A fractional order-based mixture of central Wishart (FMoCW) model for reconstructing white matter fibers from diffusion MRI.

This paper introduces an algorithm for reconstructing the brain's white matter fibers (WMFs). In particular, a fractional order mixture of central Wishart (FMoCW) model is proposed to reconstruct the WMFs from diffusion MRI data. The pseudo super diffusive modality of anomalous diffusion is coupled with the mixture of central Wishart (MoCW) model to derive the proposed model. We have shown results on multiple synthetic simulations, including fibers orientations in 2 and 3 directions per voxel and experiments on real datasets of rat optic chiasm and a healthy human brain. In synthetic simulations, a varying Rician distributed noise levels, σ=0.01-0.09 is also considered. The proposed model can efficiently distinguish multiple fibers even when the angle of separation between fibers is very small. This model outperformed, giving the least angular error when compared to fractional mixture of Gaussian (MoG), MoCW and mixture of non-central Wishart (MoNCW) models.

A generalized order mixture model for tracing connectivity of white matter fascicles complexity in brain from diffusion MRI.

This paper focuses on tracing the connectivity of white matter fascicles in the brain. In particular, a generalized order algorithm based on mixture of non-central Wishart distribution model is proposed for this purpose. The proposed algorithm utilizes the generalization of integer order based approach with the mixture of non-central Wishart distribution model. Pseudo super anomalous behavior of water diffusion inside human brain is the prime motivation of the the present study. We have shown results on multiple synthetic simulations with fibers orientations in two and three directions in each voxel as well as experiments on real data. Synthetic simulations were performed with varying noise levels and diffusion weighting gradient i.e. $b-$values. The proposed model performed outstanding especially for distinguishing closely oriented fibers.

An iterative algorithm for computing gradient directions for white matter fascicles detection in brain MRI.

This paper proposes a new iterative algorithm for computing gradient directions (GD) to reconstruct the brain's white matter fascicles. In particular, the proposed algorithm extensively overcomes the limitations of existing approaches like Uniform Gradient Directions and Adaptive Gradient Directions (AGD) for this task. The proposed algorithm uses the AGD approach to have a coarse estimation of the fibers in the initial step, and then a refinement is done using an iterative strategy. We begin with GD distributed uniformly inside a grid of bigger size and larger spacing between the points. Both (grid size and spacing between the points) reduce iteratively. The proposed algorithm has higher chance of capturing the fibers' actual position within the grid at each iteration. Hence, the solution tends to the actual position of fiber in each iteration, leading to a better estimation of fiber orientations. Multiple artificial simulations and real dataset experiments on the human brain and optic chiasm of a rat's brain are performed. The excellent performance of the proposed algorithm at different noises ensures stability and robustness. Hence, after processing the MRI data, the proposed algorithm can accurately reflect the ground truth of white matter fascicles connections in reconstructed images. The proposed algorithm helps resolve the structural complexities of the brain caused due to presence of crossing fascicles to a great extent.

An OMP-TV2 algorithm for detecting white matter fiber crossings in brain MRI.

This paper introduces a novel algorithm for solving non-Gaussian mixture models of diffusion tensor imaging (DTI). In particular, these models are used for detecting the orientations of white matter fibers in brain. In our approach, any DT-MRI model (mathematically) is represented by an under-determined system of linear equations. The proposed algorithm uses an orthogonal matching pursuit (OMP) method coupled with Tikhonov regularization for solving such an under-determined system effectively, which results in better reconstruction of the fibers orientation. These linear systems depend on the number of the gradient directions used for generating the signals and for reconstruction process. OMP is a greedy iterative algorithm that picks the column of coefficient matrix that has the maximum correlation or projection on the residual at each stage. Using OMP with Tikhonov regularization shows tremendous reduction in the angular error when compared with an existing scheme where non-negative least square method (NNLS) is used. The proposed work is validated with both artificial simulations as well as real data experiments. The reduction in angular error is more pronounced when the angle of separation between the fibers is small.

An enhanced multi-fiber reconstruction technique using adaptive gradient directions coupled with MoNCW model in diffusion MRI.

In this paper, we introduced a novel approach for generating unit gradient vectors named as adaptive gradient directions (AGD) for reconstructing single and decussating (crossing or kissing) white matter fibers in brain. The present study is focusing on reconstruction process of brain's white matter fibers but not dealing with data acquisition where scanning is performed. The gradient vectors used in the state-of-art methodologies for reconstruction are uniformly distributed vectors on a unit sphere but AGD, in contrary, are non-uniformly distributed points on a unit sphere. These points are uniformly distributed in some pattern on the surface of a unit sphere. For reconstruction, we have coupled the proposed AGD approach with mixture of non-central Wishart (MoNCW) model. We uphold the proposed approach with different simulations including synthetic as well as real data experiments. Resistivity to different Rician noise levels (σ=0.02-0.1) is demonstrated in simulated data for single as well as two and three decussating fibers. Our approach of using AGD dissipates the limitations that are encountered by the state-of-art technique of uniformly distributed points over the surface of unit sphere and outperforms showing significant reduction in angular errors.