One of the most commonly used magnetic resonance (MR) methods for fat detection and quantification is gradient recalled echo (GRE) imaging using Dixon’s 2-point technique (1
). This method assumes a simplified two component system wherein the observed MR signal is the summation of two signal sources: fat protons and water protons, which are characterized by a distinct chemical shift of approximately 3.5 parts-per-million (ppm). Images are acquired at two echo times (TEs) at which the signals from fat protons and water protons are presumed to be exactly in-phase (IP) and out-of-phase (OP). Since these images are acquired with TEs that are short relative to the T2* of healthy liver (approximately 30 ms at 1.5 T), it is normally assumed that T2* decay is negligible and all signal variation between the two TEs is due to the phase interference of the fat and water protons.
Under these assumptions, the IP image is simply the sum of the water and fat signals and the OP image is the difference between the water and fat signals. The water and fat amplitudes (S1
, respectively) can then be estimated by linear combinations of the IP and OP images.
Nominally it is assumed that S1
is water and S2
is fat although, in practice, these can only represent the “majority” and “minority” components of the signal, which is the familiar fat- water ambiguity problem (2
). Ambiguity is intimately related to B0 field homogeneity, which in turn is related to the problem of multidimensional phase unwrapping (5
The first equation provides a means of obtaining a water only image (i.e. fat-suppression contrast) and the second a fat only image. Of particular clinical interest is the fat fraction, defined by Eq 3
When the conditions leading to Eq 1
are satisfied, the fat fraction can be estimated by rearrangement of Eq 1
The 2-point Dixon technique is clinically used as an indicator for the presence of fat although it is recognized that Eq 4
is not valid for many cases of clinical importance where T2* decay is significant (6
). A regular occurrence is that the T2* decay causes signal from the later echo to be lower than the signal from the earlier echo, which leads to spurious negative values for the fat fraction when the IP image is acquired later than the OP image.
In addition to the effects of T2* relaxation, the fat fraction can be shown to be sensitive to differences in T1 relaxation (7
), which introduces a dependence on imaging parameters such as repetition time (TR) and flip-angle (α
). It is usually observed that the measured fat fraction increases with flip angle owing to the preferential suppression of longer T1 components. Since imaging parameters are typically optimized for signal-to-noise ratio (SNR) and/or scan time, a given protocol may induce significant T1-weighting bias in the fat fraction estimate.
As well as relaxation effects, fat is known to have a complicated chemical spectrum that contains a number of different spectral components (8
): CH3, CH2, CH2COOR and CH=CH groups at 0.9, 1.2, 2.2 and 5.3 ppm, respectively, which collectively represent the total fat signal. The phase interaction between different fat components can add considerable complexity to the observed signal variation with TE especially at longer TEs.
The primary goal of this paper is to overcome the limitations of the conventional 2-point method for fat quantification. This is done by starting with a comprehensive model of the MR signal that incorporates T2* relaxation effects, B0 inhomogeneity, spectral complexity and T1 relaxation effects, and then introducing simplifications with detailed examination of the consequences and validity of each step.