Design and Evaluation of Quantitative MRI Phantoms to Mimic the Simultaneous Presence of Fat, Iron, and Fibrosis in the Liver

Abstract

Purpose

To design, construct, and evaluate quantitative MR phantoms that mimic MRI signals from the liver with simultaneous control of three parameters: proton-density fat-fraction (PDFF), ${\mathrm{R}}_2^{*}$, and T₁. These parameters are established biomarkers of hepatic steatosis, iron overload, and fibrosis/inflammation, respectively, which can occur simultaneously in the liver.

Methods

Phantoms including multiple vials were constructed. Peanut oil was used to modulate PDFF, MnCl₂ and iron microspheres were used to modulate ${\mathrm{R}}_2^{*}$, and NiCl₂ was used to modulate the T₁ of water (T_1,water). Phantoms were evaluated at both 1.5T and 3.0T using stimulated echo acquisition mode MR spectroscopy (STEAM-MRS) and chemical shift encoded (CSE) MRI. STEAM-MRS data were processed to estimate T_1,water, T_1,fat, ${\mathrm{R}}_{2,\mathrm{w}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r}}^{*}$, and ${\mathrm{R}}_{2,\mathrm{f}\mathrm{a}\mathrm{t}}^{*}$ for each vial. CSE-MRI data were processed to generate PDFF and ${\mathrm{R}}_2^{*}$ maps, and measurements were obtained in each vial. Measurements were evaluated using linear regression and Bland-Altman analysis.

Results

High quality PDFF and ${\mathrm{R}}_2^{*}$ maps were obtained with homogeneous values throughout each vial. High correlation was observed between imaging PDFF with target PDFF (slope=0.94–0.97, R²=0.994–0.997) and imaging ${\mathrm{R}}_2^{*}$ with target ${\mathrm{R}}_2^{*}$ (slope=0.84–0.88, R²=0.935–0.943) at both 1.5T and 3.0T. ${\mathrm{R}}_{2,\mathrm{f}\mathrm{a}\mathrm{t}}^{*}$ and ${\mathrm{R}}_{2,\mathrm{w}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r}}^{*}$ were highly correlated with slope close to 1.0 at both 1.5T (slope=0.90, R²=0.988) and 3.0T (slope=0.99, R²=0.959), similar to the behavior observed in vivo. T_1,water (500–1200ms) was controlled with varying NiCl₂ concentration, while T_1,fat (300ms) was independent of NiCl₂ concentration.

Conclusion

Novel quantitative MRI phantoms that mimic the simultaneous presence of fat, iron, and fibrosis in the liver were successfully developed and validated.

Keywords

Quantitative imaging biomarkers, phantom, proton-density fat-fraction, ${\mathrm{R}}_2^{*}$, T₁, liver

Introduction

Abnormal deposition of fat and iron in the liver, as well as cumulative scar (fibrosis) are principal histological features of many diseases in multiple organs. In the United States, there are an estimated 100 million people afflicted by non-alcoholic fatty liver disease (NAFLD)¹, which is emerging as the leading cause of liver disease, and millions more with viral hepatitis and other forms of diffuse liver disease. Iron overload often coexists with NAFLD, and liver iron is also an important indicator of total body iron in patients with genetic hemochromatosis and those who receive multiple blood transfusions^2–5. Abnormal liver fat and iron overload often lead to liver injury and fibrosis, and eventually cirrhosis, liver failure and even hepatocellular carcinoma (HCC)⁶. Importantly, fat, iron and fibrosis also commonly co-exist as key features of many other diseases involving the heart^7–11, pancreas^12,13, and kidney^14–16, among others.

Tissue biopsy enables diagnosis of liver disease, but it is invasive, expensive, and suffers from poor sampling variability¹⁷. MRI provides multiple contrast mechanisms for the assessment of diffuse liver disease. Chemical shift encoded (CSE) MRI methods enable mapping of proton-density fat-fraction (PDFF)^6,18 for liver fat quantification. Further, MRI is very sensitive to the presence of iron in tissue, which accelerates the ${\mathrm{R}}_2^{*}$ signal decay rate, as also quantified using CSE-MRI methods¹⁹. Finally, fibrosis and inflammation increase the tissue extracellular volume, which results in increased T₁²⁰. Indeed, T₁ mapping has emerged over the past few years as a promising method for detection and staging of myocardial fibrosis⁸, as well as for assessing liver fibrosis²¹.

Noninvasive MRI biomarkers of fat (based on PDFF), iron (based on ${\mathrm{R}}_2^{*}$), and fibrosis (based on T₁) are emerging as promising quantitative biomarkers with high diagnostic performance^6,8,18,19,21, and are increasingly adopted as endpoints in clinical trials for new therapeutics. However, the disease features of fat, iron and fibrosis are rarely isolated, and these three features commonly coexist to varying degrees²². This coexistence has substantial relevance because the presence of each of these disease features impacts the acquired MR signal, and therefore the ability of quantitative MRI methods to measure the other disease features. For example, the accumulation of iron leads to both increased ${\mathrm{R}}_2^{*}$ and decreased T₁, which is well known to confound the quantification of fat if it is unaccounted for in the PDFF estimation^23–26. Similarly, the presence of liver fat can confound the quantification of ${\mathrm{R}}_2^{*}$^27,28 (i.e., small ${\mathrm{R}}_2^{*}$ increases with increasing liver fat content, likely due to magnetic susceptibility differences between fat droplets and surrounding tissue) and the quantification of T₁ with different acquisitions^26,29. For these reasons, “confounder-corrected” quantitative MRI methods have been developed to measure PDFF, ${\mathrm{R}}_2^{*}$ and T₁ while correcting for relevant coexisting factors. Importantly, development and validation of these methods require MRI test objects (“phantoms”) that mimic the simultaneous presence of these three coexisting features.

Current, commercially available MRI phantoms only attempt to change one of PDFF, ${\mathrm{R}}_2^{*}$, and T₁ independently. Quantitative fat phantoms^30,31 have been developed and used in the validation of MR fat quantification methods. Modulating ${\mathrm{R}}_2^{*}$ with chemicals (i.e., paramagnetic salts or iron oxide particles) has been demonstrated in previous works^32–34. Phantoms with controlled T₁ have been used in various applications^35,36. In summary, previous phantoms generally mimic individual tissue features (fat, iron, or fibrosis) independently^31,32,36.

