Sparse and optimal acquisition design for diffusion MRI and beyond

Authors

  • Koay Cheng Guan,

    1. Department of Medical Physics, University of Wisconsin School of Medicine and Public Health, Madison, Wisconsin 53705
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    • Author to whom correspondence should be addressed. Electronic mail: cgkoay@wisc.edu

  • Özarslan Evren,

    1. Section on Tissue Biophysics and Biomimetics, PPITS, NICHD, National Institutes of Health, Bethesda, Maryland 20892 and Center for Neuroscience and Regenerative Medicine, Uniformed Services University of the Health, Sciences, Bethesda, Maryland 20814
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  • Johnson Kevin M.,

    1. Department of Medical Physics, University of Wisconsin School of Medicine and Public Health, Madison, Wisconsin 53705
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  • Meyerand M. Elizabeth

    1. Department of Medical Physics, University of Wisconsin School of Medicine and Public Health, Madison, Wisconsin 53705 and Department of Biomedical Engineering, University of Wisconsin-Madison, Madison, Wisconsin 53705
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Abstract

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 10232 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.

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