- Top of page
- MATERIALS AND METHODS
- DISCUSSION AND CONCLUSION
This work describes observed changes in the proton T1 relaxation time of both water and lipid when they are in relatively homogeneous mixtures. Results obtained from vegetable oil–water emulsions, pork kidney and lard mixtures, and excised samples of white and brown adipose tissues are presented to demonstrate this change in T1 as a function of mixture fat fraction. As an initial proof of concept, a simpler acetone-water experiment was performed to take advantage of complete miscibility between acetone and water and both components' single chemical shift peaks. Single-voxel MR spectroscopy was used to measure the T1 of predominant methylene spins in fat and the T1 of water spins in each setup. In the vegetable oil–water emulsions, the T1 of fat varied by as much as 3-fold when water was the dominant mixture component. The T1 of pure lard increased by 170 msec (+37%) when it was blended with lean kidney tissue in a 16% fatty mixture. The fat T1 of lipid-rich white adipose tissue was 312 msec. In contrast, the fat T1 of leaner brown adipose tissue (fat fraction 53%) was 460 msec. A change in the water T1 from that of pure water was also observed in the experiments. Magn Reson Med, 2010. © 2009 Wiley-Liss, Inc.
Several reports have recently described robust chemical-shift fat-water separation methods in MRI (1–4). Fat quantification studies utilizing some of these techniques have been described in assessing hepatic steatosis (5), epicardial fat (6), and total body fat composition in obesity research (7). With methods such as the iterative decomposition of water and fat with echo asymmetry and least-squares estimation (IDEAL) approach (2), a fat-signal fraction is typically computed on a voxel-by-voxel basis as F/(F + W), where F and W denote the decomposed fat and water signals, respectively. In order for the fat-signal fraction to accurately represent the underlying fat content, several works have shown that it is important to consider a multipeak rather than a single-peak spectral model for fat (8, 9), T2* weighting (8, 10), and T1 and noise bias between F and W signals (8, 11). To specifically minimize T1-bias between fat and water spins, the use of small flip angles (≈5°) in IDEAL spoiled-gradient-echo imaging has been suggested (11). In addition to the fat-signal fraction, a fat-only signal fraction (F/FPURE) has also been reported, where FPURE is the signal from a separate reference voxel containing pure fat (12). This work specifically investigates deviation in the proton T1 spin-lattice relaxation rate of fat from its pure natural T1 value when fat is present in relatively homogeneous mixtures. Thus, it is hypothesized that the F/FPURE ratio may also be susceptible to T1-bias. Results from several phantoms constructed of acetone-water mixtures, oil-water emulsions, kidney-lard mixtures, and excised white and brown adipose tissue samples from mice are presented to corroborate this hypothesis. Although the change in the T1 of the methylene fat moiety is the primary focus in this article, we also demonstrate the change in the proton T1 of water (and acetone).
DISCUSSION AND CONCLUSION
- Top of page
- MATERIALS AND METHODS
- DISCUSSION AND CONCLUSION
We have demonstrated the phenomenon of change in the T1 of both fat and water moieties from their pure T1 values when they are present in relatively homogeneous mixtures. Fat and water are naturally immiscible and a mixture of the two can only be treated as a suspension. Acetone and water are, however, completely miscible, and results from the proof-of-concept acetone-water experiment provided compelling evidence of the T1 effect investigated in this work. For the three fat-water experiments, we observed in general an increase in the T1 of fat from its pure T1 value as the fat fraction decreased. Conversely, the T1 of water decreased from its pure T1 value when the mixture composition became less water dominant. In the oil-water emulsion experiment, the variation in the fat and water T1 values was significant when the mixture composition became less than 30% fat (water dominant) and 30% water (fat dominant), respectively. The use of MRS provided good separation of the different chemical moieties in each experimental setup, as well as excellent data fits for the saturation-recovery signal equation. Based on present results, all of our hypotheses are corroborated.
The present findings reinforce the issue of T1-bias when using fat fraction indices from chemical-shift-based methods such as IDEAL. The T1-bias between fat (F) and water (W) spins is intuitive (11). However, the variation in component fat and water T1 as a function of fat fraction is not obvious and further complicates the issue of fat quantification. Nonetheless, low-flip-angle approaches (8, 11) that minimize T1-bias or schemes that explicitly measure T1 (11) to correct for the signal bias remain important in accurate fat fraction quantification. A particularly interesting conclusion can be drawn from the current results. At low fat fractions—often encountered in liver fat quantification—the component T1 of water and fat is potentially very close in value (Fig. 3). This similarity in T1 values actually lessens the degree of T1 bias between fat and water. Consequently, the need for T1-bias correction is less of an issue, and an Ernst angle approach could potentially be favorable. A similar argument can be made for high-fat-fraction scenarios. Figure 3 further suggests that the greatest T1 bias between fat and water in mixture likely occurs at intermediate fat fractions.
