Quantifying Liver Fat Using a Low-Field Unilateral MR System

Non-alcoholic fatty liver disease (NAFLD) is a highly prevalent condition with a large impact on public health, but remains largely undetected among individual patients. MRI proton density fraction (MRI-PDFF) is the gold standard method for measuring liver fat content, but might be regarded as “overkill” for this diffuse liver disease process. There is a pressing current medical need for simpler non-invasive approaches to measure and track liver fat content over time, for which emerging unilateral permanent magnet MR technology is uniquely suited. In this study, we evaluate the potential of the barrel magnet system first described by Utsuzawa and Fukushima in 2017 to quantify liver fat content. We tested this novel unilateral MR system in oil–water emulsions and subsequently with ex vivo tissue samples from normal and fatty duck livers. In oil–water emulsions, the system provided good linear agreement between fat signal amplitudes derived from Bayesian analysis of MR signals and known oil content. Clear differences in water and fat signal amplitudes were also observed between normal and fatty liver samples. The ability to discriminate differences in fat content as little as 5% demonstrates clear potential clinical relevance for medical management of NAFLD using a scaled-up system designed for human studies.


Introduction
About one quarter of the U.S. population is believed to have non-alcoholic fatty liver disease (NAFLD), which is defined by excessive accumulation of intrahepatic triglycerides, beyond the normal low levels required for cellular housekeeping.NAFLD confers an elevated risk of cardiovascular disease [1], and moreover about one quarter of these patients will ultimately progress to non-alcoholic steatohepatitis (NASH) [2], a dangerous hepatic inflammatory condition with high risk for transition to critical liver disease states of cirrhosis and/or hepatocellular carcinoma.NASH is projected to soon become the leading cause for liver transplantation [3], due to rapidly rising incidence as well as recent advances in curing hepatitis C. Numerous therapeutic approaches for treatment of NAFLD/NASH including pharmaceutical, surgical, as well as dietary/behavioral interventions are currently under development or clinical testing, which could benefit from improved non-invasive markers of disease status [4].
Although liver biopsy is necessary for establishing a diagnosis of NASH, MRI is the gold standard diagnostic method for detecting and monitoring NAFLD, in fact providing the widely accepted definition of this condition as > 5% liver proton density fat fraction (MRI-PDFF) [5].The contribution of liver fat to total liver MRI signal in NAFLD patients ranges from 5% up to 40% and occasionally even higher, with grading of disease in increments of ~ 10%.MRI-PDFF provides exquisite depiction of fat distribution, by combining the discrimination of fat based on chemical shift with the high spatial resolution capabilities of MRI, and is widely used as an endpoint for clinical trials for NAFLD [6].A state of the art description of MRI-based markers of NAFLD/NASH is given in a recent review article [7].Unfortunately, MRI is expensive and has complex siting requirements, and it may be difficult to justify the use of MRI as a method for screening for disease or tracking disease with repeated scans over time in the case of NAFLD.
NAFLD is classified as a diffuse liver disease, and multiple prior reviews [8,9] describe its typical spatial homogeneity, suggesting that MRI-PDFF might be regarded as "overkill" for assessment of overall liver fat content.For example, one MRI study of 121 patients with T2DM (archetypal NAFLD patients, of which 59 were found to be steatotic), found an average difference of fat content of just 4% among liver segments [10].Less commonly, there can be focal fatty deposits or sparing, but such patterns are readily detectable by simple ultrasound (US) scans.Although US can often identify characteristic qualitative signal changes such as increased liver echogenicity for diagnosis of NAFLD, it cannot quantify absolute liver fat fraction, and thus unlike MRI, it cannot grade steatosis [11], nor can any other inexpensive methods to assess body composition non-invasively.Liver biopsy is a complex/expensive surgical procedure which carries risks, inappropriate for screening or serial sampling.Thus, no existing modalities are well suited for serial patient studies of NAFLD to follow the course of this chronic condition.Of course, there are differential diagnoses to consider for NAFLD, and unilateral MR with coarse localization to the liver as proposed in this work cannot replace liver MRI (or even specifically MRI-PDFF) or other medical information in 1 3 Quantifying Liver Fat Using a Low-Field Unilateral MR System such context.Nonetheless, a compact device (like ultrasound) would be ideal for detecting and following disease over time, with MRI remaining the gold standard for finer assessments of liver fat distribution and anatomic imaging as needed.
During the past few years, multiple research groups have begun investigating unilateral MR relaxometry for quantifying liver fat.One group recently showed that fat fraction can be quantified in ex vivo liver samples using a similar system to the barrel magnet [12].Two other groups recently completed human studies applying similar unilateral MR devices, showing very good correlation with MRI-PDFF [13,14].The purpose of this study was to evaluate a novel unilateral MR magnet device, the so-called "barrel magnet" first described by Utsuzawa and Fukushima in 2017 [15], for the purpose of liver fat quantitation for the first time.

