding the development of diseases exhibiting degradation such as Alzheimer's.The proposed methods are then the culmination of a research programme, starting from the basic problem of modelling the amplitude and phase of the DTI measurement in a given direction, building a coherent likelihood for the amplitude and phase, modelling the local structure whilst allowing for complicated fibre structure, and finally producing a model for the entire brain structure across voxels, where the latter can be used to answer questions of human physiognomy. The full tool-kit of methods represents a synthesis of state of the art developments in signal processing, statistics and MRI, and will help answer important physiological question of human disease progression.