However, simple combinations of the formulations applied in these PDFF, ${\mathrm{R}}_2^{*}$, or T₁ phantoms do not mimic signal characteristics observed in tissue. A super-paramagnetic iron oxide (SPIO)-based fat phantom enables the modulation of fat and iron simultaneously²³. However, this phantom did not accurately mimic the single-${\mathrm{R}}_2^{*}$ behavior (i.e., similar observed ${\mathrm{R}}_2^{*}$ relaxation decay for water and fat) that is observed in human liver^24,25. A preliminary report of a fat-iron phantom with single-${\mathrm{R}}_2^{*}$ signal based on large iron particles showed promising results^33,37, and another work using iron oxide particles also indicated the potential for single-${\mathrm{R}}_2^{*}$ signal behavior, although this was not demonstrated explicitly³⁴. The development of phantoms that simultaneously control PDFF, ${\mathrm{R}}_2^{*}$ (single-${\mathrm{R}}_2^{*}$ signal behavior: similar ${\mathrm{R}}_2^{*}$ decay behavior of fat and water signals), T₁, and other properties observed in vivo remains an unmet need for the validation and quality assurance of MRI-based methods for quantification of diffuse liver disease.

Therefore, the purpose of this study was to develop and evaluate quantitative PDFF-${\mathrm{R}}_2^{*}$-T₁ phantoms with the following design goals: i) simultaneous modulation of PDFF, ${\mathrm{R}}_2^{*}$, and T₁; ii) similar ${\mathrm{R}}_2^{*}$ relaxation rate behavior for fat and water in liver; iii) modulation of T_1,water without changing T_1,fat as seen in vivo.

Methods

Study Design

In this study, we first constructed a preliminary PDFF-${\mathrm{R}}_2^{*}$ phantom which explored two different approaches to modulate PDFF and ${\mathrm{R}}_2^{*}$ simultaneously. Two different substances, paramagnetic salt (i.e., MnCl₂) and iron microspheres, were used to control ${\mathrm{R}}_2^{*}$ in two separate sets of vials. This phantom was used to assess different ${\mathrm{R}}_2^{*}$-modulating substances (${\mathrm{R}}_2^{*}$ modulators) to evaluate their feasibility for replicating the single-${\mathrm{R}}_2^{*}$ signal behavior seen in vivo. Based on the results from the preliminary PDFF-${\mathrm{R}}_2^{*}$ phantom, two additional quantitative MRI phantoms were constructed: 1) a PDFF-single ${\mathrm{R}}_2^{*}$ phantom was designed to demonstrate simultaneous control of PDFF and ${\mathrm{R}}_2^{*}$ with single-${\mathrm{R}}_2^{*}$ behavior of fat and water; 2) a PDFF-${\mathrm{R}}_2^{*}$-T₁ phantom was designed to enable simultaneous control of PDFF, ${\mathrm{R}}_2^{*}$, and T_1,water. MR-based measurements include PDFF quantification as well as ${\mathrm{R}}_2^{*}$ and T₁ relaxometry. In addition, given the established relationship between R₂ and liver iron concentration^38,39, R₂ relaxometry measurements were also performed.

Preliminary PDFF-${\mathbf{R}}_{\mathbf{2}}^{*}$ Phantom

Two different methods for modulating ${\mathrm{R}}_2^{*}$ were evaluated in the preliminary PDFF-${\mathrm{R}}_2^{*}$ phantom, based on paramagnetic salt MnCl₂ and iron microspheres (2.9μm diameter, UMC3001, COMPEL, Bangs Labs, Fishers, IN). Two sets of vials were built with constant volume fat fraction of 20%. Details on the construction of the oil-water emulsions are provided below. The first set included five vials with varying MnCl₂ concentration (1.03 mM, 1.99 mM, 2.95 mM, 3.91 mM, and 4.86 mM) to achieve varying ${\mathrm{R}}_2^{*}$ over a range of physiological ${\mathrm{R}}_2^{*}$ values. The second set included five vials with varying concentration of iron microspheres (5.82 μg Fe/mL, 15.39 μg Fe/mL, 24.96 μg Fe/mL, 34.53 μg Fe/mL, and 44.10 μg Fe/mL) to obtain a similar ${\mathrm{R}}_2^{*}$ range as the first set. Each set was designed to have increasing target ${\mathrm{R}}_2^{*}$ on the order of 100 s⁻¹, 200 s⁻¹, 300 s⁻¹, 400 s⁻¹, and 500 s⁻¹. The required concentrations of MnCl₂ and iron microspheres were based on a preliminary 3T calibration test in the absence of fat, derived below in this work: MnCl₂ (mM) = 0.010× ${\mathrm{R}}_2^{*}$ (s⁻¹)+0.07, and iron concentration (μg Fe/mL) = 0.096× ${\mathrm{R}}_2^{*}$ (s⁻¹)−3.75.

PDFF-single ${\mathbf{R}}_{\mathbf{2}}^{*}$ Phantom

The purpose of this phantom was to demonstrate control of both ${\mathrm{R}}_2^{*}$ and PDFF in each vial, with similar ${\mathrm{R}}_2^{*}$ decay behavior of fat and water signals (i.e., “single-${\mathrm{R}}_2^{*}$” signals) as has been observed in vivo in the presence of simultaneous fat and iron deposition in the liver²⁴. Four sets of vials were constructed with varying volume fat fraction of 5%, 10%, 20% and 30% in the phantom. These volume fat fractions were chosen to cover most of PDFF observed in the liver⁴⁰. For each choice of PDFF, five vials with different ${\mathrm{R}}_2^{*}$ were constructed, with the following target ${\mathrm{R}}_2^{*}$ values: 100 s⁻¹, 200 s⁻¹, 300 s⁻¹, 400 s⁻¹, and 500 s⁻¹, for a total of 20 vials. Single ${\mathrm{R}}_2^{*}$ decay rate behavior of fat and water was controlled by modulating the combination of iron microspheres and MnCl₂ based on results obtained from the preliminary PDFF-${\mathrm{R}}_2^{*}$ phantom (see Results section below). Details (i.e., target PDFF/${\mathrm{R}}_2^{*}$, chemical concentration) regarding this proposed PDFF-single ${\mathrm{R}}_2^{*}$ phantom are listed in Table 1.

Table 1.

Composition of each vial within the proposed PDFF-single $R_2^{*}$ phantom.