MR System Hardware
The barrel magnet concept [15] is an axially symmetric generalization of an earlier dual-magnet design [16], enabled by new insights and new commercial availability of strong inexpensive NdFeB permanent magnets.This unilateral magnet design consists of a cylindrical shell or barrel polarized axially, which projects a region of uniform axial magnetic field ("sweet spot") at a distance from the magnet face.The sweet spot has a complex geometry with emanating "spider legs" as dictated by the laws of magnetostatics.We refer the reader to the paper in this issue by Conradi and Altobelli, which considers in detail the shape of the sweet spot and its potential to provide signal localization [17].Optionally, a secondary bar magnet is positioned co-axially inside the barrel to fine-tune the B 0 profile, resulting in a third-order field profile.The position of the bar magnet can be adjusted toward or away from the magnet face, resulting in a trade-off of field homogeneity and strength at the expense of depth to the sweet spot.The advantage of the barrel magnet design is its superior depth of investigation (DOI) as compared with most prior unilateral magnet systems.Since ever larger and heavier magnets can generate fields at ever deeper regions, DOI is best measured in relative units of overall magnet cross section (outer diameter), providing a better figure of merit for practical unilateral MR systems (Fig. 1).While earlier designs such as the NMR-MOUSE [18] were typically limited to DOIs of only ~ 0.05 or less, the barrel magnet can attain DOIs of ≥ 0.2, potentially facili- tating access to liver MR signals.Other newer unilateral systems may also achieve similarly large DOIs for the purpose of liver fat quantification, although the details of the magnet design for these systems is not entirely clear [13,14].The absolute depth specification is critical and may vary widely among specific versions of the system, depending on the application.For example, a preclinical magnet designed for assaying rodent liver may only require an absolute depth of ~ 1 cm or less, while a system designed for human liver as depicted in Fig. 1 will require a depth of several cm to penetrate into liver tissue.
As configured for this study, the barrel magnet consisting of N42 NdFeB rings and a central bar magnet produces a polarizing field of 0.12 T (5.1 MHz) at a sweet spot centered 1.3 cm above the deck.The magnet has a weight of 2.3 kg and is enclosed in a wooden housing.A thin figure-eight RF coil is fixed to the magnet face and produces a B 1 field that is largely orthogonal to the polarizing field within the sensitive region, for RF transmission and reception.Further details of the magnet design are given in the 2017 paper by Utsuzawa and Fukushima [15].For this work, the magnet assembly was integrated with a Magritek Kea spectrometer with built-in 100-W RF amplifier and duplexer/preamplifier covering the range of 2-5.5 MHz.Initial MR testing and signal depth profiling were performed using stacked rubber sheet phantoms, which are ideal test samples because of their short T 1 relaxation times and very low diffusivity.A photograph of the system setup and results of initial testing are shown in Fig. 2.

