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

这个项目的主要焦点是利用扩散张量成像(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，它捕捉水分子在组织中的扩散。神经对这一扩散过程的阻碍使白质结构的表征和对白质完整性的定量描述得以测量。DTI已经发现了许多疾病的白质改变，包括阿尔茨海默病、帕金森氏病、精神分裂症、艾滋病毒感染的神经系统并发症、自闭症、多发性硬化症等。DTI产生疾病进展的成像生物标志物的潜力为制药行业的药物发现和开发应用打开了大门。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数据采用复数值的形式，但目前对这类数据的分析实践涉及将复数值数据天真地转换为实值数据集。这一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，复值数据的幅度和相位都应该建模和使用。一旦复值数据得到适当的处理，估计可能会有很大的改善。通过开发更好的估计程序，可能会减少需要在治疗组之间找到统计上显著变化的受试者数量。开发更强大的具有更好灵敏度和特异度的估算器的推断程序可能有助于，例如，使用DTI数据早期识别萎缩的减少，并用于疾病进展的常规特征。现代信号处理方法也将在两个不同的层次上使用，即局部地在给定位置(体素)，以及区域地估计跨位置的结构。在局部上，多尺度方法的使用将能够在没有方向偏好方面人为限制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、接吻和/或分叉，这必须被合并到模型中。在区域上，将开发方法来描述在大脑中观察到的结构特征，例如通过设计纤维词典，即结合了脑纤维和神经的特征的局部分解。这些分解可以用于估计高度特定的特征的存在，并且即使在非常低的信噪比下也能够进行良好的估计。此外，由于结构特征在这个框架中自然地被表示，所以在纵向测量中测试潜在的结构退化是直接的，特别是与理解表现出退化的疾病(如阿尔茨海默病)的发展相关。然后，所提出的方法是研究计划的顶峰，从对给定方向上的DTI测量的幅度和相位进行建模的基本问题开始，为幅度和相位建立相干的可能性，在允许复杂的纤维结构的同时对局部结构进行建模，最后产生跨体素的整个大脑结构的模型，其中后者可以用于回答人类的地貌问题。完整的方法工具包代表了信号处理、统计学和核磁共振技术的最新发展的综合，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.