Set I: Target PDFF (%) and $R_2^{*}$ (s−1)	5/100	5/200	5/300	5/400	5/500
Volume fat-fraction (%)	5	5	5	5	5
Iron concentration (μg Fe/mL)	1.03	5.82	15.39	24.96	34.53
MnCl2 concentration (mM)	0.17	0.31	0.50	0.79	1.17
Set II: Target PDFF (%) and $R_2^{*}$ (s−1)	10/100	10/200	10/300	10/400	10/500
Volume fat-fraction (%)	10	10	10	10	10
Iron concentration (μg Fe/mL)	1.03	5.82	15.39	24.96	34.53
MnCl2 concentration (mM)	0.17	0.31	0.50	0.79	1.17
Set III: Target PDFF (%) and $R_2^{*}$ (s−1)	20/100	20/200	20/300	20/400	20/500
Volume fat-fraction (%)	20	20	20	20	20
Iron concentration (μg Fe/mL)	1.03	5.82	15.39	24.96	34.53
MnCl2 concentration (mM)	0.17	0.31	0.50	0.79	1.17
Set IV: Target PDFF (%) and $R_2^{*}$ (s−1)	30/100	30/200	30/300	30/400	30/500
Volume fat-fraction (%)	30	30	30	30	30
Iron concentration (μg Fe/mL)	1.03	5.82	15.39	24.96	34.53
MnCl2 concentration (mM)	0.17	0.31	0.50	0.79	1.17

PDFF-${\mathbf{R}}_{\mathbf{2}}^{*}$-T₁ Phantom

This phantom was intended to demonstrate simultaneous control of PDFF, ${\mathrm{R}}_2^{*}$, and T₁. Three sets of five vials were constructed by attempting to control one MRI biomarker (i.e., PDFF, ${\mathrm{R}}_2^{*}$ or T_1,water) per set. Set I was designed to modulate PDFF, with five vials of varying volume fat fractions. Iron microspheres concentration and NiCl₂ concentration were fixed in this set of vials to obtain approximately constant ${\mathrm{R}}_2^{*}$ and T_1,water. Set II was designed with five vials with different values of ${\mathrm{R}}_2^{*}$ controlled by adding varying iron microspheres concentrations. The calibration relationship between iron microspheres concentration and target ${\mathrm{R}}_2^{*}$ was the same as mentioned above (no MnCl₂ was added in order to maintain T₁ within a physiologically relevant range). In this set, the volume fat fraction and NiCl₂ concentration were held constant. Set III included five vials with varying NiCl₂ concentration, with constant volume fat fraction and iron microsphere concentration. The calibration between NiCl₂ concentration and target T_1,water was formulated as: NiCl₂ (mM) = 1.37/T₁ (s)−0.63, which was obtained in a preliminary 3T calibration test within this study. Details (i.e., target PDFF/${\mathrm{R}}_2^{*}$/T_1,water, chemical concentration) regarding this proposed PDFF-${\mathrm{R}}_2^{*}$-T₁ phantom are included in Table 2.

Table 2.

Composition of each vial within the proposed PDFF-$R_2^{*}$-T₁ phantom.

Set I: Target PDFF (%)	0	10	20	30	40
Volume fat-fraction (%)	0	10	20	30	40
Iron concentration (μg Fe/mL)	15.39	15.39	15.39	15.39	15.39
NiCl2 concentration (mM)	0.74	0.74	0.74	0.74	0.74
Set II: Target $R_2^{*}$ (s−1)	50	100	200	400	600
Volume fat-fraction (%)	20	20	20	20	20
Iron concentration (μg Fe/mL)	1.03	5.82	15.39	34.52	53.65
NiCl2 concentration (mM)	0.74	0.74	0.74	0.74	0.74
Set III: Target T1 (ms)	500	750	1000	1250	1500
Volume fat-fraction (%)	20	20	20	20	20
Iron concentration (μg Fe/mL)	15.39	15.39	15.39	15.39	15.39
NiCl2 concentration (mM)	2.10	1.19	0.74	0.46	0.28

Materials and Construction

Materials

• Fat source: Peanut oil (Planters, Glenview, IL) was chosen in this study to mimic liver triglycerides⁴¹ because it has a proton NMR spectrum similar to that of triglyceride protons in adipose tissue⁴².

• $R_2^{*}$ modulators: Two different materials were used to modulate ${\mathrm{R}}_2^{*}$ in this study. Paramagnetic salt (MnCl₂, Sigma-Aldrich, St. Louis, MO), and iron microspheres (UMC3001, COMPEL, Bangs Labs, Fishers, IN) with density: 1.23 g/mL, diameter: 2.9±0.14 μm. Iron microspheres were in the form of a saline suspension with 5% solids by weight, of which 12.5% is in the form of magnetite. Note that iron concentration in the proposed phantoms was described as iron weight (i.e., μg Fe) per volume of solution (i.e., mL). Importantly, these ${\mathrm{R}}_2^{*}$ modulators also result in increased R₂ relaxation rate, as also observed in the presence of liver iron^38,39.

• T₁ modulator: The longitudinal relaxation rate T₁ was modulated by NiCl₂ (Sigma-Aldrich, St. Louis, MO).

• Base water-agar solution components: The proposed phantoms were based on a 2% w/v agar (Sigma-Aldrich, St. Louis, MO) gel (i.e., agar mixed with DI water), including 43 mM sodium dodecyl sulfate (Sigma-Aldrich, St. Louis, MO) as surfactant, and 3 mM sodium benzoate (Sigma-Aldrich, St. Louis, MO) as preservative.

Construction

A water-agar solution (including agar, sodium dodecyl sulfate, and sodium benzoate, as described above) was heated to above 194°F in order for the mixture to gel upon returning to room temperature. Appropriate volumes of this solution were dispensed by weight into a beaker according to the desired volume agar fraction. Then, appropriate volumes of MRI biomarker modulators (i.e., peanut oil, MnCl₂, iron microspheres, and NiCl₂) were dispensed by weight or by pipetting the appropriate volume into the beaker according to the desired volume fat fraction and desired biomarker modulator concentration.

After pouring into the beaker, the mixing of MRI biomarker modulators and water-agar solution was performed using a hand-held homogenizer (Model D1000, Dot Scientific, Burton, MI) for a duration of 30 seconds in order to obtain a homogeneous emulsion with smaller fat droplets. Immediately after homogenization, the mixture in the beaker was poured into high-density polyethylene (HDPE)⁴³ vials (volume: 25 mL; diameter: 20 mm). The mixed materials in the vials were left overnight in order for the gel to form prior to subsequent imaging experiments.

The preliminary PDFF-${\mathrm{R}}_2^{*}$ phantom and the PDFF-single ${\mathrm{R}}_2^{*}$ phantom were imaged by placing the vials in the MR coil surrounded with cushioning pads. Note these vials were scanned without an additional housing because of the large number of vials. The PDFF-${\mathrm{R}}_2^{*}$-T₁ phantom vials were placed in a custom-designed spherical acrylic housing (Calimetrix, Madison, WI) that accommodates 15 vials. The housing was filled with a water bath to optimize the magnetic field homogeneity of the volume surrounding these vials and to facilitate optimal scanning conditions.