In this work, we focused only on the T1 of methylene fat protons. One limitation of this is that the observed change in water T1 may be partly influenced by the olenific fat peak (5.2-5.4 ppm), which is in close proximity to the water peak. However, the acetone-water setup was not susceptible to this limitation. Previous literature has reported that other fat components (e.g., olenific, methyl, diallyic) have individual and different natural T1 values (23, 24). It can be implied that the T1 of these minor fat peaks may also change when in mixture. Quantification of the degree of T1 change in these minor fat peaks will require a higher magnetic field strength for greater spectral resolution.
The findings of fat T1 variation will unlikely have any implications on conventional T1-based fat suppression methods (short T1/tau inversion recovery). Based on the oil-water phantom experiment (Fig. 3), pure fat had a T1 of 314 msec. The fat T1 did not begin to deviate substantially from its natural T1 value until the fat fraction was less than 30%. Let MO_F denote the fully relaxed longitudinal magnetization of pure fat. An inversion recovery (IR) sequence using inversion time = 218 msec that is set to null pure fat will more than adequately suppress not only pure fat but also a majority of voxels with fat-signal fractions between 30% and 100%. Consider a voxel with a 30% fat fraction, whose fully relaxed longitudinal magnetization can be denoted as 0.3·MO_F. According to Fig. 3, the fat T1 is 779 msec. During an IR experiment, MZ will relax at most from −0.3·MO_F to +0.3·MO_F. At inversion time = 218 msec, |MZ| will have recovered to approximately 50% of (0.3·MO_F), which results in a net detectable magnetization of only 15% of MO_F. For another voxel with a 10% fat fraction (fat T1 1332 msec), the net magnetization at inversion time = 218 msec is less than 7% of MO_F. In terms of short T1/tau inversion recovery fat suppression performance in clinical applications, these residual fat signals will not likely raise concerns.
We have also performed experiments using IDEAL with inversion-recovery fast spin echo and driven equilibrium single pulse observation of T1 (25) imaging approaches in lieu of MRS to measure fat and water T1 values in mixture (26). Comparable results and trends in T1 were observed in phantoms and in vivo. With IDEAL-inversion-recovery fast spin echo, data were acquired as a function of inversion time. With driven equilibrium single pulse observation of T1, data were acquired as a function of flip angle, similar to the approach used by Liu et al. (11). IDEAL-reconstructed fat and water signals were fitted to either inversion-recovery or spoiled-gradient-echo signal equations to determine component T1 values. Confounding factors such as T2*, T1 bias, multifat-peak modeling, and amplitude of radiofrequency field flip-angle nonuniformity were collectively considered for accurate IDEAL fat-water decomposition (8–11) and signal fitting. For both inversion-recovery fast spin echo and driven equilibrium single pulse observation of T1, a high number of signal averages (>5) were needed to ensure ample signal-to-noise ratio in the decomposed fat and water images. Physiologic constraints were also set for the T1 estimates (11) from driven equilibrium single pulse observation of T1 and inversion-recovery fast spin echo. These constraints were necessary based on our previous experience in estimating T1 values from noisy signal curves at low fat and water fractions acquired with only one to two signal averages.
The oil-water phantom results from this work bear resemblance to a recent study by Sharma et al. (16), which also used MRS to measure the water and fat T1 values, but at 1.5 T. In emulsions of 10 and 30% fat fractions, the authors found both the water and fat T1 to decrease with increasing concentrations of oil. For the 10% mixture, the T1 of water was measured as 821.7 msec, while in the 30% mixture, it was 591.7 msec. The T1 of fat in the 10% mixture was 680.3 msec, while in the 30% mixture, it was a significantly lower 185.2 msec. The emulsions also contained varying concentrations of iron additives, which were used to generate differences in T2 relaxation. Sharma et al. (16) further reported the hepatic fat T1 in a subject with a 13% fatty liver to be 485 msec, which anecdotally seems greater than reported literature values of pure fat at 1.5 T (280-340 msec) (21, 22). In another article, by Poon et al. (27), the authors performed a study at 1.5 T in thigh muscle in a patient with myositis (skeletal muscle inflammation), which is often accompanied by fatty infiltration. It was found that the fat T1 increased from 187 to 396 msec and the water T1 decreased from 1257 to 993 msec when the fat-signal fraction increased from 24 to 71% in several regions of interest. In constructing several homogeneous fat-water emulsions of different fat fractions with matched fat and water T1 values at 3 T, Dyke et al. (28) reported that it was necessary to dope the water and agarose gel ingredients with varying amounts of gadolinium contrast agent to decrease the water T1 and match it to the shorter fat T1.
