Towards quantitative brain connectomics: microstructure informed tractography via convex optimization

Tractography is the only non-invasive technique which is used to reconstruct the white mat- ter structural connectivity of the human brain. It relies on a specific Magnetic Resonance Imaging (MRI) acquisition, called diffusion MRI, which is sensitive to the displacement of water protons to varying magnetic fields, generating a signal that can be used to indirectly estimate microscopic tissue characteristics, e.g., composition and geometry. More specifically, tractography relies on two essential aspects: 1) orientations which indicates the direction of the white matter fibers in a typical 3D grid, and 2) principles of how to connect the voxels to reconstruct the white matter connections. Tractography is a relatively young technique since it was proposed only twenty years ago; however, it is already used in specific clinical applica- tions, e.g., partially in neurosurgery, and in research studies that involve reconstructions of well-known neuronal pathways. Hundreds of different tractography techniques have been proposed in the past years. In order to evaluate their performance, we participated in several international challenges. The outcomes of the challenges showed the advantages and limitations of modern tractography methods. In particular, one issue that was highlighted is the lack of a gold standard. Diffusion MRI tractography typically is validated with postmortem material and a tedious concatenation of classical 2D histological slices. In this thesis, we propose one of the first studies that use a novel 3D histological technique, named CLARITY, to validate fiber orientation in a large portion of tissue. At the typical spatial resolution of MRI, approximately 60-90% of voxels in the white matter contain multiple fiber populations. However, most of the microstructure imaging techniques proposed are not suitable to disentangle multiple populations in a voxel. In this thesis, we aimed to study the limitations of modern tractography approaches, and we proposed novel methods where tractography could play a crucial role. We propose to use microstructure informed tractography to regularize two important microstructural features, i.e., axon diameter and transversal relaxation time T2, showing the clear advantages of the use of global approaches and opening a new perspective for connectivity analysis. However, the price to pay for increasing the complexity of existing models is an increase in computational burden. In the appendix of the thesis, we propose a preliminary study which uses neural network approaches to accelerate global fitting of complex models