Data Acquisition

The preliminary PDFF-${\mathrm{R}}_2^{*}$ phantom was imaged using a clinical 3.0T MRI system (MR 750, GE Healthcare, Waukesha, WI) with an 8-channel phased-array head coil. The other two phantoms (PDFF-single ${\mathrm{R}}_2^{*}$ phantom and PDFF-${\mathrm{R}}_2^{*}$-T₁ phantom) were imaged using a clinical 1.5T MRI system (MR HDxt, GE Healthcare, Waukesha, WI) with an 8-channel phased-array head coil, and also the same clinical 3.0T MRI system mentioned above. Note all phantoms were stored in the scanner room for at least 1 hour before imaging, in order to stabilize the phantom temperature. Multiple stimulated echo acquisition mode (STEAM) MRS acquisitions⁴⁴ were performed in order to measure ${\mathrm{R}}_2^{*}$, T₁, and full width at half maximum (FWHM) of each major signal peak (i.e., main methylene fat peak and water peak) within each vial. Multi-echo CSE-MRI acquisitions were performed in order to obtain PDFF and ${\mathrm{R}}_2^{*}$ maps, and subsequently measure these parameters within each vial. Detailed descriptions of these acquisitions are provided below.

Multi-TR-TE STEAM MRS

To sample the MR spectrum and measure T_1,water and T_1,fat, single voxel multi-TR-TE STEAM-MRS was acquired with multiple repetition times (TRs) and echo times (TEs). Acquisition parameters for both 1.5T and 3.0T included spectral width = 5000 Hz, 256 samples per spectrum, and 32 spectra acquired with varying TRs (min = 150 ms, max = 1500 ms), and varying TEs (min = 10 ms, max = 110 ms)⁴⁴. A small MRS voxel with size = 8mm×8mm×8mm was carefully placed in the center of each vial within each phantom in order to minimize B₀ field inhomogeneity effects and avoid potential artifacts due to chemical shift.

Multi-TE STEAM-MRS

To sample the MR spectrum and obtain spectroscopy-based R_2,water, R_2,fat, FWHM_water, and FWHM_fat, single voxel multi-TE STEAM-MRS was acquired with multiple echo times⁴⁴. This acquisition had spectral width of 5000 Hz and higher spectral resolution (2048 samples) than multi-TR-TE STEAM, in order to enable improved assessment of spectral properties (eg: FWHM_water, and FWHM_fat). Acquisition parameters for the 1.5T MR system included five echoes with TE₁ = 10.3 ms and 5 ms spacing, TR = 3500 ms, voxel size = 8×8×8mm³. Acquisition parameters for the 3.0T MR system included ten echoes with TE₁ = 10.4 ms and 4 ms spacing, TR = 3500 ms, voxel size = 8×8×8mm³. As described above, the voxel was carefully placed in the center of each vial within each phantom.

Chemical Shift Encoded MRI

Multi-echo 3D spoiled gradient-echo (SGRE) data were acquired to perform quantitative confounder-corrected CSE-MRI-based PDFF and ${\mathrm{R}}_2^{*}$ mapping⁴⁵. Acquisition parameters included slice thickness = 2 mm, FOV = 24×16 cm², N_x×N_y = 128×128, flip angle = 5° (1.5T)/4° (3.0T), TE₁ = 1.1 ms, ΔTE = 1.1 ms (1.5T)/0.8 ms (3.0T), echo number = 12 (1.5T)/ 8 (3.0T), number of shots = 2, echo train length = 6 (1.5T)/4 (3.0T), number of signal averages = 4, bandwidth = ±83.3 kHz.

Data Processing and Statistical Analysis

Data Processing

Data from the STEAM acquisitions were processed offline using an automated custom script⁴⁶ that jointly fits all the acquired spectra and simultaneously estimates T_1,water, T_1,fat, R_2,water, R_2,fat, FWHM_fat, and FWHM_water (used to estimate ${\mathrm{R}}_2^{*}$ from MRS as described below), among other parameters. In addition, spectra were plotted for illustration of fat and water peaks in the presence of different fat and iron concentrations. In order to estimate individual ${\mathrm{R}}_2^{*}$ of water and fat, FWHM of water and fat peaks in the acquired spectra were obtained. Spectroscopy measured ${\mathrm{R}}_{2,\mathrm{w}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r}}^{*}$ and ${\mathrm{R}}_{2,\mathrm{f}\mathrm{a}\mathrm{t}}^{*}$ were approximately estimated as ${\mathrm{R}}_{2,\mathrm{f}\mathrm{a}\mathrm{t}/\mathrm{w}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r}}^{*}$=FWHM_fat/water× π. Note that these FWHM-based ${\mathrm{R}}_2^{*}$ estimates may be overestimated due to intravoxel dephasing (i.e., magnetic susceptibility-related B₀ field inhomogeneity effect) in relatively large MRS voxels. However, the relative difference between ${\mathrm{R}}_{2,\mathrm{w}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r}}^{*}$ and ${\mathrm{R}}_{2,\mathrm{f}\mathrm{a}\mathrm{t}}^{*}$ is a relevant performance metric, as water and fat signals reflect identical intravoxel dephasing. In addition, a multi-fat-peak model was applied to estimate FWHM_fat with the assumption that the FWHM of all fat peaks are equal. Note that this model does not capture the full complexity of the fat signal spectrum (e.g., additional peaks, J-coupling), but magnetic susceptibility-related B₀ inhomogeneity is likely the dominant effect introducing bias in the measured spectral linewidth. Nevertheless, the proposed ${\mathrm{R}}_{2,\mathrm{f}\mathrm{a}\mathrm{t}}^{*}$ is expected to be representative of the signal behavior observed by CSE-MRI. MRS processing was implemented in MATLAB (MathWorks, Natick, MA).

Multi-echo CSE-MRI source echo data were obtained and fitted for PDFF and ${\mathrm{R}}_2^{*}$ estimation. All the source SGRE acquisition data were processed offline using a magnitude-based algorithm^30,45 that corrects for all relevant confounding factors (including ${\mathrm{R}}_2^{*}$ decay⁴², spectral complexity of fat signals⁴², temperature effects⁴⁷ and residual phase errors^48,49) in the acquired echo data to obtain PDFF and ${\mathrm{R}}_2^{*}$ maps. CSE-MRI reconstructions were also implemented using MATLAB (MathWorks, Natick, MA). A circular region of interest (ROI) with area of approximately 1.5cm² was placed in the center of each vial to measure the imaging PDFF value and imaging ${\mathrm{R}}_2^{*}$ value from the PDFF map and ${\mathrm{R}}_2^{*}$ map, respectively.

