Mapping structural brain connectomes for living human brains typically requires expert analysis and rule-based models on diffusion-weighted magnetic resonance imaging. A data-driven approach, however, could overcome limitations in such rule-based approaches and improve precision mappings for individuals. In this work, we explore a framework that facilitates applying learning algorithms to automatically extract brain connectomes. Using a tensor encoding, we design an objective with a group-regularizer that prefers biologically plausible fascicle structure. We show that the objective is convex and has unique solutions, ensuring identifiable connectomes for an individual. We develop an efficient optimization strategy for this extremely high-dimensional sparse problem, by reducing the number of parameters using a greedy algorithm designed specifically for the problem. We show that this greedy algorithm significantly improves on a standard greedy algorithm, called Orthogonal Matching Pursuit. We conclude with an analysis of the solutions found by our method, showing we can accurately reconstruct the diffusion information while maintaining contiguous fascicles with smooth direction changes.

In this paper, we combine high-performance computing science with computational neuroscience methods to show how to speed-up cutting-edge methods for mapping and evaluation of the large-scale network of brain connections. More specifically, we use a recent factorization method of the Linear Fascicle Evaluation model (i.e., LiFE [1], [2]) that allows for statistical evaluation of brain connectomes. The method called ENCODE [3], [4] uses a Sparse Tucker Decomposition approach to represent the LiFE model. We show that we can implement the optimization step of the ENCODE method using MPI and OpenMP programming paradigms. Our approach involves the parallelization of the multiplication step of the ENCODE method. We model our design theoretically and demonstrate empirically that the design can be used to identify optimal configurations for the LiFE model optimization via ENCODE method on different hardware platforms. In addition, we co-design the MPI runtime with the LiFE model to achieve profound speed-ups. Extensive evaluation of our designs on multiple clusters corroborates our theoretical model. We show that on a single node on TACC Stampede2, we can achieve speed-ups of up to 8.7x as compared to the original approach.

Recently, linear formulations and convex optimization methods have been proposed to predict diffusion-weighted Magnetic Resonance Imaging (dMRI) data given estimates of brain connections generated using tractography algorithms. The size of the linear models comprising such methods grows with both dMRI data and connectome resolution, and can become very large when applied to modern data. In this paper, we introduce a method to encode dMRI signals and large connectomes, i.e., those that range from hundreds of thousands to millions of fascicles (bundles of neuronal axons), by using a sparse tensor decomposition. We show that this tensor decomposition accurately approximates the Linear Fascicle Evaluation (LiFE) model, one of the recently developed linear models. We provide a theoretical analysis of the accuracy of the sparse decomposed model, LiFESD, and demonstrate that it can reduce the size of the model significantly. Also, we develop algorithms to implement the optimisation solver using the tensor representation in an efficient way.

Tractography uses diffusion MRI to estimate the trajectory and cortical projection zones of white matter fascicles in the living human brain. There are many different tractography algorithms and each requires the user to set several parameters, such as curvature threshold. Choosing a single algorithm with specific parameters poses two challenges. First, different algorithms and parameter values produce different results. Second, the optimal choice of algorithm and parameter value may differ between different white matter regions or different fascicles, subjects, and acquisition parameters. We propose using ensemble methods to reduce algorithm and parameter dependencies. To do so we separate the processes of fascicle generation and evaluation. Specifically, we analyze the value of creating optimized connectomes by systematically combining candidate streamlines from an ensemble of algorithms (deterministic and probabilistic) and systematically varying parameters (curvature and stopping criterion). The ensemble approach leads to optimized connectomes that provide better cross-validated prediction error of the diffusion MRI data than optimized connectomes generated using a single-algorithm or parameter set. Furthermore, the ensemble approach produces connectomes that contain both short- and long-range fascicles, whereas single-parameter connectomes are biased towards one or the other. In summary, a systematic ensemble tractography approach can produce connectomes that are superior to standard single parameter estimates both for predicting the diffusion measurements and estimating white matter fascicles.