Oil-Water Emulsions
To assess the basic sensitivity of MR signals to sample lipid content, a series of 2 mL vial phantoms containing variable fractions of olive oil and deionized water were prepared with oil volume fractions ranging from 0 to 50% in increments of 5%.A small quantity of surfactant (dish soap) was added to each liquid phantom to facilitate mixing of the two components, and each sample was agitated prior to data collection to mix the components, with a settling period of 10 s prior to each acquisition.CPMG echo trains were acquired on the barrel magnet with 1024 echoes spaced by ΔTE = 0.5 ms, and 675 ms recycle delay between acquisitions.These parameters were optimized for detection of the oil component, as the apparent water T 1 and T 2 (~ 1000 ms) were longer than the recycle delay.A total of 8 signal averages were acquired, requiring 12 s of total scan time per sample.The 90º pulse width was ~ 12 s, which easily covered the range of resonance frequencies inside the sensitive volume.Each sample was scanned with 10 repeat acquisitions, with re-agitation and re-positioning for each scan.Relevant study parameters are collected in Table 1.Data were first analyzed using a vendor-supplied (Magritek) Quantifying Liver Fat Using a Low-Field Unilateral MR System non-negative least squares (NNLS) inverse Laplace fitting procedure to generate relaxation spectra.Specifically, data was first analyzed using the "AnalyseT2Plot" macro, with Lawson and Hanson NNLS analysis and a range of relaxation times from 80 to 850 ms, with 200 points to analyze (or bins) distributed logarithmically.Next, we used our own Bayesian double-exponential fitting procedure incorporating data priors for more optimal fitting.Specifically, data were analyzed using the Stan package [19] for Markov chain Monte Carlo analysis in Python.The following equation was fit to each data set: where 1 and 2 are the fitted amplitudes of the fat and water components and T 2,1 and T 2,2 their relaxation times, respectively, and c 0 is an empirically determined constant.The fitting code is provided as supplementary information.Both the NNLS algorithm and our own Bayesian fitting procedure considered distributions of T 2 relaxation times, not single values.To investigate the limits of our approach, we also prepared and analyzed a set of additional samples in the range of 1-10% oil content, in 1% increments.

Ex Vivo Liver Tissue Samples
A set of lean and fatty duck liver samples were also analyzed using the same procedures as applied to the oil-water emulsions.In this case, small samples of freshly butchered lean and fatty duck liver (i.e., "foie gras") (Hudson Valley Farms, NY) were loaded into sample vials.CPMG trains were acquired in this case with 512 echoes spaced by ΔTE = 0.5 ms, with a recycle delay of just 200 ms (because of the shorter relaxation times of fat and water signals within tissues as compared to bulk liquids).In this case, 16 signal averages were acquired over a total scan time of just 4 s per sample.Unlike the case of the liquid oil-water samples, in this case, the true exact fat content was not known a priori and thus, the fat content was assayed by gold standard chemical shift-based MR spectroscopy of the same samples in an Agilent 4.7 T preclinical MRI scanner, based on the area under the 1 H water and fat peaks after baseline correction.