Statistical Analysis

For the proposed preliminary PDFF-${\mathrm{R}}_2^{*}$ phantom, the correlation between ${\mathrm{R}}_{2,\mathrm{w}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r}}^{*}$ and ${\mathrm{R}}_{2,\mathrm{f}\mathrm{a}\mathrm{t}}^{*}$ was plotted for each set of vials (i.e., one set with MnCl₂ and another set with iron microspheres as ${\mathrm{R}}_2^{*}$ modulators).

For the remaining two phantoms, linear regression and Bland-Altman analysis were performed to assess several relationships: (1) Imaging PDFF/${\mathrm{R}}_2^{*}$ versus target PDFF/${\mathrm{R}}_2^{*}$ for each field strength, in order to demonstrate the accuracy of PDFF and ${\mathrm{R}}_2^{*}$ quantification; (2) R_2,water versus imaging ${\mathrm{R}}_2^{*}$ across different field strengths, in order to monitor R₂ decay rate compared with ${\mathrm{R}}_2^{*}$ decay. In previous work³⁸, R₂ and ${\mathrm{R}}_2^{*}$ both increased with increasing liver iron concentration, however R₂ increases more slowly than ${\mathrm{R}}_2^{*}$. (3) ${\mathrm{R}}_{2,\mathrm{w}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r}}^{*}$ versus ${\mathrm{R}}_{2,\mathrm{f}\mathrm{a}\mathrm{t}}^{*}$, in order to validate single ${\mathrm{R}}_2^{*}$ behavior for water and fat, for the proposed PDFF-single ${\mathrm{R}}_2^{*}$ phantom at both 1.5T and 3.0T. Comparisons between the three different sets of vials regarding PDFF, ${\mathrm{R}}_2^{*}$, T_1,water, and T_1,fat, R_2,water, and R_2,fat for the proposed PDFF-${\mathrm{R}}_2^{*}$-T₁ phantom were plotted at both 1.5T and 3.0T. In this study, all statistical analyses were implemented with MATLAB (MathWorks, Natick, MA) and Python.

Results

Preliminary PDFF-$R_2^{*}$ Phantom

Figure 1 depicts the correlation between ${\mathrm{R}}_{2,\mathrm{w}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r}}^{*}$ and ${\mathrm{R}}_{2,\mathrm{f}\mathrm{a}\mathrm{t}}^{*}$ for the two sets of vials with different ${\mathrm{R}}_2^{*}$ modulators within the preliminary PDFF-${\mathrm{R}}_2^{*}$ phantom. For the set of vials using MnCl₂ as the ${\mathrm{R}}_2^{*}$ modulator, increasing MnCl₂ concentration (indicated with a blue arrow) leads to increasing ${\mathrm{R}}_{2,\mathrm{w}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r}}^{*}$. The spectroscopy-based ${\mathrm{r}}_{2,\mathrm{w}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r}}^{*}$ relaxivity for MnCl₂ was calculated as: ${\mathrm{r}}_{2,\mathrm{w}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r}}^{*}$= 70.77 s⁻¹/mM (3.0T). However, ${\mathrm{R}}_{2,\mathrm{f}\mathrm{a}\mathrm{t}}^{*}$ was unaffected by MnCl₂ concentration. For the set of vials using iron microspheres as the ${\mathrm{R}}_2^{*}$ modulator, ${\mathrm{R}}_{2,\mathrm{w}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r}}^{*}$ and ${\mathrm{R}}_{2,\mathrm{f}\mathrm{a}\mathrm{t}}^{*}$ increased with increasing iron microsphere concentration (indicated with a red arrow), with relatively similar ${\mathrm{R}}_2^{*}$ behavior for both water and fat. However, the spectroscopy-based ${\mathrm{r}}_2^{*}$ relaxivity appears slightly higher for fat compared to water: ${\mathrm{r}}_{2,\mathrm{w}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r}}^{*}$ = 5.94 s⁻¹/μg Fe/mL, and ${\mathrm{r}}_{2,\mathrm{f}\mathrm{a}\mathrm{t}}^{*}$ = 8.99 s⁻¹/μg Fe/mL (3.0T).

Figure 1.

Correlation between $R_{2,water}^{*}$ and $R_{2,fat}^{*}$ for the two sets of vials within the preliminary PDFF-$R_2^{*}$ phantom. With increasing MnCl₂ concentration, $R_{2,water}^{*}$ increases but $R_{2,fat}^{*}$ remains unchanged. With increasing iron microspheres concentration, both $R_{2,water}^{*}$ and $R_{2,fat}^{*}$ are increased. However, the $R_2^{*}$ relaxivities for water and fat are different. Note the arrowheads represent increasing concentration of MnCl₂ and iron microspheres.

PDFF-single $R_2^{*}$ Phantom

Figure 2 depicts representative PDFF and ${\mathrm{R}}_2^{*}$ maps of the proposed PDFF-single ${\mathrm{R}}_2^{*}$ phantom at 1.5T and 3.0T. Both the PDFF map and ${\mathrm{R}}_2^{*}$ map show high image quality with homogeneous signal in each vial. PDFF remains approximately constant across varying iron and MnCl2 concentrations. ${\mathrm{R}}_2^{*}$ remains approximately constant across varying volume fat fraction. Note the high noise observed in the 1.5T PDFF map within the high ${\mathrm{R}}_2^{*}$ vials is likely due to severe noise propagation at 1.5T in the presence of high ${\mathrm{R}}_2^{*}$. In Figure 3, linear regression results (i.e., slope and intercept with standard deviation) are demonstrated regarding imaging-measured PDFF versus target PDFF and imaging-measured ${\mathrm{R}}_2^{*}$ versus target ${\mathrm{R}}_2^{*}$ at both 1.5T and 3.0T. Imaging PDFF shows high correlation with target PDFF at both 1.5T (slope = 0.99±0.04 × 10⁻¹, intercept = 1.29±0.08, R² = 0.994) and 3.0T (slope = 0.94±0.02 × 10⁻¹, intercept = 1.15±0.05, R² = 0.997). Similarly, imaging ${\mathrm{R}}_2^{*}$ shows high correlation with target ${\mathrm{R}}_2^{*}$ at both 1.5T (slope = 0.84±0.01, intercept = 23.10±3.52, R² = 0.943) and 3.0T (slope = 0.88±0.01, intercept = 57.02±3.96, R² = 0.935).

Figure 2.

Representative PDFF maps and $R_2^{*}$ maps of the proposed PDFF-single $R_2^{*}$ phantom at both 1.5T and 3.0T. Vials with varying iron and MnCl₂ concentration (i.e., varying $R_2^{*}$) are arranged along the horizontal direction, and vials with varying volume fat fraction arranged along the vertical direction. At both field strengths, the PDFF map and $R_2^{*}$ map show high image quality, and homogeneous values within each vial.

Figure 3.

