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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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Temporally resolved parametric assessment of Z‐magnetization recovery (TOPAZ): Dynamic myocardial T 1 mapping using a cine steady‐state look‐locker approach
PurposeTo develop and evaluate a cardiac phase‐resolved myocardial T1mapping sequence. MethodsThe proposed method for temporally resolved parametric assessment of Z‐magnetization recovery (TOPAZ) is based on contiguous fast low‐angle shot imaging readout after magnetization inversion from the pulsed steady state. Thereby, segmented k‐space data are acquired over multiple heartbeats, before reaching steady state. This results in sampling of the inversion‐recovery curve for each heart phase at multiple points separated by an R‐R interval. Joint T1andestimation is performed for reconstruction of cardiac phase‐resolved T1andmaps. Sequence parameters are optimized using numerical simulations. Phantom and in vivo imaging are performed to compare the proposed sequence to a spin‐echo reference and saturation pulse prepared heart rate–independent inversion‐recovery (SAPPHIRE) T1mapping sequence in terms of accuracy and precision. ResultsIn phantom, TOPAZ T1values with integratedcorrection are in good agreement with spin‐echo T1values (normalized root mean square error = 4.2%) and consistent across the cardiac cycle (coefficient of variation = 1.4 ± 0.78%) and different heart rates (coefficient of variation = 1.2 ± 1.9%). In vivo imaging shows no significant difference in TOPAZ T1times between the cardiac phases (analysis of variance:P = 0.14, coefficient of variation = 3.2 ± 0.8%), but underestimation compared with SAPPHIRE (T1time ± precision: 1431 ± 56 ms versus 1569 ± 65 ms). In vivo precision is comparable to SAPPHIRE T1mapping until middiastole (P > 0.07), but deteriorates in the later phases. ConclusionsThe proposed sequence allows cardiac phase‐resolved T1mapping with integratedassessment at a temporal resolution of 40 ms. Magn Reson Med 79:2087–2100, 2018. © 2017 International Society for Magnetic Resonance in Medicine.
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- Award ID(s):
- 1651825
- PAR ID:
- 10039740
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Magnetic Resonance in Medicine
- Volume:
- 79
- Issue:
- 4
- ISSN:
- 0740-3194
- Page Range / eLocation ID:
- p. 2087-2100
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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