Results
MR data from oil-water emulsions showed clear qualitative differences between signals across the range of fat content, which were readily captured in relaxation spectra derived from the vendor-supplied NNLS algorithm for multi-exponential fitting Quantifying Liver Fat Using a Low-Field Unilateral MR System (Fig. 3).The T 2 relaxation spectra presented in the right column of Fig. 3, obtained using the vendor's NNLS algorithm, show qualitatively that there is a fast-relaxing NMR signal component that increases with increasing oil fraction.Optimized Bayesian fitting resulted in good linear fits between the amplitude of the oil component and the known oil fraction (Fig. 4).Empirically determined priors for the Bayesian analysis were log-normal T 2 distributions with expected value of 1/log(T 2 ) of 3.6 ms −1 and standard deviation of 1/log(T 2 ) of 0.15 ms −1 for fat, and expected value of 1/log(T 2 ) of 6.0 ms −1 and standard deviation of 1/log(T 2 ) of 0.5 ms −1 for water.The starting point for estimating the priors was based on mono-exponential fitting of pure water and oil samples.Note that the values used are shorter than these values.Incorporation of the c0 constant in the Bayesian model favored use of these shorter values plus a constant for better discrimination of fat content based on fitting the magnitude data, Effective discrimination could be achieved based on differences in oil fractions of as little as 5%, although precision to the level of 1% could not be achieved using these approaches.Note that "Amplitude" in the right-most column of Fig. 3 refers to the NNLS-fitted coefficient of the component signal with the corresponding relaxation rate on the x-axis, while "Amplitude" in Fig. 4 refers specifically to the fitted coefficient of the signal assigned to fat in our Bayesian doubleexponential model.Also note that no special measures were used to ensure consistency of bubble size in the phantoms, making this a possible contributor to variation in the results [20].With ex vivo normal and fatty liver samples, "gold standard" chemical shiftbased fat measurements showed a highly bimodal distribution of fat content.These "gold standard" fat content measurements were obtained by integrating the fat and water peaks in baseline-corrected magnitude 1 H spectra.The liver fat fraction measurements were 53 ± 1.5% (fatty samples) and 6.0 ± 0.8% (normal samples).Like the gold standard MR data, characteristic signal differences between normal and fatty samples were also again clear on comparison of the raw time-domain signals as well as multi-exponential fits, with Bayesian fitting data plotted vs the corresponding gold standard fat fraction in Fig. 5.It is observed from Fig. 5 that the 0.1-T measurements exhibit greater variability than the gold standard 4.7-T results, which could Fig. 4 Oil component of the MR signal (y-axis) plotted against known oil fraction in the corresponding samples (x-axis).Samples were assayed over the range of 0-50% A in increments of 5%, and in finer increments of 1% for ≤ 10% (B).The fits are based on Bayesian double-exponential analysis incorporating data priors enforcing a fixed range of relaxation times.Means and 95% confidence intervals are shown, based on 10 repeat acquisitions per sample.Regression lines are plotted through data Fig. 5 A Ratio of fat and water signal components in duck liver samples determined from low-field relaxometry using the barrel magnet (on y-axis), plotted against gold standard ratios as determined from standard chemical shift-based MR of the same samples at 4.7 T (on x-axis).FW signal ratio refers to the integral ratio of the fat-water peaks of the transverse relaxation distribution.B Example baselinecorrected 1 H MR spectrum from one of the fatty liver samples 1 3 Quantifying Liver Fat Using a Low-Field Unilateral MR System be due to the lower SNR of the low-field MR data.In this case, it was more difficult to ascertain the true mono-exponential decay constants for water vs fat because the tissue water and fat content cannot readily be assayed separately as they can for the oil-water phantoms, but their values can be inferred from the data, and were found to be in good agreement with prior results obtained recently in the food industry using a similar inside-out scanner system operating at 4 MHz, in an application for measuring marbling within the thigh muscle of cattle [21,22].As noted in Table 1, we estimated apparent T 2 relaxation times of 35 ms for water and 145 ms for fat in liver tissue, which is comparable to the prior report of 68 ms and 156 ms in cattle muscle at a similar frequency [21,22].Interestingly, the relative relaxation rates of fat and water flipped when moving from the oil-water emulsions to the ex vivo tissue samples.We attribute the extension of the fat T 2 in tissue to restriction of diffusion, which profoundly influences the apparent T 2 in inhomogeneous field MR [23,24], and the shortening of the water T 2 in tissue to modified dipole-dipole interactions, analogous to the observed shortening of water T 2 s in MRI of tissue as compared with free water pools such as found in cerebrospinal fluid.It is also important to note that absolute quantitation of sample fat fraction may require correction for T 1 differences between fat and water, since the data were acquired without full T 1 recovery between each excitation.On the other hand, differences in T 1 with B 0 field strength do not affect the comparison between the low-field data and the 4.7-T data, since the 4.7-T data were acquired with a single excitation only.

