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Statistical Issues in Diffusion Tensor MRI 

Statistical Issues in Diffusion Tensor MRI
Statistical Issues in Diffusion Tensor MRI

Sinisa Pajevic

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date: 27 January 2020

Statistical methods are broadly divided into parametric and non-parametric approaches. The parametric approaches in DT-MRI center on the multivariate normal and the tensor-variate normal distributions which offer good parametric models of noise in the absence of motion artefacts. The weakness of these parameterizations is that they allow tensors with negative eigenvalues, a problem that can be remedied using parametric models on manifolds but with a detriment of biased description of the noise. Even when we know the parametric model of the tensor elements obtaining the parametric model of the tensor-derived quantities is usually difficult to achieve. Diffusion tensor data contain the directional information which requires various methods of directional statistics. Most notable of the directional distributions is the Bingham distribution which is a general statistical model for the axial (antipodally symmetric) directional data in three dimensions. Due to unpredictable sources of noise in DT-MRI (e.g., motion artefacts), the non-parametric statistical methods are often needed, such as bootstrap analysis, model-resampling techniques, etc. A group of mixed methods that relate the errors between different quantities or model parameterizations are error propagation methods. They can be very useful for studying the statistics of the tensor derived quantities and notable examples are perturbation methods, invariant Hessian methods, and Monte Carlo methods. Performing the hypothesis tests in DT-MRI revolve around the facts that DT-MRI data are multi-dimensional and contain directional information. While the univariate hypothesis tests can be used for the scalar tensor-derived quantities, the tests on multidimensional data can be approached either as multiple testing problems, or using multivariate hypothesis tests, or using tests for directional statistics.

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