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Original Research
Analytical error propagation in diffusion anisotropy calculations
Article first published online: 29 MAR 2004
DOI: 10.1002/jmri.20020
Copyright © 2004 Wiley-Liss, Inc.
1522-2586/asset/cover.gif?v=1&s=7744bbc5c5ee23bd9677f861606033d1d6742e48 "Journal of Magnetic Resonance Imaging")
Additional Information
How to Cite
Poonawalla, A. H. and Zhou, X. J. (2004), Analytical error propagation in diffusion anisotropy calculations. Journal of Magnetic Resonance Imaging, 19: 489–498. doi: 10.1002/jmri.20020
Publication History
- Issue published online: 29 MAR 2004
- Article first published online: 29 MAR 2004
- Manuscript Accepted: 15 DEC 2003
- Manuscript Received: 3 JUN 2003
Funded by
- Physician Referral Service at the M.D. Anderson Cancer Center (Houston, Texas)
- Dunn Foundation
- General Electric Medical Systems (Milwaukee, Wisconsin)
- Abstract
- Article
- References
- Cited By
Keywords:
- diffusion tensor imaging;
- error propagation;
- relative anisotropy;
- fractional anisotropy;
- diffusion gradient scheme
Abstract
Purpose
To develop an analytical formalism describing how noise and selection of diffusion-weighting scheme propagate through the diffusion tensor imaging (DTI) computational chain into variances of the diffusion tensor elements, and errors in the relative anisotropy (RA) and fractional anisotropy (FA) indices.
Materials and Methods
Singular-value decomposition (SVD) was used to determine the tensor variances, with diffusion-weighting scheme and measurement noise incorporated into the design matrix. Anisotropy errors were then derived using propagation of error. To illustrate the applications of the model, 12 data sets were acquired from each human subject, over a range of b-values (500–2500 seconds/mm2) and diffusion-weighting gradient directions (N = 6–55). The mean RA and FA values and their respective errors were calculated within a region of interest (ROI) in the splenium. The RA and FA errors as a function of b-value and N were evaluated, and a number of diffusion-weighting schemes were assessed based on a new metric, sum of diffusion tensor variances.
Results
When the acquisition time was held constant, the sum of the diffusion tensor variances decreased as N increased. The same trend was also observed for several diffusion-weighting schemes with constant condition number when noise in the diffusion-weighted (DW) images was assumed unity. Errors in both FA and RA increased with b-value and decreased with N. The FA error in the splenium was approximately threefold smaller than RA error, irrespective of b-value or N.
Conclusion
The condition number may not adequately characterize the noise sensitivity for a given diffusion-weighting scheme. Signal averaging may not be as effective as increasing N, especially when N is small (e.g., N < 13). Due to its smaller error, FA is preferred over RA for quantitative DTI applications. J. Magn. Reson. Imaging 2004;19:489–498. © 2004 Wiley-Liss, Inc.