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  Analytical derivation of the b matrix of a time-efficient isotropic diffusion weighting gradient waveform

Trampel, R., & Johnson, G. (2013). Analytical derivation of the b matrix of a time-efficient isotropic diffusion weighting gradient waveform. Medical Physics, 40(3), 032301-1-032301-8. doi:10.1118/1.4789489.

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Trampel, Robert1, Author              
Johnson, Glyn2, Author
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1Department Neurophysics, MPI for Human Cognitive and Brain Sciences, Max Planck Society, Leipzig, Germany, ou_634550              
2Norwich Medical School, University of East Anglia, Norwich, United Kingdom, ou_persistent22              

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Free keywords: Biodiffusion; Biomedical MRI; Helium; Lung; Statistical analysis; b matrix; Analytical derivation; Imaging gradients; Isotropic diffusion weighting; Hyperpolarized 3He
 Abstract: Purpose: Diffusion-weighted magnetic resonance imaging of 3He provides information about lung structure. If rotationally invariant measures of diffusion are desired, an equal diffusion weighting in all three spatial directions is necessary to obtain. In order to achieve such isotropic diffusion weighting, gradients have to be applied in these three spatial directions, which can be time consuming. Therefore, the purpose of this study was the analytic derivation of a time-efficient isotropic diffusion weighting scheme. Methods: The complete b matrix of a preselected gradient waveform was derived analytically. The effect of ramp times and the contribution of the imaging gradients were included in the calculation. The time-efficient waveform was compared to a standard isotropic diffusion weighting scheme by determining the mean diffusivity of hyperpolarized 3He in human lungs. Results: An analytically derived expression of the b matrix for a time-efficient gradient scheme allowing isotropic diffusion weighting was derived. Additionally, the b matrix of a common set of imaging gradients was calculated. Diffusion measurements of hyperpolarized 3He in human lungs using the derived optimized gradient scheme and a standard gradient waveform used for isotropic diffusion weighting, respectively, gave results for the mean diffusivity which did not show any statistical difference. However, the echo time using the optimized scheme was reduced by 2.5 ms in comparison with the standard scheme which leads to a theoretical signal increase of 30%. Conclusions: The analytically derived b matrix allows for the straightforward determination of time-efficient isotropic diffusion weighting schemes. By using those schemes, a substantial gain in signal can be achieved whereas the resulting values for the mean diffusivity did not show any statistical difference to the values obtained when using standard waveforms for isotropic diffusion weighting.

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Language(s): eng - English
 Dates: 2012-11-262012-09-052013-01-112013-02-082013-03
 Publication Status: Published in print
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: DOI: 10.1118/1.4789489
PMID: 23464333
 Degree: -

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Title: Medical Physics
  Other : Med. Phys.
Source Genre: Journal
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Publ. Info: New York, etc. : Published for the American Association of Physicists in Medicine by the American Institute of Physics
Pages: - Volume / Issue: 40 (3) Sequence Number: - Start / End Page: 032301-1 - 032301-8 Identifier: ISSN: 0094-2405
CoNE: https://pure.mpg.de/cone/journals/resource/991042742884000