Extremely efficient and deterministic approach to generating optimal ordering of diffusion MRI measurements

Optimizing Diffusion Imaging Protocols for Structural Connectomics in Mouse Models of Neurological Conditions

Network approaches provide sensitive biomarkers for neurological conditions, such as Alzheimer's disease (AD). Mouse models can help advance our understanding of underlying pathologies, by dissecting vulnerable circuits. While the mouse brain contains less white matter compared to the human brain, axonal diameters compare relatively well (e.g., ~0.6 μm in the mouse and ~0.65-1.05 μm in the human corpus callosum). This makes the mouse an attractive test bed for novel diffusion models and imaging protocols. Remaining questions on the accuracy and uncertainty of connectomes have prompted us to evaluate diffusion imaging protocols with various spatial and angular resolutions. We have derived structural connectomes by extracting gradient subsets from a high-spatial, high-angular resolution diffusion acquisition (120 directions, 43-μm-size voxels). We have simulated protocols with 12, 15, 20, 30, 45, 60, 80, 100, and 120 angles and at 43, 86, or 172-μm voxel sizes. The rotational stability of these schemes increased with angular resolution. The minimum condition number was achieved for 120 directions, followed by 60 and 45 directions. The percentage of voxels containing one dyad was exceeded by those with two dyads after 45 directions, and for the highest spatial resolution protocols. For the 86- or 172-μm resolutions, these ratios converged toward 55% for one and 39% for two dyads, respectively, with <7% from voxels with three dyads. Tractography errors, estimated through dyad dispersion, decreased most with angular resolution. Spatial resolution effects became noticeable at 172 μm. Smaller tracts, e.g., the fornix, were affected more than larger ones, e.g., the fimbria. We observed an inflection point for 45 directions, and an asymptotic behavior after 60 directions, corresponding to similar projection density maps. Spatially downsampling to 86 μm, while maintaining the angular resolution, achieved a subgraph similarity of 96% relative to the reference. Using 60 directions with 86- or 172-μm voxels resulted in 94% similarity. Node similarity metrics indicated that major white matter tracts were more robust to downsampling relative to cortical regions. Our study provides guidelines for new protocols in mouse models of neurological conditions, so as to achieve similar connectomes, while increasing efficiency.

Tract Orientation and Angular Dispersion Deviation Indicator (TOADDI): A framework for single-subject analysis in diffusion tensor imaging

The purpose of this work is to develop a framework for single-subject analysis of diffusion tensor imaging (DTI) data. This framework is termed Tract Orientation and Angular Dispersion Deviation Indicator (TOADDI) because it is capable of testing whether an individual tract as represented by the major eigenvector of the diffusion tensor and its corresponding angular dispersion are significantly different from a group of tracts on a voxel-by-voxel basis. This work develops two complementary statistical tests based on the elliptical cone of uncertainty, which is a model of uncertainty or dispersion of the major eigenvector of the diffusion tensor. The orientation deviation test examines whether the major eigenvector from a single subject is within the average elliptical cone of uncertainty formed by a collection of elliptical cones of uncertainty. The shape deviation test is based on the two-tailed Wilcoxon-Mann-Whitney two-sample test between the normalized shape measures (area and circumference) of the elliptical cones of uncertainty of the single subject against a group of controls. The False Discovery Rate (FDR) and False Non-discovery Rate (FNR) were incorporated in the orientation deviation test. The shape deviation test uses FDR only. TOADDI was found to be numerically accurate and statistically effective. Clinical data from two Traumatic Brain Injury (TBI) patients and one non-TBI subject were tested against the data obtained from a group of 45 non-TBI controls to illustrate the application of the proposed framework in single-subject analysis. The frontal portion of the superior longitudinal fasciculus seemed to be implicated in both tests (orientation and shape) as significantly different from that of the control group. The TBI patients and the single non-TBI subject were well separated under the shape deviation test at the chosen FDR level of 0.0005. TOADDI is a simple but novel geometrically based statistical framework for analyzing DTI data. TOADDI may be found useful in single-subject, graph-theoretic and group analyses of DTI data or DTI-based tractography techniques.

Pseudometrically constrained centroidal voronoi tessellations: Generating uniform antipodally symmetric points on the unit sphere with a novel acceleration strategy and its applications to diffusion and three-dimensional radial MRI

PURPOSE

The purpose of this work is to investigate the hypothesis that uniform sampling measurements that are endowed with antipodal symmetry play an important role in image quality when the raw data and image data are related through the Fourier relationship. Currently, it is extremely challenging to generate large and uniform antipodally symmetric point sets suitable for three-dimensional radial MRI. A novel approach is proposed to solve this long-standing problem in a unique and optimal way.

METHODS

The proposed method is based on constrained centroidal Voronoi tessellations of the upper hemisphere with a novel pseudometric.

