Probabilistic tractography using Lasso bootstrap

Tracking and validation techniques for topographically organized tractography

Topographic regularity of axonal connections is commonly understood as the preservation of spatial relationships between nearby neurons and is a fundamental structural property of the brain. In particular the retinotopic mapping of the visual pathway can even be quantitatively computed. Inspired from this previously untapped anatomical knowledge, we propose a novel tractography method that preserves both topographic and geometric regularity. We make use of parameterized curves with Frenet-Serret frame and introduce a highly flexible mechanism for controlling geometric regularity. At the same time, we incorporate a novel local data support term in order to account for topographic organization. Unifying geometry with topographic regularity, we develop a Bayesian framework for generating highly organized streamlines that accurately follow neuroanatomy. We additionally propose two novel validation techniques to quantify topographic regularity. In our experiments, we studied the results of our approach with respect to connectivity, reproducibility and topographic regularity aspects. We present both qualitative and quantitative comparisons of our technique against three algorithms from MRtrix3. We show that our method successfully generates highly organized fiber tracks while capturing bundle anatomy that are geometrically challenging for other approaches.

Joint spatial-angular sparse coding for dMRI with separable dictionaries

Diffusion MRI (dMRI) provides the ability to reconstruct neuronal fibers in the brain, in vivo, by measuring water diffusion along angular gradient directions in q-space. High angular resolution diffusion imaging (HARDI) can produce better estimates of fiber orientation than the popularly used diffusion tensor imaging, but the high number of samples needed to estimate diffusivity requires longer patient scan times. To accelerate dMRI, compressed sensing (CS) has been utilized by exploiting a sparse dictionary representation of the data, discovered through sparse coding. The sparser the representation, the fewer samples are needed to reconstruct a high resolution signal with limited information loss, and so an important area of research has focused on finding the sparsest possible representation of dMRI. Current reconstruction methods however, rely on an angular representation per voxel with added spatial regularization, and so, for non-zero signals, one is required to have at least one non-zero coefficient per voxel. This means that the global level of sparsity must be greater than the number of voxels. In contrast, we propose a joint spatial-angular representation of dMRI that will allow us to achieve levels of global sparsity that are below the number of voxels. A major challenge, however, is the computational complexity of solving a global sparse coding problem over large-scale dMRI. In this work, we present novel adaptations of popular sparse coding algorithms that become better suited for solving large-scale problems by exploiting spatial-angular separability. Our experiments show that our method achieves significantly sparser representations of HARDI than is possible by the state of the art.

Dictionary-based fiber orientation estimation with improved spatial consistency

Diffusion magnetic resonance imaging (dMRI) has enabled in vivo investigation of white matter tracts. Fiber orientation (FO) estimation is a key step in tract reconstruction and has been a popular research topic in dMRI analysis. In particular, the sparsity assumption has been used in conjunction with a dictionary-based framework to achieve reliable FO estimation with a reduced number of gradient directions. Because image noise can have a deleterious effect on the accuracy of FO estimation, previous works have incorporated spatial consistency of FOs in the dictionary-based framework to improve the estimation. However, because FOs are only indirectly determined from the mixture fractions of dictionary atoms and not modeled as variables in the objective function, these methods do not incorporate FO smoothness directly, and their ability to produce smooth FOs could be limited. In this work, we propose an improvement to Fiber Orientation Reconstruction using Neighborhood Information (FORNI), which we call FORNI+; this method estimates FOs in a dictionary-based framework where FO smoothness is better enforced than in FORNI alone. We describe an objective function that explicitly models the actual FOs and the mixture fractions of dictionary atoms. Specifically, it consists of data fidelity between the observed signals and the signals represented by the dictionary, pairwise FO dissimilarity that encourages FO smoothness, and weighted ℓ1-norm terms that ensure the consistency between the actual FOs and the FO configuration suggested by the dictionary representation. The FOs and mixture fractions are then jointly estimated by minimizing the objective function using an iterative alternating optimization strategy. FORNI+ was evaluated on a simulation phantom, a physical phantom, and real brain dMRI data. In particular, in the real brain dMRI experiment, we have qualitatively and quantitatively evaluated the reproducibility of the proposed method. Results demonstrate that FORNI+ produces FOs with better quality compared with competing methods.