Linear regression plots demonstrate high correlation between imaging PDFF versus target PDFF (top row), as well as between imaging $R_2^{*}$ versus target $R_2^{*}$ (bottom row) at both 1.5T and 3.0T for the proposed PDFF-single $R_2^{*}$ phantom.

Linear regression analysis results (i.e., slope and intercept with standard deviation) comparing R_2,water (measured using spectroscopy) and imaging ${\mathrm{R}}_2^{*}$ at both 1.5T and 3.0T are shown in Figure 4. High correlation is observed between R_2,water and imaging ${\mathrm{R}}_2^{*}$ at both 1.5T and 3.0T. R_2,water increases more slowly than ${\mathrm{R}}_2^{*}$ with increasing iron and MnCl₂ concentration. At 1.5T, the regression line has slope = 0.39 ± 0.04 × 10⁻¹, intercept = 11.54 ± 1.41, and R² = 0.947 compared with the in vivo relationship (slope = 0.17 and intercept = 47.2) from a previous study³⁸. At 3.0T, the regression line has slope = 0.36±0.04×10⁻¹, intercept = 0.54±1.69, and R² = 0.937.

Figure 4.

Linear regression plots between R_2,water and imaging $R_2^{*}$ at 1.5T and 3.0T for the proposed PDFF-single $R_2^{*}$ phantom. High correlation is observed between R_2,water and imaging $R_2^{*}$ at both 1.5T and 3.0T. However, R_2,water increases more slowly than $R_2^{*}$ with increasing iron and MnCl₂ concentration, in qualitative agreement with the behavior observed in liver imaging in the presence of iron.

Figure 5 depicts representative spectra (TE = 10.3 ms) obtained from three vials with the same target PDFF (20%) but varying iron and MnCl₂ concentration. In Figure 5 (left plot), both the water and fat peaks have moderate FWHM values (i.e., FWHM_water: 57 Hz, FWHM_fat: 63 Hz) with low iron level (1.03 μg Fe/mL) and MnCl₂ concentration (0.17 mM). In Figure 5 (middle plot), the FWHM values of water and fat peaks (i.e., FWHM_water: 75 Hz, FWHM_fat: 78 Hz) increases with increasing iron level (15.39 μg Fe/mL) and MnCl₂ concentration (0.50 mM) compared to the first vial. In Figure 5 (right plot), the FWHM values of water and fat peaks are broad (i.e., FWHM_water: 157 Hz, FWHM_fat: 138 Hz) with high iron level (34.53 μg Fe/mL) and MnCl₂ concentration (1.17 mM). Note that both the water and fat peaks demonstrate similar broadening with increasing iron level and MnCl₂ concentration. The difference between the relative amplitude of water and fat peaks is due to the different R₂ relaxation rates of water and fat (see below for R_2,water and R_2,fat measurements in the presence of iron).

Figure 5.

Spectra (TE = 10.3 ms) obtained from three vials with constant volume fat fraction (target PDFF = 20%) but increasing iron and MnCl₂ concentrations. From left to right, the water and fat peaks become broader (i.e., increasing FWHM) simultaneously with increasing iron and MnCl₂ concentration. FWHM_fat was estimated using a multi-fat-peak model with an assumption that the FWHM of all fat peaks are equal. Note the difference between the relative amplitude of water and fat peaks is due to the different R₂ relaxation rates of water and fat.

Linear regression analysis results comparing spectroscopy-measured ${\mathrm{R}}_{2,\mathrm{w}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r}}^{*}$ versus ${\mathrm{R}}_{2,\mathrm{f}\mathrm{a}\mathrm{t}}^{*}$ at both 1.5T and 3.0T are shown in Figure 6. High correlation with slope close to 1 and intercept close to zero is observed between ${\mathrm{R}}_{2,\mathrm{w}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r}}^{*}$ and ${\mathrm{R}}_{2,\mathrm{f}\mathrm{a}\mathrm{t}}^{*}$ at different field strengths. At 1.5T, the regression line has slope of 0.90±0.01 with intercept of 8.0±1.39 and R² of 0.988. At 3.0T, the regression line has slope of 0.99±0.01 with intercept of 11.1±3.42 and R² of 0.959. Bland-Altman analysis results comparing spectroscopy-measured ${\mathrm{R}}_{2,\mathrm{w}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r}}^{*}$ versus ${\mathrm{R}}_{2,\mathrm{f}\mathrm{a}\mathrm{t}}^{*}$ at both 1.5T and 3.0T are shown in Figure 6 (bottom row). Importantly, the ${\mathrm{R}}_2^{*}$ difference between water and fat is similar and small at both 1.5T (mean = 15.0 s⁻¹, 95% LoA = [−46.8 s⁻¹, 16.8 s⁻¹]) and 3.0T (mean = 13.9 s⁻¹, 95% LoA = [−59.0 s⁻¹, 31.1 s⁻¹]).

Figure 6.

High correlation and narrow limits of agreement are demonstrated by linear regression (top row) and Bland-Altman analysis (bottom row) between $R_{2,water}^{*}$ and $R_{2,fat}^{*}$ at 1.5T and 3.0T for the proposed PDFF-single $R_2^{*}$ phantom. High correlation is observed between $R_{2,water}^{*}$ and $R_{2,fat}^{*}$ at 1.5T (slope = 0.90, intercept = 7.98, R² = 0.988) and 3.0T (slope = 0.99, intercept = −11.13, R² = 0.959). Limits of agreement as assessed from Bland-Altman analysis were (−46.8 s⁻¹,16.8 s⁻¹) and (−59.0 s⁻¹, 31.1 s⁻¹) at 1.5T and 3.0T, respectively.

PDFF-$R_2^{*}$-T₁ Phantom

Figure 7 depicts representative PDFF maps and ${\mathrm{R}}_2^{*}$ maps of the proposed PDFF-${\mathrm{R}}_2^{*}$-T₁ phantom at 1.5T and 3.0T. Both the PDFF map and ${\mathrm{R}}_2^{*}$ map show excellent image quality with homogeneous signal in each vial. Set I includes vials with varying volume fat-fraction but fixed iron and NiCl₂ concentration. The five vials in Set I are labeled with white circles in the PDFF map at 1.5T. Accurate mapping of volume fat-fraction within each vial is demonstrated in the PDFF maps at both field strengths. Approximately constant ${\mathrm{R}}_2^{*}$ is demonstrated in ${\mathrm{R}}_2^{*}$ map at both field strengths. Set II contains vials with varying iron concentration but fixed volume fat fraction and NiCl₂ concentration. The five vials in Set II are labeled with yellow circles in ${\mathrm{R}}_2^{*}$ map at 1.5T. Varying ${\mathrm{R}}_2^{*}$ is clearly depicted in the ${\mathrm{R}}_2^{*}$ maps at both field strengths. Approximately constant volume fat fraction is demonstrated in the PDFF map at both field strengths across various ${\mathrm{R}}_2^{*}$ values. Set III contains vials with varying NiCl₂ concentration but fixed volume fat fraction and iron concentration. The five vials in Set III are labeled with white circles in the PDFF map at 3.0T. Approximately constant volume fat fraction is demonstrated in the PDFF map at both field strengths across various T₁ values.