RESULTS

The time complexity of the proposed tessellations was shown to be effectively linear, i.e., on the order of the number of sampling measurements. For small sample size, the proposed method was comparable with the state-of-the-art method (a direct iterative minimization of the electrostatic potential energy of a collection of electrons antipodal-symmetrically distributed on the unit sphere) in terms of the sampling uniformity. For large sample size, in which the state-of-the-art method is infeasible, the reconstructed images from the proposed method has less streak and ringing artifacts, when compared with those of the commonly used methods.

CONCLUSION

This work proposed a unique and optimal approach to solving a long-standing problem in generating uniform sampling points for three-dimensional radial MRI.

A Diffusion MRI Tractography Connectome of the Mouse Brain and Comparison with Neuronal Tracer Data

Interest in structural brain connectivity has grown with the understanding that abnormal neural connections may play a role in neurologic and psychiatric diseases. Small animal connectivity mapping techniques are particularly important for identifying aberrant connectivity in disease models. Diffusion magnetic resonance imaging tractography can provide nondestructive, 3D, brain-wide connectivity maps, but has historically been limited by low spatial resolution, low signal-to-noise ratio, and the difficulty in estimating multiple fiber orientations within a single image voxel. Small animal diffusion tractography can be substantially improved through the combination of ex vivo MRI with exogenous contrast agents, advanced diffusion acquisition and reconstruction techniques, and probabilistic fiber tracking. Here, we present a comprehensive, probabilistic tractography connectome of the mouse brain at microscopic resolution, and a comparison of these data with a neuronal tracer-based connectivity data from the Allen Brain Atlas. This work serves as a reference database for future tractography studies in the mouse brain, and demonstrates the fundamental differences between tractography and neuronal tracer data.

Sparse and optimal acquisition design for diffusion MRI and beyond

PURPOSE

Diffusion magnetic resonance imaging (MRI) in combination with functional MRI promises a whole new vista for scientists to investigate noninvasively the structural and functional connectivity of the human brain-the human connectome, which had heretofore been out of reach. As with other imaging modalities, diffusion MRI data are inherently noisy and its acquisition time-consuming. Further, a faithful representation of the human connectome that can serve as a predictive model requires a robust and accurate data-analytic pipeline. The focus of this paper is on one of the key segments of this pipeline-in particular, the development of a sparse and optimal acquisition (SOA) design for diffusion MRI multiple-shell acquisition and beyond.

METHODS

The authors propose a novel optimality criterion for sparse multiple-shell acquisition and quasimultiple-shell designs in diffusion MRI and a novel and effective semistochastic and moderately greedy combinatorial search strategy with simulated annealing to locate the optimum design or configuration. The goal of the optimality criteria is threefold: first, to maximize uniformity of the diffusion measurements in each shell, which is equivalent to maximal incoherence in angular measurements; second, to maximize coverage of the diffusion measurements around each radial line to achieve maximal incoherence in radial measurements for multiple-shell acquisition; and finally, to ensure maximum uniformity of diffusion measurement directions in the limiting case when all the shells are coincidental as in the case of a single-shell acquisition. The approach taken in evaluating the stability of various acquisition designs is based on the condition number and the A-optimal measure of the design matrix.

RESULTS

Even though the number of distinct configurations for a given set of diffusion gradient directions is very large in general-e.g., in the order of 10(232) for a set of 144 diffusion gradient directions, the proposed search strategy was found to be effective in finding the optimum configuration. It was found that the square design is the most robust (i.e., with stable condition numbers and A-optimal measures under varying experimental conditions) among many other possible designs of the same sample size. Under the same performance evaluation, the square design was found to be more robust than the widely used sampling schemes similar to that of 3D radial MRI and of diffusion spectrum imaging (DSI).

CONCLUSIONS

A novel optimality criterion for sparse multiple-shell acquisition and quasimultiple-shell designs in diffusion MRI and an effective search strategy for finding the best configuration have been developed. The results are very promising, interesting, and practical for diffusion MRI acquisitions.

A simple scheme for generating nearly uniform distribution of antipodally symmetric points on the unit sphere

A variant of the Thomson problem, which is about placing a set of points uniformly on the surface of a sphere, is that of generating uniformly distributed points on the sphere that are endowed with antipodal symmetry, i.e., if x is an element of the point set then -x is also an element of that point set. Point sets with antipodal symmetry are of special importance to many scientific and engineering applications. Although this type of point sets may be generated through the minimization of a slightly modified electrostatic potential, the optimization procedure becomes unwieldy when the size of the point set increases beyond a few thousands. Therefore, it is desirable to have a deterministic scheme capable of generating this type of point set with near uniformity. In this work, we will present a simple deterministic scheme to generate nearly uniform point sets with antipodal symmetry.