Discussion
Considering that NAFLD is typically graded in increments of ~ 10% fat content, our preliminary results showing the ability to discriminate differences in fat fractions as little as 5% has clear medical relevance.Unilateral MR systems such as the barrel magnet have the ability to grade steatosis quantitatively, a capability that is missing from all existing low-cost imaging modalities.Importantly, this demonstrates the potential of unilateral MR to accurately monitor this chronic, highly prevalent medical condition over time.Besides our approach, which is based on multi-exponential T 2 CPMG analysis as previously applied in the oil and food science industries, alternative MR methods such as based on T 1 [25] or diffusion [13] contrast could also potentially be applied to estimate liver fat content.Of course, our measurements are heavily influenced by diffusion effects because of the steep inherent B 0 field gradient.
In addition to the industrial detection of oil, an important focus of unilateral MR technology has been in the area of fat quantification.This is a natural extension of methods for in-ground detection of hydrocarbons, which are closely related to the triglycerides in fat.As reviewed in [26], unilateral MR systems have been used for a variety of applications in the food industry including fat quantitation.For example, unilateral systems have been used in the food industry to measure marbling of muscle in live cattle [21] and fat content in seafood [22].These studies paved the way for the recent work on unilateral MR in liver steatosis [12,13].Inhomogeneous T 2 relaxometry, resolved into components, has also been used biomedically to measure the water-fat body composition of small animals as well as infants [27], as an example of the field of body composition MR [28].However, this approach is not typically based on a unilateral magnet system and is not typically targeted to the study of a specific organ.A unilateral system has been applied in humans to estimate extracellular volume fraction [29], although there is yet to be any well-developed clinical application for this type of MR technology.
A crucial challenge associated with in vivo detection of liver fat using a unilateral MR system is the elimination of superficial signal contributions from subcutaneous adipose stores, which are typically substantial in patients with NAFLD and could confound the quantitation of liver fat.The barrel magnet overcomes this challenge by projecting the sensitive region ("sweet spot") to a distance away from the magnet edge, making it ideally suited for this application.Additional suppression could be provided by surface spoiling gradients such as from a meander line, if necessary [30][31][32][33].
Regarding the necessary scaling of the prototype barrel magnet used in this study into a form that would be suitable for use in human subjects, analysis of liver MRI scans from our institution across a range of body mass indices (BMI) suggests that a simple scaling of 3-4 × along each linear dimension would be sufficient to position the sensitive region well within the liver of most normal to moderately obese subjects, who represent the majority of patients with NAFLD.It is important to recognize that relaxation rates would be likely to change in the scaled-up device, because apparent T 2 s in inhomogeneous MR are influenced by diffusion effects that depend on the static field gradient [23,24], which would be less steep per unit distance in a scaled-up device.Moreover, physical laws dictate that this larger RF coil needed for the full-scale system will necessarily be less sensitive (on a "per-spin" basis) than the smaller coil used in the small-scale prototype, as the per-spin sensitivity of RF coils scales inversely with the square root of coil volume.However, the size of the sensitive volume of the barrel magnet also increases, with the 3rd power of the linear dimensions, allowing many more spins to contribute to the MR signal.This effect of more spins outweighs the loss in per-spin sensitivity associated with the larger coil, and therefore a large net SNR gain is expected for the full-scale barrel magnet system.Indeed, successful efforts by other groups in initial human studies using related unilateral magnet designs show ample sensitivity and clear feasibility for assessment of liver fat using MR systems with reasonable size and weight [13,14].
Interest in low-field MRI systems has exploded over the past few years [34,35], including new offerings from major vendors.Unilateral MR systems with true imaging capability have even been developed, with "proof of concept" medical applications in brain [36] and prostate [37], although image quality lags behind standard MRI.Considering the fundamental difficulties of imaging in inhomogeneous B 0 fields, application of unilateral MR technology to NAFLD, an inherently diffuse disease process, appears to be especially well suited for this emerging technology.

Fig. 1
Fig. 1 Illustration of the concept of "depth of investigation" (DOI) for inside-out MR magnets, measured as a fraction of magnet cross section.Magnets with larger DOI can access deeper anatomic regions

Fig. 2
Fig. 2 Unilateral barrel magnet MR system setup and initial results.A Photograph of magnet assembly (right), integrated with Magritek Kea spectrometer (left).Magnet is shown loaded with a stack of rubber sheets as the MR sample.B Resulting MR spectrum acquired at 5.1 MHz, with broad linewidth of tens of kHz.The signal shown was collected with 100 CPMG data averages over 10 s.C Rubber signal profile as a function of stack height, for assessing signal sensitivity as a function of depth

Fig. 3
Fig. 3 Time domain MR data from oil-water phantoms with oil fractions ranging from 0 to 40% are shown in left column.Echo amplitude data (green data points, normalized magnitude) and corresponding multi-exponential fits are shown in the center column.Relaxation spectra based on the vendor-supplied NNLS fitting algorithm are shown in right column.A short-T 2 component that increases proportionally with increasing oil content is clearly observed, as labeled