A detailed description behind the change in T1 is beyond the scope and intent of this article, but insights can be gleaned from literature on general relaxation theory (29), relaxation behaviors in binary liquid mixtures (30), and some intuition. It is known in chemistry that when two components (A and B) are combined to form a mixture, the critical points of the solution (e.g., freezing, boiling) will consequently vary nonlinearly as a function of the concentrations of A and B present. This principle can be extended to T1spin-lattice relaxation. Fundamentally, T1 depends on a match between the amplitude of static field–dependent Larmor frequency (fLarmor) of protons in a molecule and the tumbling rate (inverse molecule correlation time) of the local molecular lattice (flattice) surrounding the molecule of interest. When the two are equal, T1 relaxation is the most energy efficient, leading to a short T1 value. This is the primary reason underlying fat's characteristic short T1 and free water's long T1 in physiologic MRI. The tumbling rate of a molecular lattice composed of large fat molecules is closely matched the proton Larmor frequency at 1.5 and 3 T (e.g., fLarmor ≈ flattice, therefore, short T1). In contrast, the tumbling rate of a lattice composed of small, free-water molecules is significantly greater than the Larmor value (e.g., fLarmor ≠ flattice, therefore, long T1). Therefore, it is plausible that any structural change in the lattice will lead to variations in the lattice tumbling rate and thus affect T1.
In oil-water suspensions, it is conceivable that the structure of the molecular lattice will change as a function of the concentration of fat and water present in the lattice. At very low or high fat fractions, the dominant lattice is likely determined by the majority species. Large fatty acid moieties may aggregate into small micelles at low fat fractions when water is the dominant lattice. Conversely, they may link together to form large molecular sheets at high fat fractions where fat is the dominant lattice. Consequently, the observed T1 spin-lattice relaxation rates of water and fat species will likely depend on the dominant lattice. This potentially explains why the T1 values of water and fat are very close at low and high fat fractions where the dominant lattice is clearly defined by the majority species. At intermediate fat fractions where both water and fat are present in comparable amounts, an intricate and complex lattice will likely form, giving rise to distinct water and fat T1 values.
Consider the extreme case where a large fat molecule that is surrounded in a solvent consisting primarily of smaller water molecules (low fat fraction). Also consider in contrast the opposite extreme case where the fat molecule is surrounded in a solvent composed mostly of similar fat molecules (high fat fraction). In the low-fat-fraction environment, the increase in the number of local smaller water molecules with shorter correlation times and faster tumbling rates will lead to a flattice that is greater than the proton fLarmor of the fat molecule. As a result of this mismatch, the fat molecule is energetically less efficient at interacting with the water-dominant lattice. Consequently, an increase in fat T1 will occur. In contrast, fLarmor and flattice are more closely matched for the high-fat-fraction environment (fat-dominant lattice), thereby promoting fasterT1 relaxation. The same argument can be applied from the perspective of a water molecule. An increasing presence of larger, slow-tumbling fat molecules in the solvent within the immediate vicinity of a water molecule will decrease the local flattice in comparison to that of a water-rich lattice. This will effectively bring the local flattice surrounding the water molecule of interest closer to the fLarmor of the water spins, thereby lowering the water T1.
Applications involving fat infiltration of skeletal muscles and organs can potentially benefit from the present findings. Relationships between T1 and muscle fiber composition have been reported (31), where it was speculated that the proportion of slow- to fast-twitch fibers, along with their relative fat contents, plays a determining role. Assessment of muscle and organ triglyceride content remains important in studies of Duchenne muscular dystrophy (32) and Gaucher's disease (33) and in metabolic disorders and the etiology of obesity (34, 35). Furthermore, differences in triglyceride composition (fatty acid chain length, degree of saturation) may also influence T1 due to molecular size and geometry.
In conclusion, this work has described the variation in T1 of fat and water as a function mixture composition and has provided supporting evidence from MRS. It is an additional factor that falls under the complex framework of accurate fat fraction quantification in MRI and reinforces the notion that T1 bias is a required consideration.