Tensor-Based Adaptive Deconvolution for Multi-Shell Diffusion MRI

扩散加权磁共振成像(DMRI)广泛应用于神经科学和临床的无创性人脑研究。最近，获取多层扩散磁共振数据变得很常见，这涉及到多个级别的扩散加权。我们提出了一个研究议程，它将导致一个数学上有充分基础和有效的框架，从这些数据中得出新的定量参数。这些参数可以根据组织的微观结构来解释，甚至在神经纤维交叉或扩散的区域也是如此。计划的科学贡献有三个：我们的第一个目标是将现有的模型扩展到更复杂的多壳数据，该模型用高阶张量的数学语言来表示单壳扩散磁共振数据的反卷积。我们将与应用数学的合作伙伴密切合作，以确保这种方法在形式上是正确的。我们还期望这种方法将导致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具有更强的鲁棒性。第二个目标涉及反卷积核，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去卷积方法，允许内核在空间上变化。在与一位临床合作伙伴的合作中，我们发现，在存在神经退行性疾病的情况下，调整内核在受疾病影响的区域是必不可少的。我们将大大扩展这一框架，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稳健性，并允许在多壳情况下增加核参数的数量。由此产生的方法将允许在体素内任意分布神经纤维方向。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种测量方案，允许在所需测量时间方面以最低要求可靠地估计我们的模型。我们的目标是一种扫描时间不到15分钟的全脑分析方案，这将使我们的方法不仅适用于神经科学领域，甚至适用于临床。为了实现这一点，我们将利用最近关于在扩散磁共振成像中使用压缩传感的工作。

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.