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Abstract In this paper, we are interested in the following question: given an arbitrary Steiner triple systemonvertices and any 3‐uniform hypertreeonvertices, is it necessary thatcontainsas a subgraph provided? We show the answer is positive for a class of hypertrees and conjecture that the answer is always positive.
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Global sensitivity analysis of skeletal muscle dMRI metrics: Effects of microstructural and pulse parameters
PurposeEstimating microstructural parameters of skeletal muscle from diffusion MRI (dMRI) signal requires understanding the relative importance of both microstructural and dMRI sequence parameters on the signal. This study seeks to determine the sensitivity of dMRI signal to variations in microstructural and dMRI sequence parameters, as well as assess the effect of noise on sensitivity. MethodsUsing a cylindrical myocyte model of skeletal muscle, numerical solutions of the Bloch‐Torrey equation were used to calculate global sensitivity indices of dMRI metrics (FA, RD, MD,,,) for wide ranges of microstructural and dMRI sequence parameters. The microstructural parameters were: myocyte diameter, volume fraction, membrane permeability, intra‐ and extracellular diffusion coefficients, and intra‐ and extracellulartimes. Two separate pulse sequences were examined, a PGSE and a generalized diffusion‐weighted sequence that accommodates a larger range of diffusion times. The effect of noise and signal averaging on the sensitivity of the dMRI metrics was examined by adding synthetic noise to the simulated signal. ResultsAmong the examined parameters, the intracellular diffusion coefficient has the strongest effect, and myocyte diameter is more influential than permeability for FA and RD. The sensitivity indices do not vary significantly between the two pulse sequences. Also, noise strongly affects the sensitivity of the dMRI signal to microstructural variations. ConclusionsWith the identification of key microstructural features that affect dMRI measurements, the reported sensitivity results can help interpret dMRI measurements of skeletal muscle in terms of the underlying microstructure and further develop parsimonious dMRI models of skeletal muscle.
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- Award ID(s):
- 1762774
- PAR ID:
- 10241153
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Magnetic Resonance in Medicine
- Volume:
- 83
- Issue:
- 4
- ISSN:
- 0740-3194
- Page Range / eLocation ID:
- p. 1458-1470
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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