Sources of systematic error in proton density fat fraction (PDFF) quantification in the liver evaluated from magnitude images with different numbers of echoes

The purpose of this work was to investigate sources of bias in magnetic resonance imaging (MRI) liver fat quantification that lead to a dependence of the proton density fat fraction (PDFF) on the number of echoes. This was a retrospective analysis of liver MRI data from 463 subjects. The magnitude signal variation with TE from spoiled gradient echo images was curve fitted to estimate the PDFF using a model that included monoexponential R-2* decay and a multi-peak fat spectrum. Additional corrections for non-exponential decay (Gaussian), bi-exponential decay, degree of fat saturation, water frequency shift and noise bias were introduced. The fitting error was minimized with respect to 463 x 3 = 1389 subject-specific parameters and seven additional parameters associated with these corrections. The effect on PDFF was analyzed, notably the dependence on the number of echoes. The effects on R-2* were also analyzed. The results showed that the inclusion of bias corrections resulted in an increase in the quality of fit (r(2)) in 427 of 463 subjects (i.e. 92.2%) and a reduction in the total fitting error (residual norm) of 43.6%. This was largely a result of the Gaussian decay (57.8% of the reduction), fat spectrum (31.0%) and biexponential decay (8.8%) terms. The inclusion of corrections was also accompanied by a decrease in the dependence of PDFF on the number of echoes. Similar analysis of R-2* showed a decrease in the dependence on the number of echoes. Comparison of PDFF with spectroscopy indicated excellent agreement before and after correction, but the latter exhibited lower bias on a Bland-Altman plot (1.35% versus 0.41%). In conclusion, correction for known and expected biases in PDFF quantification in liver reduces the fitting error, decreases the dependence on the number of echoes and increases the accuracy.