@article{3909d07bb25d433c8a9172d987b28d41,
title = "Noise considerations of three-point water-fat separation imaging methods",
abstract = "Separation of water from fat tissues in magnetic resonance imaging is important for many applications because signals from fat tissues often interfere with diagnoses that are usually based on water signal characteristics. Water and fat can be separated with images acquired at different echo time shifts. The three-point method solves for the unknown off-resonance frequency together with the water and fat densities. Noise performance of the method, quantified by the effective number of signals averaged (NSA), is an important metric of the water and fat images. The authors use error propagation theory and Monte Carlo simulation to investigate two common reconstructive approaches: an analytic-solution based estimation and a least-squares estimation. Two water-fat chemical shift (CS) encoding strategies, the symmetric (-θ,0,θ) and the shifted (0,θ,2θ) schemes are studied and compared. Results show that NSAs of water and fat can be different and they are dependent on the ratio of intensities of the two species and each of the echo time shifts. The NSA is particularly poor for the symmetric (-θ,0,θ) CS encoding when the water and fat signals are comparable. This anomaly with equal amounts of water and fat is analyzed in a more intuitive geometric illustration. Theoretical prediction of NSA matches well with simulation results at high signal-to-noise ratio (SNR), while deviation arises at low SNR, which suggests that Monte Carlo simulation may be more appropriate to accurately predict noise performance of the algorithm when SNR is low.",
keywords = "CRB, MRI, NSA, Simulation, Three point, Water-fat separation",
author = "Zhifei Wen and Reeder, \{Scott B.\} and Pineda, \{Angel R.\} and Pelc, \{Norbert J.\}",
note = "Funding Information: This work was supported by NIH Grant No. RR09784, GE Healthcare, and the Lucas Foundation. The authors gratefully acknowledge helpful discussion with Dr. Huanzhou Yu. FIG. 1. Theoretically predicted NSA vs θ curves with Monte Carlo simulation results for MR signals with CS encoding of ( − θ , 0 , θ ) . The analytic solution was used to estimate water and fat. The water-to-fat ratios were (a) R wf = 10 , (b) R wf = 2 , (c) R wf = 1.2 , and (d) R wf = 1.01 . Data points of triangles and circles indicate NSAs for magnitudes of water and fat. FIG. 2. NSA vs θ curves given by the CRB with Monte Carlo simulation results. MR signals were generated with the CS encoding of ( − θ , 0 , θ ) and the LS solution was used to estimate water and fat. The water-to-fat ratios were (a) R wf = 10 , (b) R wf = 2 , and (c) R wf = 1.2 , and (d) R wf = 1.01 . FIG. 3. Simulation results of the RMS error vs θ of the analytic and iterative solutions with CS encoding of ( − θ , 0 , θ ) and water-to-fat ratios at (a) R wf = 10 , (b) R wf = 2 , (c) R wf = 1.2 , and (d) R wf = 1.01 . FIG. 4. Comparison of NSAs obtained with analytic and iterative (LS) solutions. Predicted NSAs are plotted as smooth curves with data points obtained with Monte Carlo simulations. The CS encoding was ( 0 , θ , 2 θ ) and the water-to-fat ratios were (a) R wf = 10 , (b) R wf = 2 , (c) R wf = 1.2 , and (d) R wf = 1 . FIG. 5. Theoretically predicted NSA vs θ curves with Monte Carlo simulation results for MR signals with CS encoding of ( − θ , 0 , θ ) . The analytic solution was used to estimate water and fat. The water-to-fat ratios were (a) R wf = 10 , (b) R wf = 2 , (c) R wf = 1.2 , and (d) R wf = 1.01 . Data points of triangles and circles indicate NSAs for magnitudes of water and fat. FIG. 6. NSA vs θ curves given by the CRB with Monte Carlo simulation results. MR signals were generated with the CS encoding of ( − θ , 0 , θ ) and the LS solution was used to estimate water and fat. The water-to-fat ratios were (a) R wf = 10 , (b) R wf = 2 , and (c) R wf = 1.2 , and (d) R wf = 1.01 . FIG. 7. Comparison of NSAs vs θ for the field-known and field-unknown cases. The CS encodings were ( − θ , 0 , θ ) and ( 0 , θ , 2 θ ) at R w f = 1 : 0 . Note that the CRB for water remained the same while the CRB for fat was different for these two encodings. FIG. 8. Schematic of geometry for MR signals with the same amount of water and fat with the CS encoding scheme of (a) ( − θ , 0 , θ ) , and (b) ( 0 , θ , 2 θ ) . The plot at the top of (b) shows signals with CS encoding angles at 0 and θ , and the plot at the bottom of (b) shows signals with encoding angles at 0 and 2 θ . FIG. 9. Signals produced by equal amounts of water and fat at CS encoding of ( − θ , 0 , θ , 2 θ ) . ",
year = "2008",
doi = "10.1118/1.2952644",
language = "English (US)",
volume = "35",
pages = "3597--3606",
journal = "Medical physics",
issn = "0094-2405",
publisher = "John Wiley and Sons Ltd",
number = "8",
}