Multi-echo chemical shift encoded (CSE) techniques provide accurate and robust fat quantification over a broad range of fat-fractions and acquisition parameters [1-3]. To maximize accuracy (i.e. minimize bias), these techniques must correct for all relevant confounding factors, including T₁ and T₂* relaxation, the spectral complexity of fat, and noise bias. However, emerging applications (e.g.: fat quantification with high spatial resolution or in iron overloaded tissues [4]) result in data with significantly lower signal-to-noise ratio (SNR) compared to previously established applications. Because CSE techniques generate fat and water signal values that may be positive or negative, noise bias correction methods are used to avoid instabilities due to negative numbers when proton density fat fractions (PDFF) are calculated on a per voxel basis. Finally, an estimated fat fraction over an ROI provides a description of the distribution of PDFF values. Typically, the estimated fat fraction is calculated using the mean of the distribution. The purpose of this work was to characterize the bias of different correction techniques for fat quantification in the low SNR regime. Specifically, we evaluate the performance of three methods for generating noise-bias corrected PDFF maps as well as the use of the mean or median over ROIs to accurately measure the estimated fat-fractions.

A summary of the six methods used to measure estimated fat fraction in an ROI and their associated noise bias correction algorithms are shown in Figure 1. Numerical simulations based on the publically available Fat/Water Toolbox [5] were performed to determine the noise performance for fat-fraction measurements made using CSE fat-water separation. Individual signal values were synthesized to model a routine 4 echo acquisition at 3T using a multi-peak fat signal model with the signal values proportional to the fat fraction and with zero mean complex Gaussian noise added. The magnitude echo fitting was then performed to determine the fat and water signals on a voxel-by-voxel basis [6]. Following this, voxel-wise PDFFs were calculated using the 3 techniques given in Figure 1 (pdff1, pdff2, and pdff3). A total of 10,000 separate simulations were run for ROIs composed of 8 x 8 voxels assuming 0, 10, 30, and 50% fat fractions and SNR values ranging from 1 - 20. Estimated fat fractions were then measured for each of the 6 methods in Figure 1, over each 8 x 8 ROI distribution. Finally the mean and variance of the individual estimated fat fractions were measured across all 10,000 runs for each initial fat fraction and SNR.

The individual signal distributions for fat and water with 0% fat and SNR = 2 from 256x256 sample voxels after magnitude echo fitting are shown in Figure 2, top row. Individual PDFF distributions are shown in Figure 2, bottom row. Distribution pdff1 includes only positive values resulting in a skewed distribution. Alternatively pdff2 demonstrates long tails due to division by very small numbers accounting for the large variability in the mean of the distribution when using this measure to report estimated fat fraction. The pdff3 distribution also displays a compact but rather a skewed non-Gaussian distribution. Estimated fat fractions were then calculated as the means and medians of each pdff.

The means and variances from the described simulations to calculate estimated fat fraction are shown in Figure 3. At SNR values of 15 and above, methods 3-6 provided very low bias and variance. Using the naïve approach of methods 1 and 2 showed bias at all SNRs for 0% fat fraction despite having relatively low variance. However for extremely low SNR settings, biases and increased variance were observed for all methods. The lowest bias for low fat fractions was observed for method 4 measuring the median of pdff 2 but this was at the expense of increased variance. The lowest variances were measured using the means of methods 1 and 5. Method 3 resulted in the highest variances.

The current work focuses on numerical simulations isolating the dependence of the reconstruction algorithm on the purely Gaussian white noise. Based on these simulations, it is important to maintain high SNR imaging data to minimize bias and variance in the reported fat fractions with a recommended SNR of 15 or higher. For very low SNR applications and fat fractions, method 4 provided the lowest bias with only moderate increase in variability where the median was found to better represent the non-Gaussian data. Future work is needed to evaluate these results in phantoms and in vivo.