Figure 7.

Representative PDFF map and $R_2^{*}$ map of the proposed PDFF-$R_2^{*}$-T₁ phantom at both 1.5T and 3.0T. Set I (labeled with white circles in the 1.5T PDFF map) includes five vials with varying target PDFF (0%, 10%, 20%, 30%, and 40%, labeled as 1, 2, 3, 4, and 5, respectively) with fixed iron and NiCl₂ concentrations. Set II (labeled with yellow circles in the 1.5T $R_2^{*}$ map) includes five vials with varying iron concentration (i.e., varying target $R_2^{*}$ (50 s⁻¹, 100 s⁻¹, 200 s⁻¹, 400 s⁻¹, and 600 s⁻¹_, labeled as 1, 2, 3, 4, and 5, respectively)) with fixed volume fat fraction and NiCl₂ concentration. Set III (labeled with white circles at 3.0T PDFF map) includes five vials with varying NiCl₂ concentration (i.e., varying target T1 (500 ms, 750 ms, 1000 ms, 1250 ms, and 1500 ms, labeled as 1, 2, 3, 4, and 5, respectively)) with fixed volume fat fraction and iron concentration.

In Figure 8, the estimated imaging-based PDFF, imaging-based ${\mathrm{R}}_2^{*}$, spectroscopy-based T_1,water, spectroscopy-based T_1,fat, spectroscopy-based R_2,water, and spectroscopy-based R_2,fat are plotted for each vial within the proposed PDFF-${\mathrm{R}}_2^{*}$-T₁ phantom, at both 1.5T and 3.0T. In each plot, vial number increases with increasing target PDFF, increasing iron concentration and decreasing NiCl₂, for Set I, II, and III, respectively. In Figure 8 (a) and (c), the five vials from Set I show increasing measured PDFF (as expected) while the vials from Set II and Set III show nearly constant PDFF. In Figure 8 (b) and (d), the five vials from Set II show increasing ${\mathrm{R}}_2^{*}$ as expected, while the ${\mathrm{R}}_2^{*}$ of the vials from Set I and Set III remain approximately constant. In Figure 8 (e) and (g), T_1,water of each vial is plotted for both 1.5T and 3.0T, respectively. The five vials of Set III show increasing T_1,water as expected. The five vials of Set I have nearly constant T_1,water of 1000 ms. However, T_1,water decreases with increasing iron concentration in the vials from Set II, in qualitative agreement with the behavior observed in vivo²⁶. In Figure 8 (f) and (h), all vials in the three Sets have nearly constant T_1,fat of approximately 280 ms at 1.5T and 310 ms at 3.0T. Note that T_1,fat is independent of iron concentration. In Figure 8 (i) and (k), R_2,water of each vial is plotted for both 1.5T and 3.0T, respectively. The five vials of Set II have increasing R_2,water, while Set I and Set III have nearly constant R_2,water. In Figure 8 (j) and (l), R_2,fat of each vial is plotted for both 1.5T and 3.0T, respectively. R_2,fat remains nearly constant for all three sets at 1.5T. At 3.0T, R_2,fat increases from 20 s⁻¹ to 40 s⁻¹ for the vials in Set II. R_2,fat of the vials in Set I and Set III remains nearly constant under 3.0T.

Figure 8.

The proposed PDFF-$R_2^{*}$-T₁ phantom enables simultaneous control of PDFF, $R_2^{*}$, and T₁ while mimicking in vivo signal behavior. The plots show measurements of imaging PDFF, imaging $R_2^{*}$, T_1,water, T_1,fat, R_2,water, and R_2,fat of each vial from different sets (Set I: varying target PDFF (0%, 10%, 20%, 30%, and 40%) with fixed iron and NiCl₂ concentration; Set II: varying target $R_2^{*}$ (50 s⁻¹, 100 s⁻¹, 200 s⁻¹, 400 s⁻¹, and 600 s⁻¹) with fixed volume fat fraction and NiCl₂ concentration; Set III: varying target T₁ (500 ms, 750 ms, 1000 ms, 1250 ms, and 1500 ms) with fixed volume fat fraction and iron concentration at 1.5T and 3.0T. Vial number increases with increasing target PDFF, increasing iron concentration and decreasing NiCl₂, for Set I, II, and III, respectively. The five vials in Set I show increasing PDFF with increasing volume fat fraction. The five vials in Set II show increasing $R_2^{*}$ and R_2,water with increasing iron concentration. The five vials in Set III show increasing T_1,water with decreasing NiCl₂ concentration.

Discussion

In this work, we have proposed and validated novel quantitative MRI phantoms designed to mimic the simultaneous presence of fat, iron, and across a range of T₁ values in the liver by controlling different MR biomarkers (i.e., PDFF, ${\mathrm{R}}_2^{*}$, and T₁, respectively). Two different phantom designs were introduced in this study. The PDFF-single ${\mathrm{R}}_2^{*}$ phantom aimed to control PDFF and ${\mathrm{R}}_2^{*}$ simultaneously with highly accurate single-${\mathrm{R}}_2^{*}$ behavior of fat and water. The PDFF-${\mathrm{R}}_2^{*}$-T₁ phantom enabled simultaneous control of PDFF, ${\mathrm{R}}_2^{*}$, and T₁ within each vial. The proposed phantoms in this study may provide a useful tool for validation and quality assurance of MRI-based fat quantification, ${\mathrm{R}}_2^{*}$/R₂ mapping, and T₁ mapping methods.

