Dataset Information

Eigenvalues of Random Matrices with Isotropic Gaussian Noise and the Design of Diffusion Tensor Imaging Experiments.

ABSTRACT: Tensor-valued and matrix-valued measurements of different physical properties are increasingly available in material sciences and medical imaging applications. The eigenvalues and eigenvectors of such multivariate data provide novel and unique information, but at the cost of requiring a more complex statistical analysis. In this work we derive the distributions of eigenvalues and eigenvectors in the special but important case of m×m symmetric random matrices, D, observed with isotropic matrix-variate Gaussian noise. The properties of these distributions depend strongly on the symmetries of the mean tensor/matrix, D?. When D? has repeated eigenvalues, the eigenvalues of D are not asymptotically Gaussian, and repulsion is observed between the eigenvalues corresponding to the same D? eigenspaces. We apply these results to diffusion tensor imaging (DTI), with m = 3, addressing an important problem of detecting the symmetries of the diffusion tensor, and seeking an experimental design that could potentially yield an isotropic Gaussian distribution. In the 3-dimensional case, when the mean tensor is spherically symmetric and the noise is Gaussian and isotropic, the asymptotic distribution of the first three eigenvalue central moment statistics is simple and can be used to test for isotropy. In order to apply such tests, we use quadrature rules of order t ? 4 with constant weights on the unit sphere to design a DTI-experiment with the property that isotropy of the underlying true tensor implies isotropy of the Fisher information. We also explain the potential implications of the methods using simulated DTI data with a Rician noise model.

SUBMITTER: Gasbarra D

PROVIDER: S-EPMC5630232 | biostudies-literature | 2017

REPOSITORIES: biostudies-literature

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Eigenvalues of Random Matrices with Isotropic Gaussian Noise and the Design of Diffusion Tensor Imaging Experiments.

Gasbarra Dario D Pajevic Sinisa S Basser Peter J PJ

SIAM journal on imaging sciences 20170914 3

Tensor-valued and matrix-valued measurements of different physical properties are increasingly available in material sciences and medical imaging applications. The eigenvalues and eigenvectors of such multivariate data provide novel and unique information, but at the cost of requiring a more complex statistical analysis. In this work we derive the distributions of eigenvalues and eigenvectors in the special but important case of <i>m×m</i> symmetric random matrices, <i>D</i>, observed with isotr ...[more]

PMID: 28989561

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Project description:This work characterizes the effect of lipid and noise signals on muscle diffusion parameter estimation in several conventional and non-Gaussian models, the ultimate objectives being to characterize popular fat suppression approaches for human muscle diffusion studies, to provide simulations to inform experimental work and to report normative non-Gaussian parameter values. The models investigated in this work were the Gaussian monoexponential and intravoxel incoherent motion (IVIM) models, and the non-Gaussian kurtosis and stretched exponential models. These were evaluated via simulations, and in vitro and in vivo experiments. Simulations were performed using literature input values, modeling fat contamination as an additive baseline to data, whereas phantom studies used a phantom containing aliphatic and olefinic fats and muscle-like gel. Human imaging was performed in the hamstring muscles of 10 volunteers. Diffusion-weighted imaging was applied with spectral attenuated inversion recovery (SPAIR), slice-select gradient reversal and water-specific excitation fat suppression, alone and in combination. Measurement bias (accuracy) and dispersion (precision) were evaluated, together with intra- and inter-scan repeatability. Simulations indicated that noise in magnitude images resulted in <6% bias in diffusion coefficients and non-Gaussian parameters (?, K), whereas baseline fitting minimized fat bias for all models, except IVIM. In vivo, popular SPAIR fat suppression proved inadequate for accurate parameter estimation, producing non-physiological parameter estimates without baseline fitting and large biases when it was used. Combining all three fat suppression techniques and fitting data with a baseline offset gave the best results of all the methods studied for both Gaussian diffusion and, overall, for non-Gaussian diffusion. It produced consistent parameter estimates for all models, except IVIM, and highlighted non-Gaussian behavior perpendicular to muscle fibers (? ~ 0.95, K ~ 3.1). These results show that effective fat suppression is crucial for accurate measurement of non-Gaussian diffusion parameters, and will be an essential component of quantitative studies of human muscle quality.

Dataset Information

Eigenvalues of Random Matrices with Isotropic Gaussian Noise and the Design of Diffusion Tensor Imaging Experiments.

Publications

Eigenvalues of Random Matrices with Isotropic Gaussian Noise and the Design of Diffusion Tensor Imaging Experiments.

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