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Variance of estimated DTI‐derived parameters via first‐order perturbation methods
Author(s) -
Chang LinChing,
Koay Cheng Guan,
Pierpaoli Carlo,
Basser Peter J.
Publication year - 2007
Publication title -
magnetic resonance in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.696
H-Index - 225
eISSN - 1522-2594
pISSN - 0740-3194
DOI - 10.1002/mrm.21111
Subject(s) - diffusion mri , parametric statistics , monte carlo method , eigenvalues and eigenvectors , mathematics , fractional anisotropy , tensor (intrinsic definition) , statistical physics , algorithm , statistics , physics , magnetic resonance imaging , medicine , quantum mechanics , pure mathematics , radiology
Abstract In typical applications of diffusion tensor imaging (DTI), DT‐derived quantities are used to make a diagnostic, therapeutic, or scientific determination. In such cases it is essential to characterize the variability of these tensor‐derived quantities. Parametric and empirical methods have been proposed to estimate the variance of the estimated DT, and quantities derived from it. However, the former method cannot be generalized since a parametric distribution cannot be found for all DT‐derived quantities. Although powerful empirical methods, such as the bootstrap, are available, they require oversampling of the diffusion‐weighted imaging (DWI) data. Statistical perturbation methods represent a hybrid between parametric and empirical approaches, and can overcome the primary limitations of both methods. In this study we used a first‐order perturbation method to obtain analytic expressions for the variance of DT‐derived quantities, such as the trace, fractional anisotropy (FA), eigenvalues, and eigenvectors, for a given experimental design. We performed Monte Carlo (MC) simulations of DTI experiments to test and validate these formulae, and to determine their range of applicability for different experimental design parameters, including the signal‐to‐noise ratio (SNR), diffusion gradient sampling scheme, and number of DWI acquisitions. This information should be useful for designing DTI studies and assessing the quality of inferences drawn from them. Magn Reson Med 57:141–149, 2007. Published 2006 Wiley‐Liss, Inc.