The proposed phantoms are able to mimic previously observed in vivo signal behavior, most notably a common, “single” effective value for ${\mathrm{R}}_2^{*}$ in the liver^24,25. As demonstrated in this study, simple combinations of previous PDFF and ${\mathrm{R}}_2^{*}$ phantom formulations (particularly using paramagnetic salts to control ${\mathrm{R}}_2^{*}$) do not result in realistic signal behavior that mimics the simultaneous presence of fat and iron in the liver. However, the combined use of MnCl₂ and iron microspheres as ${\mathrm{R}}_2^{*}$ modulators in the proposed PDFF-single ${\mathrm{R}}_2^{*}$ phantom leads to single-${\mathrm{R}}_2^{*}$ signal behavior that accurately mimics in vivo signals^24,25. In addition, both the proposed PDFF-single ${\mathrm{R}}_2^{*}$ phantom and PDFF-${\mathrm{R}}_2^{*}$-T₁ phantom demonstrate that R₂ increases more slowly than ${\mathrm{R}}_2^{*}$ with increasing iron concentration. This behavior also agrees qualitatively with what has been observed in vivo³⁸, although the quantitative relationship appears different (e.g., in vivo slope: r₂/${\mathrm{r}}_2^{*}$ = 0.18 compared to 0.39 observed in the proposed phantoms). This discrepancy may be due to differences in the magnetic susceptibility properties and microscopic iron distributions, as well as differences in the diffusion coefficient of water between the proposed phantoms and iron-loaded liver⁵⁰. Furthermore, T_1,water is shorter with increasing iron concentration in the proposed PDFF-${\mathrm{R}}_2^{*}$-T₁ phantom, which qualitatively mimics the T₁ behavior in the presence of iron deposition in the liver^26,51.

A number of previously developed quantitative MR phantoms enable the control of individual MRI biomarkers (including PDFF, ${\mathrm{R}}_2^{*}$, and T₁). Quantitative fat phantoms^30,31 have been used in previous works to demonstrate accurate and reproducible fat quantification. The ability to modulate ${\mathrm{R}}_2^{*}$ has been demonstrated in various phantoms^32–34, and phantoms that control T₁ have also been used in the past^35,36. However, these previous works did not enable simultaneous modulation of PDFF, ${\mathrm{R}}_2^{*}$, and T₁. In this study, the proposed PDFF-${\mathrm{R}}_2^{*}$-T₁ phantom is able to modulate each of three important MR biomarkers (i.e., PDFF, ${\mathrm{R}}_2^{*}$, and T_1,water) while controlling the other two.

Our study has several limitations. One assumption in our phantom construction procedure was that the small fat droplets will result after homogenization. No direct evidence proved this, even though our results demonstrated similar ${\mathrm{R}}_2^{*}$ of fat and water, which was the primary goal. Microstructural assessment of the proposed phantom (e.g., using a light or electron microscopy, particle sizing, etc.) is beyond the scope of this study, due to the potential complexity of adequate sample preparation (e.g., with controlled cooling rate) in order to replicate the structure of the proposed phantoms for microstructural analysis. Future studies may be needed for definitive assessment of the relationship between microstructural properties (e.g., droplet size and distribution) and MRI biomarkers (e.g., PDFF and ${\mathrm{R}}_2^{*}$).

Further, the ${\mathrm{R}}_2^{*}$ range targeted in the proposed phantoms was limited in this study. The highest target ${\mathrm{R}}_2^{*}$ is less than 1000 s⁻¹ in both of the proposed phantoms. Phantoms with higher ${\mathrm{R}}_2^{*}$ may be needed to validate techniques aimed at assessing high iron overload. However, robust quantification of PDFF, ${\mathrm{R}}_2^{*}$, and T₁ in these phantoms may require non-Cartesian imaging techniques. Also, the lowest ${\mathrm{R}}_2^{*}$ values in these vials were slightly above those of normal liver⁵². Nevertheless, the phantoms constructed in this study provided a relatively broad range of ${\mathrm{R}}_2^{*}$ while maintaining enough SNR to enable stable measurement of PDFF, ${\mathrm{R}}_2^{*}$, R₂, and T₁. A wider range of combinations of PDFF, ${\mathrm{R}}_2^{*}$, and T₁ than shown in this study is expected to be highly feasible with the proposed formulation. However, further evaluation with wider sets of parameters may be needed in future studies.

Another limitation of this study was that all the acquisitions were performed at room temperature (approximately 70 °F) without close temperature control, though temperature stabilization procedure was performed for each acquisition. This may introduce a small degree bias in PDFF measurements due to potential temperature variability between acquisitions, although such bias is very low with complex-based CSE-MRI⁴⁷. Note that this work used a temperature-corrected fat quantification signal model under the assumption of a constant chemical shift between water and the main fat peak (3.5 ppm, as derived in previous work⁴⁷), based on a temperature of 72°F. Furthermore, preliminary results indicate that the relaxation properties of the proposed phantoms may remain relatively stable near room temperature (e.g., between 68°F to 86°F). Importantly, excellent accuracy and high reproducibility were observed in this study without control for specific temperature across different acquisitions.

The spectroscopy-based ${\mathrm{r}}_2^{*}$ relaxivity measurements for MnCl₂ and iron might be biased (due to magnetic susceptibility related line broadening) and showed discrepancy with our imaging-based measurements in the absence of fat. However, spectroscopy acquisitions enable separate measurement of the linewidth of different chemical species and were therefore selected for this study. T_1,water and T_1,fat measurements in this work were performed using a multi-TR-TE STEAM MRS approach. This approach is sensitive to B₁ field heterogeneities which may introduce errors in the T₁ measurements. Nevertheless, the ability to reach a wide range of T_1,water is clearly demonstrated in this work. Further, the measured T_1,fat remains nearly constant, as expected, which suggests that the overall technique is adequate. The observed MRI parameter behavior (${\mathrm{r}}_2^{*}$ relaxivity, r₂ relaxivity, T_1,water and T_1,fat) is qualitatively consistent with that observed in liver at a given field strength. However, the field strength dependence of these parameters in the proposed phantom does not mimic the dependence observed in vivo (e.g., ${\mathrm{R}}_2^{*}$ and T₁ are nearly constant with field strength in the proposed phantoms, unlike in liver). Also, although a wide range of ${\mathrm{R}}_2^{*}$ values can be achieved, the specific calibration between ${\mathrm{R}}_2^{*}$ and iron concentration in the phantom does not mimic the calibrations observed in liver in the presence of iron overload. Further, the proposed phantoms are not designed to mimic other MRI-relevant properties of the liver, including magnetization transfer, stiffness, or diffusion.

In conclusion, we developed and validated a PDFF-single ${\mathrm{R}}_2^{*}$ phantom that simultaneously mimics the co-existence of fat and iron in liver with similar ${\mathrm{R}}_2^{*}$ decay rate for water and fat. Further, we were able to modulate PDFF, ${\mathrm{R}}_2^{*}$, and T₁ in a PDFF-${\mathrm{R}}_2^{*}$-T₁ phantom, in order to mimic the co-existence of fat, iron, and fibrosis. Further, this phantom was evaluated quantitatively at both 1.5T and 3.0T. The proposed phantoms may have applications for validation of novel MRI-based quantification techniques, for acceptance testing and quality assurance in multi-center clinical trials (e.g., for drug development) as well as for quality assurance in clinical applications.