Tensor-Based Adaptive Deconvolution for Multi-Shell Diffusion MRI

• Applicant: Professor Dr.-Ing. Thomas Schultz
• Subject Area: Image and Language Processing, Computer Graphics and Visualisation, Human Computer Interaction, Ubiquitous and Wearable Computing
• Term: from 2015 to 2018
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 273590161

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.

• DFG Programme: Research Grants
• International Connection: USA
• Cooperation Partners: Professor Dr. Samuel Gröschel; Professor Lek-Heng Lim, Ph.D.