Tensor-Based Adaptive Deconvolution for Multi-Shell Diffusion MRI

弥散加权磁共振成像（dMRI）被广泛用于人类大脑的非侵入性研究，无论是在神经科学还是在临床上。最近，采集多壳层扩散MR数据已经变得很常见，这涉及多级扩散加权。我们提出了一个研究议程，这将导致数学上有充分依据的和有效的框架，从这些数据中获得新的定量参数。这些参数可以解释在组织的微观结构，甚至在区域的神经纤维交叉或spread.The计划的科学贡献是三个方面：我们的第一个目标是扩展现有的模型，表示反卷积的单壳扩散MR数据的数学语言的高阶张量，更复杂的多壳数据。我们将与应用数学的合作伙伴密切合作，以确保这种方法的形式适定性。我们还希望这种方法能够对反卷积本身进行更严格的正则化，这将使其对测量噪声和误差更加鲁棒。第二个目标涉及反卷积内核，这是所有反卷积模型的重要校准参数，通常假设在整个大脑中是恒定的。我们最近提出了一种自适应反卷积方法，允许内核在空间上变化。在与临床合作伙伴的合作中，我们发现，在神经退行性疾病的存在下，适应内核在受疾病影响的区域是必不可少的。我们将显着扩展这个框架，以利用在第一部分中开发的基于张量的反卷积，通过包括空间正则化来增加鲁棒性，并允许在多壳层情况下增加核参数的数量。所得到的方法将允许在体素内神经纤维方向的任意分布。同时，它将产生新的组织微观结构的定量测量，有助于更详细地了解疾病或与学习相关的变化。最后，我们的第三个目标是建立一个测量协议，该协议将允许在所需测量时间方面的最低要求对我们的模型进行可靠的估计。我们的目标是一个协议，需要不到15分钟的扫描时间进行全脑分析，这将使我们的方法不仅适用于神经科学中的应用，甚至临床。为了实现这一点，我们将利用最近的作品在扩散MRI中使用压缩传感。

Diffusion weighted Magnetic Resonance Imaging (dMRI) is widely used for noninvasive investigation of the human brain, both in neuroscience and in the clinic. Recently, it has become common to acquire multi-shell diffusion MR data, which involves multiple levels of diffusion weighting. We propose a research agenda that will lead to a mathematically well-founded and efficient framework for deriving novel quantitative parameters from such data. These parameters can be interpreted in terms of the tissue microstructure, even in regions of nerve fiber crossings or spread.The planned scientific contribution is threefold: Our first goal is to extend an existing model, which expresses the deconvolution of single-shell diffusion MR data in the mathematical language of higher-order tensors, to the more complex multi-shell data. We will closely collaborate with a partner from applied mathematics to ensure formal well-posedness of this approach. We also expect this approach to lead to a more stringent regularization of the deconvolution itself, which will make it more robust against measurement noise and errors.The second goal addresses the deconvolution kernel, which is an important calibration parameter of all deconvolution models, and commonly assumed to be constant throughout the brain. We have recently proposed an adaptive deconvolution approach that allows the kernel to vary spatially. In collaboration with a clinical partner, we have found that, in the presence of neurodegenerative disease, adapting the kernel is essential in regions affected by the disease. We will significantly extend this framework to make use of the tensor-based deconvolution developed in the first part, to increase robustness by including spatial regularization, and to allow for the increased number of kernel parameters in the multi-shell case. The resulting method will allow for an arbitrary distribution of nerve fiber directions within a voxel. At the same time, it will yield novel quantitative measures of tissue microstructure that can contribute to a more detailed understanding of disease or changes associated with learning.Finally, it is our third goal to establish a measurement protocol that will allow reliable estimation of our model with minimum requirements in terms of the required measurement time. We aim for a protocol that requires less than 15~minutes of scan time for a full-brain analysis, which would make our method suitable not just for applications within neuroscience, but even clinically. To achieve this, we will exploit recent works on the use of compressive sensing in diffusion MRI.